Is SR really internally consistent?

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The discussion centers on the internal consistency of Special Relativity (SR) as it relates to Einstein's predictions about clock rates at different latitudes. Participants question why Einstein concluded that a clock at the equator would run slower than one at the poles, despite both being in relative motion to each other. It is clarified that the polar clock is in an inertial frame while the equatorial clock is not, due to its circular motion, leading to an asymmetry in their time measurements. The conversation also addresses the ability to test these predictions, emphasizing that SR can handle accelerated motion and that the principle of relativity applies specifically to inertial frames. Ultimately, the discussion highlights the nuanced understanding required to reconcile Einstein's predictions with the principles of SR.
  • #31
choran said:
It is confusing to me that (in the portion of the paper I originally quoted) E speaks about straight lines, then says, of course, this would also apply to constant speed on a curved line, and from that (next line) makes his unqualified and unequivocal statement about the clock on the equator, and the clock at the pole.
Yes indeed. He simply elaborates in a concrete way on the meaning of doing an integration (Δx -> dx). A circle can be (and always has been) intepreted as an infinite number of infinite straight lines. Thus, if we assume -as he explicitly did- that acceleration itself has no effect on the clock, then the effect of a circular trajectory must be about the same as the effect of many short straight trajectories, and exactly the same as an infinite number of infinitely short straight trajectories.
See in addition post # 4 by samshorn. But probably Einstein did not even consider any eventual effect of gravitation in that paper.
THEN to add a bit to the confusion, see footnote 7, which I assume was Einstein's:
"7. Not a pendulum-clock, which is physically a system to which the Earth belongs. This case had to be excluded." For all other clocks than a pendulum clock, then, Einstein rather plainly states that special relativity would apply in the polar clock/equatorial clock example that he used. He excludes a pendulum clock because of effects that the Earth's rotation and/or gravity would have on the operation of that clock, and not on his imaginary clock being used in the example.
Yes that footnote was by Einstein, [edit: OOPS, mistake: I now found back the original and see that that footnote was added later] but you misunderstand his explanation - he says nothing about the Earth's rotation or gravity, that's besides the point. To elaborate: a pendulum clock doesn't work in outer space; the Earth is part of its "spring" mechanism! Thus a moving pendulum clock is only half a moving clock, with the other half of the clock mechanism in rest (approximately).
[..] I believe, that Einstein was just wrong in his statement, especially if footnote #7, quoted above, is his. [..]
See again post # 4. His prediction was effectively wrong but technically correct: at equal temperature, gravitational potential etc. his prediction is surely correct.
 
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  • #32
"... says nothing about the Earth's gravitation or rotation." True, but that is the reason a pendulum clock would not fit into his example, is it not, because such a clock depends upon gravity to function (and will also be influenced, ala Foucault) by rotation. He's saying, I think, that no clock which depends upon or is influenced by those things would work in his polar/equator example. All others would, according to his implied exclusion of that class of clock. Why did he even use the Earth as an example? All clocks on or near the Earth's surface are affected by the motion of the earth. Otherwise, no Sagnac effect, right? Or wrong. LOL Not sure which.
 
  • #33
Whoops forgot. I have to disagree with one of your statements, "...the pendulum clock doesn't work in outer space." True, but I doubt that Einstein was thinking about outer space at all when he wrote the 1905 paper. The paper's examples are all earth-based. I think there was another reason he mentioned only pendulum clocks in his exclusion. I think he assumed that only the accuracy and/or synchronization of pendulum clocks would be affected by their differing positions on the Earth's surface, irrespective of the relativistic effects he was predicting.
 
  • #34
Another whoops: I guess what I'm saying is that (unlike in the case of general relativity) there are no "suitable clocks" with which to test special relativity in any Earth based system of experiments, for there will always be differential gravitational forces with which to content, and E has, I believed, at least impliedly excluded that type of clock.
 
  • #35
Hmm, interesting: I just read that Sommerfield added the "pendulum clock" language in a 1913 edit/reissuance of the paper, and that Einstein's original words had been "balance clock". The Sommerfield language was, some think, added to answer questions of the sort I have asked, and to reinforce (or add the caveat that) we must exclude differential gravitational effects from Einstein's clocks. I don't know one way or the other, just read it in another paper, but didn't want you to think I was sandbagging you or quoting E incorrectly. May have been Sommerfield, don't know.
 
  • #36
Trying to learn physics from the seminal works is a bad idea, as this thread clearly demonstrates. You should learn SR first from a modern textbook, and then go back and read the 1905 paper. You are getting distracted by trivialities.
 
