Theory of Relativity Published - History

Theory of Relativity Published - History

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(6/30/05) Albert Einstein, who at the time was a German physicist living in Switzerland, published the Theory of Relativity.

Theory of Relativity Published - History

The speed of light, was the central question that gave rise to the theory of relativity. The speed of light is very large compared to the speeds we experience . We have no physical intuition about speeds approaching . We can however measure the speed of light with a rotating mirror.

In what frame is the speed of light ? Newton's laws are independent of which inertial frame is chosen. Is the speed of light going to break this symmetry of physics?

Maxwell's equations predict the speed of light from some basic measurements of how fields are produced from charges and currents.

Since currents are just moving charges, they also essentially predict how the fields transform as we transform from one inertial reference frame to another. These transformations were problematic.

There was a simple way out. There could be one frame in which the medium on which EM waves propagate is at rest . The equations of EM were consistent if the speed of light is constant in one fixed frame. Physicists thought EM waves must propagate in some medium. Physicists postulated the ``ether'' (aether). They thought, space is filled with ``the ether'' in which EM waves propagate at a fixed speed. Ether gave one fixed frame for EM. But experiments, particularly Michelson-Morley disagreed. And we would loose the symmetry found in Newton's laws ``any inertial frame''.

The ether theory was testable. We should see some velocity of the ether. We should see a seasonal variation. Michelson and Morley set up to be sensitive even to the motion of the earth.

Albert Abraham Michelson (1852-1931) was a German-born U.S. physicist (at Caltech) who established the speed of light as a fundamental constant. He received the 1907 Nobel Prize for Physics. In 1878 Michelson began work on the passion of his life, the measurement of the speed of light. His attempt to measure the effect of the earth's velocity through the supposed ether laid the basis for the theory of relativity. He was the first American scientist to win the Nobel Prize.

Edward Williams Morley (1838-1923) was an American chemist whose reputation as a skilled experimenter attracted the attention of Michelson. In 1887 the pair performed what has come to be known as the Michelson-Morley experiment to measure the motion of the earth through the ether. The figure below shows the Michelson interferometer on a block of granite. A beam of light split, and reflected from two mirrors will interfere.

Oliver Heaviside (1850-1925) was a telegrapher, but deafness forced him to retire and devote himself to investigations of electricity. He became an eccentric recluse, befriended by FitzGerald and (by correspondence) by Hertz. In 1892 he introduced the operational calculus (Laplace transforms) to study transient currents in networks and theoretical aspects of problems in electrical transmission. In 1902, after wireless telegraphy proved effective over long distances, Heaviside theorized that a conducting layer of the atmosphere existed that allows radio waves to follow the Earth's curvature. He invented vector analysis and wrote Maxwell's equations as we know them today . He showed how EM fields transformed to new inertial frames.

Hendrik Antoon Lorentz (1853-1928), a professor of physics at the University of Leiden, sought to explain the origin of light by the oscillations of charged particles inside atoms. Under this assumption, a strong magnetic field would effect the wavelength. The observation of this effect by his pupil, Zeeman, won a Nobel prize for 1902 for the pair. However, the Lorentz theory could not explain the results of the Michelson-Morley experiment. Influenced by the proposal of Fitzgerald, Lorentz arrived at the (approximate) formulas known as the Lorentz transformations to describe the relation of mass, length and time for a moving body. ( Poincare did this more accurately but referred to this as the Lorentz transformation). These equations form the basis for Einstein's special theory of relativity.

George Francis FitzGerald (1851-1901), a professor at Trinity College, Dublin, was the first to suggest that an oscillating electric current would produce radio waves, laying the basis for wireless telegraphy. In 1892 FitzGerald suggested that the results of the Michelson-Morley experiment could be explained by the contraction of a body along its its direction of motion .

Einstein's ``On the Electrodynamics of Moving Bodies'' introduced Special Relativity. Einstein had read Lorentz's book and worked for a few years on the problem. He did not believe there should be one fixed frame.

Albert Einstein (1879-1955) grew up in Munich where his father and his uncle had a small electrical plant and engineering works. Einstein's special theory of relativity, first printed in 1905 with the title "On the Electrodynamics of Moving Bodies" had its beginnings in an essay Einstein wrote at age sixteen. The special theory is often regarded as the capstone of classical electrodynamic theory.

