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

[jmoorhea]

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 traveling 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

 

[PeterDonis]

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.

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]

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]

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]

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]

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 accelerating frame,,, He took account of gravitational field with SR and developed the GR.


Manish

 

[haushofer]

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 accelerating 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]

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 accelerating 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]

@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]

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 traveling 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]

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]

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]

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.

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.

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/physics/Relativity/SR/TwinParadox/twin_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]

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/physics/Relativity/SR/TwinParadox/twin_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]

"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.

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.

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]

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]

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.

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.

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.

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]

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.

 

[stevendaryl]

Gravity has no part in the classic twin paradox. It can be expressed and resolved purely in terms of SR in flat-spacetime.

I agree completely, but Einstein himself seemed a little confused, early on, anyway, about the distinction between SR and GR. I read an essay by Einstein in which he derived the differential aging of the twin paradox using "gravitational time dilation", and in the paper, he called this the application of GR to the twin paradox.

 

[stevendaryl]

I agree completely, but Einstein himself seemed a little confused, early on, anyway, about the distinction between SR and GR. I read an essay by Einstein in which he derived the differential aging of the twin paradox using "gravitational time dilation", and in the paper, he called this the application of GR to the twin paradox.

Here's a paper where he discusses it:
http://en.wikisource.org/wiki/Dialog_about_objections_against_the_theory_of_relativity

 

[PeterDonis]

I agree completely, but Einstein himself seemed a little confused, early on, anyway, about the distinction between SR and GR.

I think he was trying to argue against the idea that there has to *be* a hard and fast distinction between SR and GR. They are really just one single theory; more precisely, SR is just a subset of GR. If the question is which particular subset SR "really is" (do we just restrict to flat spacetime, or do we also restrict to inertial coordinates only?), I think Einstein would have thought that question to be an unimportant one.

I read an essay by Einstein in which he derived the differential aging of the twin paradox using "gravitational time dilation", and in the paper, he called this the application of GR to the twin paradox.

This is just what the Usenet Physics FAQ calls the Equivalence Principle Analysis. It's a valid way of analyzing the twin paradox, and since it involves a "gravitational field", it can be construed as requiring GR, since SR doesn't deal with gravity.

Of course, it's not *necessary* to analyze the twin paradox this way, since spacetime is flat in the standard twin paradox, and there is never any need to introduce a "gravitational field" in flat spacetime. But conceptually, allowing for the possibility of a "gravitational field" as a coordinate-dependent thing (as Einstein was using the term, it basically means nonzero connection coefficients) was a way of getting to the principle of general covariance--that in fact you *can* use any coordinates you like; you're not limited to inertial coordinates. But if you use non-inertial coordinates, you're going to find these "gravitational fields" present, even if no gravitating masses are present. In other words, it was a way of expressing the unity of SR and GR, that they are really just one single theory, as I said above.

 

[Mentz114]

Thanks to PeterDonis and stevendaryl for those posts and links. I was always a bit confused by Einsteins 'dialog' ( I-alog ?) but the Usenet Physics article explains how to use a gravitational field to unkink the worldlines. It is an ingenious construction.

 

[stevendaryl]

Take two twins (T1 and T2) who are at rest in an inertial frame (Frame A). They both accelerate together for a while, then stop accelerating. They are now in another inertial frame (Frame B) which is moving w.r.t. Frame A. Now T1 accelerates in such a way (decelerates) that he is again in rest in frame A. Who will age slower?

The "rate of aging" of a twin is a coordinate-dependent quantity. In the inertial coordinate system of frame A, T2 ages slowest afterward. In the inertial coordinate system of frame B, T1 ages slowest.

 

[nitsuj]

I see you still don't understand that differential ageing is a consequence of the 'clock postulate'. Do you know what proper-time means ?

What is the clock postulate? I tried google and nothing (headlined).

 

[nitsuj]

The "rate of aging" of a twin is a coordinate-dependent quantity. In the inertial coordinate system of frame A, T2 ages slowest afterward. In the inertial coordinate system of frame B, T1 ages slowest.

I find this equivalent to saying; Motion is Relative.

 

[Nugatory]

The "rate of aging" of a twin is a coordinate-dependent quantity. In the inertial coordinate system of frame A, T2 ages slowest afterward. In the inertial coordinate system of frame B, T1 ages slowest.

But note that although the "rate of aging" is a coordinate-dependent quantity, the actual amount of aging that a twin will experience on his path between two points in spacetime is not coordinate-dependent. It will be the same no matter which coordinates we use and what coordinate-dependent rate of aging those coordinates suggest. The key here is that although the "rate of aging" will be different in different coordinate systems, so will the "time" during which this aging is happening, and the two effects always balance out to give the same total amount of aging along the journey.

[Of course stevendaryl knows this already. I'm just trying to stop someone else who doesn't know this from being confused by this aging-faster/aging slower right now thing]

 

[Mentz114]

What is the clock postulate? I tried google and nothing (headlined).

I thought it was "the proper interval between two events on a clocks worldline is the time elapsed on the clock ( between those events)"

 

[PeterDonis]

What is the clock postulate? I tried google and nothing (headlined).

