Was it Einstein? Or was there someone before him to hypothesise this?


2 Answers 2


The first metric theory of gravitation, in which the effects of gravitation are treated entirely in terms of the geometry of curved spacetime, was published by Finnish physicist Gunnar Nordström in 1913. Einstein published his own theory of general relativity in 1915.

The measurement of the deflection of light passing close to the Sun during the solar eclipse of 1919 (the Eddington experiment) produced results that agreed with Einstein's theory, whereas Nordström's theory predicted no deflection. Nordström subsequently nominated Einstein for the Nobel Prize in Physics.

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    $\begingroup$ Why would there be no deflection in a geometric theory of gravitation? $\endgroup$
    – lalala
    Commented Oct 15, 2021 at 19:04
  • $\begingroup$ @lalala It did not include electromagnetism. From Wikipedia. In any metric theory of gravitation, all gravitational effects arise from the curvature of the metric. In a spacetime model in Nordström's theory...this depends only on the trace of the stress–energy tensor. But the field energy of an electromagnetic field contributes a term to the stress–energy tensor which is traceless, so in Nordström's theory, electromagnetic field energy does not gravitate! $\endgroup$
    – Schwern
    Commented Oct 17, 2021 at 19:44

The first person that I know of was the mathematician and physicist William Clifford who, on reading the Habilitationsschrift of Riemann and, almost forty years before Einstein developed general relativity, hypothesised that not only all motion was due to the curvature of space but so was matter.

This is amazingly prescient considering that Einstein only showed that gravity could be interpreted as the curvature of spacetime. However, modern unified theory also shows that the electromagnetic, the weak and the strong force can also be interpreted via curvature - not now of spacetime - but of a bundle over spacetime. Moreover, the hypothetical supersymmetry which assumes a symmetry between bosons and fermions, show that matter ought to be, if supersymmetry is correct, also an aspect of curvature.

It's interesting to speculate how much of Clifford's work was known by Einstein. It would be extraordinary if had not at least known about it, given his own preoccupations. Also, it is interesting to speculate how much of his unified field work also went down the same path as Clifgord - that is to imagine all forces and all matter was an aspect of matter.

Riemann's Habilitationsschrift was published in 1854 essay and was titled, On the Hypotheses which lie at the Bases of Geometry. Clifford translated the essay in 1867 and three years later, he reported to the Cambridge Philosophical Society the curved space concept of Riemann's including his hypothesis that both space and matter were the effects of curvature. A further three years later, his translation was published in Nature. In 1876, his report to the society was published as The Space Theory of Matter in their Proceedings.

Riemann himself suggested something similar, but his was a more general comment in the microstructure of space, closer in spirit to Wheelers spacetime foam.

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    $\begingroup$ Clifford was 9 at the time of Riemann's lecture and never visited Göttingen in his life. Nor did he develop general relativity, which uses curved spacetime, not curved space. $\endgroup$
    – Conifold
    Commented Oct 15, 2021 at 9:33
  • $\begingroup$ @conifold: No, I wasn't supposing he had visited Gottingen or had direct contact with Riemann. I read a lecture of Riemann. Perhaps a lecture of Riemann was read out? Hermann Weyl himself noted that Riemann and Clifford anticipated ideas of General Relativity. Whilst GR only explained gravity, Clifford suggested that ALL forces be explained in this way - and so electromagnetism too. His intuition was correct here too. Whilst the weak and strong force were unknown at his time, again these forces are also expressible via curvature. $\endgroup$ Commented Oct 15, 2021 at 11:09
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    $\begingroup$ @MoziburUllah: Clifford watched Riemann's lecture on youtube, $\endgroup$
    – markvs
    Commented Oct 16, 2021 at 1:33
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    $\begingroup$ @Markvs: Riemann lived between 1826-1866 in Germany. Clifford lived between 1845-1879. There was ample time for Riemann's lectures to filter through to England. Whilst his mother might have had an affinity to natural philosophy, given that she was related to Sir Thomas Bodley, a lecturer in natural philosophy at Magdalen College and the founder of the Bodliean Library, it's unlikely his mother read anything by Riemann hiven the abstruseness of the mathematics. Differential geometry is still seen as a difficult subject now, even after 150 years of shaping it to a well sharpened tool. $\endgroup$ Commented Oct 16, 2021 at 3:08
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    $\begingroup$ @markvs: No, he did not have it read to him by his mother. He probably found Riemann's Habikitationsschrift in the library, either because he was told about it or searching for Riemann's work. It could be he stumbled upon it by browsing. You never know. $\endgroup$ Commented Oct 16, 2021 at 3:38

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