#hereticalphysics

[scepticaladventure]

25  Gravity, Time and Light  6Sep18

Introduction In essence, Special Relativity is a systematic attempt to describe the physics of things that move fast, based up on postulates about light, and General Relativity is an attempt to include gravity. Hence a good question at the core of it all is “How does gravity affect the speed of light?” You might think this is a simple question but have a look at the Internet. Confusion reigns!

Sources of Confusion I think a lot of the confusion comes from lack of precision in the question. If Relativity has taught us anything it has taught us to be wary about simple questions about time, distance and speed. We have learnt we must first specify “Who is the observer and what is their situation?” We have learnt that the answers to simple questions about lengths, durations and speeds depend on how they are measured and in what circumstances are they measured - everything is relative.

Hence the speed of light in a strong gravitational field as measured by a local observer who is also embedded in that field might be different from a result obtained by a distant observer well away from the massive object creating the field.

It turns out that the speed of light is affected by a gravitational field, but so to (in fact hence) is local time keeping and so the local speed of light as measured by that local observer is the same as usual. The slowdown is undetectable. But from a more distant perspective the slowdown in the speed of light does become detectable.

Another source of confusion comes from the interrelated complexity between time, distance and speed. In a world where time can run fast or slow, distances can contract and Euclidean geometry may not hold true, the meaning of measurements and hence the quantification of physical properties becomes treacherous.

A third source of confusion comes from confused people teaching confused or confusing messages to innocent student, often with absolute conviction e.g. that the speed of light is a universal invariant that its always and everywhere the same.

What is Time? I was watching a science program the other day and the reporter asked a group of astrophysicists attending a theoretical physics conference in Ontario – what is time? Well they um’d and ah’d and said it was a difficult question and so on. They could not give a ready answer in plain English.

So let me have a go. Firstly the word itself covers two sorts of concepts – a way of tagging a river of events which may or may not be linked causally, and durations between events. Or to take a simple example – If you ask a time keeper at a sports event “What is the time?” she may reply “Do you mean the time of day, or the result of some competitor’s performance in an event?”

The underlying concept is causality. If an event A causes an event B then we say that A occurs before or simultaneously with Event B. No-one has ever witnessed causality running backwards, so we assume that it is a strictly one way affair.

When we come across physical phenomena with a repetitive regularity about them, such as the vibrations of a quartz crystal, we can use it to create a useful clock and hence create a measure of local time durations.

If we standardize such clocks to each other we can start to talk about the time more generally, and we can give an elementary answer to the question “what is the agreed exact time of day?”. But this is a man made convention. We have to be careful not to assume that our concepts can be applied well beyond the scope in which they were created. For example, we cannot assume that the whole Universe is embedded in some sort of all embracing river of time with a Universal standard clock somewhere.

Once we start to consider events on a cosmological scale, or in fast moving situations, we have come to understand that our normal day-to-day concepts of time do not suffice. Different observers can measure different time durations for the interval between the same two events. Time can be observed to run slow, not because clocks are distorted but because the finite speed of light means that the very concept of ‘what happens when’ needs to be reconsidered. Over and above that it turns out that time also runs slow in a gravitational field.

So time is nothing more than mankind’s attempt to quantify intervals between events. It is a manmade construct overlaid on reality, nothing more. It has no independent reality. In fact it can be considered to be a widely shared illusion. And a treacherous one at that.

Definitions and Standards of Measurement Let’s look at the simple equation c = D/T where c is the speed of light, D is a measure of distance travelled and T is a measure of time duration. For this to have any meaning we need an agreed way of measuring D and T and we need agreed units of measurement for both D and T. But where to start?

In the modern world our standards of measurement start with time.

Since the 1970’s there has been an international agreement that a standard second is defined by a set number of oscillations in the electromagnetic radiation (i.e. light) emitted by hyperfine transitions within Caesium 133 atoms held in certain conditions. A standard meter is then defined as being the distance travelled by this light in 1/299,792,458 standard seconds.

It then follows axiomatically that the standard speed of light is 299,792,458 meters per second. If nothing else this helps to pin down some terminology. But it does not mean that the actual speed of light will always be the same as the standard speed of light. A trivial example is if the light is travelling through glass. It’s slower. A more complicated example is if the light is travelling across a spiral galaxy.

Note that this whole approach to the definition of standards could have started in a different way. For example, a standard meter could have been defined as the distance between two scratches on a bar of metal held at a precise temperature in a specified location (e.g. Paris), and a standard second could then have been defined by the time taken for light to travel a set number of meters. Or a standard second could have been defined using an atomic clock and the speed of light could have been left out of it altogether, which is what used to happen before the current system was adopted.

There are three spatial dimensions and only one time dimension, so a democratic approach suggests we should start with defining distance and then move on to define time. Seriously though, length is a lot more observable and tangible than time. We can see and touch and run a ruler over the length of a thing. Time is invisible and intangible.

Timekeeping is always (as far as I can tell) based on motion of some sort, whether this be vibrations in a quartz crystal, the swing of a pendulum or the rotation of a planet. And since motion involves both distance and time, defining time durations based on the motions of things seems a little bit tricky. If time did not exist, how would we know anything was moving? The answer is that we could see things happening – things doing things to other things. Causality at work. But this would offer no guarantees about the nature of time. For example, if everything in the Universe speeded up by 10%, how could we tell?  

Furthermore, we know from experiments that time is affected by motion (Lorentzian time dilation) and by gravity (gravitational time dilation). So time is a rubbery phenomenon and in some situations it is a deceptive illusion.

Length is also affected by motion (Lorentzian contraction). This is a small effect in extreme circumstances, but it is nevertheless quite real. It was realized from experiments on the speed of light and came to become a key feature of the Theory of Special Relativity. But nobody, as far as I know, has been able to demonstrate length contraction in a simple experiment or demonstration. And I have never seen a photo-montage showing a Lorentz contracted object.

It is very difficult to hold up ruler against a physical object travelling at relativistic speeds in a straight line and be  able to record both ends at exactly the same time. The closest experiments I know of come from studies of high speed collisions between atomic nuclei at the Brookhaven Relativistic Heavy Ion Collider. The heavy nuclei have a non-zero radius and the dynamics of the collisions give the results expected if the nuclei are Lorentz contracted into disks. However, the Brookhaven accelerator is not a linear accelerator and this brings into play the theoretical complications of rotating and accelerated systems (see for example the Ehrenfest rotating disc paradox). Determining the effective radii of the ions is also problematical.

The three spatial dimensions of an object in spacetime are tangible. You can see and touch and measure lengths, widths and heights. You can put a ruler next to them. Time durations on the other hand are anything but simple, especially if the object is moving. You need to specify the situation of the observer very carefully. You need to carry the same clock from one event to the other or else to use a carefully synchronised set of clocks.

Time is a consequential parameter. It is the consequence of causality. At heart maybe the only thing you can be sure of is that Event A causes Event B, then Event A occurs before Event B. This also creates the Arrow of Time. In other words time is a one way phenomenon. You can never re-measure the exact same time interval, nor can you ever measure a time duration in back to front order.

The usual way to bridge from the world of tangible spatial dimensions to a world that involves time, motion, momentum and energy is to involve the speed of light.

What is an Inertial Reference Frame? After studying the results of experiments by Bradley, Eotvos, Roemer and Fizeau (and presumably Michelson and Morley, which he failed to acknowledge) Einstein simply postulated that that the speed of light in vacuum in an inertial reference frame is always the same (299,792.458 km/sec).

By inertial reference frame he meant one which is not accelerating, rotating or in a gravitational field. A frame in which test particles weigh nothing and stay still or travel in straight lines unless compelled by a force to do otherwise.

I think that an inertial reference frame is a an idealized concepts which is impossible to find in practice. Everything in the Universe is either spinning, accelerating or affected by gravity.  It was and still is common to say that an inertial reference frame is aligned to the “fixed stars”. However, no-one ever clarifies whether such stars are in our galaxy or beyond it, and what such stars can possible have to do with local physics anyway.

I all my reading I cannot find clarity about whether a satellite in orbit constitutes an inertial reference frame or not. The satellite is undoubtedly within a gravitational field or else it could not be orbiting. But the apparent effects of gravity are undone by the fact that the satellite is in free fall. Or you could consider the force of gravity to have been annulled by the effects of centrifugal acceleration. Either way you look at it test particles inside the satellite will be weightless. So are atomic clocks in this situation subject to gravitational time dilation or not?

I think this is a good question. If the answer is that the gravitational potential at which the satellite orbits does slow down the onboard observers’ clocks then they can determine whether they are free falling in gravity field by measuring the frequency of signals received from deep space, a pulsar say, on their local clock. If the signals are coming in too quickly then their clock is running slow. So they can tell that they are in fact free falling in a gravity field. This violates the Einstein Equivalence Principle, even though some authors will try to wriggle out of it by saying that the experiment is not a local one.

If the answer is no then it suggests that gravitational time dilation only occurs when matter has weight. It also suggests that a centrifugal acceleration can undo gravitational time dilation. Both aspects would be worth deep consideration. There would be interesting implications for the Clock Postulate (see an earlier essay).

As far as I can tell the answer is yes, clocks aboard an orbiting satellite are still subject to a degree of gravitational time dilation, quite apart from Special Relativity effects.

Apart from that an orbiting space station is still a potential candidate to be a localized inertial reference frame. But we have to worry about possible rotational effects.

Sagnac interferometers could be used to detect any spinning of the satellite. If the satellite is managed so that there is no spinning detected in any direction then I guess that the satellite is pretty close to being an inertial reference frame. Now let us look out of the windows of the satellite. It is generally accepted that if telescopes were positioned so that they point at very distant galaxies then those telescopes would remain pointed at those distant galaxies.

But then observers on board the satellite would perceive the Earth going round and round the satellite every orbit. And the Sun and nearly stars would all be going around and around too. So is the satellite spinning or not?

You can see that inertial reference frames are not easy to define in practice!

Einstein and the Speed of Light Between 1905 and 1911 Einstein concentrated on generalizing his description of physics and developed an approach/model that has become known as the Theory of General Relativity. By 1911 he had concluded that in the presence of gravity the speed of light is not a fixed invariant. His model of Special Relativity had to be qualified and elaborated upon. The measured speed of light in a gravitational field becomes a variable depending upon the reference frame of the observer.

His logic is contained in his paper On the Influence of Gravitation on the Propagation of Light', Annalen der Physik, 35, 1911. This predates the full description of his General Theory of Relativity by four years. The result he came up with was expressed mathematically as c’ = (1 + Φ/c2).c   where Φ is the gravitational potential relative to the point where the speed of light is measured.

In other words, light appears to travel slower in stronger gravitational fields. There is a more complete description in Section 3 of ‘The Meaning of Relativity', A. Einstein, Princeton University Press (1955).

In 1915 Einstein revised this calculation to be c’ = (1 + 2Φ/c2).c  In other words he decided the effect was twice a great as he first thought.

Unlike in the inertial reference frames of Special Relativity, the measured speed of light in gravitational fields depends upon the reference frame of the observer. What one observer sees as true, another observer sees as not true, or at least slightly different.

If you wanted to be mischievous you could say that Einstein’s Theory of Special Relativity is based upon his proposition that the speed of light is invariant, and his Theory of General Relativity is based upon his proposition that the speed of light is not invariant.

Time in a Gravity Well We know from the impressive achievements made in recent decades in developing GPS systems that atomic clocks at rest on the surface of the Earth run slower than identical clocks on orbiting satellites.

For GPS to work, atomic clocks on Earth have to be very well synchronised with identical clocks aboard specially designed satellites. There are a variety of relativistic effects in play but the main one is due to the fact that the earthbound clocks are in stronger gravity than the orbiting satellites. The effect of gravitation is slightly reduced by centrifugal accelerations caused by the spin of the Earth. The overall gravitational effect is about 45 microseconds per day.

The gravitational time dilation effect is then adjusted for smaller relativistic effects, the main one being a Special Relativistic time dilation because the satellites are moving fast relative to the earthbound clocks. This offsets the gravitational effect by about 7 microseconds per day, giving a net relative adjustment of 38 microseconds per day.

When the satellites were first deployed the scientists in charge were not totally confident how much fine tuning would be required to get perfect synchronisation, so they allowed for a large degree of post launch adjustment. Now they make most of the adjustments before launch.

Of course gravity can have a direct physical effect on clocks. For example, a pendulum clock could not work without it. But that it not what we are talking about here. We are talking about an impact on time itself.

The way I prefer to think about all this is to start with the experimental fact that gravity has an effect on the speed of light. Then I remind myself that the measure of time can be thought of as physical lengths divided by the speed of light. Hence time durations are affected by gravity. And then every physical quantity involving time, notably every form of energy, is also affected.

Shapiro Time Delay The Shapiro time delay effect, or gravitational time delay effect, is now regarded as one of the classic tests of General Relativity. Radar signals passing near a massive object take slightly longer to travel to a target and longer to return than they would if the mass of the object were not present. The time delay is caused by the slowing passage of light as it moves over a finite distance through a change in gravitational potential.

In “Fourth Test of General Relativity”, Physics Review Letters, 20 1265-1269, 1968, Irwin Shapiro wrote, “Because, according to the general theory, the speed of a light wave depends on the strength of the gravitational potential along its path, these time delays should thereby be increased by almost 2x10−4 sec when the radar pulses pass near the Sun. Such a change, equivalent to 60 km in distance, could now be measured over the required path length to within about 5 to 10% with presently obtainable equipment.”

This test was first confirmed by experiments that ‘bounced’ radar signals off the planet Venus when it was just visible on the far side of the Sun as seen from Earth. It has since been measured using Mercury as well, and also using satellites such as the Cassini probe.

Note that seen from afar the path taken by the photons is a curve in both directions. You might think that this is what makes them take longer, but that is not the best way to think of it. The photons are taking the quickest route possible, but they are still delayed by the presence of the gravity field of the Sun. They do actually slow down in the stronger gravity closer to the Sun.

Light in a Gravity Well If we throw a ball upwards in a gravity field the ball decelerates, comes to a temporary stop at the top of its trajectory, and falls again. If we throw it faster than the Earth’s escape velocity the ball can overcome the overall gravitational attraction of the Earth and fly off into space with a certain amount of residual velocity.

What happens to a photon ejected from the surface of the Sun? Several essays ago we discussed and decided that the photon arrives at its destination detector in a weakened state. By comparison to other photons we can deduce that it has less energy and momentum than when it started and the frequency of its effects upon being absorbed are slower. In other words it reveals that it has become red shifted.