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  • #37
choran said:
Hmm, interesting: I just read that Sommerfield added the "pendulum clock" language in a 1913 edit/reissuance of the paper, and that Einstein's original words had been "balance clock". [..].
See my correction: the footnote was not by Einstein. Einstein made his prediction only for a balance clock, for the reason that Sommerfeld(?) explained and which I elaborated here - the clock prediction is not valid for a partial clock. You can check the original footnotes through the link in the German Wikipedia. http://users.physik.fu-berlin.de/~kleinert/files/1905_17_891-921.pdf
 
  • #38
Yep I think it was Sommerfield, at least according a book titled "Reflections on Relativity" by Kevin Brown. I wonder then how the theory can be tested in an Earth (or near earth) setting, since (I think) that even atomic clocks vary not just according to velocity, but by altitude above the earth. I'm just saying that this makes the theory (SR, not GR) one that may be impossible for us to test. All of the tests at this point (again, SR, not GR) have of necessity involved tests on or near the earth, and I know of no clock we could use to satisfy the definition of a good clock. Maybe I'm wrong.
 
  • #39
choran said:
[..] I wonder then how the theory can be tested in an Earth (or near earth) setting, since (I think) that even atomic clocks vary not just according to velocity, but by altitude above the earth. I'm just saying that this makes the theory (SR, not GR) one that may be impossible for us to test. [..].
The prediction is valid as I stated in post 31. Thus in principle a pure SR test with transporting clocks is possible; but I don't know if anyone ever bothered. All such tests that I know about involved both velocity and height changes, and the GR prediction includes the SR prediction.
See also for other tests: http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html
 
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  • #40
Thanks Harrylin, I greatly appreciate your responses, and I understand what you're saying. I agree (if this is your position, not trying to put words in your mouth) that all tests normally referred to have been tests of GR. I also agree that a pure SR test has not been done. I don't know enough to agree or disagree that the "GR prediction includes the SR prediction", or whether a straight SR test could be done. Just don't know on that one. Thanks again for your answers. You have certainly mastered a very difficult subject matter.
 
  • #41
choran said:
Thanks Harrylin, I greatly appreciate your responses, and I understand what you're saying. I agree (if this is your position, not trying to put words in your mouth) that all tests normally referred to have been tests of GR. I also agree that a pure SR test has not been done. I don't know enough to agree or disagree that the "GR prediction includes the SR prediction", or whether a straight SR test could be done. Just don't know on that one. Thanks again for your answers. You have certainly mastered a very difficult subject matter.
Only atomic clock tests that I know of. Once more, check out the other experiments - there are several mentioned that you overlooked. http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html#Tests_of_time_dilation

PS: I had forgotten that the Hafele and Keating test involved clocks in airplanes in two directions - thus the difference between these two was largely a test of SR, similar to Einstein's thought experiment (see point 5, with the inappropriate header "Twin paradox").
 
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  • #42
There are plenty of examples of time dilation in which only the special relativistic time dilation due to speed matters. For example you can look at the lifetime of muons in particle accelerators. These muons are going very fast and so their lifetime is extended due to time dilation. This is a purely special relativistic effect and general relativity is not needed to explain it.
 
  • #43
choran said:
I'm just saying that this makes the theory (SR, not GR) one that may be impossible for us to test. All of the tests at this point (again, SR, not GR) have of necessity involved tests on or near the earth, and I know of no clock we could use to satisfy the definition of a good clock. Maybe I'm wrong.
Yes, you are wrong. Please read the sticky on experimental tests of SR. First, it is wrong that all tests of SR have involved terrestrial sources. Second, it is wrong that SR is impossible to test, it is emminently falsifiable. There are many possible tests of SR regardless of the fact that the Earth has gravity.

SR makes definite predictions about the outcomes of experiments and those predictions can be verified and falsified. It is testable.
 
  • #44
The_Duck said:
There are plenty of examples of time dilation in which only the special relativistic time dilation due to speed matters. For example you can look at the lifetime of muons in particle accelerators. These muons are going very fast and so their lifetime is extended due to time dilation. This is a purely special relativistic effect and general relativity is not needed to explain it.
To emphasize what The_Duck says here, in a typical particle accelerator the particles travel in a horizontal path, so there is no difference in gravitational potential and therefore no gravitational time dilation, even according to GR. This is just one example of a test that is carried out in a gravitational field that is nonetheless a test of SR. The sticky is full of others.
 