Einstein did not get a Nobel prize for Special Relativity. He got one for contributions to theoretical physics including the photoelectric effect . The committee did not think Special Relativity had been proved correct until the 1940s.

Einstein wanted the speed of light to be the same in every frame . This would work for E&M equations and the way the fields must transform. It would agree with experiment. Einstein did consider experiment but maybe not Michelson Morley. But velocity addition didn't make sense to anyone . How could an observer in an inertial frame moving at measure light to move at the same speed as we do in our frame at rest?

In what he called ``The Step'' , Einstein realized that by discarding the concept of a universal time , the speed of light could be the same in every frame. In going from one inertial frame to another, both and transform. The time is different in different inertial frames of reference. He derived the previously stated Lorentz transformation from the requirement that the speed of light is the same in every inertial frame.


Before Einstein, astronomers (for the most part) understood the universe in terms of three laws of motion presented by Isaac Newton in 1686. These three laws are:

(1) Objects in motion (or at rest) remain in motion (or at rest) unless an external force imposes change.

(2) Force is equal to the change in momentum per change of time. For a constant mass, force equals mass times acceleration.

(3) For every action, there is an equal and opposite reaction.

But there were cracks in the theory for decades before Einstein's arrival on the scene, according to Encyclopedia Britannica. In 1865, Scottish physicist James Clerk Maxwell demonstrated that light is a wave with both electrical and magnetic components, and established the speed of light (186,000 miles per second). Scientists supposed that the light had to be transmitted through some medium, which they called the ether. (We now know that no transmission medium is required, and that light in space moves in a vacuum.)

Twenty years later, an unexpected result threw this into question. Physicist A.A. Michelson and chemist Edward Morley (both Americans at the time) calculated how Earth's motion through this "ether" affected how the speed of light is measured, and found that the speed of light is the same no matter what Earth's motion is. This led to further musings on light's behavior &mdash and its incongruence with classical mechanics &mdash by Austrian physicist Ernst Mach and French mathematician Henri Poincare.

Einstein began thinking of light's behavior when he was just 16 years old, in 1895. He did a thought experiment, the encyclopedia said, where he rode on one light wave and looked at another light wave moving parallel to him.

Classical physics should say that the light wave Einstein was looking at would have a relative speed of zero, but this contradicted Maxwell's equations that showed light always has the same speed: 186,000 miles a second. Another problem with relative speeds is they would show that the laws of electromagnetism change depending on your vantage point, which contradicted classical physics as well (which said the laws of physics were the same for everyone.)

This led to Einstein's eventual musings on the theory of special relativity, which he broke down into the everyday example of a person standing beside a moving train, comparing observations with a person inside the train. He imagined the train being at a point in the track equally between two trees. If a bolt of lightning hit both trees at the same time, due to the motion of the train, the person on the train would see the bolt hit one tree before the other tree. But the person beside the track would see simultaneous strikes.

"Einstein concluded that simultaneity is relative events that are simultaneous for one observer may not be for another," the encyclopedia stated. "This led him to the counterintuitive idea that time flows differently according to the state of motion, and to the conclusion that distance is also relative."


If light was a wave, it was assumed that the wave must be carried by some medium, just as sound waves are carried by air and water waves are carried by water. How else could the peak and the trough of two waves annihilate one another to produce the interference patterns if the wave was not a displacement in some medium? That medium was known as the luminiferous (=light bearing) ether . The moving earth was now supposed to be moving through a medium that must stream past the earth, much as water streams past a boat moving through the ocean.

Problems Arise

However, in the early twentieth century, physicists began noticing discrepancies between Newtonian mechanics and Galilean Transformations, and the theory of electromagnetism proposed by James Clerk Maxwell in his 1873 paper, A Treatise on Electricity and Magnetism. Galilean Transformations and the theory of electromagnetism were found incompatible for two reasons. First, when Maxwell’s Equations, which describe electromagnetism, were subjected to Galilean Transformations, the equations yielded nonsensical results. 3 For example, Maxwell’s Equations changed form and failed to continue to accurately describe electromagnetic behavior. The disagreements seemed to indicate that either the theory of electromagnetic behavior was wrong, or that Galilean Transformations were inadequate for electromagnetic waves. Second, Maxwell’s Equations mathematically produce a value for the speed of electromagnetic waves, more commonly referred to as the speed of light: 186,000 miles per second. At the time, it was thought that electromagnetic waves, like all other waves, require a medium through which to propagate. According to this assumptions, the movement of this peculiar medium (called the ether) through which electromagnetic waves propagate ought to affect the speed of the electromagnetic waves. However, Maxwell’s Equations gave no indication that the speed of light should change due to a change in reference frame or the motion of a medium. 4

