Einstein's Formulation of Tensor Equation: Was He Lucky?

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SUMMARY

Einstein's formulation of the tensor equation for gravity was not merely a product of luck but a result of critical insights derived from existing data. He recognized the inconsistencies between Newtonian gravity and special relativity, particularly regarding Maxwell's equations and the absence of the aether. Additionally, he utilized the perihelion precession of Mercury as a key empirical observation that his tensor theory could explain, unlike Nordstrom's scalar theory. This combination of theoretical necessity and empirical validation solidified the efficacy of Einstein's approach.

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  • Understanding of Newtonian gravity and its limitations
  • Familiarity with special relativity and Maxwell's equations
  • Knowledge of the perihelion precession of Mercury
  • Basic concepts of tensor calculus and its application in physics
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barong
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I understand that all physical laws essentially codify mathematically observed behavior. Newton codified Kepler and Brahe data, for example. Quantum Mechanics codifies observed particle behavior at relatively low speeds, etc. But Einstein had no empirical data to work from… So, I do not understand how it was possible for him to “invent” something that ended up working empirically… I know he was a genius, but was he also “simply” lucky?
 
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Einstein was a bit lucky. He had two pieces of data. (1) Newtonian gravity was inconsistent with special relativity (Maxwell's equations and the absence of the aether), so a new theory of gravity was needed that was consistent with special relativity and that reduced to Newtonian gravity in the appropriate limit. (2) The perihelion precession of mercury appeared inconsistent with Newtonian gravity, so if the new theory of gravity could explain that, that would be a point in its favour.

At that time, (at least) two theories of gravity fulfilling (1) were known: Nordstrom's scalar theory, and Einstein's tensor theory. However, Nordstrom's theory was not consistent with the observed perihelion precession, but Einstein's was.
 

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