  • #45
I have found an article where the author says the following about einstein's SR: If we have two reference frames, S and S', with S stationary and the S' moving along the 'x' axis with speed 'v' of S, then as per SR there is length contraction in the 'x' direction but no change in the 'y' or the 'z' directions of objects in S'. That is y=y' and z=z'. If we take just the y=y', then the length y2-y1 = y'2-y'1. However, SR says that the time is slower in S' than in S. This means t2-t1 is < t'2-t'1. So, if we have a beam of light traveling along the y-axis in S then the speed of the light is C= y2-y1/t2-t1. For the observer in S' who is also looking at the same beam of light it will be C'= y'2-y'1/t'2-t'1. Now, the numerators are equal but the denominator in S' is larger than in S due to time dilation. This means C'<C, which contradicts the constancy of the speed of light postulate of SR! Also, for light traveling in x-axis direction we have from length contraction x2-x1 > x'2-x'1 and from time dilation we have t2-t1 < t'2-t'1, then the speed of light in S is C=x2-x1/t2-t1 and in S' it is C'= x'2-x'1/t'2-t'1. So, for C' we have the numerator that is smaller than in S and the denominator that is greater than that in S. This again leads to C' < C !. So, how do we resolve this? thanks.

In my previous post i should have said that S' is moving along the x-axis of S with constant speed 'v'. thanks.
 
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  • #46
Could you post a link the the article, assuming it available online? Thank you.
 
  • #47
I have made a mistake in the first post. By time dilation we have t2-t1 > t'2-t'1 and so for light beam traveling in the x-axis direction both the numerator and denominator in S' decrease by same factor thereby making C'=C. But for the light beam traveling in the y-axis direction we will have C'>C and so the problem remains as SR says C' should be equal to C in ALL directions! thanks.
 
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  • #48
tzadduki said:
I have made a mistake in the first post. By time dilation we have t2-t1 > t'2-t'1 and so for light beam traveling in the x-axis direction both the numerator and denominator in S' decrease by same factor thereby making C'=C. But for the light beam traveling in the y-axis direction we will have C'>C and so the problem remains as SR says C' should be equal to C in ALL directions! thanks.

I think you are incorrectly assuming that the light will be traveling along the y-axis in both both S and S'. If it is traveling along the y-axis in S, then it will be traveling along a diagonal path in S'. You need use the resultant path length in S' taking the both the horizontal and vertical motion. Do a search for light clock to see what I mean.
 
  • #50
Referring to post#51. The article is not published in a peer-reviewed scientific journal. A quick reading leads me to conclude that it would not be accepted.

The author has some misunderstanding of the difference between coordinate effects and invariants.
 
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  • #51
tzadduki said:
I have found an article where the author says the following about einstein's SR: If we have two reference frames, S and S', with S stationary and the S' moving along the 'x' axis with speed 'v' of S, then as per SR there is length contraction in the 'x' direction but no change in the 'y' or the 'z' directions of objects in S'. That is y=y' and z=z'. If we take just the y=y', then the length y2-y1 = y'2-y'1. However, SR says that the time is slower in S' than in S. This means t2-t1 is < t'2-t'1. So, if we have a beam of light traveling along the y-axis in S then the speed of the light is C= y2-y1/t2-t1. For the observer in S' who is also looking at the same beam of light it will be C'= y'2-y'1/t'2-t'1. Now, the numerators are equal but the denominator in S' is larger than in S due to time dilation. This means C'<C, which contradicts the constancy of the speed of light postulate of SR! Also, for light traveling in x-axis direction we have from length contraction x2-x1 > x'2-x'1 and from time dilation we have t2-t1 < t'2-t'1, then the speed of light in S is C=x2-x1/t2-t1 and in S' it is C'= x'2-x'1/t'2-t'1. So, for C' we have the numerator that is smaller than in S and the denominator that is greater than that in S. This again leads to C' < C !. So, how do we resolve this? thanks.

Either you've misunderstood the article or it's wrong.

A beam of light traveling along the y-axis in one frame is not traveling along the y-axis in the other frame - it has an x-axis component as well, and therefore travels a longer distance. The time dilation and length contraction is exactly enough to balance that effect, keep the speed of light the same.

Although a beam of light traveling along the x-axis in one frame is also traveling along the x-axis in the other frame, the distance covered from the origin of one frame as viewed from the other is different in the two frames. Again, length contraction and time dilation together exactly balance that effect.

You can see this for yourself if you choose either reference frame, imagine two pulses of light leaving the origin of that frame at time zero. After one second, the (x,y,t) coordinates of the pulse directed along the y-axis will be (0,1,1) and the coordinates of the pulse directed along the x-axis will be (1,0,1). Use the Lorentz transforms (not the contraction and dilation formulas!) to convert these into coordinates in the other frame, then calculate the distance covered by the light in one second in that frame. It'll come out to be c.
 
  • #52
yuiop said:
I think you are incorrectly assuming that the light will be traveling along the y-axis in both both S and S'. If it is traveling along the y-axis in S, then it will be traveling along a diagonal path in S'. You need use the resultant path length in S' taking the both the horizontal and vertical motion. Do a search for light clock to see what I mean.

