#Einstein GeneralRelativity Cosmology | Explore Tumblr posts and blogs

scepticaladventure · 7 years ago

Text

21 General Relativity Basics 1Sep18

Introduction In following essays/blogs I am going to make some heretical comments about General Relativity, but before that I’d like to present a summary of its background. The text is a pastiche from numerous sources.

I’d first like to say that I think General Relativity is a work of genius and that I am well aware of its successes in numerous experiments and astronomical observations. Which doesn’t mean that I think it is necessarily the perfect and final explanation of everything.

Einstein as a Young Man To understand the theory I think it helps to understand the man, the times he lived in and what else was going on in physics and maths. But there was such a lot going on that I cannot do justice to it all in a sort blog like this essay The decades from 1860 to 1930 were a golden period in physics, predominantly in northern and central Europe, Ireland, Britain, and the United States. Major advances were made in thermodynamics, electromagnetism and in atomic and nuclear physics. It was also a time of rapid industrialisation and a lot of political turmoil, notably World War I.

Albert Einstein was born in Ulm in the German Empire Kingdom of Württemberg,on 14 March 1879. (Sidenote: Sir Isaac Newtown was born in the year that Galileo died and Einstein was born in the year that James Clerk Maxwell died).

Albert’s parents were Hermann Einstein, a salesman and engineer, and Pauline Koch. In 1880, the family moved to Munich, where Einstein's father and his uncle Jakob founded a company that made electrical equipment. In 1894 the company failed to gain a bid to supply electric lighting to the city of Munich due to insufficient capital. In search of business, the Einstein family moved to Italy, first to Milan and then to Pavia where Hermann Einstein worked on installing the first electrical power plants in the region. Einstein stayed in Munich to finish his schooling, but he resented the school's strict regime and teaching method. So in December 1894, at the age of 15, he travelled to Italy to join his family in Pavia. During his time in Italy Einstein wrote a short essay with the title "On the Investigation of the State of the Ether in a Magnetic Field".

In 1895, at age 16, Einstein took the entrance examinations for the Swiss Federal Polytechnic in Zürich. He failed to reach the required standard in the general part of the examination, but obtained exceptional grades in physics and mathematics. He went to the cantonal school in Aarau, Switzerland to complete his secondary schooling.

In January 1896, and with his father's approval, Einstein renounced his German citizenship. In September 1896, he passed the Swiss Matura with mostly good grades and the highest grades in physics and mathematical subjects. He then registered at the University of Zurich to further study physics. After graduating in 1900, Einstein spent two years searching for a teaching post. He acquired Swiss citizenship in February 1901. With the help of Marcel Grossmann's father, he secured a job at the patent office in Bern as an assistant examiner. In 1902, along with a few friends from Bern, Einstein started a small discussion group that met regularly to discuss science and philosophy. Their readings included the works of Henri Poincaré, Ernst Mach, and David Hume.

In 1903 his position at the Swiss Patent Office became permanent, although he was passed over for promotion until he "fully mastered machine technology". He also married.

In 1905, at the age of 26, he completed his PhD. He sent articles to the most prestigious scientific journal of the period, the Annalen der Physik, and four of his papers were published which became recognized as outstanding contributions to physics. They were on the photoelectric effect, Brownian motion, Special Relativity, and the equivalence of mass and energy. The paper on the photo-electric effect was cited in Einstein’s award of the Nobel Prize for Physics 16 years later.

Einstein postulated that light consists of localized particles (quanta), but the idea was rejected by most leading physicists, including Max Planck and Niels Bohr. This idea only became accepted in 1919 after Robert Millikan performed detailed experiments on the photoelectric effect, and after measurements where carried out on the scattering of light in the phenomenon which we know call Compton scattering.

Einstein’s Theory of Special Relativity leapt ahead of the work being done by great scientists such as Hendrik Lorentzin Holland and Henri Poincaré in France. In essence it established a fundamentally new way to describe physics. It was based on a set of postulates about light and about the meaning of measurement. It culminated in what became the most famous equation in physics, E = mc2.

By 1908 Einstein was recognized as a leading scientific thinker. He received offers of employment from various European universities and was eventually appointed lecturer at the University of Bern. The following year, Einstein was appointed associate professor in theoretical physics, aged 30. He became a full professor at the University in Prague in April 1911, accepting Austrian citizenship in the Austro-Hungarian Empire to do so. During his stay in Prague he wrote 11 scientific works, five of them on radiation and the quantum theory of solids.