Does this mean that photons must travel slower as they climb higher – just like the ball? No – not at all! In fact the opposite is true (to a tiny extent). In the above section we discussed that the speed of light is faster in a weak field than it is in a strong field, and this is an experimental fact. Therefore the speed of photons (as measured by a distant observer) actually increases as the photons move into a weaker and weaker gravitational field.

This seems paradoxical. The arriving photon is travelling faster when its arrives than when it started, as measured from afar, but it arrives with less energy than when it started.

To understand this I think it is useful to note that the speed of a photon (as observed from afar) has no bearing on its energy level. See my earlier essay about energy remaining the same when photons travel in media with different refractive indices. I think the energy of a photon is embodied in the packet of physical properties it takes with it rather than in the speed of that packet as deduced by an external observer.

So how then does the photon become weaker? And where did the energy that is no longer contained in the photon end up? In the example of the thrown ball, what is going on is that as the ball gains in potential energy it loses kinetic energy until eventually it stops moving for a moment and then starts to fall again. There is a tradeoff between potential energy and kinetic energy. The potential energy can be thought of a being stored in the gravitational interaction between the Earth and the ball.

Much the same thing seems to happen to a photon. As it gains potential energy it loses electro-magnetic energy so that when it arrives it is weaker (i.e. redshifted).

I think this is a partially adequate description of what happens. However, if you want to adopt the Einstein Equivalence Principle as literally true and in some ways a better description of reality, and if you want to replace the greatest force in the Universe with the mathematical trickery of curved spacetime, then you can also explain the result using the language of Doppler shifts related to accelerations in curved spacetime. It also gives the right answer, so it becomes a matter of choice which point of view you want to adopt.

If you do use Einstein’s General Relativity model then note that it is only the perturbation of the time term that is needed in order to come up with the observed results for gravitational redshifts. The full field equations are not needed and there is no need to call upon any warping in the spatial aspects of the spacetime geometry.

Textbook Conventions Textbook explanations of Special Relativity invariably adopt Einstein’s postulate that the speed of light is an invariant constant. Many go further and tidy up all their equations by putting c = 1 and measuring all distances in light-seconds. They then drop c out of all the equations. They also carry over this convention into General Relativity.

However, most of the interesting predictions and effects of General Relativity depend upon the speed of light not being an invariant constant. So (in my opinion) writing c=1 and then omitting it from the equations obscures and confuses the physics of interest. Likewise, defining the speed of light to be exactly 299,792,458 meters per second is confusing unless we call this the standard speed of notional light and allow for the fact that the actual speed of light is slightly different from this in nearly all situations of interest and experience.

Conclusions Light slows down in the presence of gravity and so it is not invariant. But what you measure as its speed depends on how you measure it. A local measurement will not detect any difference. The speed of light is fundamental to the concept, meaning and measurement of time. So unless you can get this sorted out in your own mind, your physics is destined to end up in a muddle. And you would not be alone!

[scepticaladventure]

28  Fresh Perspectives Needed  13Sep18

Introduction I have three motivations in writing this series of essays. The first is to improve my own understanding through research, contemplation and organizing my ideas by writing them. The second is to be able to share this journey with others in a plain-English format, just in case anyone is interested or amused by this (which is not the case for my wife, friends and relatives!). My third reason is the hope of provoking fresh thinking in areas that seem to me to be calling out for new insights and answers.

I think modern cosmology is in trouble. 95-98% of the Universe has gone missing and cannot be found. Cosmologists claim to understand the history of the Universe, even before the so-called Big Bang, but cannot explain the motion of stars in spiral galaxies or why the Universe seems to be expanding at an accelerating rate, or why its geometry seems to be so flat. We can’t even deeply explain the motion of a simple Foucault pendulum here on Earth. And our model for light is an unsatisfactory pastiche of conflicting ideas. Paradoxes persist. How long will it take before we agree – we seem to have lost the path, it should not be as hard as this, we have missed something, we have failed to fully understand something fundamental.

So I have gone back through the foundations of modern physics with an open but skeptical mind. It has been a fascinating journey.

Here are my conclusions: 1. Our model for light is clumsy, old fashioned, contradictory and severely limiting. It needs a fresh look. Wave-particle duality is just a label for something we don’t properly understand. 2. The aether theory isn’t dead, it is just sleeping. It ran into problems and was bypassed, shelved and ignored. But maybe Lorentz, Sagnac and others were onto something that needs a fresh and further look. 3. Special Relativity is a work of genius and uncovered some fundamental aspects of Nature. But it rests on three postulates that may not be always, everywhere and entirely valid. 4. The issue of where does inertia comes from in the first place needs some deep consideration. 5. General Relativity is brilliantly successful because it recognizes that both time and the speed of light are affected by gravity. It is also a clever and powerful model that brings a whole lot of new mathematics into play. But for all that it is just a model. 6. If you add the insights of Special Relativity and the fact that gravity slows the speed of light/time back into classical physics you can successfully model, quantify and predict all of the so-called proofs of General Relativity. This shows that General Relativity is an excellent way of looking at certain aspects of Nature, but it is not the only way of understanding Nature. 7. Restricting our viewpoints restricts our understanding and progress. We need some fresh perspectives.

The Cone Here is a parable. Consider a solid cone made out of some hard shiny material. Viewed from one end it will look like a disc. Viewed from the other end it will still look like a disc, but with some indications that it has a symmetrical three dimensional nature and maybe a pointy tip. Viewed side on it will look like a triangle, again with some suggestions of curvature but this time from side to side. Which view is correct? The answer is that all three views are correct, but none is completely correct. Insisting that one view is correct and ignoring the other views is to limit understanding of the true nature of the cone.

I think it is the same with General Relativity. Insisting that it is the only correct way of interpreting the Universe is to limit our chances of developing a deeper understanding.

The Rise of the Metric Approach to Gravity There are various ways to try to describe physics involving gravity. It is clear that four dimensional spacetime is needed and that the lessons of Special Relativity need to be included. Furthermore, the fact that gravity slows down the speed of light and the rate of time points to the need to allow for flexibility in the time dimension. So a flat Minkowski spacetime is not entirely adequate. But this is where the great divide comes in. You can choose to follow Einstein and make use of a fully curved spacetime model, or not.

If you do choose Einstein’s geometric approach then you can regard this as just a model – as Einstein himself did – or you can go further and choose to regard curved spacetime as some sort of fundamental reality. This last step gained popularity after Einstein died, promulgated by luminaries such as Misner, Thorne and Wheeler in the United States and Stephen Hawking in the United Kingdom.

Necessity for Full Spacetime Curvature? N.B. In this essay I will again be making references to a heavyweight textbook on gravity by Charles Misner, Kip Thorne and John Wheeler (MTW):   “Gravitation” C W Misner, K S Thorne, J A Wheeler  Freeman Press,  1970  ISBN 0-7167-0344

MTW have played a major role in promoting the idea that gravity is nothing more than spacetime curvature. Einstein’s own approach was regarded as a curiosity by many scientists for the first forty years of its life but from the middle of the 20th century it gradually assumed the ascendency. Whereas Einstein regarded his full curvature approach to be a useful tool, MTW and others reinterpreted his approach and helped to create the modern view that gravity is just an illusion created by full spacetime curvature.

MTW do not have an open mind on the subject. On p1066 they say “Among all bodies of physical law none has ever been found that is simpler or more beautiful than Einstein’s geometric theory of gravity; nor has any theory of gravity been discovered that is more compelling”. On p1067 they say “For any adequate description of gravity, look to a metric theory”. On p 421 they say “Mass-energy curves space is the central principle of gravity”. On p429 they praise General Relativity because “It describes gravity entirely in terms of geometry; most of its competitors do not”. And John Wheeler is often quoted as saying “Matter tells spacetime how to curve and curved spacetime tell matter how to move.”

Clifford M Will was a student of Kip Thorne at Caltech and later became a leading professor of physics, specializing in General Relativity. I will use quotes from his online article “The Confrontation between General Relativity and Experiment” June 2014, SpringerLink, and his overview “Was Einstein Right? A Centenary Assessment” 33 pages, 8 figures, published in General Relativity and Gravitation: A Centennial Perspective, eds. A. Ashtekar, B. Berger, J. Isenberg and M. A. H. MacCallum (Cambridge University Press), 2015. Abridged version at arXiv:1403.7377.

Will presents the Einstein Equivalence Principle and Strong Equivalence Principle in confusing ways, with each principle containing other principles. Will then says that the equivalence principles are the heart and soul of gravitational theory, “for it is possible to argue convincingly that if they are valid, then gravitation must be a ‘curved spacetime’ phenomenon.” In other words, the effects of gravity must be equivalent to the effects of living in a curved spacetime.

I think that to whether “the effects of gravity must be equivalent to the effects of living in a curved spacetime curvature” is true or not depending on what it meant by ‘equivalent’. If the author means “can be satisfactorily modeled by” I would happily agree. If the author means we live in a curved spacetime reality and gravity does not exist, then I think that he has gone too far. Further than Einstein ever went and further than is reasonable.

The Parametrized Post Newtonian Formalism The Parameterized Post-Newtonian Framework (PPN) was developed over 50 years by illustrious physicists such as Eddington, Robertson, Schiff, Nordtvedt and Will. The PPN formalism adds ten generic parameters to a basic version of General Relativity. The parameters can be adjusted so that the PPN can represent a whole variety of competing geometric models of gravity, including subtle variations of General Relativity itself. The idea is then to use experimental results to put limits on the parameters as a way of weeding out the range of theories and preventing new weeds from taking hold.

Theories subject to this treatment include Einstein’s General Relativity (1915), Whitehead (1922), one of Bergman’s (1968) scalar-tensor theories, one of Nordstrom’s theories, theories by Birkhoff (1943), Dicke-Brans-Jordan (1961, 1959), Ni (1970, 1972) and many others.

Suffice it to say that plain vanilla General Relativity complies neatly with these tests and the other models struggle.

The work by Will also covers a lot of metric theories, classified into General Relativity, scalar-tensor theories (of which the Jordan–Fierz–Brans–Dicke theory is a good example), vector-tensor theories and scalar-vector-tensor theories. Let me quote from the second of the Will references mentioned above: • A number of theories fall into the class of “prior-geometric” theories, with absolute elements such as a flat background metric in addition to the physical metric. Most of these theories predict “preferred-frame” effects that have been tightly constrained by observations. An example is Rosen’s bi-metric theory. • A large number of alternative theories of gravity predict gravitational wave emission substantially different from that of general relativity, in strong disagreement with observations of the binary pulsar. • Scalar-tensor modifications of general relativity have become very popular in unification schemes such as string theory, and in cosmological model building. Because the scalar fields could be massive, the potentials in the post-Newtonian limit could be modified by Yukawa-like terms. • Theories that also incorporate vector fields have attracted recent attention, in the spirit of the Extension of the Standard Model (of sub-atomic particles), as models for violations of Lorentz invariance in the gravitational sector, and as potential candidates to account for phenomena such as galaxy rotation curves without resorting to dark matter.

Again Will uses a range of experimental results and concludes that plain vanilla General Relativity complies neatly with these tests and the other models do not.

My problem with all this work is not its intention, but the way it is carried out. MTW, Will and Nordtvedt make up the rules, act as prosecutor, select the evidence, interpret the evidence and act as jury and judge. If they encounter a problem in a theory they allow no attempt to fix it. They simply bayonet the wounded theory, declare it dead and buried, and move on to the next.

Einstein struggled for ten years to develop his General Relativity model, with many twists and turns. He produced an initial calculation for the light bending effect that was half the final result. He argued for, then against, and finally for the existence of gravitational waves. He introduced a cosmological constant and then called it a mistake. So it may be a bit harsh and possibly premature to kill off other models at the first sign of a problem.

Models with Backgrounds The antagonism by MTW towards alternate theories of gravity and alternate interpretations of Einstein’s approach shows up in the discussion by MTW of attempts to view gravity as a standard type of field situated in a flat spacetime background.

This approach has been developed and explored by notable theorists such as Gupta, Kraichman, Thirring, Feyman, Weinberg and Deser (see MTW p436). It offers one of several routes to the field equations of Einstein’s General Relativity.

One version (Fierz and Pauli 1939) borrowed from quantum theory and envisages gravity as occurring via the exchange of gravitons – hypothetical zero rest mass particles with a spin number of 2. MTW claim that by the time this approach is fully developed the original flat spacetime has become unobservable. MTW dismiss the theory (p437) because it is silent about the emergence of the Universe from an initial singularity - the Big Bang Theory. Hence MTW dismiss a serious attempt to bring together the two pillars of modern physics because it is silent about something else that they like.

MTW start their more general discussion of models with backgrounds by stating that any flat background must be unobservable (p424). This is the same point of view put to Lorentz by Einstein in relation to Special Relativity.

Einstein did not deny the possibility of a background that may or may not correspond to a lumiferous aether. He just argued that if it cannot show up in Michelson-Morley type experiments it must be unobservable and hence not useful.

MTW praise General Relativity for being free of any ‘prior geometry’, and criticize any competitors which admit this as a possibility. I think they have a point because I think that all geometry is a man-made overlay and hence has no prior reality. In fact no reality at all except in our own minds. But I think that that agreeing that there is no prior geometry is not quite the same as agreeing that there is no background. It might just mean that the background has no prior geometry.

I think this subtle difference is vitally and fundamentally important.

In my view, Newton’s rotating bucket, the Foucault pendulum and the Sagnac interferometer all readily distinguish reference frames which are rotating or accelerating from ones which are not. The Cosmic Microwave Background does the same. Conversely, Einstein’s attempt to explain why some objects demonstrate rotational phenomena and others do not by imposing boundary conditions on his cosmological models was a failure. Einstein thought so anyway, even though it suits many modern cosmologists to disagree.

So why do MTW show such antagonism to the idea of a cosmological background? I think it might be because they conflate it with ‘prior geometry’. However, to their credit they attempt to clarify their language. On p 429 they say “By ‘prior geometry’ one means any aspect of the geometry of spacetime that is fixed immutably, i.e. that cannot be changed by changing the distribution of gravitating sources”.

So what about a background geometry that is affected by the distribution of gravitating sources in the Universe? This echoes the argument put forward by Ernst Mach towards the end of the 19th century. Einstein admired the idea so much that he dubbed it “Mach’s Principle.” (Einstein endeavored to incorporate the idea into his theories all his life, but eventually concluded that he had not been successful.) If the background is given a Machian interpretation then I think it has to be taken very seriously.

