#ClassicalRelativity

[scepticaladventure]

13  Relativity à la Lorentz 24Aug17

Introduction

In my last four blogs I suggested a model of light that seems to me to be a better fit to the experimental evidence than the inherently self contradictory wave-particle duality interpretation. Which was a lot of fun to write and I hope will spark some fresh thinking by persons more talented than myself.

In the adventure through the experiments on light and the foundations of Special Relativity it struck me that the concept of a lumiferous aether might have been killed off too soon, and that Special Relativity rests on some key assumptions or postulates that are not absolutely proven beyond doubt in every aspect. In fact there are some troublesome paradoxes that hint at the same thing.

So, with due regard for the many remarkable predictions of Special Relativity that are well proven experimentally, the next part of “Heretical Adventures” is going to develop a modified version of Special Relativity in the way that Lorentz might have done if he had lived longer and had not been overshadowed by Einstein’s approach.  It is written for fun and in the hope of being a stimulus to thought.

The approach starts from where Lorentz left off. It comes up with a slightly different version of Special Relativity and in the process suggests solutions to the Ehrenfest paradox and to the Symmetrical Twin Paradox. The new theory is open to experimental verification. Who knows, it might even be a step forward.

Background

Throughout the 19th century, astronomers and other physicists struggled to decipher the nature of light. A lot was discovered, but problems remained. Of particular difficulty was the result of the Michelson Morley aether drift experiment in 1887. The round trip travel time of light going to and fro parallel to the aether stream was supposed to take longer than the travel time back and forth over the same distance but across the aether stream, but it did not.

In developing his Theory of Special Relativity, Einstein leapfrogged the whole issue. He just assumed that the speed of light in vacuo, when measured in an inertial reference frame, was always the same. Combined with a few other postulates, Einstein logically developed a new approach to the description of physics and came up with some marvellous new insights.

A hundred years later, I for one do not think that Einstein’ approach has solved everything. We still can’t properly account for Newton’s pail of water, the Foucault pendulum or Ehrenfest’s rapidly rotating disc, let alone the physics of rotating spiral galaxies. Nor can we work out why the expansion of the Universe is accelerating, if indeed that is the case.

Hence this essay goes back to about a hundred years and re-litigates some old issues. What if the aether theorists were right? What does all the modern evidence suggest? What are facts and what are assumptions?

Approach:  I am going to try to stick to the evidence revealed by experiments and will be careful of just repeating everyone else’s assumptions and interpretations. If I followed the same path as everyone else I would just end up in the same place.

I am also going to try to maintain a distinction between linear accelerations, rotations and rotational accelerations because I think they are fundamentally different.

And I am going to use the old fashioned spelling of ‘aether’ because ‘ether’ is a class of organic chemicals that was sometimes used as an anaesthetic.

The Aether

In 1913 Georges Sagnac thought that his closed path interferometer had proved the existence of the aether. I am going to agree with him.

I am going to imagine the aether to be everywhere and that it is the medium in which light travels. I will think of light as being made up of disturbances in this aether, travelling as fast as anything can travel, and by the quickest route possible. But I reject the description of light as being a wriggly little wave. I think of it as being made up of phots, which are basically two dimensional electromagnetic disturbances. See an earlier blog for more details.

What Sagnac discovered was that you can always detect rotations simply by using a closed path interferometer. You can detect whether you are rotating or not, and if the rate of rotating is accelerating or not. Light will take longer to go around one way than the other.

Mach’s Galactic Reference Frame

I’m not going to agree with Ernst Mach that the distant stars provide a universal reference frame. When Mach was thinking about the origins of inertia no-one had any idea that there were other galaxies other than the Milky Way. So when Mach referred to the “fixed stars” as providing the self evident reference frame for rotational and linear inertial effects, he did not realise that many of the so-called “fixed stars” are in fact other galaxies and that our Milky Way is a rotating spiral galaxy amongst an infinite multitude of others.

What I am going to do is to link the concept of an aether with the concept of a more localised inertial reference frame.  I am going to assume that an inertial reference frame is one which is not rotating or accelerating with respect to the aether.

This would mean that, instead of being undetectable, the aether is extremely detectable in many respects. You do not even need a Sagnac interferometer. You can use a spinning bucket of water. In fact you do not need any device at all. Use your eyes and ears. If you do not feel giddy, and the stars in the night sky are not wheeling around before your eyes, then you are not rotating with respect to the aether.

