Before Einstein came up with General Relativity, was there any serious reason to doubt Newton's theory (and its various developments)?

I only know about the discrepancy in Mercury's orbit, which may have been caused by an error (e.g. similar to the one that caused people to make up Planet X).

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    $\begingroup$ It was incompatible with special relativity and couldn't explain the motion of Mercury. $\endgroup$ – MBN Mar 29 '15 at 10:06
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    $\begingroup$ Newton had trouble explaining action at a distance, so if the moon vanished now, for example, in Newton's theory, the tides should be affected immediately on earth, whereas Einstein's theory said gravitational waves would travel at light speed, so there should be a time lag of around 250 milliseconds before our tides reacted. Regards $\endgroup$ – user74893 Mar 29 '15 at 11:06
  • $\begingroup$ @irish mercury and action at a distance: true, of course, but probably not that relevant in the development of GR. $\endgroup$ – innisfree Mar 29 '15 at 11:36
  • $\begingroup$ @innisfree good point and fully accepted thanks regards $\endgroup$ – user74893 Mar 29 '15 at 11:39
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    $\begingroup$ @Just Greg: Is the question about before or after special relativity? $\endgroup$ – Qmechanic Mar 29 '15 at 12:51

You raise an interesting point about the role of experiment and falsifiability in science. Despite a long-standing anomaly in Mercury's perihelion, Newton's theory of gravity itself wasn't heavily questioned, let alone rejected or falsified. Rather, auxiliary assumptions were concocted that saved Newton's theory, such as an erroneous mass of Venus, a planet inside Mercury's orbit and that Mercury had a moon.

Imre Lakatos developed this idea in his criticisms of falsifiability, see e.g.

Auxiliary hypotheses are considered expendable by the adherents of the research programme—they may be altered or abandoned as empirical discoveries require in order to 'protect' the 'hard core'. Lakatos was following Pierre Duhem's idea that one can always protect a cherished theory (or part of one) from hostile evidence by redirecting the criticism toward other theories or parts thereof (wiki)

Kuhn explicitly discussed the case of Mercury's perihelion in his seminal The Structure of Scientific Revolutions (1962):

No one seriously questioned Newtonian theory because of the long-recognized discrepancies between predictions from that theory and both the speed of sound and the motion of Mercury ... [The discrepancy] vanished with the general theory of relativity after a crisis that it had had no role in creating.

Einstein, for example, seems not to have anticipated that general relativity would account with precision for the well-known anomaly in the motion of Mercury’s perihelion, and he experienced a corresponding triumph when it did so

The development of general relativity followed from theoretical inconsistencies between Newton's theory and Einstein's relativity, rather than evidence that contradicted Newtonian theory.

That said, Newton's theory didn't have to wait for Einstein for theoretical criticisms. Even in Newton's day, his theory was criticized on conceptual grounds as being "occult," for it permitted action at a distance, especially by Leibniz. However, Kuhn suggests that these criticisms died away and only returned in light of general relativity:

When Newton’s theory had been accepted, a question [the origin of gravitational attraction] was therefore banished from science. That question, however, was one that general relativity may proudly claim to have solved.

  • $\begingroup$ See Newton's letter to Richard Bentley in 1692 where he said this: ""That gravity should be innate inherent & {essential} to matter so that one body may act upon another at a distance through a vacuum without the mediation of any thing else by & through which their action or force {may} be conveyed from one to another is to me so great an absurdity that I beleive no man who has in philosophical matters any competent faculty of thinking can ever fall into it." $\endgroup$ – John Duffield Mar 29 '15 at 12:50
  • $\begingroup$ Also see Opticks query 20 where Newton said this: "Doth not this aethereal medium in passing out of water, glass, crystal, and other compact and dense bodies in empty spaces, grow denser and denser by degrees, and by that means refract the rays of light not in a point, but by bending them gradually in curve lines?" Newton's gravity wasn't some magical mysterious action at a distance. $\endgroup$ – John Duffield Mar 29 '15 at 12:54
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    $\begingroup$ Thanks @John, but I'm not exactly sure what you're getting at? $\endgroup$ – innisfree Mar 29 '15 at 13:32
  • $\begingroup$ Innisfree: Newton's gravity didn't involve action-at-a-distance, he was totally against that, and instead he talked of a local phenomena. He didn't push it because he preferred to feign no hypothesis. His outline description is however rather similar to Einstein's explanation. Amazingly, even Einstein talked about space as an "aether". $\endgroup$ – John Duffield Mar 29 '15 at 16:35
  • $\begingroup$ the correspondence with bentley is discussed in the SEP article in my answer: "Newton apparently regarded action at a distance as perfectly possible when writing the Principia. Indeed, it is difficult to reconcile the Principia with the Bentley correspondence ... regardless of Newton's personal attitude toward distant action among material bodies, his mechanist interlocutors and readers continued to object to the physical theory outlined in Book III of the Principia on the grounds that ... it left open the conceptual possibility of a kind of action that cannot in fact exist anywhere in nature. $\endgroup$ – innisfree Mar 29 '15 at 17:34

Mach et al. criticized Newton's absolute space and formulated alternative explanations of Newton's bucket experiment.

More recently, Schrödinger applied Weber's force law to gravitation/cosmology:



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