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What motivated Einstein to start thinking about a General Theory of Relativity?

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jmoorhea
#1
Jan27-13, 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 Michelson-Morley experiment which tried to detect movement of Earth relative to the supposed ether. He probably knew about the Lorentz-Fitzgerald 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
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PeterDonis
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Jan27-13, 02:21 PM
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Quote Quote by jmoorhea View Post
why did he think that Special Relativity was not the full story?
Because SR doesn't include gravity, and Newtonian gravity is obviously incompatible with SR because Newtonian gravity implies that the gravitational force propagates instantaneously, but "instantaneously" can't be given a frame-invariant meaning in SR.

Quote Quote by jmoorhea View Post
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.
It was; that's why it took Einstein 8 years to get from the "elevator" thought experiment in 1907, to the full theory of GR in 1915.
ModusPwnd
#3
Jan27-13, 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.

jmoorhea
#4
Jan27-13, 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.
haushofer
#5
Jan28-13, 04:08 AM
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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.
manishvasoya
#6
Jan28-13, 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
haushofer
#7
Jan28-13, 04:20 AM
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Quote Quote by manishvasoya View Post
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.
I'm not sure whether this is true. SR is perfectly capable of handling accelerations without invoking spacetime curvature (just as classical mechanics can handle accelerating observers without invoking gravity via the equivalence principle), although I'm not sure how this was realized historically.
Nugatory
#8
Jan28-13, 04:46 AM
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Quote Quote by manishvasoya View Post
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.
It might be more accurate to say that SR is the special case of GR that applies in flat uncurved space-time. SR works just fine in accelerating frames, as long as the space-time is flat.
manishvasoya
#9
Jan28-13, 05:02 AM
P: 2
@Nugatory : Yes, its full consequence, I was trying to say..in SR the space is flat (straight line) and GR is for general space...,,,
Thinkor
#10
Feb3-13, 05:42 PM
P: 36
Quote Quote by jmoorhea View Post
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 Michelson-Morley experiment which tried to detect movement of Earth relative to the supposed ether. He probably knew about the Lorentz-Fitzgerald 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
A problem with special relativity as it stood in 1905 was that it could not explain the twin paradox, but the Lorentz theory could. That may be one reason, as it would require a generalization of special relativity to deal with accelerated motion, including, I suppose, accelerations due to gravity. Another reason is that Poincare had begun work on a relativistic theory of gravitation even before Einstein, mentioning the problem of gravitation in his own 1905 paper, and had made some progress, including the introduction of a 4 dimensional geometry. Unfortunately, he died after a prostate operation in 1912. Also, probably both were aware of Soldner's speculations about a slower light speed at higher potentials being one way to explain how the frequency of light, rising against the gravitational potential, could remain the same as it ascended. Einstein's 1911 paper showed how he proposed to reconcile the two by having clocks at a higher potential running faster than those at a lower potential. This required that the speed of light not be a universal constant, which, along with other problems, I think probably led him to the idea of using the curved spacetime approach.
stevendaryl
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Feb3-13, 05:53 PM
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Quote Quote by Thinkor View Post
A problem with special relativity as it stood in 1905 was that it could not explain the twin paradox, but the Lorentz theory could.
I don't know why you would say that. Under some pretty natural assumptions, SR correctly predicts that the traveling twin is younger when he returns to Earth.
Thinkor
#12
Feb3-13, 06:04 PM
P: 36
Quote Quote by stevendaryl View Post
I don't know why you would say that. Under some pretty natural assumptions, SR correctly predicts that the traveling twin is younger when he returns to Earth.
I don't want to get too much into the history of it, because I don't want to waste time tracking down references, but I read somewhere that Einstein himself said the problem could not be solved within SR when he provided a resolution of it in GR in 1918(?). I also heard from a physicist (I'm not one, incidentally), that SR initially only dealt with uniform motion. However, since then I've seen the claim that the twin paradox can be resolved in SR, and I assume that's because the basic concept, of exactly what SR is, has been extended.
PeterDonis
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Feb3-13, 06:30 PM
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Quote Quote by Thinkor View Post
I read somewhere that Einstein himself said the problem could not be solved within SR when he provided a resolution of it in GR in 1918(?).
This is the sort of claim you should *not* make just on the basis of "I read somewhere". If you don't have the time to track down an actual reference, don't make the claim. I would be surprised if Einstein actually said such a thing in the extreme form you state it.

Quote Quote by Thinkor View Post
I also heard from a physicist (I'm not one, incidentally), that SR initially only dealt with uniform motion.
People may not have *used* SR to deal with non-uniform motion initially, but that's not the same as saying it couldn't have been so used, if someone had tried. See further comments below.