Now make use of a linear accelerometer. A bucket of water will do if your research grant cannot sponsor anything more sophisticated. If the surface of the water is level and flat then you have detected that the aether and you are not accelerating or rotating with respect to each other.

But maybe you are moving in a smooth constant linear fashion relative to the aether? Or maybe you are at rest in the aether? This is harder to detect. A localized physical experiment is not going to give you the answer. Which is good in a way because it makes day to day physics in real life a lot simpler.

The only way I can think of to detect smooth linear motion relative to the aether is to observe the heavens. If the light from distant stars, or the cosmic microwave background, does not show a higher degree of redshift in one direction or another then you can more or less infer that you are stationary in the aether. Which, by the way, almost nothing in the Universe ever is.

Is the Aether Stationary?

I do not consider it to be self evident or even likely that the aether is everywhere uniform, even and at rest. It is certainly not safe to assume this. In fact I am inclined to think that it would be disturbed by massive objects and may even form giant whirlpools in the vicinity of spiral galaxies. Or maybe spiral galaxies form because there are whirlpools in the aether. But that is a topic for a later blog.

However, I am going to make a working assumption that our own solar system is moving through a three dimensional aether field that is more or less aligned to the gross distribution of galaxies in the Universe, though possibly with some drag effects within the Milky Way.

Time, Distance and the Speed of Light

If nothing else, Einstein managed to highlight that our ordinary everyday notions of measuring time durations, lengths and masses are naïve and do not work well at high speeds. The speed of light affects everything and even the simple task of coordinating clocks in order to be able the measure the speed of a travelling object is fraught with difficulty.

So what do we know? Let’s start with time. We have developed atomic clocks that are extremely precise and stable. For example the modern definition of a second is 9,192,631,770 periods of fluctuation in the hyperfine structure of Cesium 133.

If we put an atomic clock into a centrifuge and spin it up we find that it runs more slowly (see the experiment of Hay et al in 1960 as described in Wikipedia article on the Ives-Stilwell experiment). If we shake a clock back and forth then it also runs more slowly (see experiment of Chou in the same article and again in Science magazine 2010). 

We know that atomic clocks aboard Global Positioning System satellites have to be adjusted for at least 3 separate relativistic effects in order to stay in step with exactly the same clocks back on Earth. So time is anything but straightforward.

The modern definition of a meter is 1/(299,792,458) of the distance that light travels in one standard second. So the modern definition of a meter is derived from the standard definition for one second and is stable only if one standard second is stable.

The modern value for the speed of light is 299,792,458 meters per second. This is clearly dependent on the atomic clock definition for both for the meaning of a meter and the meaning of a second.

You can see that these definitions are interrelated, circular even.

In 1905 Einstein simply cut through all the confusion and postulated that the speed of light in vacuo was an invariant for all inertial observers. It then followed from this and other postulates that time durations and measurements of lengths must vary according to how they were observed.

However the forerunner of Special Relativity, Hendrik Lorentz, had a subtle but fundamentally different perspective. He thought that moving clocks, when viewed from a non-moving reference point, would appear to run slowly. In fact he came up with the concept of time dilation in the first place. But he also thought that a physical system moving against the aether would contract in the direction of motion by the same factor, now called the Lorentz factor   (g = √(1 – v2/c2)  where v is the speed of movement and c is the speed of light). (I would type the gamma symbol if I knew how to do so in Tumblr’s text system)

Observers moving with the experiment would be unable to detect the shrinkage because all their measuring instruments would be affected by the shrinkage. However, non-moving observers standing nearly would measure the shrinkage if they did the measurements properly (which requires that they measure both ends at the same synchronised time in their own reference frame).

Lorentz’ idea would explain the null result of Michelson-Morley experiment. This experiment was designed to try to detect the effects of the earth’s movement through the aether but it failed to find any effects.

In this blog essay I am going to agree with Lorentz. I will assert that the Michelson-Morley experiment did not prove that the aether drift did not exist, it just showed that result of moving through the aether was to affect time durations and lengths in such as way that these types of round-trip interference experiments will always give a null result.

Einstein decided that if the aether was not going to show any effects then it was just a metaphysical concept and served no purpose. His concept of light was (I suppose) that it was a particle travelling through nothing at all. Or maybe that he thought of spacetime as being the fabric of the Universe.

Inertial Frame Physics

If moving through the aether causes time to slow down and lengths to contract then we have to distinguish between two types of inertial systems – those that are moving in a uniform straight line through the aether and those that are at rest in the aether. Let us describe the latter as being stationary.

