Paradoxes in relativity, and an absolute reality

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  • #26
phinds
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But to say that Special Relativity proves that an absolute rest frame cannot exist or does not exist is to misunderstand the foundation of SR
OK, THAT'S the part I was not aware of. So what DOES say that an absoute rest from does not exist? (Or is everyone here who says it doesn't wrong? I seem to remember having seen that here many times but perhaps I misunderstood what I was reading)
 
  • #27
ghwellsjr
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But to say that Special Relativity proves that an absolute rest frame cannot exist or does not exist is to misunderstand the foundation of SR.
OK, THAT'S the part I was not aware of. So what DOES say that an absoute rest from does not exist? (Or is everyone here who says it doesn't wrong? I seem to remember having seen that here many times but perhaps I misunderstood what I was reading)
Every inertial frame defined according to Special Relativity is a candidate for an absolute rest frame so we cannot rule out the possibility of its existence. But we can rule out the possibility of our being able to identify which frame it is so it becomes a moot point. Whether it exists or not has no bearing on our theory of SR. Just like we say there is no preferred frame of reference, even if there were an absolute rest frame and even if there were some way to identify it (God told me), we could still relegate it to the realm of insignificance because we would not be able to distinguish that "preferred" frame from any other. Or to put it another way, we could treat any other frame with the same degree of "priviledge" that the ether frame should get.

Maybe you could find some of these posts that say an absolute rest frame does not exist and we can deal with them on a case by case basis.
 
  • #28
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OK, THAT'S the part I was not aware of. So what DOES say that an absoute rest from does not exist? (Or is everyone here who says it doesn't wrong? I seem to remember having seen that here many times but perhaps I misunderstood what I was reading)
I would say, they may be right but that there is no basis in SR or logic that makes this inevitable. So any such positive assertion would seem questionable. IMO
 
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  • #29
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If it were possible for the gears to actually continue to stay meshed throughout the trip then the odometer will always register the same distance no matter what the speed. I think you're going to have to find another way to build an odometer.
You are partly correct. I was wrong to introduce the meshing gears thing. I was trying to emphasize the rolling without slipping part, but meshing gears would not work at relativistic speeds. However, if we had a wheels with regular rubber tyres (that could withstand the forces) and a regular car odometer, then the distance measured by a car travelling at relativistic speeds would be less than the distance measured by a slow moving car along a given track. For each revolution of the wheel the proper distance rolled along the track (measured in the rest frame of the track) is greater by the gamma factor at relativistic speeds.
I don't understand your particular wording here as it unnecessarily restricts what you are saying. All observers agree with the displayed time on any clock at every event, not just the accumulated times between two events so obviously they're also going to agree on the accumulated time between events.
I agree as long as we are talking about elapsed times measured on individual clocks. If the times are measured by spatially separated and synchronised clocks, then different observers will disagree on the coordinate times.
Also, your definition of "proper time" is unnecessarily restrictive as it implies that any clock that is present at two events will measure the same interval of time which is not true. It depends on how the clock travels between the two events. So two clocks that were both present at two events can accumulate different "proper time" intervals. Every clock always displays "proper time" all the time, no exceptions.
Again you right to pull me up here. Sometimes we loosely talk about the time between events using two separate clocks and I was focusing on excluding that situation. An accelerating clock present at both events would indeed record a lower elapsed time than the proper time interval between those events. Perhaps I should of said the "proper time interval" is the time measured by a single inertial clock that is present at both events, which works fine in SR where we exclude gravitational effects.
 
  • #30
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Seems to me he has it right and you have it backwards. It doesn't exist for the reason he stated, NOT because we can't measure it.
I would tend to agree with AustinO and ghwellsjr that stating an absolute reference frame does not exist is perhaps too strong a statement. Lorentz Ether Theory shows that an absolute light medium with properties that affect the time dilation and length contraction of objects with motion relative to the absolute medium, is completely consistent with the predictions of SR. It just so happens that those properties of the absolute medium make identifying the rest frame of the medium impossible. In other words LET posits that an absolute medium exists but is unmeasurable and SR does not really care whether it exists or not. Either way, the predictions of LET and SR are identical. LET gives a mechanical description of the universe that is entirely logical and perhaps less paradoxical, while SR just says things happens the way they do, because they "just do" and takes the pragmatic approach of only considering relative velocities of objects and can seem paradoxical at times.
But those rotations and distortions and curvature effects are only in what an observer sees. In other words, it is an optical illusion, not something actually happening.
I also agree with this statement. A long rod that fits comfortably inside a hollow cylinder, will not become wedged as result of Penrose-Terrell rotation when it has motion relative to the cylinder, as it is not a physical effect.
 