Quote Quote by Thinkor View Post
However, since then I've seen the claim that the twin paradox can be resolved in SR, and I assume that's because the basic concept, of exactly what SR is, has been extended.
No, it's because people physicists don't always immediately appreciate all of the implications of a new theory. That certainly happened with GR; it took decades for a lot of the implications of the Einstein Field Equation to be worked out. That doesn't mean GR was "extended"; the Einstein Field Equation hasn't changed since Einstein published it in 1915. It just means it took time to work out all its implications.

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.
Thinkor
#14
Feb3-13, 07:00 PM
P: 36
Quote Quote by PeterDonis View Post
This is the sort of claim you should *not* make just on the basis of "I read somewhere". If you don't have the time to track down an actual reference, don't make the claim. I would be surprised if Einstein actually said such a thing in the extreme form you state it.



People may not have *used* SR to deal with non-uniform motion initially, but that's not the same as saying it couldn't have been so used, if someone had tried. See further comments below.



No, it's because people physicists don't always immediately appreciate all of the implications of a new theory. That certainly happened with GR; it took decades for a lot of the implications of the Einstein Field Equation to be worked out. That doesn't mean GR was "extended"; the Einstein Field Equation hasn't changed since Einstein published it in 1915. It just means it took time to work out all its implications.

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.
Actually, I found my copy of Einstein's 1918 paper, which I believe I downloaded from Wikipedia, and it says:

"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.
PeterDonis
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Feb3-13, 07:39 PM
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Quote Quote by Thinkor View Post
"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."
This is talking about coordinate systems, not objects. It does not say that accelerating objects can't be handled by SR.

Quote Quote by Thinkor View Post
The Baez paper or article is still making an analysis where there is acceleration.
The traveling twin does have to accelerate to turn around, yes. But you don't need to use an accelerating reference frame to analyze his motion.

Quote Quote by Thinkor View Post
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.
Once again, Einstein did not say that 1905 SR could not deal with accelerated objects; he only said that 1905 SR had to use inertial reference frames. You can analyze the motion of an accelerated object in an inertial reference frame. So the Doppler Shift analysis, which is done in an inertial reference frame, is a perfectly valid use of 1905 SR.
Thinkor
#16
Feb3-13, 08:21 PM
P: 36
Quote Quote by PeterDonis View Post
This is talking about coordinate systems, not objects. It does not say that accelerating objects can't be handled by SR.



The traveling twin does have to accelerate to turn around, yes. But you don't need to use an accelerating reference frame to analyze his motion.



Once again, Einstein did not say that 1905 SR could not deal with accelerated objects; he only said that 1905 SR had to use inertial reference frames. You can analyze the motion of an accelerated object in an inertial reference frame. So the Doppler Shift analysis, which is done in an inertial reference frame, is a perfectly valid use of 1905 SR.
Einstein essentially said SR deals only with unaccelerated coordinate systems relative to which material points ("objects" in modern parlance) move uniformly in straight lines. Therefore, SR did not, according to Einstein, in 1918, deal with accelerated coordinate systems or accelerated objects.

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.
PeterDonis
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Feb3-13, 08:39 PM
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Quote Quote by Thinkor View Post
Einstein essentially said SR deals only with unaccelerated coordinate systems relative to which material points ("objects" in modern parlance) move uniformly in straight lines.
He did not just say "material points". He said "sufficiently isolated material points" (emphasis mine). Big difference. See further comments, below.

Quote Quote by Thinkor View Post
The Doppler shift analysis deals with an accelerated object ("material point" in 1918 parlance)
A material point, yes (because we're not dealing with its internal structure). But not sufficiently isolated, because it has to interact with something in order to accelerate. If it fires a rocket engine, for example, it exchanges momentum with the rocket exhaust. By "sufficiently isolated material points" Einstein meant "material points that are very far away from all gravitating bodies (so spacetime can be treated as flat), and have no non-gravitational interactions with other objects (so they're in inertial motion, i.e., in free fall, not feeling any force). The traveling twin is not in inertial motion while he's turning around.

Quote Quote by Thinkor View Post
According to Einstein, once again, the material points move uniformly and in straight lines.
The sufficiently isolated material points do, but they're the only ones that do. See above.

Quote Quote by Thinkor View Post
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.
I think we're coming to different conclusions because you have not taken the words "sufficiently isolated" into account in the Einstein quote you gave. Whether you want to give that any additional thought is up to you, of course. I don't have any hard feelings.
PeterDonis
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Feb3-13, 09:03 PM
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Quote Quote by Thinkor View Post
SR only deals with unaccelerated coordinate systems and objects moving uniformly in straight lines.
On re-reading, this may help to make it clearer where we disagree. To me it's clear that Einstein was not saying that 1905 SR could not deal with accelerated objects. He was only saying that accelerated objects couldn't be used in 1905 SR to define coordinate systems; for that you need to use inertial objects.

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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