The Usenet Physics FAQ has a good explanation:

http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html

Basically, it's the postulate that a clock's "rate of time flow", as seen by an observer, is not affected by its acceleration; it's only affected by the clock's velocity relative to the observer.

 

[nitsuj]

The Usenet Physics FAQ has a good explanation:

http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html

Basically, it's the postulate that a clock's "rate of time flow", as seen by an observer, is not affected by its acceleration; it's only affected by the clock's velocity relative to the observer.

Cool, Thanks PeterDonis

 

[Mentz114]

This diagram is the scenario where the twins T1 (blue) and T2 (green) comove, then part company. The measurements are made between times t₀ and t₂.

The proper times of interest are AB, along T2's worldline, and CD+DE along T1's worldline. Without doing any calculations ( I think these proper times are stevendaryl's τ₂ and τ₁), it is obvious that whether AB is greater than or less than CD+DE, this relationship will be true from any inertial frame.

The reason being, that proper time is invariant under LT.

Definition of proper time
$$d\tau^2 = dt^2-dx^2$$
Transform the intervals dx->dX, dt->dT with a Lorentz transformation
$$dT=\gamma dt + \gamma\beta dx,\ \ dX=\gamma dx + \gamma\beta dt$$
Calculate new proper time

$$\begin{align} dT^2-dX^2 &= (\gamma dt + \gamma\beta dx)^2 - (\gamma dx + \gamma\beta dt)^2\\ &= \gamma^2(1-\beta^2)dt^2- \gamma^2(1-\beta^2)dx^2\\ &= dt^2 - dx^2 \end{align}$$

Any decent, simple book on relativity tells us this.

 

[PeterDonis]

This diagram is the scenario where the twins T1 (blue) and T2 (green) comove, then part company.

This is what we thought the scenario was, but now we're not sure. You have T1 and T2 separated in the x direction and moving in the x direction; but we think arindamsinha meant to have them separated in the y direction (no initial separation in the x direction) and moving in the x direction.

 

[PeterDonis]

Is that a correct description of the scenario as seen from Frame A?

I'm going to assume that it is and go ahead and post the analysis, since it's pretty simple.

We have the following events (coordinates t, x, y are given relative to Frame A):

#1: $(0, 0, 0)$ T1 starts the experiment, moving in the x direction at velocity v.

#2: $(0, 0, 1)$ T2 starts the experiment, moving in the x direction at velocity v.

#3: $(t_1, v t_1, 0)$ T1 stops moving.

#4: $(t_2, v t_2, 1)$ T2 stops moving and ends the experiment.

#5: $(t_2, v t_1, 0)$ T1 ends the experiment.

We have, by hypothesis, $t_2 > t_1$, and for convenience I will define $\delta t = t_2 - t_1$.

The proper times in Frame A are then:

$$\tau_1 = \frac{t_1}{\gamma} + \left( t_2 - t_1 \right) = \frac{t_1}{\gamma} + \delta t$$

$$\tau_2 = \frac{t_2}{\gamma} = \frac{t_1 + \delta t}{\gamma}$$

This makes it obvious that $\tau_1 > \tau_2$.

Now let's look at things in Frame B. Here are the event coordinates t', x', y' in that frame, obtained by Lorentz transforming the coordinates given above (note that we have assumed the origins of both frames are the same, at event #1):

#1: $(0, 0, 0)$ T1 starts moving in the x direction at velocity v.

#2: $(0, 0, 1)$ T2 starts moving in the x direction at velocity v.

#3: $(t_1 / \gamma, 0, 0)$ T1 stops moving.

#4: $(t_2 / \gamma, 0, 1)$ T2 stops moving.

#5: $(t_1 / \gamma + \gamma \delta t, - \gamma v \delta t, 0)$ T1 ends the experiment.

The proper times in this frame are then:

$$\tau_1 = \frac{t_1}{\gamma} + \frac{t_1 / \gamma + \gamma \delta t - t_1 / \gamma}{\gamma} = \frac{t_1}{\gamma} + \delta t$$

$$\tau_2 = \frac{t_2}{\gamma} = \frac{t_1 + \delta t}{\gamma}$$

In other words, the proper times are the same in both frames, as they should be. The key thing to note, of course, is that in Frame B, event #5 happens *later* than event #4, and the additional coordinate time that this adds to T1's "moving" segment in that frame more than compensates for the fact that T1 is moving while T2 is at rest. This is basically the same resolution as the previous scenario; the y coordinate drops out of the analysis since all the motion is in the x direction, but there is still separation in the x direction at the end of the experiment (even though there isn't at the start), so relativity of simultaneity still comes into play in making event #5 later than event #4 in Frame B.

 

[D H]

Thread locked pending cleanup.

Metz114 et al: Please remember to use the report button to let the mentors know about nonsense such as that which you highlighted.
OK. Cleanup complete. I deleted 50 posts. That's a bit much, perhaps too much. Those posts are still here; I soft-deleted them. Let me know if there's anything that you members strongly feel needs to be restored.