Re: Are SR effects real or not? Simplified case.
- From: Alen <alen1@xxxxxxxxxxxxxxx>
- Date: Mon, 14 Jul 2008 06:58:13 -0700 (PDT)
On Jul 13, 1:59 am, Uncle Ben <b...@xxxxxxxxxxx> wrote:
There is another thread in sci.physics.relativity entitled "Are
'observed' SR effects real?" I have trouble following the discussion,
as maybe you do too. I prefer to phrase the question in a way that to
me is much clearer.
The following thought experiment is an old problem, not original with
me, but I will not give any reference to it just yet. Just think
about it and draw your own conclusion. I'll post my explanation in
about a week.
*****************
Imagine two rocket ships at rest, one behind the other at a distance
x0, in intergalactic space. Let's tie a light string between the two
ships -- so light that it cannot affect the motion of the ships.
Let both ships be aimed at a distant galaxy that is on the line
connecting the ships. The ships synchronize watches and fire their
identical rocket engines at the same time.
Theorem: According to either classical mechanics or relativistic
mechanics, as the two ships accelerate, they keep a constant distance
between them with respect to (w.r.t.) their intial rest frames.
-------------------------------
Proof:
1) According to Newton, the position of a ship under constant
acceleration is given by x=t*t in some units. In an obvious notation,
the equations of motion are
x1 = t*t + x0,
x2 = t*t,
so
x1-x2 = x0.
2) According to Einstein, the position of a ship under constant proper
acceleration is given by x=cosh(t). The equations of motion will be
x1 = cosh(t) + x0,
x2 = cosh(t).
so
x1-x2 = x0.
QED
-------------------------------
But what about the string? When the ships are moving at almost the
speed of light, the string must have tried to contract a lot. But it
is constrained to stay at a fixed length x0. Sooner or later it will
reach its breaking point and will snap!
Do you believe this? Does the string break or not? Is the Lorentz-
Fitzgerad contraction real or not real?
Uncle Ben
The following Wikipedia article supposedly gives the correct
spacetime explanation, but the spacetime explanation cannot
possibly be correct, as I have argued before:
http://en.wikipedia.org/wiki/Bell_spaceship_paradox#Analysis
In the Wikipedia article illustration we have the spacetime
trajectory AA' for one acceleration, and BB'' for the other.
We thus have physically identical accelerations producing
results dependent on location, if the acceleration is viewed in
the context of the moving frame. This means that an experiment
that is physically unchanged will produce a different result in
the moving frame, simply my moving its location, thus making
the laws of physics dependent on location. Further, the events
A' and B'' have a relationship to one another specified by the
supposed nonsimultaneity effect between the frames. If the
initial distance AB is large enough, we will therefore have a
faster than light connection between the accelerations and
their results in the moving frame. Again, if we have a third
identical acceleration of a ship, C, placed initially to the left
of A, then both A' and B'' will be different, and C' will be the
same as A'. All this is completely impossible to reconcile
with the known working of the laws of physics, in that their
results are not dependent on location, and there is no faster
than light connecting principle by which experiments might
modify one another's results.
This is why I have argued before that the Lorentz transformation
equations cannot be simple spacetime coordinate transformations,
and SR cannot be a spacetime theory. I therefore suggested that
SR is properly a theory of light, rather than spacetime, and the
transformation equations are relationships created by the working
of light, and not of spacetime. It follows, also, that Lorentz
invariance is a feature of interactions involving lightspeed bosons,
and not a property of spacetime coordinate transformations.
The result, therefore, in the experiment, must be that AB ends
up as A'B', and the string does not stretch or break. The distance
A'B' will appear length contracted in the stationary frame only if
it is measured by sending a pulse of light along it, and not
otherwise.
Alen
.
- References:
- Are SR effects real or not? Simplified case.
- From: Uncle Ben
- Are SR effects real or not? Simplified case.
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