It was 1905, and Albert Einstein had just turned theoretical physics on its head by publishing a paper on what later became known as special relativity. This showed that space and time could not be considered in absolute terms: time could speed up or slow down; standard lengths could contract; and masses could increase.

And, most famously, energy was equivalent to mass, proportional to each other based on the famous equation *E = mc²*.

Although there is no doubting Einstein's genius in formulating special relativity, it is generally accepted that had Einstein not published the theory in 1905, some other physicist would have done so shortly thereafter.

It was not until 1915 that Einstein's unparalleled genius was demonstrated when he published his general theory of relativity. This theory made the claim that space–time curvature is proportional to, and is caused by, the "energy-momentum density", that is, the energy and the momentum associated with all and any kind of matter in a unit volume of space.

This claim was subsequently confirmed when it was shown to fit with observations of Mercury's unusual orbit and the bending of starlight around the sun.

And over the course of the last century, general relativity has been tested to remarkable accuracy and has withstood critique each time. General relativity was such a giant leap forward that it is arguable that had Einstein not formulated the theory, it may have remained undiscovered for a very long time.

**Path to general relativity**

In 1907, Einstein had the "happiest thought of my life" when he was sitting in a chair at the patent office in Bern:

*If a person falls freely he will not feel his own weight.*

This led him to the postulate the "equivalence principle", which states that one cannot tell the difference between an accelerating reference frame and a gravitational field. For example, standing on the Earth feels the same as standing in a space craft accelerating at 9.81 meters per second per second, which is the acceleration due to gravity on the Earth's surface.

This was the crucial first step in Einstein's formulation of a new theory of gravity.

Next, Einstein believed that, "all physics is geometry". By that he meant we can think of space-time and all the universe in terms of geometry. The most startling conclusion from special relativity – the dynamic nature of time and space – must have led Einstein to start considering "geometric" space-time to be in need of modification.

Einstein then embarked on a series of careful thought experiments, comparing observations made by observers in inertial and rotating frames.

Einstein deduced that for observers in a rotating frame, space time could not be Euclidean, i.e. it could not be like the kind of flat geometry we all learn about in school. Rather, we need to introduce "curved space" to account for the anomalies predicted by relativity. Curvature thus became the second key assumption that underpinned his general theory.

To describe curved space-time, Einstein called upon the earlier work of Bernhard Riemann, a 19th century mathematician. And with the help of his friend Marcel Grossman, also a mathematician, Einstein spent several exhausting years learning the mathematics of curved spaces, or what mathematicians call "differential geometry". As Einstein commented, "compared with understanding gravity, special relativity was mere child's play".

Now Einstein had the mathematical tools to finalise his theory. His equivalence principle stated that an accelerating reference frame is equivalent to a gravitational field. From his geometrical studies, he believed the gravitational field was simply a manifestation of curved space-time. Hence, Einstein could show that accelerating frames were represented by non-Euclidean space.

**It follows**

The third key step for Einstein involved resolving complications that had arisen when special relativity was applied to Newtonian gravitational physics. In special relativity, the constancy of the speed of light in all reference frames, and the conclusion that the speed of light set the universal speed limit, was in direct contradiction to Newton's theory of gravity, which postulated the instantaneous effect of gravity.

Put simply: Newtonian gravity predicted that if the sun was removed from the centre of the solar system, the gravitational effect on the Earth would be instantaneous. However, special relativity says that even the gravitational effect of the sun disappearing ought to travel at the speed of light.

Einstein also knew that gravitational force between two bodies was directly proportional to their masses, from Newton's equation F = GMm/r². So mass clearly determined the strength of the gravitational field. Special relativity tells us that mass is equivalent to energy, so the energy–momentum density must also determine the gravitational force.

Thus the three key assumptions that Einstein used to formulate his theory were:

- Rotating frames (non-inertial) imply non-Euclidean (or curved) space-time
- The equivalence principle asserts that accelerating frames (i.e. non inertial frames) are equivalent to gravitational fields
- From special relativity, mass is equal to energy, and from Newtonian physics, mass is proportional to strength of gravity.

Hence, Einstein was able to conclude that energy-momentum density causes, and is proportional to, space-time curvature.