There seems to be a confused belief that the idea of a background conflicts with something that Einstein called the Principle of General Covariance. This principle states that the outcome of physical experiments does not depend on the choice of reference frame in which to view them. In other words, physics is agnostic to reference frames invented by observers for their own convenience.

This principle is entirely reasonable, but has little to do with the fact that some reference frames are more equal than others. For example, frames that are not accelerating or rotating do not contain spurious forces deflecting unattached test particles all over the place.

It is robustly true that the physical outcomes are the same whatever reference frame you chose to use – it is just that the ease of describing what is going on them is vastly different depending on the frame you happen to choose to describe them in. Choose your frame right and you do not have to invent  ‘fictitious’ forces to balance the books.

An example of the type of effort that I admire is a modeling approach developed by W T Ni in 1970 and 1972 (see MTW p1070). This has a background geometry and treats gravity as a scalar field. MTW agree that the theory satisfies the equivalence principle (which version is not clear), and that the model is self-consistent and complete. But then they say “If the solar system were at rest in the ‘rest frame of the Universe’, the theory would agree with all experiments to date – except possibly for the expansion of the Universe. But the motion of the solar system through the Universe leads to serious disagreement with experiment (Will and Nordtvedt 1972)”.

The alleged fatal flaw comes from work by Will in 1971 that suggests that the force between two massive objects will depend on the way in which they are travelling through the background metric. This is calculated to create a twice-a-day fluctuation in the tides on Earth and also to tidal fluctuations within the Earth that conflicts with the experimental evidence. This leads Will to claim that the theory of Whitehead (1922) and of Ni (1972) cannot be correct. But is Will correct?

When Galileo presented his model of a spinning Earth orbiting a stationary Sun, the wise men of the day calculated that the tangential speed of the Earth’s surface could be anything up to 1600km/hour and said that Galileo’s model could not possibly be true because no bird could fly that fast in order to keep up. It was not an unreasonable point because this was in the days prior to Torricelli and hence there was not yet a concept of the atmosphere being a thin layer coating the earth with no viscous drag where it meets the vacuum of space. Likewise Will’s objection could be perfectly reasonable and clever, but nevertheless wrong.

Since General Relativity and modern physics generally cannot explain the enormous anomaly in the motion of stars in the discs of all spiral galaxies (without inventing hypothetical dark matter) there is clearly something occurring that is not well explained by the conventional paradigm. So it may be unwise to be too definite about what is right and what is wrong at this stage. What if the type of thinking put forward by Ni resolves the galaxy rotation curve crisis?

The Fabric of Spacetime? It is common to hear expressions such as “the fabric of spacetime”, and “spacetime tells matter how to move”. It is also common to see diagrams with spacetime depicted as a curved or distorted rubber sheet with dimples around massive objects forcing the path of freely moving bodies into curves and orbits.

This is a bit unfortunate. It tends to create the impression that spacetime is a real thing, an actual entity. That moving objects are deflected because they hit a bump in the road.

Spacetime is a just way of defining places and moments, lengths and times in a satisfactory way so we can describe what is going on. We do this sort of thing all the time, but we need to be careful not to get confused between our imagined constructs and actual reality.  

For example, we have an agreed way of assigning lines of latitude and longitude to the surface of the Earth. This creates a two dimensional grid. But it is not real. You cannot see it, touch it, taste it, smell it or hear it. You cannot detect it with any instruments. It does not interact with matter in any shape or form. The motion of everything on Earth is oblivious to the imaginary grid that we have imagined and agreed upon for our own convenience of reference.

It is the same with spacetime. Curved or not. It is just a reference frame that we overlay onto physical reality to make it easier to talk about what is going on. If it proves convenient to use a warped geometry then use that. If some other representation is more convenient then use that one instead. It makes no difference to actual reality.

Imaginary reference frames are useful for describing physical systems. That is all. Spacetime does not exist as a thing in its own right, any more than the lines of latitude and longitude exist on the surface of the Earth. Spacetime curvature does not tell matter how to move any more than the lines of latitude and longitude tell ships and planes how to move, or ducks how to migrate. It is important not to become confused between descriptions of reality that we happen to find useful and reality itself.

When someone says “matter tells spacetime how to curve and spacetime curvature tells matter how to move” we should not take the words too literally. It would be better to remind ourselves that we have imposed an imaginary and somewhat arbitrary reference frame across the physical system we are trying to describe and that for some purposes we find it convenient to model the effects of gravity by using a warped four dimensional framework.

I know that General Relativity can be recast in terms so generic that the convenience of coordinates can be dispensed with all together. However I do not think this alters my point.

I am also familiar with the argument that goes as follows. By applying geometry to the surface of the Earth we can discover that two dimensional geometry which is locally Euclidean no longer works on a larger scale, thus revealing that the surface of the Earth is a curved manifold in three dimensional space. Similarly, applying four dimensional geometry which is locally Lorentzian on a larger scale reveals that spacetime curvature is necessary to account for physical dynamics in the presence of gravity. I would agree with this if I thought that Einstein’s Equivalence Principle was literally true. But I don’t. I think that gravity can be mimicked by a linear acceleration to a certain degree, and that it is possible to build clever mathematical models based on this fact. But is gravity, the most dominant force in the Universe, just an illusion created by a quirk of geometry? I don’t think so.

Is General Relativity Perfect? Yes, you can get rid of gravity by imagining spacetime is curved. Yes this is brilliant stuff. Yes this produces a small number of remarkable (very small) predictions that turn out to be true. And yes it is possible to build innumerable wonderful cosmological models using curved spacetime geometries. But that is not conclusive proof that the modern version of General Relativity is the only way to look at the Universe, the best way to look at the Universe, or even the most convenient way to look at the Universe.

General Relativity is very hard to use and I think the results of its over complicated mathematics throw up more questions than they answer. And while I am being heretical, I may as well produce a list of criticisms. In my naive opinion, the modern version of General Relativity: 1. is based on a Principle of Equivalence which is just a mathematical assumption 2. elevates spacetime to a status it does not deserve 3. does not explain why matter, stress and energy distort spacetime 4. does not explain the origins of linear or rotational inertia 5. does not explain why matter has mass 6. is so complicated that it enables mathematicians to come up with a whole range of solutions which have no correspondence in Nature 7. creates red herrings that waste everyone’s time 8. has not helped with the dilemmas of missing Cold Dark Matter and Dark Energy 9. has predictions which can be accounted for in other ways 10. obscures, bypasses or overshadows a lot of fundamental issues that deserve more attention.

In many ways, the proof of the pudding is in the eating. A century after General Relativity was produced, most astronomers do not use it except in special circumstances such as gravitational lensing and black holes. In day-to-day discussions they just use a post-Newtonian approximation. And although Einstein and modern ‘metricists’ seem to be averse to any ‘a priori’ geometry in the Universe, astronomers nevertheless find it convenient to have agreed reference frames for the Solar System, the Milky Way and the wider Universe. Are they are instinctively using something that has physical significance?

Spatial Curvature on a Cosmological Scale Einstein’s General Relativity model requires mass/energy to warp spacetime. Its equations involve mass/stress/energy tensor warping the 4x4 spacetime metric tensor in all of its sixteen components (six of which are duplicates due to symmetry).

Suppose there are three spacecraft at rest with respect to each other and the cosmic microwave background. Connect them by laser beams and measure the angles between the three beams. The beams form a triangle. If the interior angles always add up to 180 degrees, then spacetime is flat. If the sum of the angles is more or less than that, then space has positive or negative curvature.

As far as we can tell, on a very large spatial scale our Universe is flat. Very flat. Parallel lines in intergalactic space will never meet. But this requires a very particular value for the universal stress energy tensor. Theorists have been struggling for nearly a century to explain why this might be so. It would be a remarkable coincidence if the average mass/stress/energy in our Universe happens to be exactly the right amount for universal spacetime to have neither positive nor negative curvature on a macro scale.

So Why is our Universe so Flat? The Einstein-Friedmann-Robertson-Walker models of the Universe involve solutions for Einstein’s equations based on the assumption that the Universe is more or less uniformly filled with mass/stress/energy, a bit like a perfect fluid. The equations have solutions which have positive curvature (like a sphere in 3D), negative curvature (like a hyperbolic surface in 3D) or zero curvature (i.e. flat) depending on the energy density measured by the omnipresent mass/stress/energy tensor.

But observations show the Universe is flat. So how did the Universe come up with exactly the right amount of mass/stress/energy to arrive at this special case? Theorists have come up with all sorts of suggestions, but it is still a mystery.

I have a much simpler answer. The Universe is flat because is has always been flat and that is the only thing it can be. The non-flat Friedmann solutions are just artifacts of the model and the assumptions used in obtaining its generic solutions. Not all aspects of the solutions have to correspond to reality.

When I read the debate between cosmologists about possible values for the cosmological constant I cannot help but be reminded of the debate between medieval theologians about how many angels can dance on the head on a pin. All very clever, but maybe not very useful.

Consider the Cartesian map analogy again. It is possible to map the surface of the earth onto a two dimensional surface by allowing the lines of longitude to move further and further apart as the distance from the equator increases. This is very useful, especially when reproducing maps on paper. But it produces singularities at the north and south poles. It is no good worrying about the meaning of these singularities and what bizarre things might be happening at the poles because the singularities do not exist in reality – they are just an artifact of the mathematical approach used to build the two dimensional model.

Likewise, you can waste time worrying why the Universe is flat, or you can just accept that the non-flat mathematical solutions are an artifact of a particular set of solutions to a peculiar model of the Universe based on a peculiar approach to describing physics.

I say peculiar model of the Universe because it seems to me that the Einstein-Friedmann-Robertson-Walker models of the Universe rest on some doubtful assumptions. Friedmann was not making assumptions summarizing actual experimental observations – he was just making gross simplifications in order to be able to get a handle on the mathematics. I don’t think the Universe is anything like a homogeneous perfect fluid. The more we look the more we find macro patterns in its structure. Huge super-clusters of galaxies, filaments, voids and walls. The analogy to the particles in a fluid are the galaxies. However, unlike the molecules in a fluid, the space between the galaxies contains a lot of intergalactic dust, neutrinos and photons. Furthermore galaxies collide with each other in ways that are totally different to the ways that molecules collide in a fluid. And the list of differences goes on.

I think the large scale geometry of our Universe is so flat because it was never curved. Cosmological curvature is our idea – not Nature’s.

Conclusion Inspired by Einstein’s great work there have been literally dozens of other models of gravitation over the last hundred years or so.

At first gravitation theory was a theorist’s paradise but an experimenter’s purgatory. Since the 1960’s however, developments in space technology and astronomy have created the ability to test many aspects of this work. The clear winner has been Einstein’s original theory. So much so that many scientists regard spacetime curvature not as a model of what is going on in nature, but as a fundamental new reality.

I think this is a mistake. I think that General Relativity is a very clever and successful model, but a model none-the-less. There is plenty that we do not yet understand properly about the Universe, how it works and how it evolved. Refusing to consider alternative approaches has the strong likelihood of unnecessarily limiting our understanding and delaying the next generation of breakthroughs.

General Relativity leaves key questions unanswered, e.g. in relation to the origins of inertia and the dynamics of spiral galaxies. The fact that 98% of the Universe required by theory cannot actually be found may be trying to tell us something - we have missed something fundamental. We have got off track. Something is wrong somewhere.

The current orthodoxy is a cage to our thinking and it deserves to be rattled and shaken. And finally a message to young scientists – please do not stop asking questions and do not stop questioning what they tell you, especially if it seems fudged.

A quote from a lecture Einstein gave in 1921: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain they do not refer to reality.”

[scepticaladventure]

29  Bells Inequality  30Sep18

Bell’s Inequality is a simple mathematical result that can be applied to any set of objects where there are three potential properties for those objects and the objects must have one, two or three of those properties. For example, consider a set of 100 men who are wearing hats and/or scarves and/or gloves.

It is called Bell’s Inequality not because it was discovered by the Irish physicist John Stewart Bell but because it was used by him in an influential argument about the nature of quantum mechanics and reality. His argument is generally known as Bell’s Theorem. Experiments that follow his suggestion as to how to test his ideas are called Bell’s Experiments.

I will be discussing all that in the next few essays but first I’d like to get Bell’s Inequality out of the way.

Bell’s Inequality Consider a set of objects, fixed in number, and three properties X, Y and Z. For each object the simple question “does it have property X?” must be answerable by a simple Yes or No and that answer must remain fixed. For each object the simple question “does it have property Y?” must be answerable by a simple Yes or No and that answer must remain fixed. For each object the simple question “does it have property Z?” must be answerable by a simple Yes or No and that answer must remain fixed. Hence a particular object can have one, two or three of the properties.

Denote: 

the number of objects that have property X and not property Y by <X, Y>.   the number of objects that have property Y and not property Z by <Y, Z>.   the number of objects that have property X and not property Z by <X, Z>.  

Bells’ Inequality is simply that  <X,Y> + <Y,Z>   ≥   <X,Z> i.e. the number of objects with property X and not property Y plus the number of objects with property Y and not property Z must equal or exceed the number of objects with property X and not property Z.

Note the pattern in the equation. Y is repeated on the left hand side (the first time in the negative) but does not appear on the right hand side.  It ‘drops out’ on the right hand side leaving just the extremities of the left hand side to create the solitary term on the right.

Example: A fixed group of men and the three properties  ….  wearing hats, wearing scarves and wearing gloves.  Bell’s Inequality says: The number of men wearing hats but not scarves, plus the number of men wearing scarves but not gloves, must equal or exceed the number of men wearing hats but not gloves.

In fact there are six inequalities like this.  The first symbol can be any one of the three properties and the second symbol can be any one of the remaining two symbols. For example  <Z,Y> + <Y,X>  ≥  <Z,X>  must also be true. There is nothing mysterious about this – it is just simple mathematics.

Proof of the Inequality The simplest way to demonstrate the proof of the inequality is to use a Venn Diagram.

Figure:   Venn diagram of a set of objects with properties X and/or Y and/or Z.  The lower case letters represent numbers. The number of objects with only property X is a, the number with all three properties is e and so on. Adding up all the numbers gives the total number of objects. If you want to get fancy you can make the size of each separate area proportional to the number of objects it represents.

Proof:   <X,Y>  +  <Y,Z>   ≥   <X,Z> becomes (a + d) + (b + c)  ≥  (a + b) which must be true because the left hand side contains the extra numbers d and c.

If you want an intuitive explanation try this. The left hand side is bigger than the right because it is boosted by some objects in X that do in fact have property Z and also by objects which have only property Y.

Example: 

 Figure:   Venn diagram of a set of men wearing hats and/or scarves and/or gloves.  