In 1887, in order to investigate whether or not the speed of light changes with the motion of the ether, physicists Albert Michaelson and Edward Morley performed an experiment at Case Western Reserve University designed to detect the motion of the ether. 5 The experiment involved firing pulses of light perpendicular to each other over the same distance and measuring whether one pulse of light covered the distance in less time than the other (Figure 2). A discrepancy in time elapsed would indicate that the motion of the ether had affected the speed of light that passed through it. However, in repeated trials, Michelson and Morley detected no difference in the time required for both pulses of light to cover the same distance. 6 The results of the Michelson-Morley experiment indicate that there is no ether, and the speed of light is invariant. Clearly, another explanation was required.

Theory of Relativity Published - History

When he was 16, Albert Einstein, having failed his exams, took a gap year. He read philosophy books, attended university lectures, and dreamed up thought experiments – this is how he would become a genius. He thought about chasing the light.

Chasing the light is the kind of experiment theoretical physicists perform in the lab of the mind. Teenage Einstein imagined running after a beam of light, and this became the start of asking himself fiendish questions – about the speed of light, about space and time, about how gravity really works. This was about a decade before E = mc 2 .

In 1905, Einstein published the four papers that would earn him acclaim, including the special theory of relativity and the one containing the world’s most famous equation. Yet something bugged him about special relativity: it was too … theoretical. It proved the validity of all natural laws except one: Isaac Newton’s law of universal gravity. This law had formed the bedrock of physics for 220 years, so a theory of the universe that didn’t take it into account was, in Einstein’s own word, “unsatisfactory.”

He was sitting in his office a couple of years later, gazing at the roofs outside the window. “Suddenly a thought struck me,” he would recall. “If a man falls freely, he would not feel his weight. This simple thought experiment made a deep impression on me.” It took him eight more years to solve the problem. His general theory of relativity came out in Annalen der Physik, the German physics journal that had published all his papers, on March 20, 1916.

Mathematical world view

I know what you’re thinking: roofs, light beams – what does it all mean? Good question! As Einstein himself said, “The important thing is not to stop questioning.”

Physicists use mathematics to describe the universe. Consider Pythagoras’ theorem (a 2 + b 2 = c 2 ). Use it on the triangle pictured here, and you can predict that c is 5 cm. Then draw a triangle to those measurements, and you’ll see that your prediction was right. Make the two straight sides any length at all and the theorem will always, always tell you the length of the third side. That’s the whole point – the beauty – of the mathematical world view.

That’s why Einstein took a decade each time to formulate his two theories they had to predict measurements as vast as the cosmos, not to mention conform to the theories of previous thinkers such as Newton and Galileo. Well, except when his theory said that Newton’s was obsolete. Classical mechanics needed an update.

For two centuries, gravity was presented as a force between two objects, like apple and Earth or Earth and sun, traveling through “empty” space. But where did this mysterious force come from? Newtonian mathematics didn’t explain. So Einstein re-imagined gravity.

Certain physicists talk about spacetime, not the two separately, because every object occupies time as well as space. Consider the moon. What we see is always what the actual thing was 1.25 seconds ago, because that’s how long light takes to reach us from there. Since we’re all traveling through time continuously, from past to present, we’re traveling through space nonstop too.

It gets weirder. Astronomical objects bend this multidimensionality like a blanket around themselves. This is why the moon orbits the Earth, and the Earth orbits the sun – like a marble around a bowling ball on a trampoline. Our world is hurtling across the part of spacetime wrapped around the densest mass in the system, and it’s taking us along for the ride. We experience this motion as gravity.

So, according to general relativity, a man doesn’t fall because gravity is pulling him to the ground, but because the Earth is always traveling continuously in curved spacetime. If it were flat, the man might float across the air until he reached the next roof. Instead, he follows this warped trajectory until the ground stops it. The rough illustration here (not drawn to scale at all) attempts to show snapshots of this process.

Wacky, I know … even if we could understand it. When it was first verified three years later, even fellow scientists had to admit the theory was inscrutable! That first verification showed that even light from distant stars bends around the sun as it travels across the universe to reach us.