In July 1912, he returned to his alma mater in Zürich. From 1912 until 1914 he was professor of theoretical physics at the ETH Zurich, where he taught analytical mechanics and thermodynamics. He also studied continuum mechanics, the molecular theory of heat, and the problem of gravitation, on which he worked with mathematician and friend Marcel Grossmann.

In July 1913 Einstein was voted membership of the Prussian Academy of Sciences in Berlin. Max Planck and Walther Nernst offered him the post of director at a new Institute for Physics. Einstein accepted the move to Berlin just as World War I was beginning. His decision to move to Berlin was influenced by the prospect of living near his cousin Elsa, with whom he had developed a romantic realtionship. Einstein joined the academy and thus Berlin University and became Director of Kaiser Wilhelm Institute for Physics in 1917. He was the elected president of the German Physical Society from 1916 to 1918.

Einstein did not work in isolation. Northern Europe was awash with great scientists and mathematicians. In some ways it was a competition between nations and individuals but there was also a lot of cooperation. Lorentz graciously said that Einstein had taken his own efforts to a new level. Lorentz wanted Einstein to succeed him at Leiden University but Einstein went to Berlin and Paul Ehrenfest succeeded Lorentz at Leiden.

One of Einstein’s professors of mathematics, Herman Minkowski, was surprised when he read Einstein’s paper on Special Relativity, since he was working on much the same thing. In fact, it was Minkowski who invented the concept of spacetime. Max Planck was a consistent supporter of Einstein. Ehrenfest a good friend. And so on.

Einstein’s success in Germany was in spite of anti-Semitic prejudice. One German physicist, himself a Nobel Laureate in1905, scornfully called Einstein’s work “Jewish physics”. In 1933 Einstein realised that he could not continue to live in Germany due to the rise of Nazism and he managed to move to the United States. He was always an avowed pacifist.

Origins of General Relativity In one of his books, Einstein recalled: “I was dissatisfied with the special theory of relativity, since the theory was restricted to frames of reference moving with constant velocity relative to each other and could not be applied to the general motion of a reference frame. I struggled to remove this restriction and wanted to formulate the problem in the general case.”

There were other things on Einstein’s mind as well. Lorentz’s successor at Leiden University, Paul Ehrenfest, had posed a paradox about a rapidly rotating disc. In Special Relativity, the radius of the disc is supposed to stay the same but the circumference is supposed to undergo a Lorentz contraction, thus violating the usual Euclidean ratio. This was one of the things that started Einstein wondering if the generalised geometry of four dimensional spacetime was in fact “flat”.

Curved space geometry had been developed by Bernhard Riemann just before Einstein was born and Einstein would have learnt about it at University. So this is another of the key strands involved in the development of Einstein’s approach and thinking.

But perhaps Einstein’s main concerns had to do with inertia and with gravity. Ernst Mach a had suggested that the distant stars were somehow responsible for the phenomenon of inertia since there was a striking correspondence between non-rotation and the reference frame provided by the “fixed stars”. But this suggested action at a distance, which was itself problematical. Newtonian gravity also inferred action at a distance and the force of gravity was anomalous when compared to other known forces in nature e.g. it was always one-way.

So after publishing his work on Special Relativity in 1905, Einstein started thinking about how to incorporate gravity into his new framework. In 1907, he came up with as simple thought involving an observer in free fall and another observer at rest in a gravitational field. He later said: “The breakthrough came suddenly one day. I was sitting on a chair in my patent office in Bern. Suddenly the thought struck me: If a man falls freely, he would not feel his own weight. I was taken aback. This simple thought experiment made a deep impression on me. This led me to the theory of gravity. I continued my thought: A falling man is accelerated. Then what he feels and judges is happening in the accelerated frame of reference. I decided to extend the theory of relativity to the reference frame with acceleration. I felt that in doing so I could solve the problem of gravity at the same time. A falling man does not feel his weight because in his reference frame there is a new gravitational field, which cancels the gravitational field due to the Earth. In the accelerated frame of reference, we need a new gravitational field.”

Einstein decided to further explore his idea that the observable physics in a gravitational field and in an accelerated reference frame not only looked the same but that they could be described in the same way.

Einstein embarked on what would be an eight-year quest to develop his extended theory. In 1912 he started to use a new branch of mathematics that had been developed in Germany over the previous fifty years – non-Euclidean geometry. This led him to use a curved spacetime model as a way of describing gravity. (It was later theorists that introduced the idea that curved spacetime actually replaces gravity). After numerous detours and false starts, his work culminated in presentation to the Prussian Academy of Science in November 1915 of what are now known as the Einstein field equations. These equations specify how the geometry of space and time is influenced by whatever matter and radiation are present, and they form the core of Einstein's General Theory of Relativity.

