🚀 go-pugleaf

harry wrote in news:1170327863_2682@sicinfo3.epfl.ch :

: Of course, you could say that in SRT one has an "expanded" view of the
: moving distance that is at any time next to one's ruler due to the
: apparent contraction of the moving system.

My impression is that our positions have converged at least a little.
And such a convergence of different beliefs should be a goal in any
discussion. Here I'll content myself with a revised version of the
contraction/expansion part of my previous posting.

Cheers, Wolfgang
________________________________________________________________________

Let us take a 6 m long (rest length) ruler moving at v = 0.8 c in
the ether, as described in the article:
http://groups.google.com/group/sci.physics.relativity/msg/9db6b5df54b79f1d
(See APPENDIX for my treatment/summary of the example)

In Lorentz ether theory the ether-length dx = 3.6 m of the contracted
ruler corresponds to physical reality. Nevertheless, a local "proper
length" of dx' = 6 m' is ascribed to the ruler. If we assume moving-
ruler simultaneity dt' = 0, we get from the Lorentz transformation:

  dx = gamma * (dx' + v*dt')  -->   dx  = gamma * dx'
                                        = (5/3) * 6 m' = 10 m

This ether distance of 10 m has a very concrete meaning. Let us assume
that along the whole length of the ruler are small flash lamps next to
each other. If they fire all at the same time (S'-simultaneity) then
the distance between the first and the last flash is 10 m in the ether.

However, the flashes do not appear at the same time in the ether
(S-simultaneity): at first appears the flash from the rear end, and
80/3 nano-seconds later the last flash from the front end. During
these 26.666 ns the ruler moves 6.4 m, so increasing the distance
from the contracted length of 3.6 m to the expanded of 10 m.

Let us further assume that the flash lamps fire at t' = 0 in red,
at t' = 25 ns' in blue, at t' = 50 ns' again in red, and so on.
Because the next firing always occurs, when the rear end passes the
ether position where the flash from the front end fired the last time,
this represents a measurement of ether distances using the ruler
length of 6 m'. In the ether this results in a light source apparently
moving at 0.8 c and changing after each a length unit of 10 m from
red to blue or inversely.

So it should be obvious that only inasfar (S'-simultaneity) as the
ruler expands from 6 m' to 10 m wrt the ether, ether distances can
contract wrt the ruler, e.g. from 6 m to 3.6 m'.

So in Lorentz ether theory, three basic length-unit changes can be
distinguished:

  1) Contraction of objects moving wrt the ether, caused by concrete
     physical effects
  2) Expansion of moving objects, caused by different durations
     (wrt ether simultaneity) of the movements of the different
     points of the moving objects
  3) Apparent contraction of the ether, resulting from the expanded
     length units of moving objects.

The expanded length of a moving object is physically real also
inasfar, as it is the sum of the paths of synchronization light
signals from the center to both ends. For an apparent contraction
of ether distances wrt the WHOLE moving object, it is therefore
required that the FRONT END of the contracted object moves
inertially long enough in the ether, so that ITS distance from
the rear end can increase from L/gamma to L*gamma.

Let us assume a ruler with rest length of 2 light years moving at
v = 0.9999995 c  (gamma = 1000). So the distances from the center to
each end are contracted to 0.001 LY wrt the ether. Ether distances
passed by synchronization light signals from the center to the rear
and to the front each are:

   to_rear  = 0.001 LY / (c + v) * c  =     0.0005 LY
   to_front = 0.001 LY / (c - v) * c  =  1999.9995 LY
                                         ------------
                                         2000.0000 LY

The physical expansion in the ether from the contracted 0.002 LY to
2000 LY is caused by constant MOVEMENT of the front, STARTING when
the rear after 0.0005 years receives the synchronization signal, and
ENDING 1999.999 years later when also the front receives the signal.
Such expansions by physical movement are a precondition for any
apparent contraction of ether distances wrt to moving objects.