If we set up an arbitrary reference frame then it could be stationary, moving, accelerating, rotating, increasingly rotating or any combinations of these. So we have to be very careful in our choice of reference frame or things could get very messy.

Physics can be described from the viewpoint of observers who are moving the same way as their system, or one type of system can be described from the reference frame of another type of system.

The easiest situation is where the reference frame is stationary. This is pretty much the same as the starting point in standard Special Relativity but in this essay the interpretation is a little different. I will assume that there will be an absence of non-inertial effects because the reference frame is either stationary in the local aether or it is moving in a smooth constant linear fashion within the local aether.

Fast moving objects display relativist effects – time dilation, length contraction, mass increase etc. not because they are fast moving objects per se, but because they are fast moving objects in the aether.

The second easiest situation is a moving but still inertial reference frame. Same physics as the previous case but again there is a twist. On top of the usual physics we have now introduced a locally undetectable, relativistic Lorentz contraction of length, and also a Lorentz dilation of time.

What happens if we wish to switch the description of physics from the viewpoint of a moving observer across to the viewpoint of a stationary observer? When the observer was based in the moving system their clock was slow and their rulers were short in the dimension parallel to the direction of travel.

The answer is that there is not a problem.

Let us start with the principle of classical relativity. If the moving system sees the stationary system moving past at velocity v, then the stationary system must see the moving system moving past at velocity –v. This remains true because the moving system calculates v with a short ruler and a slow clock, and the stationary system calculates v with a ‘normal’ clock and a ‘normal’ ruler. Since v is distance divided by time, the Lorentzian effects cancel each other and both sets of observers get the same answer for v.

The One Way Speed of Light

Most of the experiments that try to detect aether wind effects, and most experiments measuring the speed of light, involve mirrors and interference effects and can be labeled as two-way path experiments.

One way speed of light measurement experiments are hard to find.

Suppose a group of phots is coming towards you through the aether and you are moving through the aether towards them in the opposite direction. You would expect to meet them sooner than if you remained standing still. But what if your clock slowed down as soon as you started moving? What would the time durations be then? It is not trivial.

And when you meet up and try to measure how fast the phots are travelling in your reference frame you face the further problem that your ruler is contracted. Plus you now have a further issue in getting your measurements done correctly – you have to get your clocks properly synchronised. You need one clock to be able to record the time at which the phots passed Point A and you need another clock to be able to record the time at which the phots passed Point B. The duration of the travel time is the difference between the two times, but this is only meaningful if the two clocks are synchronised. Getting the two clocks to run at the same rate is not the problem. It is getting a meaningful synchronisation that is hard.

Let us use an analogy. Suppose there is a lighthouse and a pilot station set N kilometres apart and the light house keeper and the pilot master try to coordinate their clocks by the use of foghorns. Suppose sound takes 10 seconds to travel between then when the wind is not blowing. They will eventually figure out that if they send a signal and the other one replies instantly then the return signal will take 20 seconds to be heard. They can use that information to synchronise their clocks.

Now suppose there is a constant onshore breeze such that the signal from the lighthouse to the shore takes 9 seconds and the signal from the shore to the lighthouse takes 12 seconds. They both get a return signal in 21 seconds, but if they each set their clock to be 10.5 seconds ahead of when they heard the other’s signal they would not be properly synchronised.

If they take turns to send a signal on the hour, and keep on adjusting their clock so that it records the other’s signal as being heard at 10.5 seconds past the hour, then they will never be able to synchronise properly.

In other words, if they keep on using the Einstein-Poincaré method of clock synchronisation they will fail.

Eventually the lighthouse keeper will have to put his clock into his rowboat and take it to the pilot on shore so that they can both get back on track. Or they will have to realize that the speed of their clock signals is not the same in both directions.

Back to our phots story.

We postulate that if some phots are recorded at A at a certain time and the rest are recorded at B’s clock at a later time then, even with the slow clocks and the short ruler, the time of travel between A and B will be less that the time of travel for phots approaching in the other direction and travelling from B to A.

In other words, the one way speed of light is affected by moving through the aether.

This would be very difficult to check by experiment but in principle it could be done. I don’t know if such an experiment has ever been done. There are a lot of round trip experiments but the difference would not show up in these.

Using the Earth as a test bed has problems. The speed of the earth through the aether is about 1/1000 the speed of light, which is hardly what you would call relativistic.

