🚀 go-pugleaf

"Wolfgang G. Gasser" <z@z.lol.li> wrote in message 
news:ep6cfd$3uk$1@atlas.ip-plus.net...
> :: = Wolfgang G. Gasser in news:ep2hvi$qli$1@atlas.ip-plus.net
> :  = harry in news:1169540586_1789@sicinfo3.epfl.ch
>
> ::  "...             However, if he uses his own effective time as
> ::  indicated on his own co-moving transverse light clock, he will
> ::  have dt' = dt * (1 - v^2)^1/2, so the effective length is
> ::  v * [(L/v) * (1 - v2)^1/2] = L * (1 - v^2)^1/2. Thus, effective
> ::  length contraction (and no transverse expansion) is logically
> ::  unavoidable given the effective time dilation."
> :
> : What problem do you have with that? I think that the author of
> : mathpages is (as usual) correct on the math.
>
> The author is discussing as possible explanations of the Michelson-
> Morley experiment: "transverse expansion" versus "longitudinal
> contraction" of "the material comprising Michelson's apparatus".
>
> In order to decide this question, he makes a (consistent) reasoning
> (starting from time dilation) leading to the conclusion that the
> ether contracts wrt a moving object. Using this contraction of the
> ether, he decides the open question in favour of "longitudinal
> contraction" of Michelson's apparatus (and against "transverse
> expansion").

I did not interpret his writing that way - instead I interpreted it as I 
indicated in my next sentence.
For sure an "ether contraction" interpretation would not work and you would 
be right to go against it.

> However, the author does not notice, that contraction of the ether
> wrt to the apparatus is the EXACT OPPOSITE of contraction of the
> apparatus wrt the ether. The only way to get a contraction of the
> ether wrt to moving objects is an expansion of the moving objects
> (and their rulers) wrt the ether. See [1]. But e.g. Tom Roberts
> claims (or at least claimed in January 2000) that "there is never
> any sort of 'Lorentz expansion'" [2].

See above.

> : The earth's atmosphere appears contracted to a muon
>
> and the muon appears contracted to the earth's atmosphere.

Exactly.

> However, inasfar as the atmosphere appears contracted to the muon,
> the muon itself is expanded wrt the atmosphere,

Uncontracted you should mean; and only in the rest-frame of the muon...

> and inasfar the
> atmosphere appears contracted, the muon is expanded.

Not so: moving objects appear to *contract* in SRT, while proper lengths are 
unaffected.

> This reciprocal contraction/expansion in SR

See above: you must be confused...

> is only possible
> if we adopt Einstein's simulaneity concept, where v/c^2*x of
> the time transformation is as 'real' as v*t of the x-coordinate
> transformation:
>
>  x' = gamma * (x -     v*t)
>  t' = gamma * (t - v/c^2*x)
>
> The claim that v/c^2*x is only a convention has no more
> justification than the claim that v*t is only a convention.

The convention is to declare the frame of choice to be "in rest".

> :: Generally accepted premisses of LET are:
> ::
> :: - the ether is rigid
> :: - moving time dt' dilates/expands with respect to ether time dt:
> ::   dt = dt' * gamma
> :
> : Yes, as measured in a "stationary" system:
> :
> :   dt' = dt/gamma  (a moving clock appears to slow down; thus a really
> :                    moving clock really slows down)
>
> Correct. Slowing down corresponds to EXPANSION of time intervals.
>
> :: - moving length dx' in direction of motion contracts wrt the ether:
> ::   dx = dx' / gamma
> :
> : No, not in a "stationary" system:
> :
> :   dx' = dx/gamma  (a moving rod appears to contract; thus a really
> :                    moving rod really contracts)
>
> Here also you are a victim of the confusion (resp. fatal error) I'm
> dealing with. According to SR,  dx' = dx/gamma  means contraction
> of rest-frame distances wrt the moving-frame.

dx = dx'/gamma is valid in S' only. It's an often.made mistake of 
contributors to this group to mix reference frames, which implies making 
transformation errors. One should not mix values of miles and and km in one 
calculation.

> An ether distance of
> e.g.  dx = 1 light-year  is contracted to  dx' = l LY / gamma  in the
> moving-frame.

"ether" and "is contracted" are incompatible, just as "proper" and 
"contracted" are incompatible. You could say: a rest frame distance of e.g. 
dx = 1 light-year appears to be contracted to  dx' = l LY / gamma  in the 
moving-frame.

> However, you correctly have deduced your wrong interpretation of
> dx' = dx/gamma  from premisses which are assumed to be valid:
>
> (1) In LET there is neither expansion of moving objects nor
>     contraction of the ether.
> (2) dt' = dt/gamma

(2) is only valid in S.
In S': dt' = dt*gamma. Just check the textbooks -they also explain why 
(hint: simultaneity).

> (3) dx'/dt' = v = dx/dt

> From (2) and (3) you conclude  dx' = dx/gamma

Only in S.

> and according to (1)
> contraction of the moving object is the only valid interpretation.

Indeed: "the moving object" means dx' as determined in S.

> So your point of view no more justifiable than the one of 'rotchm' [3]
> who came to the opposite conclusion:
>
>  "Your quoted example is wrong. It should be the other way."
>  "The author ... has either screwed up or ..."

I think that both of you misunderstand what the author of mathpages wrote.

> The existence of contradicting conclusions in a theoretical system is
> a clear indication of inconsistence.
>
> :: However, the basic reasoning exemplified in the above quoted text
> :: implies instead of contraction of moving objects the exact contrary:
> :: contraction of the rigid ether with respect to moving objects.
> :
> : No, in SRT - no matter what your interpretation - the observations are
> : reciprocal. That's mentioned in your ref. 2 as well as in your ref. 3
> : ("These transformations, ..., must form a group").
>
> Do you mean by "the observations are reciprocal" that rest-frame
> distances contract in the same way wrt a moving-frame as the
> corresponding moving-frame distances wrt to the rest-frame?

Do you mean by "distances contract", not the objects themselves but the 
measures thereof? Then indeed, that's well known to be the case.

> If yes,
> do you suggest that this kind of reciprocity somehow follows from
> the group-property of the Lorentz transformation? If yes, how?

Sure - it means that the inverse transform (with v' = -v) has the same form, 
so that observers in both frames measure the same effects.
Most textbooks give the derivation. For those who don't trust that or want 
to see how that works in practice, I also gave an example with numbers:

http://tinyurl.com/2xcga8

See also the long recent thread where people tried to explain that to Ken 
Seto ("Question on the LT and the inverse LT").

Cheers,
Harald

> Cheers, Wolfgang
>
> [1] Simulation of Special Relativity by LET:
> 
> http://groups.google.com/group/sci.physics.relativity/msg/9d447bb45109a585
> [2] http://groups.google.com/group/sci.math/msg/171c14a33690331b
> [3] news:1169478732.985047.109090@q2g2000cwa.googlegroups.com
>
>