As an accentuation of the thought experiment, let us ask what
happens if the 2 LY long ruler performs a circular movement with
an orbit of 2000 LY. In the ether, the length of the ruler is
contracted to 0.002 LY. As measured by the ruler, the orbit must
contract in the same way as local time is expanded, because
otherwise dx'/dt' does not result in v.

Thus the 2 LY' long moving ruler has to ascribe the same length
to the orbit as to itself: 2000 LY / gamma = 2 LY'. This means
concretely: under moving-ruler simultaneity', the ruler is expanded
over the whole 2000 LY of the orbit, and the front of the ruler is
next to the rear at the same time'.

________________________________________________________________________

APPENDIX:

A ruler with a rest length of 6 m passes at v = 0.8 c a rod of the
same length at rest in the ether.

The length dL' = 6 m' of the ruler is contracted by gamma in the ether:

   gamma = 1/sqrt(1-v^2/c^2) = 1/sqrt(1-0.8^2) = 5/3 = 1.666

   dL  =  dL' / gamma  =  6 m' / (5/3)  =  3.6 m

Time intervals dt' of clocks fixed on the ruler (x' = const) are
dilated/expanded wrt to the ether time:  dt = dt' * gamma

         ruler                                         --> v = 0.8c
  |--------+--------|               rod
                      |=============================|      v = 0
   < - - 3.6 m - - >   < - - - - -  6 m  - - - - - >
   < - - - - - - - - - -  10 m - - - - - - - - - - >

Clocks on both ends of the ruler are synchronized using a light signal
from the center of the ruler. In the ether system, the light signal to
the right clock (in front) needs

  1.8 m / (c-v) = 1.8 m / 0.2 c = 30 ns

and passes an ether distance of 30 ns * c = 9 m. The light signal to
the left clock (in the rear) needs only

  1.8 m / (c+v) ) 1.8 m / 1.8 c = 10/3 ns = 3.333 ns

and passes an ether distance of only 3.333 ns * c = 1 m. Thus in the
ether, the rear clock is ahead of the front clock by:

  time_offset = 30 ns - 10/3 ns = 80/3 ns = 26.666 ns

Wrt the dilated/expanded time of the moving clocks, the time offset' is
time_offset / gamma = 26.666 ns * (3/5) = 16 ns'.


 t'=0           t'=-16ns'
  |--------+--------|
                      |=============================|
Fig. 1


  t'=1ns'          t'=-15ns'
    |--------+--------|
                      |=============================|
Fig. 2

                    t'=10ns'           t'=-6ns'
                      |--------+--------|
Fig. 3                |=============================|


                                t'=16ns'           t'=0
                                  |--------+--------|
Fig. 4                |=============================|


                                                t'=25ns'             9ns'
                                                    |--------+--------|
Fig. 5                |=============================|


Let us define t' = 0 as the moment, the right clock of the ruler
passes the right end of the rod (Fig. 4). The left clock then
(ether simultaneity) indicates t' = 16 ns'.

The distance passed by the left clock of the ruler between Fig 1. and
Fig 5. is 10 m. During a movement of 10 meters a clock advances (local
time) by

  dt' = 10 m / 0.8 c * gamma = 10 m = (0.24 m/ns) / (5/3) = 25 ns'

In order to determine the proper speed v' as measured from the moving
ruler, we can use Fig. 4 und Fig. 5. The right end of the rod passes
at t' = 0 the right clock of the ruler, and at t' = 25 ns' the left
clock. So wrt the ruler, the right rod end moves dL' = 6 m' in
dt' = 25 ns', resulting in a proper speed of v' = dL'/dt' = 0.8 c.

In order to determine length contraction of the rod at rest wrt to
the moving ruler, we can take the left ruler end of Fig. 1 and the
right ruler end of Fig. 4, both at the same local time t' = 0. The
distance between these two ends is 10 m in the ether. And because to
these 10 m corresponds a proper length of 6 m', the 6 m long rod
contracts to 6 m' * (6 m / 10 m) = 3.6 m' wrt the ruler.
_______________

--  The Lorentz transformation today plays the role the principle
--  of circular motion played in the old (pre-Keplerian) astronomy