Mathematical Obscurities in Special Relativity

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I think you should re-read the problem, you are reading things into it that arent there. The $2 is left on the table, period. Nowhere does it say that the salesmen made any attempt to split it. Even if it is left there for all eternity and not pocketed by the innkeeper or whoever that does not change the problem. The missing dollar illusion arises from the inappropriate summing of debits and credits in the accounting of the transaction. In that, Mark's version is no different than any other.


JR
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If the salesmen were given $5 back, why would they think they paid $27 for the room? What is $30 - $5? And if the Innkeeper and his wife were also aware of the fact that $5 were refunded to the salesmen, from who's viewpoint
is there a missing dollar?

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by MarkVitrone</i>
Arguments about SR and discrepancies in the mathematics remind me of a story if you all will indulge me:
Three travelling salesmen break down and are forced to spend the night at a small town inn. They go in the innkeeper tells them, "The rooms are $30". Each man pays $10 and they go up to the room. The husband of the innkeeper says to her, "Did you charge them the full amount? Why not give them five bucks back since their car is broken and they hadn't planned to stay here." She then brings the men five $1 bills and each man takes one while the other $2 rests on the table.
Originally each man paid ten dollars (10x3=30), now each man has paid nine dollars (9x3=27) there are $2 sitting on the counter (27+2=29). The last dollar disappears.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
<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>

No, I think you should reread the problem. If the salesmen were given $5 back, why would they think they paid $27 for the room? What is $30 - $5? And if the Innkeeper and his wife were also aware of the fact that $5 were refunded to the salesmen, from who's viewpoint
is there a missing dollar?
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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:

<b>The Salesmen </b>- 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). 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>The Innkeeper </b>- 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. If the salesmen leave the $2 for her, then she will calculate that they spent $30 - $3 = $27. 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.

<b>The Innkeeper's husband </b>- As far as he knows the salesmen gave his wife $30 for the room and he told her to refund $5, so $30 - $5 = $25. If the salesmen don't keep the $2, he's screwed, because his wife has just pocketed $2 that he's never going to see []


JR

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, then it seems to me that mass and gravitational mass will both actually increase for the same reason. In this case the gravitational fields in very rapidly spinning objects of stellar size and above will tend to be highest towards the outside where absolute velocities are highest. This may lead to a situation where such objects can stabilise in the form of spinning squashed donuts, which radially may act as 'black holes' and axially as sources of relativistic jets. Is there any evidence that would refute this hypothesis that would resolve the current paradox of how relativistic jets emerge from objects with the mass/size indicative of a black hole?

Tony J Carey

<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
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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.

<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
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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.

"..... if their motion is straight-line and unaccelerated, they think they are “resting” and not moving at all."

You might wish this to be true, but the experimental astronomical evidence is in conflict with this. The measured existence of a transverse Doppler effect in the jets of stellar object SS 433 (see Sc Am Oct 1980, article by Bruce Margon) that are moving with a constant absolute velocity in relation to the universal black body frame of reference of 0.26 c shows that atomic time is slowed by passage through space, which is therefore not nothing and has, amongst its properties the ability to interact with matter at high velocities, increasing the mass of atomic particles and thereby slowing down their rates of internal oscillation that determine atomic time.

Particles moving at high absolute velocities in relation to the black body frame of reference, therefore do not "think" they are resting, but experience some force due to their interaction with the quantum vacuum/ether/neutrino gas (Their are billions of these little fellows going through us and the earth every second and they are now recognized to have mass, so they are good candidates for an ether, or significant ether constituent)

I agree that Einstein's theory should be replaced by that of Lorentz, who assumed that real changes took place when objects were moved at different absolute speeds relative to the ether. The physicist Joseph Levy who, with a reference to his book, can be found through Google, has worked out some of the relevant theory. As Essen said in his 1968 letter to nature entitled 'The Error in the Special Theory of Relativity (Vol. 217, January 6, p.19) "Einstein stressed the tentative nature of his theory and the need for experimental checks". Until SS 433 there were no measurements on unaccelerated objects in force-free space(of course galactic gravitational fields permeate all space, so in an absolute sense nothing is totally force-free).

With best wishes
Yours absolutely,
Tony J Carey

Tony J Carey