In essence, Einstein’s approach replaced the Newtonian description of gravity as a force acting instantaneously over the distance between massive objects. The Einstein description is now interpreted as suggesting that gravity does not actually exist as such. Rather, the effects of matter/stress/energy are to curve spacetime in such a way that the natural trajectories of objects gives the appearance that they are being acted upon by a external force. Gravity is not regarded as a physical force transmitted through space and time but is instead regarded as an effect caused by the curvature of spacetime. Spacetime is curved and objects moving through space over time follow the “straightest” path along the curve, which explains why their paths appear to be curved.

For example, the Sun bends spacetime around it and the natural paths of the planets around the Sun belong to the family of the shortest closed paths possible (which also require the least amount of energy), resulting in the same elliptical orbits so accurately described by Copernicus and Kepler in the 17th century.

One of the earliest successes of General Relativity was in being able to provide an explanation for a slow “anomalous” advance (precession) in the axis of the orbit of Mercury around the Sun.

Another success came via a prediction that was soon proved experimentally. When he published his complete theory of General Relativity in 1915, Einstein modified his 1911 prediction of how much bending would occur in the path of light coming to earth from a distant star and just grazing the edge of the Sun’s disc. In effect he doubled it.

In 1919, an expedition led by the British astronomer Arthur Eddington went to the west African island of Principe to observe the deflection of starlight by the Sun. It was possible to see stars (which were in the constellation of Taurus) near the Sun because Principe was in the path of a total solar eclipse at the time. Eddington, (later Sir Arthur Eddington) was a strong supporter of Einstein and was delighted to report that the observed deflection was exactly as Einstein had predicted.

Einstein became world famous and a media darling. In 1921 he received the Nobel Prize for physics. In a visit to the United States in the same year he received film star treatment and his name became synonymous with “genius”. (In truth, Eddington’s result was not conclusive and Einstein’s predictions were not conclusively verified until several decades later.)

In spite of the media headlines, Einstein’s approach was regarded by scientists of the day as a bit of a curiosity. Neither Einstein’s Theory of Special Relativity or his Theory of General Relativity was specifically mentioned in the citation to Einstein’s Nobel Prize.

In 1955, aged 76, Einstein died in Princeton from an abdominal aneurism.

In my opinion Einstein’s extraordinary rate of contribution to science between 1905 and 1915 was not matched by his subsequent achievements, but that does not detract from his great contribution to science. I regard Einstein as the second greatest physicist of all time, surpassed only by Sir Isaac Newton.

Einstein is widely regarded as having created one of the two main pillars of modern physics (the other pillar being quantum mechanics). General Relativity is regarded as an advance over Special Relativity and Newton's much earlier law of universal gravitation.

The Einstein field equations are a set of ten nonlinear partial differential equations and are very difficult to solve. Einstein used approximation methods in working out initial predictions of the theory. The curvature of spacetime is mathematically related to the energy and momentum of whatever matter and radiation are present by the Einstein field equations.

In 1916, the astrophysicist Karl Schwarzschild found the first non-trivial exact solution to the Einstein field equations, the Schwarzschild metric. This solution laid the groundwork for the description of the final stages of gravitational collapse, and the objects known today as black holes. (I find this all the more remarkable because Schwarzschild was serving on the Russian front and suffering from an auto-immune disease at the same time).

Examples of alleged differences from the predictions of classical theory include gravitational time dilation, gravitational lensing, the gravitational redshift of light, and the gravitational time delay. (I say ‘alleged’ differences because in later chapters I will explore whether or not classical physics can come up with the same predictions.)

The predictions of General Relativity have been confirmed in all appropriate observations and experiments to date, and to a very high degree of accuracy. Furthermore, although General Relativity is not the only relativistic geometric theory of gravity, it is the simplest geometric based theory that is consistent with this experimental data.

However, unanswered questions remain. The one usually mentioned is how general relativity can be reconciled with the laws of quantum physics to produce a complete and self-consistent theory of quantum gravity. Personally I think that this is a red herring and that are many other shortfalls that are more important.

The main one (in my lonely and humble opinion) is that General Relativity fails to adequately explain Mach’s Principle and the origins of inertia. Einstein grappled with this all his life and eventually concluded he had not succeeded.

My other main objection is that General Relativity and quantum mechanics between them do not even come close to explaining the motion of stars in spiral galaxies. This is called the Galactic Rotation Curve problem.