With this theory, this stupendous thought experiment supported by 10 impenetrable field equations, Einstein predicted several astrophysical phenomena back when no one had the instruments to prove they existed. Now consider Allan Adams’ recent TED talk about a discovery made at the LIGO observatory in September 2015. The observatory’s detectors had picked up the sound of gravitational waves made by a couple of black holes as they crashed into each other in a distant galaxy 1.3 billion years ago. Einstein’s equations had calculated that when dying stars collapse or collide, they ripple spacetime, creating gravitational waves. The waves heard at LIGO rippled through the Earth, finally announcing their existence to us.

The physicists were ecstatic, and I just couldn’t understand why – until I read about general relativity. One hundred years later, and Einstein’s mathematical world view is still correct.

How Albert Einstein Developed the Theory of General Relativity

In 1907, two years after the publication of his theory of special relativity, Albert Einstein came to a key realization: special relativity could not be applied to gravity or to an object undergoing acceleration. Imagine someone inside a closed room sitting on Earth. That person can feel Earth’s gravitational field. Now put that same room out in space, far from the gravitational influence of any object, and give it an acceleration of 9.8 meters per second (the same as Earth’s gravitational acceleration). There would be no way for someone inside the room to distinguish whether what they were feeling was gravity or just uniform acceleration.

Einstein then wondered how light would behave in the accelerating room. If one were to shine a flashlight across the room, the light would appear to bend downward. This would happen because the floor of the room would be coming up to the light beam at an ever-faster speed, so the floor would catch up with the light. Since gravity and acceleration are equivalent, light would bend in a gravitational field.

Finding the correct mathematical expression of these ideas took Einstein several more years. In 1912, Einstein’s friend, mathematician Marcel Grossman, introduced him to the tensor analysis of Bernhard Riemann, Tullio Levi-Civita, and Gregorio Ricci-Curbastro, which allowed him to express the laws of physics in the same way in different coordinate systems. Three more years of wrong turns and hard work followed, but in November 1915 the work was complete.

In his four papers, published in November 1915, Einstein laid the foundation of the theory. In the third in particular he used general relativity to explain the precession of the perihelion of Mercury. The point at which Mercury has its closest approach to the Sun, its perihelion, moves. This movement could not be explained by the gravitational influence of the Sun and other planets. It was such a mystery that in the 19th century a new planet, Vulcan, orbiting close to the Sun, had even been proposed. No such planet was needed. Einstein could calculate the shift in Mercury’s perihelion from first principles.

However, the true test of any theory is if it can predict something that has not yet been observed. General relativity predicted that light would bend in a gravitational field. In 1919, British expeditions to Africa and South America observed a total solar eclipse to see if the position of stars near the Sun had changed. The observed effect was exactly what Einstein had predicted. Einstein instantly became world-famous. (Read The Solar Eclipse That Made Albert Einstein a Science Celebrity for more on that.)

Einstein: Ether and Relativity

How does it come about that alongside of the idea of ponderable matter, which is derived by abstraction from everyday life, the physicists set the idea of the existence of another kind of matter, the ether? The explanation is probably to be sought in those phenomena which have given rise to the theory of action at a distance, and in the properties of light which have led to the undulatory theory. Let us devote a little while to the consideration of these two subjects.

Outside of physics we know nothing of action at a distance. When we try to connect cause and effect in the experiences which natural objects afford us, it seems at first as if there were no other mutual actions than those of immediate contact, e.g. the communication of motion by impact, push and pull, heating or inducing combustion by means of a flame, etc. It is true that even in everyday experience weight, which is in a sense action at a distance, plays a very important part. But since in daily experience the weight of bodies meets us as something constant, something not linked to any cause which is variable in time or place, we do not in everyday life speculate as to the cause of gravity, and therefore do not become conscious of its character as action at a distance. It was Newton's theory of gravitation that first assigned a cause for gravity by interpreting it as action at a distance, proceeding from masses. Newton's theory is probably the greatest stride ever made in the effort towards the causal nexus of natural phenomena. And yet this theory evoked a lively sense of discomfort among Newton's contemporaries, because it seemed to be in conflict with the principle springing from the rest of experience, that there can be reciprocal action only through contact, and not through immediate action at a distance.