  • #31
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[..] I was wrong to introduce the meshing gears thing. I was trying to emphasize the rolling without slipping part, but meshing gears would not work at relativistic speeds. However, if we had a wheels with regular rubber tyres (that could withstand the forces) and a regular car odometer, then the distance measured by a car travelling at relativistic speeds would be less than the distance measured by a slow moving car along a given track. For each revolution of the wheel the proper distance rolled along the track (measured in the rest frame of the track) is greater by the gamma factor at relativistic speeds. [..]
Sorry, I don't think that that can be right. A rubber (non-slipping) wheel has zero speed relative to the road at the point of contact; when used as a flexible ruler (odometer), it necessarily measures the proper distance of the road.
 
  • #32
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I would tend to agree with AustinO and ghwellsjr that stating an absolute reference frame does not exist is perhaps too strong a statement. [..]
And I already stated the same in post #16, before the discussion of the same stated. :tongue2: Was my post to succinct perhaps?
 
  • #33
ghwellsjr
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Also, your definition of "proper time" is unnecessarily restrictive as it implies that any clock that is present at two events will measure the same interval of time which is not true. It depends on how the clock travels between the two events. So two clocks that were both present at two events can accumulate different "proper time" intervals. Every clock always displays "proper time" all the time, no exceptions.
Again you right to pull me up here. Sometimes we loosely talk about the time between events using two separate clocks and I was focusing on excluding that situation. An accelerating clock present at both events would indeed record a lower elapsed time than the proper time interval between those events. Perhaps I should of said the "proper time interval" is the time measured by a single inertial clock that is present at both events, which works fine in SR where we exclude gravitational effects.
You are still being too restrictive. I think the source of confusion is the wikipedia article on Spacetime under the section called "Spacetime intervals" and more specifically near the end of the subsection called "Time-like interval" where you see the sentence beginning with "The proper time interval..." which implies that a specific definition of that phrase is being given. They should have started the sentence with "The proper time of time-like intervals..." They did use that phrase at the end of the subsection "Space-like interval" but look at the phrase that follows: "the proper distance of space-like spacetime intervals". That avoids all confusion because what they are talking about are different kinds of frame-invariant "spacetime intervals" between any two events. So instead of saying "The proper time interval..." the complete phrase "The proper time of time-like spacetime intervals..." avoids all confusion. The phrase, "proper time interval" does not have a specific meaning limited to spacetime intervals, it can apply to the accumulated time on any clock.

If you look up the wikipedia article on "proper time", you will see that proper time is not invariant between two events but depends on the motion of a clock carried between the two events.
 
  • #34
ghwellsjr
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I would tend to agree with AustinO and ghwellsjr that stating an absolute reference frame does not exist is perhaps too strong a statement. Lorentz Ether Theory shows that an absolute light medium with properties that affect the time dilation and length contraction of objects with motion relative to the absolute medium, is completely consistent with the predictions of SR. It just so happens that those properties of the absolute medium make identifying the rest frame of the medium impossible. In other words LET posits that an absolute medium exists but is unmeasurable and SR does not really care whether it exists or not. Either way, the predictions of LET and SR are identical. LET gives a mechanical description of the universe that is entirely logical and perhaps less paradoxical, while SR just says things happens the way they do, because they "just do" and takes the pragmatic approach of only considering relative velocities of objects and can seem paradoxical at times.
I would not speak so glowingly of LET. When I refer to LET, I mean the version of it that was, shall we say, reverse engineered from SR after SR was developed by Einstein in 1905. Lorentz never developed it on his own and his theory was in a continual state of evolution and never arrived at the state of being identical to SR. Even the so-called Lorentz Transformation had an evolution prior to 1905. And even though Lorentz and others tried to provide a mechanical description of the universe, it was never complete and never arrived at the sweeping paradigm shift that Einstein introduced. And I wouldn't say that LET (before Einstein) was less paradoxical than SR. SR does not say things happen the way they "just do", it provides the principle under which all of physics must operate, that of the Lorentz Transformation. So all the rest of physics had to be redone to abide by the principles of SR and that eliminates all paradoxes. So after Einstein showed the clear, unequivocal way to establish a consistent all-encompassing physics, the embattled LET plagiarizes all the predictions and principles of SR but says, oh, by the way, we still think there is a preferred frame so we'll just say that everything SR concludes, we would have concluded too if we just had enough time to figure it all out (but I even doubt that).
 
  • #35
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[..] the embattled LET plagiarizes all the predictions and principles of SR but says, oh, by the way, we still think there is a preferred frame so we'll just say that everything SR concludes, we would have concluded too if we just had enough time to figure it all out (but I even doubt that).
As it's completely off-topic just one remark: your comment reminds me of Bjerknes "The incorrigible plagiarist", only your view is opposite to his - and I disagree with both.
 

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