What, if any, was Einstein's biggest mistake, the one most affecting our physics today? There is a perhaps apocryphal story, recounted by George Gamow, that he counted his cosmological constant as his biggest blunder. We now know his hypothesized cosmological constant to be correct. His lifelong rejection of quantum mechanics, an interesting side-story in the evolution of 20th-century physics, is a candidate. None of these introduced difficulties in how our physics is done today. It can be argued that his biggest actual mistake, one that affects many subfields of physics and chemistry and bewilders students today, occurred in his naming of his A and B coefficients.Yes, his lifelong rejection of quantum mechanics is a candidate for his biggest mistake. So is his pursuit of unified field theory.
I think his biggest mistake was his failure to accept relativity as a geometric theory. Students today learn relativity as a geometric theory, and they are taught that Einstein discovered it all, but Einstein refused to accept the geometric view in both special and general relativity. I explain this point on this blog, such as here.
Lee Smolin wrote:
Einstein’s search for a unified field theory failed, and the roots of this failure are his embrace of mathematical beauty as a guiding principle. Over the thirty-five years between 1920 and his death in 1955 Einstein attempted many versions of a unified field theory. ...Einstein had a similar objection to extending from three-dimensional space to four-dimensional spacetime, with time having a different geometry.
Einstein already understood by 1922 that the hypothesis that there are extra, hidden dimensions could not give a unification of the forces. ...
As Einstein wrote to his friend Paul Ehrenfest, “It is anomalous to replace the four dimensional continuum by a five dimensional one and then to subsequently tie up artificially one of those five dimensions in order to account for the fact that it does not manifest itself.”.
 Quoted in Abraham Pais, Subtle is the lord (New York: Oxford Univ. Press, 1982) p.334
The problem here is that Einstein did not truly recognize the significance of geometry. He had this blind spot all of his life.
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