Dingle's Paradoxes

In my opinion the real question is why does special relativity predict any effect on the clock at all. It seems to me that if the Michaelson-Morley experiment gives a null result because time and space "adjust" in order to keep the speed of light the same in all moving reference frames, then there is no reason why there should be a change in the clock rate due to motion. In fact special relativity says that the proper time is the same in all reference frames. So clocks all run at the same rate. But for some puzzling reason the theory says that they appear to run slow to an observer in the opposite reference frame. This idea is peculiar and strange. Most books fail to make it clear how this happens.

The theory actually gives two different answers to this question. One answer says that the moving clock runs slow and points to the Ives Stillwell experiment as proof. But is this only an apparent effect or does time in the moving frame actually slow down? In 1905 Einstein claimed that moving clocks run slow because time slows down. Hence an astronaut lives longer. But then in 1907 he said that the slowing down of the clock was not real but apparent. Both answers are wrong but that doesnt remove the confusion.

In my view there should be no slowing of the moving clock in relativity because time adjusts to keep the rate an invarient constant independent of the state of motion of the clock. That is what relativity really means, that physics is independent of the state of motion.

This question was touched on in another thread at this web site. The was to see this is with three signal/observers going at different rates. One is at rest, one is moving at ~.5C and one is moving at~.9C All three send the signal at the same time. You can figure out who receives what signal and when the observer receives it and that should make the answer clear.

In 1907 J. Stark asked Einstein to write a review of relativity. One of the things Einstein tried to do was prove that Stark's observation of a redshift of canal rays was a prediction of relativity. But when Einstein tried to do this his theory developed in 1905 failed to give the desired result. The reason for this was that his 1905 theory was in error. It gave the result that the moving clock runs fast. Einstein tried to fix this up by changing the theory. He gave a proof that claimed to show that the moving canal ray atom redshift was "apparent". This is a peculiar result. The reason he says this is because his 1905 prediction said the spectrum should be blueshifted, ie the clock runs fast. So he changed the meaning of the symbols in the equations. The correct answer was that the rest frame reference atoms are redshifted, so the moving atom is blue-shifted, ie it runs fast. To make it appear that the theory predicted the correct result, Einstein changed the meaning of the symbol for the rest frame clock rate so that it appeared to be the observed rate of the moving clock. But the calculation is clearly wrong because what it really says is that the moving clock or atom runs fast or is blue shifted. This contradicts the experimental result. So we see that Einstein tried to fudge the theory to make it appear to be consistent with experiment. All this leads to the confusing reinterpretation of the theory which asserts that moving clocks only appear to run slow but they really dont.

The point here is that Einstein's 1905 theory predicted that the moving clock runs slow based on the fact that time is contracted in the moving frame. In the 1907 paper Einstein had to make a calculation that compared the frequency of the moving clock with the rest clock. This calculation showed the moving clock runs fast. This was contrary to the experimental result. Einstein fudged the theory to make it appear that the moving clock runs slow. He did this by a calculation that is wrong mathematically. But nobody checked the math he used so the theory was accepted even though it is based upon a mathematical mistake.

kc3mx,


<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by kc3mx</i>
<br />In 1907 J. Stark asked Einstein to write a review of relativity. One of the things Einstein tried to do was prove that Stark's observation of a redshift of canal rays was a prediction of relativity. But when Einstein tried to do this his theory developed in 1905 failed to give the desired result. The reason for this was that his 1905 theory was in error. It gave the result that the moving clock runs fast. Einstein tried to fix this up by changing the theory. He gave a proof that claimed to show that the moving canal ray atom redshift was "apparent". This is a peculiar result. The reason he says this is because his 1905 prediction said the spectrum should be blueshifted, ie the clock runs fast. So he changed the meaning of the symbols in the equations. The correct answer was that the rest frame reference atoms are redshifted, so the moving atom is blue-shifted, ie it runs fast. To make it appear that the theory predicted the correct result, Einstein changed the meaning of the symbol for the rest frame clock rate so that it appeared to be the observed rate of the moving clock. But the calculation is clearly wrong because what it really says is that the moving clock or atom runs fast or is blue shifted. This contradicts the experimental result. So we see that Einstein tried to fudge the theory to make it appear to be consistent with experiment. All this leads to the confusing reinterpretation of the theory which asserts that moving clocks only appear to run slow but they really dont.

