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Language in which einstein intuitively discovered GR

  1. Feb 21, 2012 #1


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    Hi all,

    Einstein definitely had to learn tensors from someone else <via correspondence>.
    But he did not need tensors to intuitively get idea of curvature.

    So, Can some one share in that simple language, How he got the intuition that space time should be curved in accelerated/ gravitional frame.

    Thank You.
  2. jcsd
  3. Feb 22, 2012 #2


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    In special relativity the worldline of a body travelling uniformly ( force-free) is a straight line. If two bodies are accelerating towards one another in force-free motion, the worldlines will curve towards each other. But because they are in free-fall they are travelling on a path which is straight in a different way, so the curvature of the 'straight' (geodesic) worldlines is transferred to the spacetime. That seems intuitive to me.

    If the rate of approach is between worldlines is calculated it turns out to depend solely on the Riemann curvature tensor. This quantity is called the geodesic deviation. So the identification of gravity with curvature follows.


    Last edited: Feb 22, 2012
  4. Feb 24, 2012 #3
    Einstein claims (perhaps with a touch of poetic licence) that he saw a worker falling from a roof (perhaps together with his work tools) and pondered what the free falling tools would look like from the point of view of the free falling worker. He concluded they would look stationary and that in free falling reference frame things (at least locally) look exactly the same as in flat space. From there he considered what things would look like in an artificially accelerated laboratory in flat space and what they would like in a laboratory that was stationary in a gravitational field and concluded that they would be equivalent. This gave him a bare bones intuitive way to start extending Special Relativity to the more general case that included gravity. He also described this idea (the equivalence principle) as the happiest thought of his life.

    I have not bothered to look up exact references and my recall my be coloured by my own poetic licence, but I think that is very rough outline of his initial intuitive thought processes in simple layman's terms.
  5. Feb 24, 2012 #4


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    The following analogy may be useful.

    Draw a four-sided figure, where all the angles are 90 degrees, on a plane, with all four sides equal.

    Try to do the same thing on a curved surface - and find that in general, all four sides don't have the same length.

    For specifics, say that the sphere is the Earth, and one side of the figure is on the equator and is 1 nautical mile, where one nautical mile represents a minute of arc at the equator.

    Then you draw two lines at right angles, going north, that are also 1 nautical mile long, for t he next two sides. This leaves one remaining side, which will not be a great circle, unlike the others. And it will have a length that's less than one nautical mile, because one minute of arc is the longest at the equator, and shrinks to a distance of zero at the poles.

    Now imagine that you are drawing a space-time digram on the surface of the sphere, and not just a space diagram. Let the N-S lines represent distances, and the E-W llines represent duration, or "proper time". So our quadrilateral has two equal distances, and two unequal proper times.

    Then the curved space-time diagram shows that clocks at a higher lattitude will appear to run at a different rate than the clocks at a lower lattitude, due to the curvature.

    This is, roughly speackig, how curved space-time geometry generates gravitational time dilation.
  6. Feb 25, 2012 #5


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    I believe it was something like this. Deformed observer in flat spacetime is eqivalent to "flat" observer in deformed spacetime. He knew how to describe deformed observer in flat spacetime and how to describe "flat" observer. So he just had to find how to describe deformed spacetime.
    And probably in addition it was idea (or just a possibility worth exploring) that extrapolating "flat" observer in deformed spacetime to global case will somehow turn out better than deformed observer in flat spacetime. But I am not sure about this.
  7. Feb 25, 2012 #6
    What he wanted to establish was that no matter what was happening from any other perspective, all laws of physics would appear the same to the physicist experimenter. That was a very appealing notion and goal to obtain because in that way, the same equations could be used regardless of the situation of the experimenter.

    In mere linear motion, assuming light to always appear constant, he got Special Relativity. He merely had to slow time and shorten lengths, comparatively easy.

    But going from stationary to motion, the changing process, posed a problem of having to slow and shorten as a function of time. That is the issue of acceleration. As yuiop explained, the concept is embodied in a man falling along side his tools yet not accepting that it was he who was falling, but rather the rest of the universe was accelerating.

    In order to shorten length and slow time as a function of time, a "bending of space and time" is required. The idea is that a length must change as time proceeds. But time is changing as relative location extends. That length changing per relative location is the "bending".
    Last edited: Feb 25, 2012
  8. Feb 25, 2012 #7
    He illustrated that in simple language here (chapters 23+24):

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