Paradoxes in relativity, and an absolute reality

[harrylin]

[..] 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 traveling 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.

 

[harrylin]

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. Was my post to succinct perhaps?

 

[ghwellsjr]

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.

 

[ghwellsjr]

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).

 

[harrylin]

[..] 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.