There are 42 men in total. Let’s check the Bell Inequality that says that the number of men wearing hats but not scarves, plus the number of men wearing scarves but not gloves, must equal or exceed the number of men wearing hats but not gloves. The number wearing hats but not gloves is 12+5 = 17. The number wearing hats but not scarves is 14 and the number wearing scarves but not gloves is 15, giving a combined total of 29 and this is greater than 17 so the inequality holds (as it must).

A strange case of Hats, Scarves and Gloves Suppose that we replace all the men by twins and put half of each twin pair in a group on the left and the other half in a group on the right. When we do our survey of how many men are wearing hats but not scarves, how many are wearing scarves but not gloves, and how many are wearing hats but not gloves, we get the first part of our answer by surveying the group on the left, and the answer to the second part of each question by surveying the group on the right.

This is analogous to what happens in the Bell experiment. But note that it is more complicated than in the simple Bell Inequality. Some additional assumptions have crept into the story. We have to assume that each member of each twin pair is always dressed exactly the same as the other. We also have to assume that splitting our sampling method is not distorting the results.

What happens if the sample set’s behaviours are not simple and static? I think problems arise.

Suppose the men wearing hats have a fickle habit in relation to wearing scarves and if they are not wearing a scarf and feel a bit cold they pull a scarf out of their pocket and wear it for short periods of time. Each twin does exactly the same as their sibling. The men not wearing hats do not do this.

Likewise suppose the men wearing scarves have a fickle habit in relation to wearing gloves. If they are not wearing gloves and are feeling a bit cold they tend to pull a pair of gloves out of their pocket and put them on for short periods of time. Each twin does exactly the same as the other. The men with no scarves do not do this.

If we count hats on one side and no scarves on the other side we will get a low statistic due to the extra scarves that have been put on. If we count scarves on one side and no gloves on the other side we will get a low statistic due to the extra gloves that have been put on. If we count hats on one side and no gloves on the other side we will get the same answer as always because wearing hats does not influence glove wearing behaviour.

In these circumstances Bell’s Inequality does not apply.  The statistics could easily give a relationship that does not comply with the relationship set out in Bell’s Inequality.

The Simple Pub Crawl I’ll give some more examples and increase the complexity a bit in a way that will be relevant to some of the physics I want to discuss in subsequent essays.

Let us suppose that a group of people are in a village with three pubs/hotels/bars and they have all decided to go on a pub crawl. They can each visit one, two or three pubs (and each pub no more than once). Let us call the pubs X, Y and Z.

Let us take an example where 10 people visit X only, 6 people visit Y only and 4 people visit Z only.  1 person visits X and Y (but not Z), 2 people visit Y and Z (but not X) and 3 people visit X and Z (but not (Y).  Two hardy souls visit all three pubs.

How many people are there? Just add all the numbers together. Answer is 28. Which pub is the most popular? Answer is X with 16 visits. How many people visit at least 2 pubs? Answer is 8. OK – got the picture? Now let’s try Bells Inequality.

For each person we can ask – did you exit pub X, yes or no? Did you exit pub Y, yes or no? Did you exit pub Z, yes or no? We have the conditions for Bell’s Inequality to apply.

We can now ask every person ‘Did you leave X but not Y? Did you leave Y but not Z? Did you leave X but not Z?’ Add together the number of people that visited X but not Y, and the number that visited Y but not Z. Answer is 13 + 7 = 20. Compare this to the number visiting X but not Z. Answer is 11. Bells Inequality is satisfied because 20 is greater than 11.  Note that the number of people who visited all three pubs doesn’t come into it.

A month later the pub crawl is held again. Word has got around and 100 people turn up for the event. The organisers add a new rule. The participants can visit 1, 2 or 3 pubs as they prefer, but they have to visit X first and any of the others in alphabetical order. The organisers monitor the event by placing motion detectors outside each pub.

They note that 100 people emerged from pub X, 85 people emerged from pub Y and 50 people emerged from pub Z.  (XY) is the number that emerged from X but not Y and so is 100 – 15 = 85.  (YZ) is the number that emerged from Y but not Z and so is 85 - 50 = 35.  (XZ) is the number that emerged from X but not Z and so is 100 – 50 = 50. Arranged in the form of Bell’s inequality gives 85 + 35 ≥ 50 which is clearly true.

The Triple Pub Crawl Let me use a new version of the pub crawl story. The participants have to visit two or three pubs. The pubs they do visit have to be visited in alphabetical order (i.e. XY, YZ and XZ). Furthermore if they visit a pub they do not have to leave it again. If they do exit a pub they will pass through a person-counter. The pubs act a bit like filters. Some participants get stuck in X, some get stuck in Y and some get stuck in Z.

Disaster strikes! On the occasion of the new format pub crawl it turns out that pub Y has been booked for a wedding and is not available. However the organisers decide to proceed anyway as 64 people have turned up for the event. When they collect the counters the next morning they observe that 32 participants exited pub X but none exited Pub Z. Curious, especially as the organisers are sure that quite a few people that left pub X did go into pub Z.

The next time they hold the same event, pub Y is not closed and so all three pubs are available. 64 people again turn up for the event. The organisers decide that everyone has to visit all three pubs, starting with X. When the organisers collect the counters the next morning they observe that 32 people exited pub X, 16 exited pub Y and 8 exited club Z.

So again we have a set of objects (in this case people). And for each person we can ask – did you exit pub X, yes or no? Likewise pub Y and pub Z. And then we can ask each person Did you leave X but not Y? did you leave Y but not Z?  and  Did you leave X but not Z?

So we have the conditions for Bells Inequality to apply. Let’s check it.  <X,Y> + <Y,Z> = 16 + 8 = 24  whereas <X,Z> = 24.  So Bell’s Inequality holds (just).

The more interesting thing to note here is that adding back the middle pub Y has led to more people managing to exit the third pub Z than when pub Y was missing. It seems that pub Y has somehow conditioned participants to survive pub Z a lot better.

That would be a bit surprising in a real pub crawl experiment. But perhaps possible, especially if the participants are Australian.

What is surprising is that it always happens in what I call the three polarizers experiment. The photons are replaced by people and the pubs are replaced by linearly polarized filters. A beam of photons is aimed to pass through all three polarizers. Polarizer Z is turned at an angle of somewhere between zero and 90 degrees to the first polarizer and the middle polarizer is oriented with half that angle of turn. When the middle polarizer is taken away the number of photons leaving the last filter is low. Putting the middle polarizer back again increases the total number of photons exiting the last filter. The brightness of the emergent light increases even though an extra filter has been added. It is a simple neat experiment that you can do at home.

I hope you enjoyed this brief excursion into some mathematics.

[scepticaladventure]

27  Gravitational Waves  12Sep18

Introduction This essay continues my series of essays discussing tests of Einstein’s Theory of General Relativity. More detailed descriptions of the test themselves can be found online and in the literature. See for example the literature review in May 2017 by Estelle Asmodelle from the University of Central Lancashire Ref:  arXiv:1705.04397 [gr-qc] or arXiv:1705.04397v1 [gr-qc].

I have questioned whether the experimental tests exclude any other explanations for the same phenomenon. So far I have examined gravitational redshifts and gravitational light bending, the Shapiro round-trip light delay and the ‘anomalous’ precession of Mercury. The evidence so far is that while General Relativity provides a satisfying explanation for all of these experimental observations, other ways of describing the outcomes are also viable. Hence there may be more than one way to include all the evidence within a different but still complete and consistent model or theory.

In this essay I will look at the latest of the five so-called tests – gravitational waves.

Gravitational Waves Gravitational waves are generated in certain gravitational interactions and propagate as waves outward from their source at the speed of light. Their possibility was discussed in 1893 by the polymath Oliver Heaviside, using the analogy between the inverse-square laws in both gravitation and electricity.

In 1905, Henri Poincaré suggested that a model of physics using the Lorentz transformations (then being incorporated into Special Relativity) required the possibility of gravitational waves (‘ondes gravifiques’) emanating from a body and propagating at the speed of light.

Some authors claim that gravitational waves disprove Newton’s mechanics since Newton assumed that gravity acted instantaneously at a distance. I think this is unfair to Newton. Whether or not Newton explicitly claimed that gravity acted instantaneously at a distance I do not know, but it would have been a reasonable and pragmatic working assumption to make at the time. Furthermore whether he assumed instantaneous effects or delays at the speed of light makes no practical difference to the validity of Newton’s work for the type of celestial mechanics he was interested in.

In 1916, Einstein suggested that gravitational waves were a firm prediction of General Relativity. He said that that large accelerations of mass/energy would cause disturbances in the spacetime metric around them and that such disturbances would travel outwards at the speed of light. A spherical acceleration of a star would not suffice because the gravity effects would still be felt as coming from the centre of mass. The cause would have to be a large asymmetric mass that was rotating rapidly. Or better still, two very large masses that were rotating around each other.

In general terms, gravitational waves are radiated by objects whose motion involves acceleration and changes in that acceleration, provided that the motion is not spherically symmetric (like an expanding or contracting sphere) or rotationally symmetric (like a spinning disk or sphere).

A simple example is a spinning dumbbell. If the dumbbell spins around its axis of its connecting bar, it will not radiate gravitational waves. If it tumbles end over end, like in the case of two planets orbiting each other, it will radiate gravitational waves. The heavier the dumbbell, or the faster it tumbles, the greater the gravitational radiation. In an extreme case, such as when two massive stars like neutron stars or black holes are orbiting each other very quickly, then significant amounts of gravitational radiation will be given off.

Over the next twenty years the idea developed slowly. Even Einstein had his doubts about whether gravitational waves should exist or not. He said as much to Karl Schwarzschild and later started a collaboration with Nathan Rosen to debunk the whole idea. But instead of debunking the idea Einstein and Rosen further developed it and by 1937 they had published a reasonably complete version of gravitational waves in General Relativity. Note that this is 22 years after the General Theory was first published.  

In 1956, the year after Einstein’s death, Felix Pirani reduced some of the confusion by representing gravitational waves in terms of the manifestly observable Riemann curvature tensor.

In 1957 Richard Feynman argued that gravitational waves should be able to carry energy and so might be able to be detected. Note that gravitational waves are also expected to be able to carry away angular or linear momentum. Feynman’s insight inspired Joseph Weber to try to build the first gravity wave detectors. However his efforts were not successful. The incredible weakness of the effects being sought cannot be over emphasized.

More support came from indirect sources. Theorists predicted that gravity waves would sap energy out of an intensely strong gravitational system. In 1974, Russell Alan Hulse and Joseph Hooton Taylor, Jr. discovered the first binary pulsar (a discovery that would earn them the 1993 Nobel Prize in Physics). In 1979, results were published detailing measurement of the gradual decay of the orbital period of the Hulse-Taylor pulsar, and these measurements fitted precisely with the loss of energy and angular momentum through gravitational radiation as predicted by calculations using General Relativity.

Four types of gravitational waves (GWs) have been predicted. Firstly, there are ‘continuous GWs,’ which have almost constant frequency and relatively small amplitude, and are expected to come from binary systems in rotation, or from a single extended asymmetric mass object rotating about its axis.

Secondly, there are ‘Inspiral GWs,’ which are produced by massive binary systems that are spiralling in towards one another. As their orbital distance lessens, their rotational velocity increases rapidly.

Then there are ‘Burst GWs,’ which are produced by an extreme event such as asymmetric gamma ray bursters or supernovae.

Lastly, there are ‘Stochastic GWs,’ which are predicted to have been created in the very early universe by sonic waves within the primordial soup. These are sometimes called primordial GWs and they are predicted to produce a GW background. Personally I doubt that this last type of GW exists.

On February 11, 2016, the LIGO and Virgo Scientific Collaboration announced they had made the first observation of gravitational waves. The observation itself was made on 14 September 2015, using the Advanced LIGO detectors. The gravity waves originated from a pair of merging black holes millions of years ago that released energy equivalent to a billion trillion stars within seconds. For the first time in human history, mankind could ‘feel and hear’ something happening in deep space and not just ‘see’ it. The black holes were estimated to be 36 and 29 solar masses respectively and circling each other at 250 times per second when the signal was first detected.

By August 2017 half a dozen other detections of gravitational waves were announced. I think all of them have been in-spiral GW’s. These produce a characteristic ‘chirp’ in which the signal becomes quicker and stronger and then stops. This is very useful for finding the signal amongst all the background noise. The flickering light pattern signal in the interferometer detector can be turned directly into a sound wave and actually does sound like a chirp.

In 2017, the Nobel Prize in Physics was awarded to Rainer Weiss, Kip Thorne and Barry Barish for their role in the detection of gravitational waves. (The same Kip Thorne who co-authored the heavyweight textbook on gravity that I have referred to so often in these essays that I gave it its own acronym -  MTW).

As I first drafted this essay in 2017 there was considerable excitement in the world of astronomy because the Large Interferometer Gravity Wave Observatories (LIGO) suggested that a pair of neutron starts were in the process of collapsing. Space based telescopes were then able to look in that direction and they observed an intense burst of gamma rays. This is the first example of the two types of observational instruments working together and the dual result confirms that LIGO had been observing what they thought they were observing. Furthermore it provides evidence that gravitational waves travel at the speed of light.

Detection LIGO is a large-scale long-term physics project that includes the design, construction and operation of observatories designed to detect cosmic gravitational waves and applied theoretical work to develop gravitational-wave observations as an astronomical tool. It has been a struggle lasting many decades. It took many attempts to achieve funding for the observatories and nearly a decade to make the first successful observations. A triumph of persistence, optimism and the begrudging willingness of the USA National Science Foundation to fund a speculative fundamental science project to the tune of US$1.1 billion over the course of 40 years.

To my mind the experimental set up is reminiscent of Michelson Morley experiments 140 years ago. But it is on a much larger scale and is incredibly more sensitive, with all sorts of very clever tricks to increase the sensitivity and to get unwanted noise out of the system. Two large observatories have been built in the United States (in the states of Washington and Louisiana) with the aim of detecting gravitational waves by enhanced laser interferometry. The observatories have mirrors 4 km apart. Each arm contains resonant cavities at the end.

When a gravitational wave passes through the interferometer, the spacetime in the local area is altered. Depending on the source of the wave and its polarization, this results in an effective change in length of one or both of the beams. The effective length change between the beams will cause the light currently in the cavity to become very slightly out of phase (anti-phase) with the incoming light. The cavity will therefore periodically get very slightly out of coherence and the beams, which are tuned to destructively interfere at the detector, will have a very slight periodically varying detuning. This results in a measurable signal.

