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 />
Tony J Carey
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">


Tony,

You might want to order a copy of this book. This is the 1895 version of the full Lorentz theory, and it contains a lot of information that was later used by Einstein in his papers.

At this web address, you can click on “Preview Pages” and you will see three pages of the book.

[url] www.elibron.com/english/other/item_detail.phtml?msg_id=10017783 [/url]

Here is a page I copied from the book that shows where he introduced the Lorentz transformation. In his equations, p = v and V = c. He used the old German symbols for velocity and light speed.

http://im1.shutterfly.com/procserv/47b4dc32b3127cceb821b68ead3f0000001610

This is a very rare book today, and I think the website I linked you to is the only source for it. It needs to be translated into English, because this is the main basic fundamental Lorentz theory that Einstein copied so much. This is also the book in which Lorentz introduced slow “clock” rates. His “clocks” were basically atomic clocks. Einstein began replacing his mechanical clocks with atomic clocks in his 1911 paper. He finally removed mechanical clocks from the 1905 SR theory in 1918 and he added atomic clocks to his “moving” system, but Lorentz had already done that 23 years earlier in his 1895 book.

The 1905 SR theory was Einstein’s attempt to “correct” and “improve” on this 1895 Lorentz book, but Einstein left out all the acceleration and fields and wound up with no “forces” on any of his clocks, and also all his clocks were mechanical, not atomic. He later realized his errors and he added the fields and acceleration and the atomic clocks. Lorentz already knew this stuff since he had been writing about it since as early as 1892.

The 1904 Lorentz paper is just a slight extension to his 1895 book.

Einstein got all the publicity in the newspapers with his 1905 SR theory, because he used regular mechanical watches and clocks, and he made everyone think that it was “all of time” that slowed down in his “moving system”, but he was wrong. Mechanical clocks do not react to a Lorentz force like atomic clocks do. And it is not “all of time” that slows down, just the atomic oscillation rates and some atomic processes. But in reality, where an atomic oscillation slows down, a molecular vibration rate often speeds up. So while atomic “time” might slow down, “thermodynamic” time can speed up among the very same atoms and molecules. So it is not “time” that is slowing down, it is merely an atom experiencing a lower internal atomic oscillation rate. Biologists don’t even use “atomic time”, they use molecular “heat time”, i.e. “thermodynamic” time.

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

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. <b><u>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. </b></u>



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

Read the underlined part. If you still don't get it, I might
explain it again. Then again, maybe I won't.

1234567890,

I give up! What do you consider the correct answer? Please show your work.


JR

<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 />1234567890,

I give up! What do you consider the correct answer? Please show your work.


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

Nevermind, I apologize. I got stupid there for a minute.

1234567890,
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Nevermind, I apologize. I got stupid there for a minute.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
No sweat. It happens to me more frequently than I would like and usually at the point at which it will generate maximum embarassment.


JR

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by DAVID</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 TonyJCarey</i>
<br />If the physical reality is that moving clocks are actually slowed due to interaction with the quantum vacuum/ether/neutrino gas or whatever space actually is,
Tony J Carey
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

I think it’s pretty obvious that moving clocks that aren’t accelerating and that are only moving “relatively” and that aren't moving through fields 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.

However, atomic clocks apparently do slow down if they are moved through fields. But this is Lorentz theory, not Einstein theory.

Einstein got his clock “slow-down” idea from Lorentz’s 1895 book, in which Lorentz said that atoms moving through fields could slow down their oscillation rates.

Einstein mistook the oscillation rate “slow-down” for a full “time” slow-down in that moving system, and he also mistook the “cause” as being only the “relative motion” and not a motion through “fields”.

His 1905 paper is filled with flaws, which he gradually corrected as time went by, but he didn’t correct them in an obvious manner and he pretended that the 1905 theory continued to apply under “special circumstances”. Actually, it doesn’t apply under any circumstances. However, the Lorentz theory does apply, and it should replace SR, while SR should be totally disregarded. SR was based on Einstein’s misinterpretation of Lorentz theory.



<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">This is a good example of the real problems posed by Einstein's relativity. The essence of the problem is that we really don't know what time and space are. We don't even have a very good idea of how to analyse the problem because we have preconceived ideas concerning what we mean by time and space. Einstein used the old preconceived ideas of time and space derived from Newtonian mechanics and turned them around and showed that they lead to to a new vision of what they mean. But this Einsteinian interpretation leads to absurdities that create confusion. The result is that if we hold on to the Newtonian ideas we get the bizzare conclusions of Einstein. But this is mostly due to a sleight of hand in Einsteins mathematics which is not really rigorous. He kind of patched this up and covered up the confusion in general relativity. The real problem is that when you don't have a clear idea of what is meant by time and space or space-time you get the current confusion in concepts which result from these theories.

Another point is that I dont think Lorentz derived a time dilation in an 1895 book. What book are you citing here? I would like to look this up. My understanding is that Larmor was the first to derive a time dilation using a theory of the ether. This point is not clearly resolved for me. Most books make the incorrect claim that Einstein was the first to derive time dilation. But this is not correct.

The basic issue is the following. Does the derived time dilation reflect a fundamental property of time,ie, that time actualy slows down? This being opposed to the view that time remains the same but that the clock used to measure time is effected by the motion so that its calibration is changed to indicate a different time. In this case the clock reads slow because the physical process by which time is measured has changed such that the clock calibration relativer to a standard clock has been changed.The answer to this question depends upon whether time is conceived as an actual physical entity or as an artifical concept invented to explain the Newtonian laws of physics.

The anwser depends upon what you think time is. This is not at all a question which can be glibly answered as many textbooks like to do. Now of course, the same problem applies for space. We don't know what it is either.

There are two recent books that discuss these issues. One titled "The End Of Time", and the other "Nothingness". These summarise the current research on space and time at a popular level.