Altered Foundations for a Theory of Relativity

In the above conjecture, the key foundations of Special Relativity would have to be split into two parts to become:

The one-way and two-way speed of light in vacuo is always the same in any stationary inertial reference frame, irrespective of how that frame is oriented.

The measured two-way speed of light in vacuo is always the same in any inertial reference frame, irrespective of how that frame oriented or moving.

(An inertial reference frame is of course one that is not rotating, accelerating or decelerating or in a gravitational field).

Another postulate underlying Special Relativity is going to be dropped altogether – the Principle of Classical Relativity. I do not know why it was ever included in the first place. It might appear to be obvious, but Special Relativity teaches us that a lot of naively obvious things are not true at relativistic speeds. Nor am I aware of any experimental tests of this postulate at relativistic speeds, let along verifications.

I think that the effect of these changes in the foundation will be a theory which is consistent with Special Relativity in most respects, but which opens up an easier way to understand accelerated and rotating reference frames.

Let us make a start by means of some thought experiments.

A Spaceship in Uniform Linear Acceleration

Consider a long empty rocket undergoing constant linear acceleration towards some distant galaxy. It is moving through the aether at an ever increasing speed. On account of this movement relative to the aether, clocks aboard the spaceship will be slowed by the usual gamma factor and lengths in the direction of the movement will be shortened by the same factor.

Observers aboard the rocket will be unable to detect these Lorentzian effects by most normal experiments. If they had a reliable way to measure the one-way speed of light in their rocket they might be able to tell that the duration for a phot to travel from tail to tip is longer than the duration for a phot to travel from tip to tail. The two-way speed of light however, is the same in any orientation. 

Any attempts to measure the speed of light, or to detect its path, would be significantly affected by the acceleration of the rocket.

If the rocket has parallel mirrors down each side and phots are directed across the rocket at right angles to the axis of acceleration, their path would be a series of curves that creates a kind of curvy zig-zag pattern down towards the rear of the rocket.

As the speed of the rocket increases, phots directed from an emitter at the rear of the rocket towards an absorber at the front would take longer and longer to arrive. Furthermore they would be increasingly Doppler red shifted upon detection. For phots directed from the front of the rocket to the back there would be an ever increasing blue shift.

Would there be a difference in the rate of clocks at the front and at the back? I don’t think so. They are moving as fast as each other and they are at rest relative to each other, and they are both experiencing the same degree of acceleration.

What about other physics? I expect that the inertial resistance of matter to forces would be increasing. You can think of this as the inertia of the matter increasing, or you might prefer to think that they are acquiring extra relativistic mass.

The Very Fast Train Revisited

Let us revisit the very fast train thought experiment from an earlier blog essay, but this time using the above modified postulates. What is different?

Remember, there is a straight station platform just under 300 million kilometres long, with observers every million kilometres who have well synchronised clocks equipped with cameras. We will imagine this platform to be stationary in the aether.

Hurtling down a long straight track comes a train that is the same length as the station when it at rest, but it is travelling at half the speed of light. The train has a driver at one end and a guard at the other and they also have clocks that are synchronised in their reference frame. If they measure the two-way speed of light is comes out to be c. If they do a Michelson-Morley experiment then they do not detect any aether wind effects.

The set of clocks on the train and the set of clocks on the platform have been zeroed so that the driver’s clocks shows zero at the precise moment (Event 1) he passed the stationmaster at the start of the platform, and the latter’s clock is also zero at that Event, as confirmed in everyone’s photos.

The interpretation of what happens is relatively simple. Due to its movement through the aether, the train shrinks by the factor g  (= 1.1547 in this example) and it’s clocks slow down by the same factor.

When the guard passes the stationmaster, the station cameras show the driver has only reached 259.92 million km up the platform. When the driver reaches the end of the platform (Event 2) a station camera back down the platform (Event 3) shows the guard has only reached 259.92 million km back down the platform. The train is definitely shorter. By the usual factor of g.

The driver reaches the end of the platform in 2 seconds on the station clocks, confirming the train is travelling at c/2. The photograph taken by the station clock at that event also shows the driver’s clock, and it shows it to read 1.732 seconds. The driver’s clock is running slow by a factor of g. The platform clock and camera at Event 3 shows the guard’s clock is running slow by the same factor.

So far so good, and all consistent with normal Special Relativity.

