
#1
Jan2713, 02:17 PM

P: 7

So basically I have always wondered what motivated Einstein to move from Special Relativity to General Relativity.
Anyone care to tell me what was going on in Einsteins mind after he completed his Special Theory of Relativity? I have done a course in Special Relativity, understand it and I can see how Einstein arrived at all the equations derived from the theory. Essentially he was wondering what would happen if he was looking at himself in a mirror and travelling at the speed of light. He then came across the null results of MichelsonMorley experiment which tried to detect movement of Earth relative to the supposed ether. He probably knew about the LorentzFitzgerald equation of length contraction. So when he proposed that the speed of light was constant c and physical objects could not travel faster than the speed of light, then using a simple thought experiment (as described in Young and Freedmans University Physics) he was able to derive Fitzgerald Length contraction equation from basic principles. Then the rest of Special Rel followed suit. I have also done a course in General Rel. and read most of D'Inverno's "An introduction to Einsteins Relativity" a few times since then. But I cannot for the life of me see why Einstein decided to move from Special Rel to General Rel. I mean like what was going through his head, what did he know and why did he think that Special Relativity was not the full story? I know he was thinking about a person trapped in an elevator, how gravitational field of earth was the same as an accelerated frame (like if the elevator had rocket boosters attached to outside of it and accelerating at value g) but it just seems like a quantum leap to go from this thought experiment to the full field equations and the equation of geodesic deviation. Thanks Justin 



#2
Jan2713, 02:21 PM

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PF Gold
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#3
Jan2713, 02:23 PM

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One problem is Newton's Force Law for gravity. It has no time dependence at all, according to it the gravitational force is "instantaneous". But if we get a limit on the speed of "communication" via relativity how does that mesh with the classical force of gravity? I believe this is one problem that came to mind before gen. rel. was developed.




#4
Jan2713, 03:19 PM

P: 7

What motivated Einstein to start thinking about a General Theory of Relativity?
Thanks guys.
That basically fills in the gaps for me. I basically knew already what you just said about Newtons theory implying instanteous propagation of force but never tied it in with why Einstein starting thinking about a more general theory of relativity. 



#5
Jan2813, 04:08 AM

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P: 869

Some nice articles about the history of GR are written by e.g. John Norton or John Stachel. :) One very important stumbling block Einstein encountered was that his theory could be viewed as a gauge theory, something which he formulated in the "hole argument". It made him abandon the notion of general covariance for a while. It's also nice to see the different scalar gravity models which were developed by him and others soon after his SRT.




#6
Jan2813, 04:15 AM

P: 2

SR is just special case of relativity to one kind of frame of reference (frame with constant velocity (accelaration=0)).
And to extend the theory to general case with accelarating frame,,, He took account of gravitational field with SR and developed the GR. Manish 



#7
Jan2813, 04:20 AM

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#8
Jan2813, 04:46 AM

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#9
Jan2813, 05:02 AM

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@Nugatory : Yes, its full consequence, I was trying to say..in SR the space is flat (straight line) and GR is for general space...,,,




#10
Feb313, 05:42 PM

P: 23





#11
Feb313, 05:53 PM

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#12
Feb313, 06:04 PM

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#13
Feb313, 06:30 PM

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In the case of SR, take a look at the Usenet Physics FAQ entry on the twin paradox: http://math.ucr.edu/home/baez/physic...n_paradox.html You'll see three main ways of analyzing and solving the "paradox": (1) The Doppler Shift Analysis: This doesn't use anything that isn't in Einstein's 1905 paper on SR, so it could have been done at any time after that paper was published. But it may have taken quite a while before anyone actually realized this; see above. (2) The Spacetime Diagram Analysis: The concept of spacetime wasn't introduced into SR until 1907, when Minkowski did it; so this analysis couldn't have been done based on Einstein's 1905 publication alone. But it could have been done at any time after 1907. (3) The Equivalence Principle Analysis: This is the one that, in a sense, "uses GR", because the equivalence principle is a central principle in GR, not SR; it involves gravity, and SR doesn't deal with gravity. This analysis is, I believe, basically the one Einstein used in the 1918 "resolution" you referred to. 



#14
Feb313, 07:00 PM

P: 23

"Indeed this theory [meaning Special Relativity  thinkor] asserts only the equivalence of all Galilean (unaccelerated) coordinate systems, that is, coordinate systems relative to which sufficiently isolated, material points move in straight lines and uniformly." Prior to this Einstein says that there has been opposition to SR, because what is essentially the twin paradox (my characterization thinkor) has elicited opposition "with good reasons". He goes on to show that the paradox does not contradict SR for the reason given by the quote. Einstein then accounts for the paradox referencing gravitational potential etc. The Baez paper or article is still making an analysis where there is acceleration. Therefore, per Einstein's quote above, I feel justified in saying SR could not deal with it under any circumstances, as it stood in 1905, assuming, as Einstein says, that in 1918 it only deals with unaccelerated systems and there wasn't a regression in SR between 1905 and 1918. 



#15
Feb313, 07:39 PM

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#16
Feb313, 08:21 PM

P: 23

The Doppler shift analysis deals with an accelerated object ("material point" in 1918 parlance) and therefore Einstein's SR of 1918, and presumably of 1905, did not deal with it. According to Einstein, once again, the material points move uniformly and in straight lines. In the twin paradox, at least one material point is not moving uniformly in a straight line. A brief summary of the Einstein's 1918 paper is as follows: Criticisms of SR were made with good reasons, but SR was not disproved because SR only deals with unaccelerated coordinate systems and objects moving uniformly in straight lines. In GR the paradox is easily resolved. So far as I can tell, everything Einstein said in this paper was correct, although I admit that I haven't examined the GR solution closely. I'm happy to let other readers make their own judgment. I've made mine. I can't put any more time into a matter that seems so clear to me. I hope you have no hard feelings about our coming to different conclusions. 



#17
Feb313, 08:39 PM

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#18
Feb313, 09:03 PM

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Part of what Einstein discovered in developing GR was that curvilinear coordinate systems *can* be used even in flat spacetime, so they can be used even in SR problems. So in that sense I think Einstein's understanding of SR evolved. But you don't need a curvilinear coordinate system for the Doppler Shift analysis of the twin paradox; as I said before, that analysis doesn't use anything that isn't in 1905 SR. 


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