🚀 go-pugleaf

"Wolfgang G. Gasser" <z@z.lol.li> wrote in message
news:ep2hvi$qli$1@atlas.ip-plus.net...
> Adherents of LET often make statements such as "Lorentz ether theory
> does not know any paradoxes of relative motion" [1]. Even some of
> those who adhere to Special Relativity use LET in order to defend
> SR from paradoxes. They argue that LET, based only on time dilation
> and length contraction, makes the same predictions as SRT without the
> seemingly paradox SR simultaneity concept.

Your summary is a bit incomplete: it omits increase of inertia with speed as 
well as the fact that conventionality of simultaneity is necessary in any 
interpretation. BTW, what you call "LET" is simply the earliest 
interpretation of SRT, and thus it's a bit historical.

> The perported equivalence between SR and LET however stems from an
> astonishingly huge error, exemplified in this text [2]:
>
> "... two mirrors in parallel motion, with a pulse of light bouncing
>  between them. In this case the motion of the mirrors actually does
>  diminish the frequency of bounces, relative to the stationary ether
>  frame, because the light must travel further between each reflection.
>  Thus the time intervals 'expand' (i.e., dilate). Given this time
>  dilation of the local moving coordinates, it's fairly obvious
>  that there must be a corresponding change in the effective space
>  coordinate (since spatial lengths are directly related to time
>  intervals by dx = v*dt). In other words, if an observer moves at
>  speed v relative to the ground, and passes over an object of length
>  L at rest on the ground, the length of the object as assessed by the
>  moving observer is affected by his measure of time. Since he is
>  moving at speed v, the length of the object is v*dt, where dt is the
>  time it takes him to traverse the length of the object - but which
>  "dt" will he use?  Naturally if he bases his length estimate on the
>  measure of the time interval recorded on a ground clock, he will
>  have dt = L/v, so he will judge the object to be v*(L/v) = L
>  units in length. 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 earth's atmosphere appears contracted to 
a muon (if a muon had brains). Where do you claim that he made a mistake?

> 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)

> - 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)

> 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").

> In
> LET (inasfar as it is not "a clever restatement" of SR)

You have it upside down...

> , contraction
> results from the motion through the ether [3], so contraction of the
> ether with respect to moving objects is impossible.

The "astonishingly huge error", as you call it, is all yours.

Cheers,
Harald

> References:
>
> [1] The Twin Paradox in Special Relativity and in Lorentz Ether Theory,
>    http://redshift.vif.com/JournalFiles/V10NO3PDF/V10N3KHO.pdf
> [2] Reflections on Relativity, 1.5 Corresponding States,
>    http://www.mathpages.com/rr/s1-05/1-05.htm
> [3] "... assuming that the electron, deformable and compressible, is
>    subject to a kind of exterior constant pressure whose effect ..."
>    Poincar�, June 1905, see:
>    http://groups.google.com/group/sci.physics/msg/4e5049b2c4a76432