It is not clear when Einstein had the "light bulb moment", the moment when he was able to put the puzzle together and link mass/energy with the curvature of space.

From 1913 to 1915, Einstein published several papers as he laboured to complete the general theory. Some of these papers contained errors and took Einstein down theoretical pathways that ultimately were not productive.

But the final result, that the energy–momentum density of matter curves space-time, like a bowling ball curves a flat sheet of rubber, and that the motion of a mass in a gravitational field is based on the curvature of space time, just as a bowling ball moves freely on a curved rubber sheet, is surely one of the greatest insights of human intellect.

**Head start**

How long would it have taken us to understand gravity without Einstein's sheer genius? It is possible we would have had to wait many decades.

However, in 1979 the cat would have been out of the bag. In that year, astronomers discovered the "twin quasar", QSO 0957+561, the first gravitationally-lensed quasar.

This astonishing discovery could only have made sense if space-time was curved. It would surely have attracted a Nobel Prize if it hadn't been for Einstein's genius. Maybe it still should.

**Explore further:**
From Newton to Einstein—the origins of general relativity

## indio007

## viko_mx

## Noumenon

This is a questionable claim.

In fact David Hilbert submitted for publication the correct field equations for general relativity five days before Einstein (although they may have been amended before actual publication).

Hilbert eventually let Einstein take full credit though, perhaps because he (Hilbert) would not have worked on the problem had it not been for Einstein's previous talks and correspondence. Then again perhaps it would have taken Einstein longer without correspondence with the greatest mathematician of the twentieth century.

However, Einstein correctly pointed out to Hilbert, that the difficulty was not in resolving the final covariant form of the equations, as this could be done by contracting the Riemann tensor via the Bianchi identities (Einstein having already settled of differential geometry years before),.... but was in recognizing them as a natural generalization of Newton's.

## estudios

If Hilbert had choosen litigation we would had another similar bitter dispute ala Newton vs. Leibnnitz over the calculus with supporters on each side, surely something amusing, and in the end we would learn that both great men with some cross correspondence did the same discovery. Of course, as in the case of Hook vs. Newton with the inverse square law, the math advantage could let Hilbert claim the upper hand.

And don't forget about Lorentz who formulated a form of Special Relativity before Einstein.

## ichisan

## ichisan

Except that this is not true. Time cannot change by definition since that would introduce a self-reference. Clocks speed up or slow down but time never changes.

## Noumenon

Lorentz was stuck in his box and didn't see that his equations could "transcended its connection with Maxwell's equations [to be] concerned with the nature of space and time in general",..... from mere dynamics of electromagnetism to kinematics of space-time.

@ ichisan,... Special Relativity concerns itself with Defined time, as a physical system unto itself, as Einstein had to take an operationalist approach in forming a mathematical theory. Also, an observer traveling along with the clock would never see the clock rate slow down. So, it is a valid physical Definition of time as it will correspond to the observers intuition of time that rides with it.

## Noumenon

## ichisan

Man, give it a rest.

## Noumenon

You stated "Time cannot change by definition since that would introduce a self-reference. Clocks speed up or slow down but time never changes",...... but want me to "give it a rest"?!

## flag

## my2cts

You have to explain what is the "structure of the vacuum of space.". Let me guess: it is the Holy Matrix with the Creator in the Holy Driving Driver Seat.

## Hyperfuzzy

## Hyperfuzzy

## Schrodinger_Heisenberg

Kant would surely disapprove of your name - an apparent champion of Kantian ontology shouldn't be so incessantly enamored with diminishing genius. You remind me of those aroused to point out that it was Hooke who in fact discovered the inverse square law, not Newton; and that without Descartes, Newton never formulates his "fluxions"; and that Laplace standardized the principia (and corrected some of Newton's math) in his masterwork "Celestial Mechanics"; or that the greatest polymath of his age, Leibniz, an autodidact whose formulation of calculus was ultimately more useful given what the Bernoulli brothers - and subsequently Euler - were able to do with his discrete notation, published a far more clear and comprehensible formulation of D/I calculus.

## Schrodinger_Heisenberg

A few contentions.