Scientists of the 19th century were faced with a theoretical challenge of similar magnitude. They recognized their challenge as being a major issue and called it the Ultraviolet Catastrophe. Einstein and Planck made major contributions to the resolution of the Ultraviolet Catastrophe issue and in doing so they greatly assisted the development of quantum mechanics.

By way of contrast, modern scientists just leapt to an assumption about the solution to the Galactic Rotation Curve issue. They decided that the solution must be the presence of some hitherto unknown, exotic and undetected type of ‘cold dark matter’. They have been vainly looking for cold dark matter ever since. I wonder how many more decades will go by before they achieve enough humility and open mindedness to realize they might be barking up the wrong tree?

Of course if cold dark matter is ever actually discovered then I will take this comment back, with appropriate humble apologies.

General Relativity and Cosmology In 1917, Einstein applied his theory to the Universe as a whole, initiating the field of relativistic cosmology. In line with what everyone else naturally assumed at the time, Einstein assumed that the Universe was unchanging. So he incorporated a new parameter to his original field equations - the cosmological constant - to make sure that any solution to his set of equations could be adjusted to ensure that this was the case.

By 1929, the work of Hubble and others had shown our Milky Way galaxy is in fact just one of countless galaxies and also that the distances between all these galaxies is expanding. Einstein later said that introducing the cosmological constant had been a “big blunder”. However, recent astronomical evidence is suggesting that the rate of expansion is accelerating and the cosmological constant is now back in favor.

Alexandr Friedmann solved Einstein’s equations for a particular model of the Universe in 1922. Lemaître used these solutions to formulate the earliest version of the Big Bang models, in which our Universe is envisioned as evolving from an extremely hot and dense earlier state.

With the developments in astronomy between approximately 1960 and 1975 General Relativity began to dominate the mainstream of theoretical astrophysics. Physicists began to understand the concept of a black hole, and to identify quasars as one of these objects' astrophysical manifestations. Ever more precise solar system tests confirmed the General Relativity’s predictive powers. Relativistic cosmology became amenable to direct observational tests and General Relativity fared so well that it slowly became the orthodox paradigm. In 2016 another success came about when scientists were able to observed gravitational waves for the first time.

In the current era General Relativity reigns supreme and almost any alternative idea is politely or impolitely ignored. In 1999 Time Magazine selected Einstein as the most significant person of the 20th century. He is popularly considered to be the greatest scientist of all time (without, as far as I can tell, having actually performed any actual physical experiments). Personally I think that honor still belongs to Sir Isaac Newton.

The elephant in the room is that modern cosmology now requires that about 98% of the Universe has to consist of cold dark matter and dark energy. Both of these are fabrications completely outside of the rest of known physics and there is no direct well-confirmed experimental evidence for either of them. I think that the something is very wrong somewhere. I strongly suspect we are missing something fundamental, not in the Universe, but in our understanding of the fundamentals of the Universe.

Next Steps In the next few essays I am going to have some fun. • I will argue that the Equivalence Principle is just a mathematical abstraction – a conjectural hypothesis. An assumption for the sake of a model. An excursion into mathematical imaginings. And that it is patently untrue. • Then I will look at some of the classic test of relativity involving gravity and light. • Next I will challenge Schild’s interpretation of the Pound-Rebka experiments demonstrating and measuring gravitational redshifts. I do not disagree with the conclusion, just the argument itself. • After that I may look at Einstein’s insistence that there in no universally preferred reference frame. I will present a paradox that I call “Two fat trains”. And I will suggest that physics is a lot simpler if we do admit that some reference frames “are more equal than others.” • Then I want to take a fresh look at the modern attitude to spacetime. I will argue that we have got confused between our mathematical imaginings and reality. • Next I plan to explore if there are any ways to merge Newtonian gravity into four dimensional spacetime without going to the full geometric approach. As pat of this I am going to search the literature for the sort of model I have in mind (for surely people better than me have tried this already). • If this comes to fruition I will try to explain how an alternate model might be able to handle all the classic experimental verifications for General Relativity. • Then it would be very nice to find or predict some experimental or observational outcomes that do not accord with conventional General Relativity but which are explained in the new approach • And finally it would be very nice to be able to make some predictions that experimenters could then look for.

It is a Quixotic quest, but I will enjoy it and who knows. I might even come up with something. Or inspire someone better than me to come up with a breakthrough. Or at least amuse a reader or two.

#Einstein GeneralRelativity Cosmology

1 note · View note