Or, to put it another way: After approximately 280 trips up and down the 4 km long evaluated tube arms to the far mirrors and back again, the two beams leave the arms and recombine at the beam splitter. The beams returning from two arms are kept out of phase so that when the arms are both in coherence and interference (as when there is no gravitational wave or extraneous disturbance passing through), their light waves subtract, and no light should arrive at the final photodiode. When a gravitational wave passes through the interferometer, the distances along the arms of the interferometer are repeatedly shortened and lengthened, creating a resonance and causing the beams to become slightly less out of phase and thus allowing some of the laser light to arrives at the final photodiode, thus creating a signal.

Light that does not contain a signal is returned to the interferometer using a power recycling mirror, thus increasing the power of the light in the arms. In actual operation, noise sources can cause movement in the optics that produces similar effects to real gravitational wave signals. A great deal of the art and skill in the design of the observatories, and in the complexity of their construction, is associated with the reduction of spurious motions of the mirrors. Observers also compare signals from both sites to reduce the effects of noise.

The observatories are so sensitive that they can detect a change in the length of their arms equivalent to ten-thousandth the charge diameter of a proton. This is equivalent to measuring the distance to Proxima Centauri with an error smaller than the width of a human hair.

Although the official description of LIGO talks about gravitational waves shortening and lengthening the arms of the interferometers by almost infinitesimal amounts, I think it might also be reasonable to describe what is going on as very slight changes in the speed of the photons being reflected back and forth 280 times in the 4 km long arms, as compared to the reference photons in the resonant cavities.

Some Comments on the Interpretation Commentators continually refer to gravitational waves as being “ripples in the fabric of spacetime”. There seems to be some deep-seated human desire to regard spacetime as being real and tangible, more or less like some sort of four dimensional fluid in in which the Universe is immersed. Computer based animations invariably depict empty space as some sort of rubberized sheet being dimpled by massive ball bearings and this promotes the same sort of mental images, attitudes and beliefs. Which is a pity.

It may be a lost cause but I point out once again that spacetime is a human construct for measuring, modeling and discussing what is going on in the Universe. It has no more reality that the Cartesian coordinate grid of latitude and longitude lines here on Earth.

It was not Einstein who promoted the idea that curved spacetime is an actual physical reality. This only happened after his death and was promoted by authors such as MTW and Stephen Hawking. For example, John Wheeler often made the comment that “mass/energy tells spacetime how to curve, and spacetime curvature tells matter how to move”. The cover of MTW classic textbook shows a little ant wandering around on the surface of an apple and dutifully following its curvature.

I would say to John Wheeler that he has started to confuse mathematical models with reality and that the analogy with the ant is a false one. The ant can feel the curvature of the apple with its little feet. The surface and its curvature is real and tangible. But spacetime is a manmade imagination created for our own convenience. A better analogy is the lines of latitude and longitude we have invented for talking about movement on the surface of our home planet. These lines do not actually exist. They cannot be observed. They are not tangible. I would say to John Wheeler that spacetime does not tell matter how to move any more than the latitude and longitude grid on Earth tells ducks how to migrate.

Which is not to say that I think that spacetime does not correspond to something that it observable. In fact I do. But this is a heretical idea that I will explore in other essays.

I also agree that applying a spacetime metric to this “something” is a good idea. But spacetime is not that something, and that something is not spacetime. In other words, do not get a reference system invented by mankind for convenience of describing physics mentally confused with reality itself.

Another crime in my book is commentators who compare gravitational waves with electromagnetic waves. Unless such commentators can explain how two stars orbiting each other can produce quantized packets of energy and then how these packets can be reflected, polarized, refracted etc. I suggest that they refrain from such analogies. If they must use analogies I suggest that they try acoustic comparisons instead.

Note that Doppler effects are a familiar phenomenon in sound waves and they should also occur for other moving disturbances such as gravitational waves. But where gravitational waves are concerned the effects should not be called red-shifting. The Doppler effect is not called red-shifting when it applies to acoustic waves and I think it should not be called red-shifting for gravitational waves either. It is just a plain old Doppler effect.

Discussion I do not find it surprising that a pair of massive pair of stars rotating about each other might have tiny push-pull effects a long way away. I think this is what you would expect to find even with a basics inverse-square law based on classical physics. For example, if a large asteroid suddenly knocked the moon out of its orbit, I think it reasonable to expect that observers on Earth would notice changes in gravity very soon afterwards.

Nor am I surprised that gravitational disturbances travel at the speed of light. In fact I am surprised that this has not been measured experimentally years ago. For example, the passage of the Moon overhead produces a noticeable gravitational tidal effect on the surface of the Earth. Since the centre of the pattern of this disturbance coincides exactly with where the Moon appears to be then that is evidence for the gravitational effect to be arriving hand in hand with the visible light from the Moon.

I would be surprised if gravitational waves are ever found to consist of discrete quantized packets, analogous to photons. In my currently preferred conceptual model of the Universe, photons are disturbances in something that can be modelled by spacetime constructs, and gravitational waves are disturbances of that something itself.

This is more than a semantic difference. Consider a laser beam that is pointed at the sky and turned on and off again. This sends bunches of well-collimated photons off on a journey into deep space which, in principle, can continue travelling indefinitely. Barring absorption by dust or blocking by some solid barrier, the beam of photons stands a chance of being able to be detected on some distant galaxy at some time in the future. Not so a gravitational wave. The energy from a gravitational wave spreads outwards in all directions and becomes increasingly weak with distance from its source. I think there is almost no chance of being able to detect gravitational waves coming from binary star events and suchlike outside of their local galaxy. Colliding galaxies might be a different story.

Conclusion After initial doubts, Einstein eventually decided that gravitational waves were a necessary feature of his Theory of General Relativity. The recent detection of gravitational waves, apart from being a remarkable achievement, is further confirmation that General Relativity works well as a model. However I think it is not proof that General Relativity is the only viable and useful way of looking at physics in our Universe.

[scepticaladventure]

23  Gravitational Redshift  2Sep18

Introduction Earlier essays in this series of blogs provided a plain English synopsis of the foundations of General Relativity, presented some heretical comments about Einstein’s Equivalence Principle and introduced the Clock Postulate. In this essay I would like to take a closer look at gravitational redshifts. [Note: In this essay I will again be using references from the heavyweight textbook on gravity by Charles Misner, Kip Thorne and John Wheeler  (MTW):   “Gravitation” C W Misner, K S Thorne, J A Wheeler  Freeman Press,  1970  ISBN 0-7167-0344]

Effects of Gravity on the Propagation of Light The effects of gravity on light are not straightforward. Einstein’s ideas evolved over more than a decade and involved discussions with and by other great scientists such as Max Planck, Hermann Minkowski, Max Born, Willem de Sitter, Max von Laue, Hermann Weyl and John L Synge. Einstein wrote on the subject repeatedly, e.g. in 1907, 1908, 1911, 1915 and 1916. His 1915 paper contained significant corrections to his 1911 formulae. His 1915 work opened with the remark “‘I return to this theme because my previous presentation does not satisfy me.”

Einstein came to the conclusion that one of the basic tenets of the Special Theory of Relativity - the constancy of the velocity of light – had to be abandoned when gravity is taken into account. Einstein embraced this consequence and made it the basis of a further prediction – the bending of light passing near a massive body. His 1911 prediction for the light bending was the same as that of classical physicists.

In 1912 Einstein’s approach to modeling the effects of gravity on light using only his principle of equivalence ran into problem after problem. This motivated him to begin studying in earnest the differential calculus of Ricci and Levi-Civita as applied to curved geometrical manifolds (involving tensors, co-variant derivatives, Christoffel symbols and the like.)

Einstein revised his 1911 calculation in his 1915 paper and came up with a prediction twice as large as the original estimate. Sir Arthur Eddington famously claimed to have verified this prediction several years later in 1919. [In spite of World War I, Eddington had received a copy of Einstein’s work on General Relativity and he quickly became an early supporter of its ideas. Eddington came up with the idea of measuring the bending of light during a total eclipse and he obtained support from the Royal Astronomical Society to do so. I think this is a nice example of scientific cooperation transcending national hostilities.]

Einstein’s theory of General Relativity eventually contained three effects of gravity on light: 1. Gravity slows the speed of light, 2. photons climbing out of a gravity well arrive redshifted, and 3. gravity bends the path of light.

The degree to which the second and third effects are were predicted by Einstein’s 2015 theory became important tests for the new theory, along with the calculation of the anomalous precession in the perihelion of Mercury (see latter essays).

As to the redshift, Einstein wrote in a letter to Arnold Sommerfeld in 1912, ”The clock goes more slowly if set up in the neighborhood of ponderable masses. From this it follows that the spectral lines of light reaching us from the surface of large stars must appear displaced towards the red end of the spectrum”.

This makes it clear that Einstein was attributing some or all of the gravitational redshift to the time dilation caused by gravity, which in turn is intimately connected to the speed of light in gravity (for as we discussed earlier, the very meaning of time is intrinsically intertwined with the concepts of distance and the speed of light).

I like these comments by two American writers in 1980 (John Earman and A Glymour): “Einstein’s early derivations of the red shift show his most characteristic style of work - heuristic, allusive, sometimes baffling, but unfailingly fruitful.” They go on to say “Altogether, there may be no other single topic which so vividly illustrates the intellectual ferment, the styles of work, the profundity and the confusion associated with the general theory of relativity.”

We can argue at length about the exact meanings of the language used by Einstein and others to describe the three effects, as many good physicists, mathematicians and philosophers have done for the last century, especially if they are inclined to the modern view that gravity is an illusion created by spacetime curvature.

The more important thing is that the three effects led to new predictions for the size of gravitational redshift and gravitational light bending which became early tests for the new Theory of General Relativity.

The success of Einstein’s new general theory in predicting the size of gravitational redshift and light bending effects has led textbook writers to assert that classical physics has shortcomings that required the genius of Einstein’s curved spacetime theory to correct.

However, I think that the experimental results are what Sir Isaac Newton, Pierre-Simon Laplace and many other great classical physicists scientists over the previous three hundred years had already anticipated to some degree and would not have been surprised at all to see confirmed.

I think that General Relativity is a powerful new approach that brings in a whole new class of mathematical tools and so lends itself to a better description of some small effects in extreme situations. But I also think that if you add Special Relativity and the fact that gravity slows the speed of light to classical physics you can get the same answers. Certainly for the three effects on light (the first result is axiomatic) and possibly also for the anomalous precession in the perihelion of Mercury.  

This is what the next few essays are going to examine. Starting with gravitational redshifts.

Gravitational Redshift - The Long Hollow Rocket Imagine that the very tall elevator shaft in the previous essay has become a long hollow rocket which is in deep space somewhere and that this rocket is accelerating at a high constant rate forwards. Imagine there is a source of photons with a very tightly defined frequency range (a laser for example) situated at the back of the rocket and that this has just fired a burst of photons towards the front of the rocket. When this burst of photons was sent on its way, the back of the rocket was travelling at a certain speed. Due to the rocket’s acceleration, by the time the photons reach the front of the rocket the front of the rocket will have reached a higher speed. In other words there will be a relative speed difference increase from the back to the front of the rocket due to the acceleration that takes place while the photons are in flight.

Detectors at the front of the rocket will find the arriving photons to have lower energy (hence lower frequency and longer (redder) wavelengths) than they had when the photons started. Furthermore, if the arrangement of laser and detectors is reversed, then the detectors when positioned at the back of the rocket will find photons arriving from the laser at the front of the rocket to have acquired extra energy and thus been blue-shifted. It is a straightforward Doppler effect. (There will be infinitesimal Lorentzian effects as well but these can be safely ignored for our purposes).

Einstein’s Equivalence Principle says that the above situation is the same if the rocket is actually a very tall elevator shaft sitting in a uniform gravitational field. Photons fired upwards in the shaft will arrive redshifted and photons fired downwards in the shaft will arrive with a degree of blue shift.

The redshift effect has been confirmed by experiments such as that of Pound and Rebka at Harvard in 1960.

It is possible to persuade ourselves that light must be red shifted in this way using Einstein’s discovery that energy and mass are equivalent to each other, and applying this to a thought experiment (see MTW p187) as follows.

Imagine that a well defined amount of mass falls through gravity and does some work on the way (turning a treadmill for example). It is then entirely converted into photons that are beamed back up to the starting point. Unless these photons lose some energy they could be turned back into the same initial starting mass and the process could be repeated endlessly, performing work on every loop. But this would violate the principle of Conservation of Energy. Hence Einstein reasoned that the photons must lose energy on their way back up to the starting point.

Does Gravitational Redshift Imply Spacetime Curvature? (MTW p 187)  “An argument by Schild (1960, 1962, 1967) yields an important conclusion: the existence of gravitational redshift shows that a consistent theory of gravity cannot be constructed within the framework of special relativity”.

(MTW p189) “Schild’s redshift argument … does say … quite unambiguously, that the flat spacetime of special relativity is inadequate to describe the situation, and it should therefore motivate one to undertake the mathematical analysis of curvature.”

The Schild argument builds on the experimental demonstration of gravitational redshift by Robert Pound and Glen Rebka at Harvard University in 1960.

In 1958 a way had been found to use the Mossbauer resonance effect to emit and absorb gamma rays in a very narrow and precise frequency range using solid samples containing radioactive Fe57. Pound and Rebka made use of this discovery and placed two such samples vertically in a tower at Harvard with a height difference h (and so at a gravitational potential difference of gh in the language of Newton).

General Relativity predicts photons emitted from one sample will no longer be absorbed by the other. But if the absorber is vibrated so that it obtains a range of vertical motions relative to the source, the resulting Doppler effects can restore some absorption.

It is common to see this experimental result described mathematically as ∆t2 = (1 –(Φ2 – Φ1)/c2) ∆t1  where (Φ2 – Φ1) = gh is the difference in gravitational potential.

In essence Schild invites the reader to consider a Lorentz reference frame aligned to the Earth and containing an electromagnetic wave generator at one level and a suitable detector at a higher level, both at rest with respect to each other. Schild’s argument goes like this: The bottom generator emits a wave of exactly N cycles of well defined frequency √ in time interval T and this is received by the top detector. The observer at the top detector is asked to determine how long this signal lasts. In flat spacetime the answer should be T, since the top and bottom observers are at rest with respect to each other. However, the signal undergoes a gravitational wavelength change, lengthening as it climbs up towards the top observer. N cycles of a longer wavelength should last longer than T. The conflict can only be resolved if spacetime is curved.