The light clock example is just to show the phenomenon of time dilation in S' compared to S. The person in S' who is moving with speed 'v' will not see the light beam traveling diagonally as the horizontal component equal to 'vt' will be canceled out by the actual movement of S' along the x'-axis. Hence, the S' person will also see the light beam traveling along y'. But the person in S will see the light beam travel diagonally in S'. In this way the light travels along y in S and y' in S'. This is the relativistic principle i.e that any phenomenon in S has to be exactly the same in S'. thanks.

in the above post i should have said:...the horizontal component equal to '-vt' will be cancelled...movement of S' along the x'-axis equal to '+vt'.
 
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  • #53
Nugatory said:
Either you've misunderstood the article or it's wrong.

A beam of light traveling along the y-axis in one frame is not traveling along the y-axis in the other frame - it has an x-axis component as well, and therefore travels a longer distance. The time dilation and length contraction is exactly enough to balance that effect, keep the speed of light the same.

Although a beam of light traveling along the x-axis in one frame is also traveling along the x-axis in the other frame, the distance covered from the origin of one frame as viewed from the other is different in the two frames. Again, length contraction and time dilation together exactly balance that effect.

You can see this for yourself if you choose either reference frame, imagine two pulses of light leaving the origin of that frame at time zero. After one second, the (x,y,t) coordinates of the pulse directed along the y-axis will be (0,1,1) and the coordinates of the pulse directed along the x-axis will be (1,0,1). Use the Lorentz transforms (not the contraction and dilation formulas!) to convert these into coordinates in the other frame, then calculate the distance covered by the light in one second in that frame. It'll come out to be c.

The x which is equal to +vt, where t is the time in S, will be canceled out by the movement of S' with respect to S by -vt where again t is the time in S, thereby resulting in the light traveling straight along y' with respect to the person in S', even though it is diagonal for a person in S looking at the beam in S'. This has to be the case according to the principle of relativity.
 
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  • #54
Mentz114 said:
Referring to post#51. The article is not published in a peer-reviewed scientific journal. A quick reading leads me to conclude that it would not be accepted.

The author has some misunderstanding of the difference between coordinate effects and invariants.

I like you to read the article by Weinberg regarding the article by de Broglie. He says that, and i am paraphrasing, given the political environment today regarding publishing it would not have been possible that de Broglie's article would have been accepted for publication by any journal. thanks.
 
  • #55
tzadduki said:
The x which is equal to +vt, where t is the time in S, will be canceled out by the movement of S' with respect to S by -vt where again t is the time in S, thereby resulting in the light traveling straight along y' with respect to the person in S', even though it is diagonal for a person in S looking at the beam in S'. This has to be the case according to the principle of relativity.

I think you are confusing your frames. If the light ray is parallel to the y-axis it cannot be parallel to the y' axis because the two axes are moving apart. If the ray remains on one axis it must be getting further away from the other.

An analogy might help. A train crosses a bridge over a road just as a car goes under. In the frame of a person standing by the roadside, the train is moving in the +x direction and the car in the +y direction. In the frame of an observer on the train, however, the car is moving diagonally: it is moving along the road in the +y' direction, and also both the car and the road are moving in the -x' direction.

The extra effects in relativity conspire so that if the car is replaced by a photon, its speed is equal in any frame. The direction is not.
 
  • #56
tzadduki said:
I have found an article where the author says the following about einstein's SR: If we have two reference frames, S and S', with S stationary and the S' moving along the 'x' axis with speed 'v' of S, then as per SR there is length contraction in the 'x' direction but no change in the 'y' or the 'z' directions of objects in S'. That is y=y' and z=z'. If we take just the y=y', then the length y2-y1 = y'2-y'1. However, SR says that the time is slower in S' than in S. This means t2-t1 is < t'2-t'1. So, if we have a beam of light traveling along the y-axis in S then the speed of the light is C= y2-y1/t2-t1. For the observer in S' who is also looking at the same beam of light it will be C'= y'2-y'1/t'2-t'1. Now, the numerators are equal but the denominator in S' is larger than in S due to time dilation. This means C'<C, which contradicts the constancy of the speed of light postulate of SR!
The article referenced is not from an acceptable source, which is not surprising given how eggregiously flawed the reasoning is. You cannot use the time dilation formula for light since there is no frame in which it is at rest, nor can you use the length contraction formula for the same reason. You must use the full Lorentz transform which includes all effects including length contraction, time dilation, relativity of simultaneity, abberation, Doppler, etc.

The equation:
##c^2 t^2 = x^2 + y^2 + z^2##
is the equation for a sphere of radius ct about the origin. I.e. it is a sphere expanding at c in all directions. If you use the Lorentz transform on that it takes only a couple of minutes worth of algebra to show that in any other frame you get
##c^2 t'^2 = x'^2 + y'^2 + z'^2##
which is also a sphere expanding at c in all directions.

Any insinuation that SR preserves c in one direction but not in another direction is nonsense.
 
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