The point here is that Einstein's 1905 theory predicted that the moving clock runs slow based on the fact that time is contracted in the moving frame. In the 1907 paper Einstein had to make a calculation that compared the frequency of the moving clock with the rest clock. This calculation showed the moving clock runs fast. This was contrary to the experimental result. Einstein fudged the theory to make it appear that the moving clock runs slow. He did this by a calculation that is wrong mathematically. But nobody checked the math he used so the theory was accepted even though it is based upon a mathematical mistake.
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">


When you look at the first papers by Einstein, it becomes apparent that a high degree of heuristics is involved, such as the definition of simultaneity.

But there are also other terms that are rather vague. For example, consider the definition of "v", the relative velocity of the two frames S and S'. This parameter is not carefully explained and has been pulled out of "nowhere". One would expect, with more rigour, that we really need to treat everything strictly local.

If we look at the Lorentz Transformation again, we have the map

T(v) --&gt; S'.

We all know that "v" is the velocity of S' as measured from S. However, it is rather "sloppy" to take this parameter as self-evident and assume right away the "v" is the same as measured from S'. Therefore, we need to treat this parameter completely local at first. We could say that "v" belongs to the parameter space of S, which we denote as P, our space of parameters.

Likewise, we can look at the inverse mapping

1/T(v'): S' --&gt; S.

We now define the parameter space P', where v' in P' is the velocity of the frame S as measured from S'. Note, we should not take v = v' at first: everything must be seen absolutely local. Thus, it is safe to say that one has enlarged the field of enquiry to the cartesian products S x P and S' x P'. From here, we can equip our spaces with additional properties for further developments.

The above is just a simple example which shows that SR is shrouded in heuristics and subjectivism. Furthermore, the highly non-trivial physical phenomena SR intends to explain are presented very lightly and are seen as self-evident. The damage has been done, and there is no turning back.

When you do the inverse mapping, don't you have to switch the sign of the v? V' = -v?

Also,
How do you write the Lorentz transformation in a function form? Seems
that originally, coordinates in the K frame r being transformed to
the K' frame so X' depends on v, x and t? X'(v,x,t) = (x-vt)/gamma?

So if you solved for x, you get x = (X'(v,t)+ vt) (gamma)?
But now X depends on t' and -v, no? So that
X(t',v',x') = (X' - vt') (1+v^2/c^2) ?

Anyways, Einstein rearranged the equation to make X dependent
on the values of X' in his argument on length contraction but set the t = 0, and I presume t'=0 as well. So in order
to claim length contraction, he had to assume simultaneity.
And his reverse transformation also seems inaccurate if he was actually mapping X' coordinates to the X frame.

How can you compare two lengths anyway if there is no remote
simultaneity in SR? A measurement made simultaneous in one frame
is not made simultaneously from another frame so it would be
like comparing apples with papayas.

BTW, why didn't Einstein just make a straight forward
transformation of X and t measurements to the K' frame?

123,
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">
When you do the inverse mapping, don't you have to switch the sign of the v? V' = -v?
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">


It depends, we can define v' = v if we regard these as parameters (magnitudes), which we could take as positive real numbers: The correct signs are incorporated when we really define the mapping T(v). So, we could define 1/T(v') merely as a function of v', the correct sign is embedded in the mapping. But in strict sense you are 100% correct, v' = - v in vectorial sense.


In the derivation of the LT, the locality has been broken to assume that v' = - v (vectors). But there is no apparant reason to do this, especially when we take everything local. Who guarantees that the observed speeds are identical in magnitude? In the derivation of the Lorentz Transformation, some classical arguments were used implicitly, which should have been explained. When one takes v' = -v, then explain why this is the case from a relative point of view.


<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">How can you compare two lengths anyway if there is no remote
simultaneity in SR? A measurement made simultaneous in one frame
is not made simultaneously from another frame so it would be
like comparing apples with papayas. <hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

Nicely put. Let us take a textbook example when measuring a rod stationary in S' having length L'= x2'-x1'. We write down:

x2' - x1' = g*(x2 - x1) - g*v*(t2 - t1)

t2' - t1' = g*(t2 - t1) - g*(v/c^2)*(x2 - x1)

Then they argue that t2 = t1 because the measurements are simultaneous in frame S. So L' = g*(x2 -x1) = g*L. But I thought that the observer in S', the frame for which the rod is stationary, can claim simultaneous measurements. After all, S' is the proper frame and the darn rod is moving in S. Moreover, how are measurements of a moving object being performed?

It is probably the case that measurements taken in one frame can be done simultaneous, but not between different frames.


<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">BTW, why didn't Einstein just make a straight forward
transformation of X and t measurements to the K' frame?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

Only Einstein knows.