I agree that gravitational redshift occurs in reality, and I also accept that gravitational time dilation occurs in reality. And if the time dimension is significantly slowed by the presence of gravity, then the usual Lorentz-Minkowski flat four dimensional spacetime framework becomes suboptimal for describing what is going on in the physics.

However, I do not accept the argument that the Pound-Rebka demonstration of gravitational redshift proves that it is necessary to invoke curvature in all four dimensions of spacetime because I think the Schild argument is inherently flawed and in any case it would only introduce a degree of flexibility in the time dimension.

For a start, the Pound-Rebka experiment example used by Schild does not take place in a Lorentz reference frame at all. Very few experiments do. Inertial setups are so rare and to be almost non-existent. Orbiting space stations come close but even then there is still rotation relative to the so-called “fixed stars”. But my concern is mainly about the misuse of wave concepts.

What is the ‘wave’ talked about by Schild (as described by MTW)? It seems Schild is thinking about the emissions being electromagnetic waves with spatial properties related to their wavelength and temporal properties related to their frequency. He talks as if the wavelength gets ‘stretched’ in transit between the bottom and the top of the tower. He talks as if the signal has a well defined frequency in time T and hence acts as a type of clock.

But Einstein himself was instrumental in demonstrating that electromagnetic radiation takes the form of photons. These are emitted with precise energy level. If they have to climb against a gravitational potential then when they arrive they are detected as having less energy. That is the relatively simple experimental fact.

And as I discussed earlier (and summarise in the box below) I think the whole schizophrenic particle/wave duality concept of light is seriously old fashioned and that it can be resolved simply by following the evidence with a fresh and open mind.

I think of the precise electro-magnetic emissions in the Pound- Rebka experiment as being phots. They have no length, they do not wriggle about as they travel and they are not little clocks. They are just packets of energy with some intrinsic properties that are only revealed upon absorption.

Schild is suggesting that the bottom generator emits a wave that has a well defined frequency in time T and therefore acts as some sort of clock. Now it is perfectly possible to incorporate a beat into an overall emission of lots of phots. Just synchronise their phase at time of emission and change this in a structured manner as time progresses. It is what happens all the time in a radio signal. The signal is encoded in the overall pattern. But not in each individual phot.  

Do not get mixed up between what happens to the pattern of phots and what happens to the phots themselves, which is what I think Schild (and others) have done. And forget about anything with a finite length being “stretched” somehow. Phots have no length.

All the Pound Rebka experiment does is demonstrate that phots emitted in precise circumstances at one point in a gravitational field and absorbed at another point in the gravitational field lose energy consistent with the change in gravitational potential. This shows up upon their absorption/detection/destruction as a decrease in the frequency of their embedded signal. If you insist on using the phots as a way of standardising time in reference frame covering the whole experiment, you are entitled to conclude that time runs more slowly at the bottom of the tower than at the top.

So does a gravitational redshift as demonstrated by a single Pound and Rebka experiment demonstrate that gravity has to be modeled by a fully curved spacetime approach? I do not think so. In fact I think that a gravitational redshift occurring between two specific points in flat spacetime can be understood perfectly well just using classical physics augmented by Special Relativity and the recognition that gravity slows the speed of light (and hence time).

A single gravitational redshift experiment in one particular location is not proof of full spacetime curvature. However, if you consider how to interpret the results of many different redshift experiments spread around a gravitationally perturbed region of the Universe at more or less the same time, then the argument becomes stronger.

Take Earth for instance. If we consider a whole set of Pound-Rebka experiments occurring at different locations around the Earth, then while each experiment might have something to say about its local spacetime environment and local inertial reference frames, the only way to connect all the frames is to admit curvature into the dimensions of spacetime more generally. This is the conventional route to Einstein’s General Relativity.

So I’m saying that while curving all the dimensions of spacetime is not necessary to understand gravity per se, it is still a very useful approach to modeling some subtle effects in physics in gravity fields surrounding massive celestial objects.

How to Interpret Gravitational Redshifting? Pound-Rebka and many others showed that gravitational redshift does occur, and a variety of thought experiments suggest that this is a perfectly reasonable outcome. But how should we interpret the results? It is a debate that went on for decades from about 1911 onwards and it is a question that is still open, although many minds are not.

I will let the photons speak for themselves. Let us turn them into little cartoon characters. On arrival at the top detector the photons could explain what has happened in one of three possible ways: (1) “Hi, we are from bottomland. Time runs slow down there, so please excuse us if we are a bit slow. We are all slow down there. Apart from that we are exactly like you.” (2) “Hi, we are your identical counterparts from bottomland. We have had a tough journey and now we find that we have to give up some of our energy in the form of a tax. So please excuse us for being a bit redder than when we started out.” (3) “Hi, we are your identical counterparts from bottomland. You guys seem to have been accelerating upwards while we were travelling. We can’t climb aboard your detector, even though it is identical to the one that gave us birth, unless you lower the bar a bit and retune it to a lower frequency, or push it towards us to shake off all that extra speed you’ve acquired.”

The first explanation suggests gravity causes time to slow down and any and all processes that involve time to slow down as well. This by itself is enough to distort the time dimension in a four dimensional spacetime reference frame. But it does not say anything about curvature in the three spatial dimensions and hence is not an argument for Einstein’s curved spacetime ‘geometric’ model per se.

The second explanation is akin to a standard Newtonian approach. Newton thought of light as consisting of “corpuscules” and fully expected them to be able to be influenced by gravity. See the following essay about the bending of light by the Sun.

The third explanation of gravitational redshifting uses the Einstein Equivalence Principle to suggest that what is going on is that both the bottom and the top of the tower are being accelerated in curved spacetime. This is what causes the redshift as per our discussion of the long hollow rocket. You could say that this is an explanation in terms of the Doppler effect.

A student of Special Relativity might not be surprised by gravitational redshifting since, if a photon is energy, and energy is equivalent to mass, and mass loses energy when it climbs out of a gravity well, then why would anyone not expect a photon to lose energy also? So such a student might be inclined towards explanation (2).

One of things that intriques me about gravitational redshifting is this. If the photons arrive at the top of the experiment with less energy than they started out with – where did that energy go? If the photon were a little rocket then it would end up in the heat and kinetic energy of the exhaust gases. If the photon was a solid projectile the lost energy is apparent in the gradual loss of kinetic energy. If the photon was pulled upwards by a string it would clearly come from whatever was winding up the string. But in the case of a photon it starts off with one amount of energy and arrives with an amount that is lower than that of photons being created in exactly the same way but at the ‘higher altitude’. Where did the difference go?

I think that the question goes to the heart of understanding gravity and hence is a quite profound. But most lecturers will just say “It has ended up as a reduction in negative potential energy” and leave it at that. Personally I think that this ‘papers over’ a gap in a better understanding of the situation. The same thing happens is you ask questions like – what gives matter its mass? or what gives mass its inertia? or why does a moving object want to travel in a straight line? Just giving physical phenomena names instead of explanations tends to block our minds to deeper understandings.

The first and third of the explanations require a non-flat spacetime reference frame due to distortion in the time duration dimension.

If one of the answers is correct it does not necessarily mean that the others are incorrect. In principle the correct answer might depend upon what point of view you are using. Then the best answer is then the one that is consistent with the point of view you are using. And the best point of view is generally the one that is the most convenient for your purposes at hand.

Furthermore, it is also possible in principle that the best answer requires a combination of the various explanations. In fact I think it does, as I will explain later.

So what about explanation (3) that interprets the redshift as a Doppler effect? My take on this is that if you want to adopt the Einstein Equivalence Principle, and if you want to replace the greatest force in the Universe with the mathematical trickery of curved spacetime, then this is the explanation you should use. It also gives the right answer, so it becomes a matter of choice.

But the fact that you could prefer Explanation (2) shows that the curved spacetime approach is not the only way to understand the Pound Rebka experiment. And even if you do want to use Explanation (3) you should note that this does not require you to use Einstein’s full model. If you do use Einstein’s General Relativity model then it is only the perturbation of the time term that is needed in order to come up with the observed results for gravitational redshifts. The full field equations are not needed and there is no need to call upon any warping in the spatial aspects of the spacetime geometry.

Gravitational Redshift in the Solar Spectrum Light reaching Earth from the Sun’s surface has climbed a long distance up the Sun’s considerable gravity well, and has fallen into the Earth’s smaller gravity well. The light itself comes from a large number of sources with known spectral frequencies, but these spectral lines are complicated by the extreme thermal motion of the sources, the Sun’s rotation and the Earth’s own motion. All of this creates a blur of Doppler shifts. Nevertheless it is possible to screen and correct for the blurring effects and the resultant redshifts are consistent with the expected result.

Early attempts to measure the gravitational redshift of light reaching Earth from the Sun were plagued by practical difficulties. The earliest results tended to disprove Einstein’s predictions. When Einstein’s fame and reputation soared towards the end of the second decade of the 20th century, the trend reversed and it became more fashionable to produce results corresponding to Einstein’s predictions. Modern results do confirm Einstein’s predictions.

It is interesting that the earlier attempts to explain the spectral shifts in light from the Sun did not use General Relativity. This shows that while on one level Einstein’s general theory won wide acceptance, on another level there was a reluctance to fully adopt the curved spacetime approach. General Relativity was thought of as being impressive and interesting, but also a bit too weird and not to be taken literally.

The Best Way to Interpret Gravitational Redshifts? General Relativity has now become the orthodox paradigm but even today arguments continue about how best way to tie in the experimental evidence about gravitational redshifts. Some authors/teachers prefer one type of explanation, others prefer another.

I’m pretty sure many students find this confusing. But I also think that there may be more than one way to look at it. I do not think that one view corresponds to “reality” and the others are fallacies. They are all just mental models created for our own convenience of understanding.

Here is an analogy. A cone can be seen as a triangle from one perspective and a circle from another. The real nature of a cone transcends both views.

In this spirit I object to those who insist that spacetime curvature is real and gravity is not real. I say that you can use a curved spacetime model if you like, but it is only a model. Likewise you can hold the view that gravity is a real force of nature, but you still also have to recognize the lessons revealed to us by Einstein.

My preferred way of explaining gravitational redshift is as follows. When a photon reaches a zone of space where everything has a higher gravitational potential than things did where the photon came from, it arrives in a new environment. It may have been created in outer shell of a certain type of atom, but it now finds itself unable to join similar situations in similar atoms in the new environment. It has to pay a tax to be allowed to join in. Its energy wallet now longer buys what it used to. The photon can now longer afford the sort of home it came from. It has to settle for a lower energy type of accommodation. One with lower energy levels. For example, a photon than came from a green home might have to settle for a new home in the red light district.

So if we go back a couple of sections and eavesdrop on our animated photon’s conversation when they arrive, what they are saying is (2) “Hi, we are your identical counterparts from bottomland. We have had a tough journey and now we find that we have to give up some of our energy in the form of a tax. So please excuse us for being a bit redder than when we started out.” And their newfound friends say “Don’t worry about it. It happens to everyone. And you haven’t lost any value – it is just that some of your energy is now embedded into your relationship with your new environment all around. You can have it back again should you return home.”

Conclusion Gravitational redshifts can be described in Einstein’s General Relativity model but it is not necessary to invoke the full field equations and curvature in all of the dimensions in order to do so. The basics effect was predicted well before Einstein using nothing more than Newtonian gravity and Galileo’s Weak Equivalence Principle.

Once Special Relativity is taken into account the phenomenon can still be understood in terms of differences in gravitational potential.

The mystery is why this phenomenon is considered to be one of the proofs that General Relativity is the only valid way to look at gravity. I think that what happens to photons encountering changes in gravitational potential can be described without reference to Einstein’s General Relativity field equations at all.

Here is a bit of basic logic. “If General Relativity is to be a useful model then it must not contradict the evidence of gravitational redshifts.” Let us agree that this is true. Then we also have to accept the contra-positive argument that goes as follows. “If General Relativity contradicts the evidence of gravitational redshifts, then it is not a useful model.” What we do not have to agree is the argument that “If General Relativity is consistent with the evidence of gravitational redshifts, then it is a useful model”. This statement may or may not be true. And we certainly do not have to agree without question the insistence by many modern physicists that because General Relativity is a useful model then its method of approach is the only interpretation of Nature that we should agree to be “reality”.

On this I am pretty sure that Einstein would agree.

[scepticaladventure]

14  Relativity and GPS Satellites 25Aug17

Relativistic Effects and GPS Satellite Clocks

Good evidence for relativistic effects on time comes from Global Positioning Systems. The NAVSTAR system has a network of 24-30 satellites in high orbits (not geostationary) about 20,000 km above the surface of the Earth and travelling at about 14,000 km/hour. There are four satellites in each of six orbital planes inclined at 55° with respect to the Earth’s equatorial plane, distributed so that from any point on the Earth, four or more satellites are almost always above the local horizon.

Each satellite has an atomic clock aboard with an accuracy of a nanosecond or better. The satellites emit extremely well coordinated radio signals. Earth bound GPS detectors can receive signals from 6-12 satellites at a time and by comparing the small differences in the arrival time of the signals they can compute their location on Earth with an accuracy of a few meters. More advanced detection systems can get this accuracy down to centimetres. To achieve this level of precision, the clock ticks from the GPS satellites must be stable with an accuracy of 20-30 nanoseconds and be perfectly coordinated with each other.

The main GPS is designed so that satellite clocks appear to an observer on the surface of the Earth (a geoid) to beat at a frequency of 10.23 MHz. The signal from each satellite also tells the detector where the satellite is at the time its signal is sent.

The detectors on Earth do not contain atomic clocks. They get all the information they need from the satellite signals. For example, if the detector receives signals from two satellites at the same time then it deduces that it is equidistant from those two satellites. (One of the adjustments made for super fine accuracy is to allow for different levels of moisture in the atmosphere since this can affect the refractive index of air to a small degree and hence the signal path time).

It is often said that in order to work the GPS satellite clocks have to be adjusted to take into account the effects predicted by the Special and General Theories of Relativity. This is not strictly correct for the main purpose of the system, which as its name suggests is global positioning. The satellites communicate and coordinate with each other and GPS will work as long their clock ticking stays stable and coordinated.

What is more relevant for this essay is the potential drift in time between the satellite clocks and earth bound clocks. There are two main relativistic effects to take into account, plus a small Sagnac effect and then some other, really small effects such as the Shapiro signal delay.

The biggest effect comes from the Earth’s gravitational field. Earth bound detectors feel the effects of the Earth’s gravity at 9.8m/s2. A calculation using General Relativity predicts that the ground-based clocks will run slower than the GPS satellite clocks by about 45 microseconds per day. A little less if the detector is above sea level. And also a little less because the effect of gravity can be offset slightly by centripetal acceleration caused by the Earth’s rotation, which of course varies with latitude. But this is a very small adjustment.

