Wednesday, April 4, 2012

No technology uses curved spacetime

An Amazon review gives my book a low rating because "General Relativity ... sprang full-blown from the mind of Albert Einstein", and "curved, multidimensional space ... underlies much of modern technology, including GPS satellites." He points to this site to show that GPS satellites use relativistic time corrections.

I wish that were true, but it is not. GPS uses some relativity formulas to correct its clocks based on velocity and gravity, but does not require anything about curved spacetime. No other technology does either, as far as I know, except for experiments designed to test general relativity.

Yes, general relativity is a theory that models all gravity with curved spacetime. So if I drop an apple to the ground, then its fall can be explained by curved spacetime. So in that sense, everything using gravity is also using curved spacetime. But you do not need general relativity or curved spacetime to predict when that apple hits the ground, and you do not need it for apples, cars, GPS, or other technologies.

It is a historical fact that the formulas for the relativistic time corrections needed for GPS were discovered without any use of curved spacetime. The velocity clock corrections were published by Lorentz (1904), Poincare (1905), and Einstein (1905). Einstein says that he discovered the gravity correction in 1907 with the happiest thought of his life, and published it in 1908. It is a simple application of special relativity. Neither Einstein nor anyone else had said anything about curved spacetime by 1908.

Yes, you could say that the GPS formulas could be re-derived using curved spacetime. You can also re-derive them using string theory. But it is a mistake to say that curved spacetime or string theory underlies much of modern technology.

Explaining gravity with curved spacetime was not a wholly original idea of Einstein's either. As far as I can determine, it was Marcel Grossmann's idea. Grossmann proposed it in 1913, but Einstein refused to believe that it could really be a geometric spacetime curvature until Levi-Civita and Hilbert convinced him a couple of years later.


  1. I note your critic's last comment:-

    "And, surely, you must have better ways to use your time than to to cross swords with an old and retired physicist, who has free time on his hands and a bad attitude against revisionist mathematicians."

    I think you proved your point but he does not seem willing to concede with good grace.

    1. >> Grossmann proposed it in 1913

      Having read your Einstein book, even paying scant attention thereto while doing so, I was thinking you were going to make that above-cited thought something like "Minkowski proposed it in 1908" or "Minkowski proposed it in 1907". But you instead refer to Grossman. (?)

  2. Minkowski proposed spacetime, and non-Euclidean geometry, but he died in 1909 and no one talked about curved spacetime until several years later.