It is only with reluctance that man's desire for knowledge endures a dualism of this kind. How was unity to be preserved in his comprehension of the forces of nature? Either by trying to look upon contact forces as being themselves distant forces which admittedly are observable only at a very small distance and this was the road which Newton's followers, who were entirely under the spell of his doctrine, mostly preferred to take or by assuming that the Newtonian action at a distance is only apparently immediate action at a distance, but in truth is conveyed by a medium permeating space, whether by movements or by elastic deformation of this medium. Thus the endeavour toward a unified view of the nature of forces leads to the hypothesis of an ether. This hypothesis, to be sure, did not at first bring with it any advance in the theory of gravitation or in physics generally, so that it became customary to treat Newton's law of force as an axiom not further reducible. But the ether hypothesis was bound always to play some part in physical science, even if at first only a latent part.

When in the first half of the nineteenth century the far-reaching similarity was revealed which subsists between the properties of light and those of elastic waves in ponderable bodies, the ether hypothesis found fresh support. It appeared beyond question that light must be interpreted as a vibratory process in an elastic, inert medium filling up universal space. It also seemed to be a necessary consequence of the fact that light is capable of polarisation that this medium, the ether, must be of the nature of a solid body, because transverse waves are not possible in a fluid, but only in a solid. Thus the physicists were bound to arrive at the theory of the "quasi-rigid" luminiferous ether, the parts of which can carry out no movements relatively to one another except the small movements of deformation which correspond to light-waves.

This theory - also called the theory of the stationary luminiferous ether - moreover found a strong support in an experiment which is also of fundamental importance in the special theory of relativity, the experiment of Fizeau, from which one was obliged to infer that the luminiferous ether does not take part in the movements of bodies. The phenomenon of aberration also favoured the theory of the quasi-rigid ether.

The development of the theory of electricity along the path opened up by Maxwell and Lorentz gave the development of our ideas concerning the ether quite a peculiar and unexpected turn. For Maxwell himself the ether indeed still had properties which were purely mechanical, although of a much more complicated kind than the mechanical properties of tangible solid bodies. But neither Maxwell nor his followers succeeded in elaborating a mechanical model for the ether which might furnish a satisfactory mechanical interpretation of Maxwell's laws of the electro-magnetic field. The laws were clear and simple, the mechanical interpretations clumsy and contradictory. Almost imperceptibly the theoretical physicists adapted themselves to a situation which, from the standpoint of their mechanical programme, was very depressing. They were particularly influenced by the electro-dynamical investigations of Heinrich Hertz. For whereas they previously had required of a conclusive theory that it should content itself with the fundamental concepts which belong exclusively to mechanics ( e.g. densities, velocities, deformations, stresses ) they gradually accustomed themselves to admitting electric and magnetic force as fundamental concepts side by side with those of mechanics, without requiring a mechanical interpretation for them. Thus the purely mechanical view of nature was gradually abandoned. But this change led to a fundamental dualism which in the long-run was insupportable. A way of escape was now sought in the reverse direction, by reducing the principles of mechanics to those of electricity, and this especially as confidence in the strict validity of the equations of Newton's mechanics was shaken by the experiments with b-rays and rapid cathode rays.

This dualism still confronts us in unextenuated form in the theory of Hertz, where matter appears not only as the bearer of velocities, kinetic energy, and mechanical pressures, but also as the bearer of electromagnetic fields. Since such fields also occur in vacuo - i.e. in free ether-the ether also appears as bearer of electromagnetic fields. The ether appears indistinguishable in its functions from ordinary matter. Within matter it takes part in the motion of matter and in empty space it has everywhere a velocity so that the ether has a definitely assigned velocity throughout the whole of space. There is no fundamental difference between Hertz's ether and ponderable matter ( which in part subsists in the ether ) .

The Hertz theory suffered not only from the defect of ascribing to matter and ether, on the one hand mechanical states, and on the other hand electrical states, which do not stand in any conceivable relation to each other it was also at variance with the result of Fizeau's important experiment on the velocity of the propagation of light in moving fluids, and with other established experimental results.

Such was the state of things when H A Lorentz entered upon the scene. He brought theory into harmony with experience by means of a wonderful simplification of theoretical principles. He achieved this, the most important advance in the theory of electricity since Maxwell, by taking from ether its mechanical, and from matter its electromagnetic qualities. As in empty space, so too in the interior of material bodies, the ether, and not matter viewed atomistically, was exclusively the seat of electromagnetic fields. According to Lorentz the elementary particles of matter alone are capable of carrying out movements their electromagnetic activity is entirely confined to the carrying of electric charges. Thus Lorentz succeeded in reducing all electromagnetic happenings to Maxwell's equations for free space.