Most texts say that the gravitational effect occurs because the satellite clocks are at a higher gravitational potential than the Earth bound clocks. I prefer to think of it as occurring because the satellites are in a weaker gravitational firld than the Earth bound clocks.

Note that the fact that the satellites are in free fall does not affect the gravitational slow down effect.  It does however come into play through the tangential velocity of the satellites in their orbits.

The second biggest effect comes from this relative movement of the satellites with respect to stationary Earth bound clocks. Earth bound clocks near the poles see the satellite clocks running slow by about 7 microseconds per day, and if they are near the equator they see the difference as being about 6.3 microseconds per day.

Adding the above two main effects together gives a net figure of about 38 microseconds per day. So, before they are launched, the satellite clocks are tuned to run faster than the Earth bound clocks by 38 microseconds per day.

Apparently, when the first GPS satellites were launched, the organisers were not 100% confident that the relativistic effects would be present as expected and so they made the clocks just a little bit more adjustable post launch than is the case today.

There is a third and smaller adjustment due to the Sagnac effect arising from the Earth’s rotation. Synchronising clocks in or on a rotating body is difficult. Simple-minded use of the Einstein synchronisation method in the rotating frame of the Earth’s surface leads to a significant error. Traversing the equator once eastward, the last clock in the synchronisation path would lag the first clock by 207.4 nanoseconds. Traversing the equator once westward, the last clock in the synchronisation path would lead the first clock by 207.4 nanoseconds.

In an inertial frame a portable clock can be used to synchronise the others. The clock must be moved so slowly that changes in the moving clock’s rate due to time dilation, relative to a reference clock at rest on earth’s surface, are extremely small.

However, observers in a rotating frame who attempt this method will find that the proper time elapsed on the portable clock is affected by earth’s rotation rate. Path-dependent discrepancies in the rotating frame are thus inescapable whatever method one attempts to use.

However, synchronisation in the underlying inertial frame using either method is self-consistent. Identifying this frame with absolute precision would be an interesting exercise. Is it non-rotating with respect to the Milky Way? Or to distant galaxies?  Or to something in between?

With all the adjustments mentioned above GPS satellites provide not only accurate positioning but also a good basis for a synchronised time standard around the globe. Just add a certain number of hours adjustment so that the solar maximum is somewhere close to 12 noon in that time zone and there you have it – a very good standard for clocks in any location right around the world.

The rate of GPS coordinate time is closely related to International Atomic Time, which is a time scale computed in Paris on the basis of inputs from hundreds of primary time standards, hydrogen masers, and other clocks from all over the world.

Universal Coordinated Time (UTC) is another time scale, which differs from International Atomic Time by a whole number of leap seconds. These leap seconds are inserted every so often into UTC so that UTC continues to correspond to time determined by Earth’s rotation.

Having discussed time keeping using atomic clocks and orbiting satellites, let us consider another thought experiment.

The Lonely Planet

This thought experiment is similar to the rotating disc except in that the disc is now imagined to be a massive spherical planet which is rotating slowly relative to distant galaxies. The planet is drifting in deep space far from neighboring objects. To make it a bit less abstract imagine that the sphere is about as massive as the Earth. There are four satellites in a circular orbit around the planet’s equator. One is in an orbit which is stationary with respect to the planet’s surface far below. The other three satellites are orbiting in the other direction.

The diagram show a cross section through the equator of the lonely planet. There is an surface based observer with a clock at R. An identical clock is in a geostationary orbit at S. Another three identical satellites A, B and C are carrying identical clocks but they are orbiting in the other direction (clockwise).

How can we describe this system and how does it compare to what we know from Earth based experiments and Global Positioning Systems using satellites?

Use a reference frame aligned to the distant galaxies. Use a reference time coordinate in this reference frame which is based on clocks at rest in the frame but positioned so far away from the planet that any gravitational effects can be ignored.

There are several key aspects to this new thought experiment. The main new feature is gravity. This is holding material objects to the surface of the planet. All four satellites are in free fall around the planet, but one is geo-stationary and the other three are orbiting clockwise. The planet is not moving through the aether as such, but it is rotating in the aether, as are all the satellites.

We know that there are several effects to take into account. We know that the planet based Clock R will run slow by about 45 nanoseconds per day because it is in a gravitational field such as experienced on the surface of Earth.

We also know that we need to take into account the small amount of rotation that is going on. But here it is a bit more complicated. The centripetal acceleration offsets the gravitational pull slightly and this seems to make a small difference (judging from real life experience with GPS systems). But it also results in a gross circular motion through the conjectured aether, and we have argued that this should contribute to a Lorentzian slowing down of time compared to our reference clock.

We are interested in the rate of time on Clock R compared to Clock S in the geo-stationary orbiting satellite and to the other three clocks in the other satellites.

All the satellites are in free fall. None of the clocks aboard the satellites are feeling any effects of gravity. Hence I think there is no gravitational time dilation on clocks S, A, B or C, in spite of the fact that all four satellites have gravitational potential energy. The only clock with gravitational time dilation is Clock R.

Of particularly interest is the extent of any clock drift caused by the relative motion of the satellite clocks with respect to the surface bound clock R.

I think Special Relativity would predict that there would not be any time drift between R and S other than the gravitational effect on R because clock R is effectively at rest with respect to the geostationary satellite clock S.

However, in my Lorentzian version of Relativity I am going to suggest that there will be a motion based relativistic difference in the clock rates between R and S because S is moving through the aether faster than R, simply because it is further from the centre of rotation of the lonely planet.

What about the other three satellite clocks A, B and C?

I think Special Relativity would predict that A, B and C run slower than R due to their motion relative to R, with a gamma factor based on the speed of the three clocks as they pass overhead.

However, in my Lorentzian version of Relativity I am going to suggest that clock R will run slow according to how fast it is moving through the aether, and clocks A, B and C will run slow according to how fast they are moving through the aether and that the net drift will be the difference between this and the effect for R.

What about any difference in the rate on clock S and the other three satellite clocks? In essence what we have here is the Twin Paradox with a twist.

Clock S will see the other three clocks passing by at great speed, over and over again. I think that Special Relativity predicts that an observer on satellite S would see the other satellite clocks run slow compared to the local clock S. But it could be argued that observers on each of the other satellites would see clock S pass by at great speed, over and over again, and so clock S should be running slow compared to their clock, and not the other way round.

The textbook resolution of the twin paradox usually assumes that one twin experiences accelerations and decelerations and claims that this breaks the symmetry and resolves the paradox. But in this thought experiment, all four satellite clocks are in free fall orbits and all four clocks are in essentially the same situation.

In my Lorentzian version of Relativity I am going to suggest that all four clocks will be moving through the aether at the same speed, which depends solely on their Keplerian orbits around the lonely planet, and hence they will all have the same Lorentzian time dilation. Therefore there will be no effect due to their movements relative to each other.  Hence no paradox.

This can be generalized in a way that makes it easier to test. The Lorentzian version of relativity predicts that there will be no clock drift between any group of satellites in identical orbits, apart from possible very minor effects of a lower order.

Experimental Verification

I do not know which of the innumerable satellites in orbit around the Earth carry atomic clocks, other than the GPS satellites. However, I suppose that may of them do. Someone with a lot more access to data than me, and a lot more computational power at their disposal (e.g. the experts in GPS at the University of Colorado) might be able to work out which set of predictions comes closest to actual experimental evidence.

If the Lorentzian version gives the better results then it would provide a very interesting new interpretation and understanding of relativity.

With time and effort and talent, many other experimental tests comparing the two interpretations should be possible. I think it is worth checking which theory works best - Einstein’s original version of Special Relativity or this heretical version inspired by the thinking of Hendrik Lorentz.

[scepticaladventure]

12  Michelson-Morley Revisited 23Aug17

The experimental apparatus set up by Michelson and Morley in Ohio in 1886-87 was designed to measure the effects of the earth’s movement through the aether field that was thought to be the medium in which light travelled.  It consisted of a beam splitter (half silvered mirror angled at 45 degrees to incoming light), plus two mirrors mounted on arms at right angles to each other and exactly the same length as each other. The whole apparatus was on mounted on a massive stone block floating on a bed of mercury in order to reduce vibrations and to allow everything to be rotated.  

In principle, light travelling with the aether drift and then back again would take longer to complete such journey than light travelling across the aether wind and back again (simply because the light would lose more time a swimming against the tide on the way back than it gained getting on the way forward). (See swimmer in the stream story in an earlier blog). Any travel time differences would show up as an interference pattern. No such pattern could be generated, no matter which way the apparatus was oriented. It became perhaps the most famous null experiment in physics.

Simplified Michelson Morley experiment. The red lines are mirrors. There are three mirrors. The angled mirror is shown twice. Everything is moving to the left (which we will call west) at velocity V. Coincident phots come in from the west. One phot is absorbed by the angled mirror at Event 1, and its child then travels “north” and hits a mirror at Event 2, whereupon it is absorbed and reemitted in the form of a grandchild phot. The grandchild phot travels back southwards to the detector at Event 4. The phots’ total travel time T is the same as the travel time for the apparatus to continue on its path westwards at velocity V, so that the angled mirror arrives exactly at the same place and time (Event 4) as the southbound grandchild phot.  

The other coincident phot goes straight through the angled mirror in the “east” direction and hits a mirror at Event 3. This path is shorter than L because the whole apparatus is moving leftwards/westwards at constant velocity V. The phot is reborn at Event 3 and the child phot returns westwards and hits the angled mirror at Event 4, where it is detected, along with the grandchild phot travelling south from Event 2.

The experimental result is that there is no interference between the southbound and the westbound phots. They arrive at Event 4 at exactly the same time no matter which way the apparatus is oriented.  The north south phots travel 2 x L1 in the same time as the east west phots travel between Event 1 and Event 3 and back again to Event 4.

The result was interpreted as proving that the Earth was not moving through a stationary aether, and that the speed of light through this apparatus was the same in both arms no matter which way the apparatus was oriented direction.

This suggested that the Earth must be dragging the aether field with it. But other earlier experiments had ruled out the possibility that the earth was dragging an aether cloud around with it. Hence the result of the experiment was very perplexing.

Lorentz (assisted by Poincaré) started to think that maybe the motion of the Earth into an aether wind was somehow causing lengths of things oriented in that direction to shrink slightly. Lorentz calculated the size of the required shrinkage. His formula is now called the Lorentz contraction factor and is denoted by the Greek letter gamma.

Einstein did not acknowledge the Michelson Morley experiment in his 1905 paper on Special Relativity, though it is implausible that he did not know of it. Einstein simply took it as axiomatic that the speed of light was the same (for a particular medium such as a vacuum or a gas at a given temperature and pressure) for any inertial reference frame, no matter how fast that frame is moving or in what direction it is moving.

I have some comments to make on this experiment and would like to describe and explain it in the language of phots.

I do not consider the light to have been split. You cannot split a phot. And I argue that you cannot “watch a phot” either. All you can do is to detect it – once only and then it is destroyed. However, let us assume that there are a few more phots in the incident beam and that some of these are detected at Event 1 so that the experimenter knows the experiment has begun.

First consider observers riding along with the angled mirror. As far as they are concerned some phots have travelled north-south for a total distance of 2L meters, and other phots have travelled east-west for a for a total distance of 2L meters. The two phots arrive at Event 4 at the same time. (It is convenient to consider phot, child phot and grandchild phot sequences to be the same phot). This is strong evidence that both the north-south and the east-west phots have all been travelling consistently at the same speed.  

It is vaguely possible that a phot has travelled fast or slow on one leg of the journey and another member of their relay team has made up the difference on another leg. This is not plausible for the north south phots, but it is worth checking out for the east west phots.  

The aether wind idea was that the eastbound phot would be travelling fast “with the wind” and the westbound phot slowly “against the wind”. But the time delay effects could not be the same size as each other because the headwind effect applies for a longer duration than the tailwind effect.  

We could imagine a variable tail wind effect to accord with the fact that the return phots are coincident at Event 4. But this would be a different correction for every value of V.  It is too complicated to be plausible.

Ultimately we are forced to the conclusion that the round trip duration times are the same in both arms of the experiment and that there is no aether wind effect.

This is not the same as concluding that there is no aether. An alternative conclusion is that the experiment is unable to detect an aether wind effect.

Lorentz eventually decided that the aether was undetectable and the whole idea of an aether gradually became unfashionable.

I think that the Michelson Morley experiment set out to detect the aether wind but discovered relativistic length contraction instead. The slight shortening in whatever arm is pointing east west is what enables the east west phot to arrive back at Event 4 at the same time as the north south phot.

This interpretation is similar to what I think Lorentz was thinking. But be warned that it is probably a heretical idea nowadays. It suggests that a Lorentz contraction occurs due to movement in an invisible aether, rather than movement which is simply relative to an observer in an inertial reference frame. The effect is therefore not always symmetrical and this would violate the Principle of Classical Relativity (Postulate 2 in an earlier blog) in some circumstances.

I do not see that as a weakness. Instead I think it could be a very important realization which I will be investigating and commenting on in a later blog.

Note that the experiment is not a measurement of the speed of light. The Michelson Morley experiment is just a test of the relative times of travel between the north-south journey and the east-west journey. It is not designed to measure the speed of light itself.

Conclusion

The concept of light as consisting of phots - two dimensional electromagnetic bundles of energy – is not only able to describe what goes on in the famous Michelson Morley experiment, but also helps to interpret this experiment in a new and interesting way.

[scepticaladventure]

24  Gravitational Light Bending  3Sep18

Introduction This essay continues the focus on the collection of experimental results involving light, gravity and General Relativity. It takes a closer look at the fact that the path of light is bent when it passes close to a massive object such as our Sun, and similar phenomena arising when light from distant sources passes close to a massive celestial body on its way to our telescopes.

History of the Bending of Light by Gravity In the latter part of the 17th century, just after the English Civil War, Sir Isaac Newton came up with an expression for the gravitational force between two massive objects. It was hard work - Newton almost had to invent integral calculus to arrive at his result, but it gives beautifully simple results that depend only on the masses of the two objects and the distance between their centers of mass. It then provides a good way to calculate the trajectory of planets around the Sun and these calculations accord almost perfectly with observations.

But what about the path of photons arriving at Earth from a distant star when a massive gravitating object like the Sun gets so close that the photons are forced to graze its edge?

