Re: Are SR effects real or not? Simplified case.



On Jul 12, 9:40 pm, Uncle Ben <b...@xxxxxxxxxxx> wrote:
On Jul 12, 5:28 pm, Dono <sa...@xxxxxxxxxxx> wrote:



On Jul 12, 12:30 pm, Uncle Ben <b...@xxxxxxxxxxx> wrote:

On Jul 12, 1:42 pm, "Sue..." <suzysewns...@xxxxxxxxxxxx> wrote:

On Jul 12, 11:59 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?

The contraction is just as real as the light particles
which Einstein did not win a Nobel prize for.

~The famous Lorentz transformation ensures that the velocity
of [inertially moving] light [particles] is invariant
between different inertial frames~http://farside.ph.utexas.edu/teaching/em/lectures/node109.html

<<The Nobel Committee avoids committing itself to the
particle concept. Light-quanta or with modern terminology,
photons, were explicitly mentioned in the reports on
which the prize decision rested only in connection with
emission and absorption processes. The Committee says
that the most important application of Einstein's photoelectric
law and also its most convincing confirmation has come from
the use Bohr made of it in his theory of atoms, which explains
a vast amount of spectroscopic data. >>http://nobelprize.org/physics/articles/ekspong/index.html

<< where $\epsilon_0$ and $\mu_0$ are physical constants
which can be evaluated by performing two simple experiments
which involve measuring the force of attraction between
two fixed changes and two fixed parallel current carrying
wires. According to the relativity principle,
these experiments must yield the same values for
$\epsilon_0$ and $\mu_0$ in all inertial frames.
Thus, the speed of light must be the same in
all inertial frames. >>http://farside.ph.utexas.edu/teaching/em/lectures/node108.html

IOW the string neither breaks nor slacks.

See also:

4-velocity and 4-accelerationhttp://farside.ph.utexas.edu/teaching/em/lectures/node115.html

Sue...

Uncle Ben- Hide quoted text -

- Show quoted text -- Hide quoted text -

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Dono: breaks
Sue: doesn't
Androcles: <snarl>

1:1 so far. (And you thought the question was too old!)

This is not a sports contest. Science shows the answer quite clearly.
Do you have a problem with the answer?- Hide quoted text -

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No, I have no problem with the answer. But I think the answer can be
explained much more simply than in the Wikipedia article or in the
sci.physics.relativity FAQ paper on the Bell paradox. I will post the
simple argument next weekend.

I was at MIT a year or so after the problem appeared in the Am. J. of
Physics. I was delighted with the short paper explaining the result,
because I had bet several of my colleagues a small amount that the
paper was correct and that I could persuade them of it with a simple
argument. Somehow none of them had the time to spend to settle the
question.

It happened that the editor of the AJP was on the faculty of the
physics department and later told us that the little paper had been
greatly delayed in publication because various reviewers were arguing
among themselves whether the result was correct. It took the
authority of respected specialists in relativity theory, special and
general, to beat down the sceptics!

I had had a pet peeve about physics textbook authors using language in
describing relativity thought experiments in terms like "appears to be
shortened" and "according to observer B" and the like. I preferred
language that says straight out that the length with respect to frame
A is shorter than the length with respect to frame B. Nothing about
"appearing" or involving observers and their human frailties. The key
word in my version is "IS", in place of "appears to be."

(All of this is about what the theory of special relativity says; not
about whether it is true or not. The theory says that moving clocks
run slow and moving meter sticks are shorter. It does not say anthing
about thoughts or illusions or mere appearances.)

That was a long time ago, but the question is far from settled in the
minds of many practicing physicsts of my acquaintance with endowed
chairs in famous universities, not to mention in the minds of physics
afficianados writing confidently in newsgroups. So I think it proper
to bring up the problem from time to time for the enlightenment of
subsequent generations.

Uncle Ben
Age 78



I think the wiki explanation is excellent. I don't care much for the
FAQ explanation.
.