As to the mechanical nature of the Lorentzian ether, it may be said of it, in a somewhat playful spirit, that immobility is the only mechanical property of which it has not been deprived by H A Lorentz. It may be added that the whole change in the conception of the ether which the special theory of relativity brought about, consisted in taking away from the ether its last mechanical quality, namely, its immobility. How this is to be understood will forthwith be expounded.

The next position which it was possible to take up in face of this state of things appeared to be the following. The ether does not exist at all. The electromagnetic fields are not states of a medium, and are not bound down to any bearer, but they are independent realities which are not reducible to anything else, exactly like the atoms of ponderable matter. This conception suggests itself the more readily as, according to Lorentz's theory, electromagnetic radiation, like ponderable matter, brings impulse and energy with it, and as, according to the special theory of relativity, both matter and radiation are but special forms of distributed energy, ponderable mass losing its isolation and appearing as a special form of energy.

More careful reflection teaches us however, that the special theory of relativity does not compel us to deny ether. We may assume the existence of an ether only we must give up ascribing a definite state of motion to it, i.e. we must by abstraction take from it the last mechanical characteristic which Lorentz had still left it. We shall see later that this point of view, the conceivability of which I shall at once endeavour to make more intelligible by a somewhat halting comparison, is justified by the results of the general theory of relativity.

Think of waves on the surface of water. Here we can describe two entirely different things. Either we may observe how the undulatory surface forming the boundary between water and air alters in the course of time or else-with the help of small floats, for instance - we can observe how the position of the separate particles of water alters in the course of time. If the existence of such floats for tracking the motion of the particles of a fluid were a fundamental impossibility in physics - if, in fact nothing else whatever were observable than the shape of the space occupied by the water as it varies in time, we should have no ground for the assumption that water consists of movable particles. But all the same we could characterise it as a medium.

We have something like this in the electromagnetic field. For we may picture the field to ourselves as consisting of lines of force. If we wish to interpret these lines of force to ourselves as something material in the ordinary sense, we are tempted to interpret the dynamic processes as motions of these lines of force, such that each separate line of force is tracked through the course of time. It is well known, however, that this way of regarding the electromagnetic field leads to contradictions.

Generalising we must say this:- There may be supposed to be extended physical objects to which the idea of motion cannot be applied. They may not be thought of as consisting of particles which allow themselves to be separately tracked through time. In Minkowski's idiom this is expressed as follows:- Not every extended conformation in the four-dimensional world can be regarded as composed of world-threads. The special theory of relativity forbids us to assume the ether to consist of particles observable through time, but the hypothesis of ether in itself is not in conflict with the special theory of relativity. Only we must be on our guard against ascribing a state of motion to the ether.

Certainly, from the standpoint of the special theory of relativity, the ether hypothesis appears at first to be an empty hypothesis. In the equations of the electromagnetic field there occur, in addition to the densities of the electric charge, only the intensities of the field. The career of electromagnetic processes in vacuo appears to be completely determined by these equations, uninfluenced by other physical quantities. The electromagnetic fields appear as ultimate, irreducible realities, and at first it seems superfluous to postulate a homogeneous, isotropic ether-medium, and to envisage electromagnetic fields as states of this medium.

But on the other hand there is a weighty argument to be adduced in favour of the ether hypothesis. To deny the ether is ultimately to assume that empty space has no physical qualities whatever. The fundamental facts of mechanics do not harmonize with this view. For the mechanical behaviour of a corporeal system hovering freely in empty space depends not only on relative positions ( distances ) and relative velocities, but also on its state of rotation, which physically may be taken as a characteristic not appertaining to the system in itself. In order to be able to look upon the rotation of the system, at least formally, as something real, Newton objectivises space. Since he classes his absolute space together with real things, for him rotation relative to an absolute space is also something real. Newton might no less well have called his absolute space "Ether" what is essential is merely that besides observable objects, another thing, which is not perceptible, must be looked upon as real, to enable acceleration or rotation to be looked upon as something real.