Some people think that Newton’s Law of Gravitation implies that since the photon has no mass, there can be no gravitational force to deflect its path and hence it should not deflect at all.

But this makes several unjustified assumptions. Who says a photon has no mass? It may have no rest mass, but it does have something called relativistic mass. [The term relativistic mass is one which Einstein eventually came to regret, but the concept is still meaningful. Note that the famous Einstein equation is actually E2 = p2c2 + m2c4  and only becomes E = mc2 for an object which has rest mass m but no momentum p. A photon (or neutrino) does not have rest mass but does have momentum, so the equation becomes E2 = p2c2 and hence E = pc. It does not make much difference, but it does reveal that many commentators have only a poor grasp of what they are talking about.

Experiments on photons also show that E = hf  where h is Planck’s constant and f is the frequency of the disturbance created by the photon when it is absorbed/observed, so it is easy to infer the momentum of a photon from its frequency effects when detected. It is also possible to feel the impact of photons when they are detected – (look up “solar sails” for example).

Newton did not know about relativistic mass and hence was silent about it. Nevertheless he thought of light as having a well defined path and robust nature and hence thought of light as being “corpuscular” in nature rather than some of sort of diffuse wave. So he fully expected it to be deflected by gravity (see below). In fact he even calculated the extent to which a massive object would deflect a passing “corpuscule”. Laplace went further and calculated the strength of gravity that would prevent light from escaping upwards – anticipating future considerations of back hole physics by about three hundred years.

Even if a photon has no mass of any sort then it is still not safe to assume that it cannot be deflected, for it would have absolutely no resistance to being deflected either. There is a popular conundrum that asks “what happens if an irresistible force meets an immoveable object?” Well the situation with light is a bit like the opposite conundrum – “what happens if a zero force applies to an entity with zero resistance to being deflected?”

Galileo (who died in the year Newton was born) had already realized that the rate of attractive acceleration towards a massive object is independent of the mass or composition of the attracted object. This is now called the Weak Equivalence Principle. Hence, in the absence of air resistance, a feather falls as quickly as a cannonball. Continuing the argument, an atom falls as quickly as a feather and a neutron falls as quickly as an atom. Whey then should not a neutrino or a photon fall just as quickly as anything else?

Here is a synopsis of how this issue has been handled over the centuries: • In 1704, Newton suggests the bending of light as an aside in his treatise, Opticks. • In 1784, Henry Cavendish calculates the bending of light due to Newtonian gravity but does not publish the result. The evidence of his calculation only surfaced in the 1900s. • In 1801, Johann von Soldner calculates the bending of light as it passes by a massive object in 1801 (taking 25 pages to do it!). The calculation uses Newton's theory of light as a stream of corpuscles with an unspecified mass. However, the mass of the corpuscle (photon) drops out of the calculation, and the angle only depends on the mass of the object and the closest approach to the massive object (e.g. our Sun). The angle of deflection turns out to be:  angle ~ 2m/r, where m = GM/c2, M is the mass of the object and r is the closest approach distance of the photon to the object. This solution is an approximation, because it is the first term in a series. All of the other terms in the series are much smaller. Von Soldner's calculation is very close to Cavendish's, and to a first-order approximation, they are the same. • In 1911, Albert Einstein published a paper called "On the Influence of Gravitation on the Propagation of Light", which calculated the bending effect of gravity on light using his Equivalence Principle. This calculation was not based on the equations of General Relativity, since these had not yet been developed. It did rely on Einstein’s recent conclusion that gravity must have an effect on the speed of light. Einstein’s calculation in this paper was identical to von Soldner's approximation. • In 1915, Einstein finished his theory of General Relativity, and developed a full set of ten partial differential equations for the curvature of spacetime in a gravitational field. When Einstein used his full theory and recalculated of the deflection of starlight due to the Sun he obtained exactly twice the prediction he published in 1911. The additional bending was due to the curvature of space itself. [In mathematical terms it arises from non-zero off-diagonal terms in the 4x4 Riemannian metric tensor that describes the spacetime curvature]. Note that equal contributions are made by both the space and time perturbations of the metric. • In May 1919, Sir Frank Dyson and Sir Arthur Eddington and led an expedition to the equatorial African island of Principe and their colleague Andrew Crommelin led an expedition to Sobral in Brazil to observe what happened to the apparent position of stars in the constellation of Taurus when the Sun got in the way. They could see these stars because they situated their telescopes in the moving shadow path of the moon during a total eclipse of the Sun. They reported, and the Royal Astronomical Society announced, that the degree of starlight bending (‘aberration’) was exactly as predicted by General Relativity. This announcement became headlines in a world hungry for interesting good news and Einstein became a media superstar. Which may have helped him retain his job in Berlin in spite of the rise of anti-Semitism. However, it is interesting to note that there is some question as to whether or not the equipment and results of the 1919 eclipse expeditions really had the ability to conclusively determine the deflections as claimed. It is not a simple experiment. For example, the Sun’s corona has strong magnetic fields and emits a lot of plasma that can complicate the interpretation of the results, and the observed effect is tiny. It may be that the researchers injected some of their expectations into the reported results. However, subsequent and more robust observations have confirmed the deflection as predicted.

So there you have it. Modern physics interprets the bending of light by a massive object such as the Sun as being partly due to a combination of factors, neatly modeled by the spacetime solution to Einstein’s field equations for the spacetime region around the Sun.

The textbooks invariably show the stretched rubber sheet attempt to suggest what spacetime is like in Einstein’s model. There is a big depression caused by the ponderable mass of the Sun. Light comes in and is deflected slightly because of the curved topology. A bit like when you just miss a putt in golf. To be frank, it is not an analogy that I particularly admire.

A Heretical Alternative? Since the theme of these essays is to re-examine the foundations of modern physics and try to provoke some fresh thinking about them, I am going to suggest an alternative interpretation.

We already have a good explanation for half of the effect, due to classical luminaries like Sir Isaac Newton, Henry Cavendish and Simon Laplace. You can think of it as a kind of scattering effect due to the Sun’s gravity trying to pull the passing photons a bit closer. If you like you can think of the Sun’s gravity working on the mass equivalent to the photon’s energy, resisted by the inertia of the photon’s momentum.

It is the other half of the observed effect that presents the issue.  I suggest that the earlier classical calculations do not get the full answer because they do not take into account the fact that gravity also slows down the speed of light. Classical physicists did not have the means to know this. But I suspect that if Isaac Newton knew that light travels more slowly when the presence of gravity is more intense, then he would have started to think about the phenomenon of refraction.

[Most transparent media have a refractive index higher than that of a vacuum, which we have assigned index value 1. This signifies that light travels more slowly in such media than it does in a vacuum. When light passes from one medium to another at an inclined angle the path it travels bends at the interface (see Snell’s Law, Fermat’s Principle etc).]

Gravity also slows down light so it is not unreasonable to conceive of “gravitational refraction”.  We could say that the gravitational index of empty space in the absence of any discernable gravity fields is 1 and that near a back hole it is very high.  Elsewhere it takes an intermediate value.

Note that ordinary refraction affects the speeds of photons, but not their energy level. We can deduce this by using a beam consisting of a large number of identical photons and sampling some of them at each stage of their collective journey. When the surviving photons emerge from the refractive medium they have the same energy level as those photons sampled as they attempt to enter the medium.

I suggest the same thing happens with gravitational refraction. Photons enter a region of high gravitational field and are slowed down and deflected (in accord with Fermat’s Principle, overlaid with a Newtonian gravity deflection) but when they emerge they speed up again. The photons emerge with the same energy level as when they went in.

Furthermore I suggest that if the gravitational refraction is added to the normal Newtonian scattering deflection the answer will be as observed experimentally. Curvature of spatial coordinate system not required.

Finally I would like to suggest that gravitational light bending and gravitational redshifts are closely related. In the case of gravitational light bending the photons traverse the gravitational field at high angles to the gravitational field but in typical gravitational redshift situations the photons travel more or less parallel to the direction of gravitational field.  If the photons are travelling at an intermediate angle through a gravitational field, I suggest it is reasonable that the result would be a combination of the gravitational redshift effect and the gravitational light bending effect.  

A spectrum? I have asked myself whether the gravitational bending of the light should create a spectrum effect. I think this is a reasonable question.

A spectrum effect might be expected if what is going on is similar to an ordinary refraction effect. Consider what happens if a beam of light passes through a medium with a refractive index greater than one, such as a glass prism. I will shun the usual explanation based on what I think is an old fashioned wave model of light and will talk about phots instead.

Consider a beam of light consisting of many phots, all travelling at the same speed in a vacuum. When they encounter a medium with a higher refractive index than 1, such as glass or water, they slow down, sometimes quite considerably. Some textbooks say this is because multiple scattering events makes their path longer, but I doubt this is true because well collimated beams of a single frequency, such as from a laser, remain well collimated and are not scattered. If the initial and final surfaces of the prism are perfectly parallel, the incident and emergent phot paths are also perfectly parallel.

If the phots emerge from a transparent medium they continue with the same energy they had before they entered it. This is a further reason to doubt the scattering explanation, for then it is reasonable to suppose that the medium itself would absorb some of the energy from individual phots. What I think happens is that the phots actually do slow down when they are in the denser medium. High energy photos slow down more than low energy phots. It would be interesting to explore the electromagnetic field reasons for this but let us not get distracted.

If the beam of light of light encounters the new medium at an angle, the path of the phots develops a kink at the interface. If the transition is more gradual the change in direction is a curved bend. Either way the light beam path is refracted. High energy phots are refracted more than low energy phots. The beam is spread out according to the energy of the phots. As far as visible light is concerned, a rainbow spectrum is formed, with red at the top and violet at the bottom.

If the light is passing through a prism say, then when it emerges at the final interface the opposite refraction occurs. Depending on the shape of the prism, the rainbow effect can be undone or not.

The whole process follows something called Fermat’s Principle. Fermat's Principle states that “light travels between two points along the path that requires the least time, as compared to other nearby paths.” From Fermat's principle, one can derive (a) the law of reflection [the angle of incidence is equal to the angle of reflection] and (b) the law of refraction [Snell's law].

In the case of refraction, think about cross country runners encountering a strip of boggy ground that slows down their running speed. If they want to minimize their overall effort and maximize their overall rate of progress, it makes sense to shorten their path across the boggy ground, even if this makes their overall path a little longer.

Returning to the case of a photon (to use the conventional term) traversing a gravity field around a spherical celestial object. The more energy the photon has, the more momentum it has and this might make it more difficult to bend its path. However, no spectrum effect is detected.

The Weak Equivalence Principle gives a naïve explanation. The more energy a photon has, the more momentum it has, and this offsets the bigger deflecting force. However, a modern physicist would probably prefer to say that all the photons, of whatever energy level, are following the same geodesic pathway as determined by the non-Euclidean four dimensional spacetime.

As a photon passes through a strong gravity field at a shallow angle. gravity slows down the speed of light (as viewed from a distance). More on the side closer to the Sun than on the other.  Hence it is not unreasonable to think that the light will follow Fermat’s Principle and take the quickest overall path through the gravity field, even if this means bending away from its initial direction.

However, unlike ordinary refraction through glass or water, there is no rainbow effect. Gravitational slowdown applies equally to photons of all frequency/energy and the speed of all photons remains the same relative to each other. There is no dispersion and they all bend by the same amount.

Conclusion The bending of light by gravity is generally regarded as one of the key experimental results supporting Einstein’s theory of General Relativity, and its model of a spacetime with curvature in all of its time-time and space-time coordinate pairs. However, half of the effect was already predicted and explained in terms of classical physics.

In the next essay I will discuss the fact that gravity slows down both time and the speed of light.

We know that slowing the speed of light by passing it through a transparent medium that is not a vacuum causes the path of the light to bend in according with Fermat’s Principle. Why then is it not reasonable to consider that slowing down the speed of light by passing it through a gravity field might not also cause a degree of bending in accordance with Fermat’s Principle?

Adding the classical gravitational effect to a gravitational time-dilation refraction effect might give a satisfactory explanation for light bending in accord with experimental observation, without calling upon the full spacetime curvature model adopted by Einstein.

[scepticaladventure]

20a  A Note from the Author - Sep18

I have had a lot of fun re-examining the foundations of modern cosmology and challenging the current paradigms. Whether there is any merit in my new model for electromagnetic radiation, or my modified version of Special Relativity, or my solution to the galaxy rotation curve issue without resorting to imaginary Cold Dark Matter, or my fanciful Q Theory of nearly everything, only time will tell. At the very least I hope to provoke others into questioning what they are taught and to challenge anything that seems not right.

For anyone who may have read the chapters published thus far, I apologize for this 12 month break in putting more chapters online. I can reveal that I continued the journey and have drafted the rest of the story in about another dozen chapters, mainly looking at General Relativity.  I now intend to put the remaining chapters online.

My main objective for this journey was my own interest. It turned out so interesting that I decided I would like share it with other people. I’m hoping that some open minded physicists might be inspired to develop some new insights. My intention is to provoke and challenge, not to pretend I know the answers.

But to have any effect at all people will need to read what I have written. In this era of information overload we are all beset by so much dross that I will be surprised and pleased if anyone invests in reading such esoteric stuff by an unknown author. Assuming they come across it at all.

I am pitching it at the level of bright young undergraduates in physics. To make it accessible I am going to keep using plain English, keep away from fancy mathematics, and keep it light and bright. It contains some solid historical information and signposts to some interesting associated topics. But I have also included some highly original speculations and ideas of my own, just to be provocative. For example my Q Theory of nearly everything.

Call me a skeptic or a heretic, a genius or a fool - I don’t care. But I do think that modern theoretical physics has dug itself into a hole and that it need to take stock of how it got there. I think that any mainstream model that has managed to lose about 95% of the Universe ought to do the same. Plus of course there are all those awkward questions and paradoxes that just seem to keep on hanging around. “We can fool all people some of the time and some people all of the time … etc.” But let us hope we never stop questioning.

When I have finished putting the remaining chapters online I think I will edit them and then maybe open up the feedback option. I also want to write the whole thing over again. The trouble with an online blog is that people see the last chapters first, thus making the adventure a bit muddled up. Conscious of what the journey uncovered and discovered and invented, I may recast the content into a small number of books.

So here goes. The next few chapters will be taking a skeptical look looking at Einstein’s General Theory of Relativity and the experimental tests that it has handled so brilliantly. I will reach conclusions that may discomfit and annoy a few people, but may resonate with a few others and may even inspire a subset of those to think deeply about some of the points I raise.

In any case I hope that you, dear reader, enjoy the rest of this journey.