Mathematical Obscurities in Special Relativity

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by TonyJCarey</i>
<br />With best wishes
Yours absolutely,
Tony J Carey

Tony J Carey
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I agree with you. Notice that I explicitly said, in reference to SR theory:

“I think it’s pretty obvious that moving clocks that aren’t accelerating and that are only moving “relatively” and <b><u>that aren't moving through fields</b></u> can’t possibly “slow down” due only to “relative motion”, since there is no force place on the clocks and since, as far as they are concerned, if their motion is straight-line and unaccelerated, they think they are “resting” and not moving at all.”

What you have described is Lorentz theory, not SR theory, since there are no fields and no “ether” in SR theory.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by 1234567890</i>
<br /><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">
I reposted the story above for reference.
I don't know what the salesmen are thinking and nor do you, since the story is told as a third person narrative and the author has not provided that insight. If you want to know how much the salesmen have spent from the point of view of the various characters, here is your answer:

The Salesmen - They originally spent $30, $10 each. The Innkeeper gave $5 back to them, and they each took $1 and left $2 undistributed. If they later intend to split the $2 three ways then David is correct. But the story provides no evidence that this is their intent so I don't see how this interpretation is justified, especially since in all other versions of the story they do not keep the $2. The only thing we know for sure is that at the end of the story the $2 is left on the table. If the salesmen intend on keeping the $2, then they will calculate that they have paid ($10 - $1) * 3 - $2 = $25 (This is the calculation in the story, but the $2 is incorrectly ADDED instead of being SUBTRACTED which leads to the illusion that $1 has disappeared).<b><u> If the salesmen intend to leave the $2 as a tip or something, then they will calculate that they have spent ($10 - $1) * 3 = $27 </b></u>.

The Innkeeper - She receives $30 from the salesmen and then gives $5 back to them at her husband's insistence. If the salesmen keep the $2, then she will calculate that they spent $30 - $5 = $25. <b><u> If the salesmen leave the $2 for her, then she will calculate that they spent $30 - $3 = $27. </b></u>. These numbers agree with what the salesmen calculate in both cases and demonstrate that the final disposition of the $2 is immaterial to the problem.


jr
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

Read the underlined parts in your explanation. What is $27 + $2?
Here you repeat the error that led to the missing dollar
in the orignal problem. Apparently the $2 is not so irrelevant.

The original version was successful in tricking the reader into
believing $27 was spent by the salesmen because the focus
was placed on the $3 they received from the bellgirl. In Mark's
version, the reader is always mindful of the $5 refunded to
the salesmen and he gave no cause as to why the reader
should ever think the salesmen paid $27 for the room. And
as you demonstrated above, the $27 amount is necessary to
create the confusion leading to the missing dollar.
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I never said the $2 was immaterial to the trick - it is essential, only that the <b>final disposition</b> of the $2 was immaterial to solving it correctly. I don't understand your point. The accounting trick that leads to the "missing dollar" is the same in all versions of the story.


JR

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by 1234567890</i>
<br /><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by jrich</i>
<br /><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by 1234567890</i>
<br /><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">
I reposted the story above for reference.
I don't know what the salesmen are thinking and nor do you, since the story is told as a third person narrative and the author has not provided that insight. If you want to know how much the salesmen have spent from the point of view of the various characters, here is your answer:

The Salesmen - They originally spent $30, $10 each. The Innkeeper gave $5 back to them, and they each took $1 and left $2 undistributed. If they later intend to split the $2 three ways then David is correct. But the story provides no evidence that this is their intent so I don't see how this interpretation is justified, especially since in all other versions of the story they do not keep the $2. The only thing we know for sure is that at the end of the story the $2 is left on the table. If the salesmen intend on keeping the $2, then they will calculate that they have paid ($10 - $1) * 3 - $2 = $25 (This is the calculation in the story, but the $2 is incorrectly ADDED instead of being SUBTRACTED which leads to the illusion that $1 has disappeared).<b><u> If the salesmen intend to leave the $2 as a tip or something, then they will calculate that they have spent ($10 - $1) * 3 = $27 </b></u>.

The Innkeeper - She receives $30 from the salesmen and then gives $5 back to them at her husband's insistence. If the salesmen keep the $2, then she will calculate that they spent $30 - $5 = $25. <b><u> If the salesmen leave the $2 for her, then she will calculate that they spent $30 - $3 = $27. </b></u>. These numbers agree with what the salesmen calculate in both cases and demonstrate that the final disposition of the $2 is immaterial to the problem.


jr
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

Read the underlined parts in your explanation. What is $27 + $2?
Here you repeat the error that led to the missing dollar
in the orignal problem. Apparently the $2 is not so irrelevant.

The original version was successful in tricking the reader into
believing $27 was spent by the salesmen because the focus
was placed on the $3 they received from the bellgirl. In Mark's
version, the reader is always mindful of the $5 refunded to
the salesmen and he gave no cause as to why the reader
should ever think the salesmen paid $27 for the room. And
as you demonstrated above, the $27 amount is necessary to
create the confusion leading to the missing dollar.
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
I never said the $2 was immaterial to the trick - it is essential, only that the <b>final disposition</b> of the $2 was immaterial to solving it correctly. I don't understand your point. The accounting trick that leads to the "missing dollar" is the same in all versions of the story.