1. It was Einstein who introduced Hilbert to the mathematical and conceptual nuances of General Relativity prior and subsequent to his failed Entwurf theory. Hilbert had never done ANY work on General Relativity prior to Einsteins lectures on GR at Gottingen (at HIlbert's request, no less).

2. Einstein had actually written down the correct field equations for GR two years earlier in a draft he had dismissed, but then returned to when HIlbert had tried to usurp his theoretical birthchild in October 15'.

3. As of the year 2000 we now know that Hilbert did NOT in fact write down the correct field equations before Einstein as his field equations in his published draft were not generally covariant: nytimes.com/1997/11/18/science/findings-back-einstein-in-a-plagiarism-dispute.html

## Schrodinger_Heisenberg

I applaud your diligence and understanding of the theoretical difficulties at the heart of this silly quibble. However, it behooves you to read more about the history of Einstein's thought pattern concerning both Special and General Relativity. If you read the translated papers between Hilbert and Einstein, you'll find that Hilbert gained much more from those correspondences than Einstein did. In FACT, Einstein learned far more about non-symmetrical variances, the so called 'scale' problem, and much else concerning tensor calculus from Tullio Levi-Civita himself. Civita, as you surely know, wrote the definitive work on the subject in 1900 (a work whose brilliance Hilbert commended). Einstein corresponded with Civita from 1907 onward and probably learned more about differential geometry from Civita than from Grossman & Hilbert combined

## Schrodinger_Heisenberg

This is patently wrong. Hilbert was undoubtedly a mathematical genius, a man whose natural ability would certainly give Newton a run for his money had he been born 400 years earlier. However, Hilbert's was not a great physicist. Big difference. Without Einstein Hilbert never even makes an attempt at GR; this had been rehashed over and over again but without Einstein's lectures at Gottingen Hilbert never understands the axiomatic parameters from which a constructive theory, a la T.S. Kuhn, can be built.

Lorentz did NOT invent SR. If you believe that, you haven't read Lorentz work. Hell, even Lorentz invariance owes homage to both Fitzgerald and Maxwell (the same way Newton's laws of motion owe homage to Galileo - science is a team sport, lest we forget).

## Schrodinger_Heisenberg

I suspect you do not know more about Lorentz's own work than Lorentz himself:

"And at a conference on the Michelson–Morley experiment in 1927 at which Lorentz and Michelson were present, Michelson suggested that Lorentz was the initiator of the theory of relativity. Lorentz then replied:[15]

I considered my time transformation only as a heuristic working hypothesis. So the theory of relativity is really solely Einstein's work. And there can be no doubt that he would have conceived it even if the work of all his predecessors in the theory of this field had not been done at all. His work is in this respect independent of the previous theories." -Hendrik Lorentz

He would later remark, "the theory is all his"

## Schrodinger_Heisenberg

"Roger Cerf (2006) gave priority to Einstein for developing special relativity, and criticized the assertions of Leveugle and others concerning the priority of Poincaré. While Cerf agreed that Poincaré made important contributions to relativity, he argued (following Pais) that Poincaré "stopped short before the crucial step" because he handled length contraction as a "third hypothesis", therefore Poincaré lacked a complete understanding of the basic principles of relativity. "Einstein's crucial step was that he abandoned the mechanistic ether in favor of a new kinematics." He also denies the idea, that Poincaré invented E=mc² in its modern relativistic sense, because he did not realize the implications of this relationship..."

## Schrodinger_Heisenberg

## Schrodinger_Heisenberg

Poincare, whom you seem to love to appropriate all of Einstein's work to, actually 4-dimensionalized space-time years before Minkowski did. I don't see anybody accusing MInkowski of plagiarism, or of some trumped up "priority dispute." Without the work of Wein, Planck never becomes world famous, and so on and so forth.

Apropos Einstein, the greatest intellect of the 20th century should receive universal praise - much like one of his idols, Newton. Photoelectric effect, SR, Brownian Motion, Emc2, GR, On the Specific Heat of Solids, Bose-Einstein Condensates; on Spontaneous & Stimulated Emission, on Quantization of Chaos;W-P Duality, Probability Waves, etc.GENIUS