🚀 go-pugleaf

:: = 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").

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].

: The earth's atmosphere appears contracted to a muon

and the muon appears contracted to the earth's atmosphere.

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

This reciprocal contraction/expansion in SR 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.

:: 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. An ether distance of
e.g.  dx = 1 light-year  is 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
 (3) dx'/dt' = v = dx/dt

From (2) and (3) you conclude  dx' = dx/gamma  and according to (1)
contraction of the moving object is the only valid interpretation.

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 ..."

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

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