JR
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Well, when the $2 was given as tip to the Innkeeper, it made
you miscalculate the total amount the salesmen spent on
the room so apparently the final disposition of the $2 is
not so irrelevant either. Btw, do you have a proof
for how $30 - $2 = $30 - $5?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
If they keep the $2, they spent $25 total, all of it on the room. If they don't keep the $2, they spent $27 total, $25 for the room and $2 in tips. This is exactly what I said before. I still don't see where I miscalculated anything or what your point is.



JR

David wrote: "What you have described is Lorentz theory, not SR theory, since there are no fields and no “ether” in SR theory."

David
I am glad we are in basic agreement. However, I think it is worth making two points to check that we are in full agreement:
* What I described in the case of SS 433 was NOT any theory. It was an observation of the physical reality of our universe. What I think we are in agreement about is that it is Lorentz's theory rather than SR theory that best explains the physical reality of SS 433's transverse doppler effect.
* However, the core of the Twin Paradox and the reason that there is SO much difficulty in getting general agreement about this whole area is that the SR people can argue that Einstein, in his 1905 paper predicted that moving clocks run more slowly "Thence" (i.e. from the theory he had just expounded, which takes no account of acceleration, gravitation or any difference at all between the clocks except their state of uniform motion) "we conclude that a balance-clock at the equator must go more slowly than a precisely similar clock situated at one of the poles under otherwise identical conditions". Dingle (1972, Science at the Crossroads) followed this quote with his question:
"Applied to this example, the question is: what entitled Einstein to conclude FROM HIS THEORY that the equatorial, and not the polar, clock worked more slowly" No one has ever been able to give a satisfactory answer to Dingle's question.
As Essen (Nature, 1968) and others have pointed out there never was a Twin Paradox because, as Essen wrote: "The result given by Einstein does not follow from" (the round trip thought)""experiment" but from an assumption made implicitly that the clock that does the round trip is actually going slower than the one regarded as stationary and does not simply appear to be going more slowly as viewed by the stationary observer". PARADOX RESOLVED ?
Therefore, Einstein's prediction about moving clocks does not follow from his postulates - an error that Essen suggests he would not have made had he used four symbols, instead of just the two symbols in the paper, to represent four different quantities.

Are we in agreement about these two points?
Best wishes,
Tony
(Carey)

Tony J Carey

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by TonyJCarey</i>
<br />
Tony J Carey
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My point of view about the SR theory is that Einstein had no physical “forces” that could slow down any of his clocks, since he left out the fields and acceleration, and the motion was just “relative”. So, either or both “systems” could be considered to be either moving or stationary, or both moving at the same speed.

I think he mentioned the clock at the equator because that was the fastest he could think of a clock moving on earth, i.e. about 1,000 mph. I don’t think he had any ideas about gravity fields or centrifugal force at that time. I think he was thinking of 1,000 mph as compared to 0 mph. But, again, he had no force placed on his clock that could slow it down.

He got the clock slow-down idea directly from Lorentz’s 1895 book, which I have a copy of. His SR paper was an attempt to duplicate the best ideas in the book but leave out the fields and the “ether”. So, while Lorentz had the “ether” acting like a “field”, Einstein just left out the “ether” and “fields” altogether, and he had the slowdown due only to a mystical “kinematical” effect that he postulted is supposed to take place at high “relative” speeds. But, of there is no pressure or force on a clock at slow relative speeds, then there isn’t going to be any force on the clock at high relative speeds either. There is nothing in the SR theory that could cause any clock to slow down.

Are you aware that he modified the theory in 1918 and converted it over to his GR theory by adding acceleration, a gravity field, and atomic clocks? The SR theory actually disappeared as of his 1918 paper. There hasn’t been an SR theory since 1918. There is only Lorentz theory and GR theory.

As far as his “moving clocks” going slower in the SR theory, he actually sets the rates of the clocks himself, or he has the “moving observers” do it, so they will measure “c” as the speed of light, as measured in thier system by those clocks. In the 1905 SR theory, the clocks don’t “slow down” due to the motion, they “slow down” because someone sets them to run slow. He requires them to be set to run low.

Note this line in the paper:

“Further, we imagine one of the clocks which are qualified to mark the time t when at rest relatively to the stationary system, and the time t’ when at rest relatively to the moving system, to be located at the origin of the co-ordinates of k, <b><u>and so adjusted that it marks the time t’</b></u>.”

See?

He purposely “adjusts” the clocks to run slow so they will follow all of his postulates.

After so much criticism, and especially after he repeated some of his same errors in his 1916 book, he felt compelled to make the necessary changes in his 1918 paper. Many physicists and professors have been ignoring that paper for the past 86 years. I don’t think Essen or Dingle knew about it. It was translated into English only in the late 1980s.

David
Thanks for all that background. I was aware of the 1918 GR theory.
Following the vindication of the Lorentz approach through the SS 433 observations, what I think we now need is a general theory based on Lorentz's 1904 paper. In line with my earlier hypothesis, such a theory will, I expect, generate the relevant mathematics to predict the squashed donut shapes for relativistically spinning astronomical objects, that seem to be intuitively possible if gravitational as well as inertial mass increases with absolute velocity.
Best wishes,
Tony

Tony J Carey