But our alternative theory is not as symmetrical as Special Relativity. It does not postulate that classical relativity has to hold true at relativistic speeds. In the case above it is the train that is moving through the aether and not the platform.

What difference does this make? Nothing at all from the point of view of the stationary observers, but what about from the point of view of a reference frame co-moving with the train?

Let us start with time. As the driver (and then the guard) move past the platform they notice that the platform clocks are ahead of theirs. By the time the driver gets to the end, his clock says 1.732 seconds and the platform clock says 2 seconds. The driver can take a photograph to prove it. It tells the same story as the photograph taken from the station.

There are only two possibilities, either the train’s clocks must be slow or the station clocks must be running fast. The driver and the guard  consult their revised textbooks and decide that it must be that their clocks are running slow by the factor g.

What about lengths? The textbooks also tell them that their train will have shrunk by the factor g. The observers on the platform tell them the same thing.

So how fast is the outside world passing by according to their calculations? The best way for them to measure this is to choose a marker in the outside world and derive the time duration for this marker to go from being abreast of the driver to being abreast of the guard. 

So the driver asks the guard to photograph the time on his clock when the back of the train passes the stationmaster standing at leading edge of the platform (call this Event 1a). At the same simultaneous instant (in the train frame) the driver is further up the platform (call this Event 1b).

The stationary observers photograph Event 1b as occurring at location 259.92 million km up the platform at their time of 1.732 seconds. They have no doubt that the driver is travelling at half the speed of light. Their photograph reveals the driver’s clock to be reading 1.5 seconds (= 2seconds/g2) and the driver agrees with this as his camera shows the same data. But it is Event 1a we are most interested in.

The Stationmaster’s clock and camera show that Event 1a happened at time 1.732 seconds in the stationary (platform) frame and 1.5 seconds on the guard’s clock. So the driver and guard are confident that the stationmaster has gone from the tip of the train to the back of the train in 1.5 of their seconds. They divide what they now know to be the length of their train by this duration and come up with the answer of g.c/2. In other words they measure and calculate that the outside world is passing them by at a factor of gamma more than the outside world thinks they are passing by.

The platform based observers see the train going past at c/2 but the train based observers see the platform going past at g.c/2.  

The postulate of Classical Relativity has been broken. Basically because the train shrinks but the platform doesn’t.  And this is because the train is moving very fast relative to the aether but the platform isn’t.

Or you can interpret the result as follows. The moving system has clocks which are running slow by the gamma factor, so they see the outside world moving past at a rate which is increased by the gamma factor.

Surely this would have shown up in some experimental results by now! But has it? Where has there been an experiment based on a reference frame which is moving at relativistic speeds?

Lorentzian Relativity and the Symmetrical Twin Paradox

The new theory resolves the symmetrical twin paradox (see earlier blog) in simple way. Both twins are moving through the aether, so both experience time dilation and both age at the same slower rate. They also age less than their colleagues aboard the stationary mother ship by the same amount.

Rapidly Rotating Disc

Return to the earlier discussion on the Ehrenfest Paradox. This has a rigid disc spinning so fast that points on its circumference are moving at an appreciable proportion of the speed of light. Suppose the external observers see points on the rim moving at X million meters per second in an anti-clockwise direction. The principle of classical relativity says that observers on the rim should measure the territory immediately outside the rim moving at the same speed in the opposite direction. But will this in fact be true?

I am going to argue that they this will not happen. I am going to suggest that the passage of time for the rim based observers will slow down and so they will see the outside world going past faster than X million meters per second.

My argument is simple. External observers see one rim circumference go by in T seconds. A rim based observer sees one rim circumference go by in T’ seconds where T’ is the duration on their local clock and T’<T because their local clock is slow.

Both the external inertial observers are measuring the circumference properly. The external observers can just run a tape measure around it. The rim based observers cannot dispute that this is in fact the length of their rim. The same observer can see both ends of the tape in the same place at the same instant.

Dividing the rim circumference by the smaller value T’ give a bigger answer. The rim based observers see the outside world going fast by a factor of g, and this is simply because their clocks are running slow by a factor of g.

The so-called principle of Classical Relativity is broken, but it makes the situation a lot less paradoxical.

Experimental Verification

The new theory has the same predictions as Special Relativity for all the well know time dilation and relativistic mass increase experiments that I can think of. The best place to look for different predictions is situations where observers are likely to be travelling very fast relative to the conjectured aether, and other observers are not.  And I think a good place to try this out is using satellite systems orbiting the Earth. See next blog.