It is true that Mach tried to avoid having to accept as real something which is not observable by endeavouring to substitute in mechanics a mean acceleration with reference to the totality of the masses in the universe in place of an acceleration with reference to absolute space. But inertial resistance opposed to relative acceleration of distant masses presupposes action at a distance and as the modern physicist does not believe that he may accept this action at a distance, he comes back once more, if he follows Mach, to the ether, which has to serve as medium for the effects of inertia. But this conception of the ether to which we are led by Mach's way of thinking differs essentially from the ether as conceived by Newton, by Fresnel, and by Lorentz. Mach's ether not only conditions the behaviour of inert masses, but is also conditioned in its state by them.

Mach's idea finds its full development in the ether of the general theory of relativity. According to this theory the metrical qualities of the continuum of space-time differ in the environment of different points of space-time, and are partly conditioned by the matter existing outside of the territory under consideration. This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that "empty space" in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions ( the gravitation potentials g m n g_ g m n ​ ) , has, I think, finally disposed of the view that space is physically empty. But therewith the conception of the ether has again acquired an intelligible content although this content differs widely from that of the ether of the mechanical undulatory theory of light. The ether of the general theory of relativity is a medium which is itself devoid of all mechanical and kinematical qualities, but helps to determine mechanical ( and electromagnetic ) events.

What is fundamentally new in the ether of the general theory of relativity as opposed to the ether of Lorentz consists in this, that the state of the former is at every place determined by connections with the matter and the state of the ether in neighbouring places, which are amenable to law in the form of differential equations whereas the state of the Lorentzian ether in the absence of electromagnetic fields is conditioned by nothing outside itself, and is everywhere the same. The ether of the general theory of relativity is transmuted conceptually into the ether of Lorentz if we substitute constants for the functions of space which describe the former, disregarding the causes which condition its state. Thus we may also say, I think, that the ether of the general theory of relativity is the outcome of the Lorentzian ether, through relativation.

As to the part which the new ether is to play in the physics of the future we are not yet clear. We know that it determines the metrical relations in the space-time continuum, e.g. the configurative possibilities of solid bodies as well as the gravitational fields but we do not know whether it has an essential share in the structure of the electrical elementary particles constituting matter. Nor do we know whether it is only in the proximity of ponderable masses that its structure differs essentially from that of the Lorentzian ether whether the geometry of spaces of cosmic extent is approximately Euclidean. But we can assert by reason of the relativistic equations of gravitation that there must be a departure from Euclidean relations, with spaces of cosmic order of magnitude, if there exists a positive mean density, no matter how small, of the matter in the universe.

In this case the universe must of necessity be spatially unbounded and of finite magnitude, its magnitude being determined by the value of that mean density.

If we consider the gravitational field and the electromagnetic field from the standpoint of the ether hypothesis, we find a remarkable difference between the two. There can be no space nor any part of space without gravitational potentials for these confer upon space its metrical qualities, without which it cannot be imagined at all. The existence of the gravitational field is inseparably bound up with the existence of space. On the other hand a part of space may very well be imagined without an electromagnetic field thus in contrast with the gravitational field, the electromagnetic field seems to be only secondarily linked to the ether, the formal nature of the electromagnetic field being as yet in no way determined by that of gravitational ether. From the present state of theory it looks as if the electromagnetic field, as opposed to the gravitational field, rests upon an entirely new formal motif, as though nature might just as well have endowed the gravitational ether with fields of quite another type, for example, with fields of a scalar potential, instead of fields of the electromagnetic type.

Since according to our present conceptions the elementary particles of matter are also, in their essence, nothing else than condensations of the electromagnetic field, our present view of the universe presents two realities which are completely separated from each other conceptually, although connected causally, namely, gravitational ether and electromagnetic field, or - as they might also be called - space and matter.

Of course it would be a great advance if we could succeed in comprehending the gravitational field and the electromagnetic field together as one unified conformation. Then for the first time the epoch of theoretical physics founded by Faraday and Maxwell would reach a satisfactory conclusion. The contrast between ether and matter would fade away, and, through the general theory of relativity, the whole of physics would become a complete system of thought, like geometry, kinematics, and the theory of gravitation. An exceedingly ingenious attempt in this direction has been made by the mathematician H Weyl but I do not believe that his theory will hold its ground in relation to reality. Further, in contemplating the immediate future of theoretical physics we ought not unconditionally to reject the possibility that the facts comprised in the quantum theory may set bounds to the field theory beyond which it cannot pass.

Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities in this sense, therefore, there exists an ether. According to the general theory of relativity space without ether is unthinkable for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time ( measuring-rods and clocks ) , nor therefore any space-time intervals in the physical sense. But this ether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it.

General relativity

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General relativity, part of the wide-ranging physical theory of relativity formed by the German-born physicist Albert Einstein. It was conceived by Einstein in 1916. General relativity is concerned with gravity, one of the fundamental forces in the universe. Gravity defines macroscopic behaviour, and so general relativity describes large-scale physical phenomena.

General relativity follows from Einstein’s principle of equivalence: on a local scale it is impossible to distinguish between physical effects due to gravity and those due to acceleration. Gravity is treated as a geometric phenomenon that arises from the curvature of space-time. The solution of the field equations that describe general relativity can yield answers to different physical situations, such as planetary dynamics, the birth and death of stars, black holes, and the evolution of the universe. General relativity has been experimentally verified by observations of gravitational lenses, the orbit of the planet Mercury, the dilation of time in Earth’s gravitational field, and gravitational waves from merging black holes. (For a more detailed treatment of general relativity, see relativity: General relativity.)

This article was most recently revised and updated by Erik Gregersen, Senior Editor.

When testing Einstein's theory of general relativity, small modeling errors add up fast

Small modeling errors may accumulate faster than previously expected when physicists combine multiple gravitational wave events (such as colliding black holes) to test Albert Einstein's theory of general relativity, suggest researchers at the University of Birmingham in the United Kingdom. The findings, published June 16 in the journal iScience, suggest that catalogs with as few as 10 to 30 events with a signal-to-background noise ratio of 20 (which is typical for events used in this type of test) could provide misleading deviations from general relativity, erroneously pointing to new physics where none exists. Because this is close to the size of current catalogs used to assess Einstein's theory, the authors conclude that physicists should proceed with caution when performing such experiments.

"Testing general relativity with catalogs of gravitational wave events is a very new area of research," says Christopher J. Moore, a lecturer at the School of Physics and Astronomy & Institute for Gravitational Wave Astronomy at the University of Birmingham in the United Kingdom and the lead author of the study. "This is one of the first studies to look in detail at the importance of theoretical model errors in this new type of test. While it is well known that errors in theoretical models need to be treated carefully when you are trying to test a theory, we were surprised by how quickly small model errors can accumulate when you start combining events together in catalogs."

In 1916, Einstein published his theory of general relativity, which explains how massive celestial objects warp the interconnected fabric of space and time, resulting in gravity. The theory predicts that violent outer space incidents such as black hole collisions disrupt space-time so severely that they produce ripples called gravitational waves, which zoom through space at the speed of light. Instruments such as LIGO and Virgo have now detected gravitational wave signals from dozens of merging black holes, which researchers have been using to put Einstein's theory to the test. So far, it has always passed. To push the theory even further, physicists are now testing it on catalogs of multiple grouped gravitational wave events.

"When I got interested in gravitational wave research, one of the main attractions was the possibility to do new and more stringent tests of general relativity," says Riccardo Buscicchio, a Ph.D. student at the School of Physics and Astronomy & Institute for Gravitational Wave Astronomy and a co-author of the study. "The theory is fantastic and has already passed a hugely impressive array of other tests. But we know from other areas of physics that it can't be completely correct. Trying to find exactly where it fails is one of the most important questions in physics."

However, while larger gravitational wave catalogs could bring scientists closer to the answer in the near future, they also amplify the potential for errors. Since waveform models inevitably involve some approximations, simplifications, and modeling errors, models with a high degree of accuracy for individual events could prove misleading when applied to large catalogs.

To determine how waveform errors grow as catalog size increases, Moore and colleagues used simplified, linearized mock catalogs to perform large numbers of test calculations, which involved drawing signal-to-noise ratios, mismatch, and model error alignment angles for each gravitational wave event. The researchers found that the rate at which modeling errors accumulate depends on whether or not modeling errors tend to average out across many different catalog events, whether deviations have the same value for each event, and the distribution of waveform modeling errors across events.

"The next step will be for us to find ways to target these specific cases using more realistic but also more computationally expensive models," says Moore. "If we are ever to have confidence in the results of such tests, we must first have as a good an understanding as possible of the errors in our models."

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