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

On Jul 12, 8:59 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

Here are the correct calculations :

http://en.wikipedia.org/wiki/Bell_spaceship_paradox#Analysis

.

Relevant Pages

  • Re: Are SR effects real or not? Simplified case.
    ... ships -- so light that it cannot affect the motion of the ships. ... acceleration is given by x=t*t in some units. ... $\epsilon_0$ and $\mu_0$ in all inertial frames. ...
    (sci.physics.relativity)
  • Re: Are SR effects real or not? Simplified case.
    ...  Let's tie a light string between the two ... ships -- so light that it cannot affect the motion of the ships. ... acceleration is given by x=t*t in some units. ...
    (sci.physics.relativity)
  • Re: Are SR effects real or not? Simplified case.
    ... Imagine two rocket ships at rest, one behind the other at a distance ... ships -- so light that it cannot affect the motion of the ships. ... acceleration is given by x=t*t in some units. ... But what about the string? ...
    (sci.physics.relativity)
  • Re: Are SR effects real or not? Simplified case.
    ... Let's tie a light string between the two ... ships -- so light that it cannot affect the motion of the ships. ... acceleration is given by x=t*t in some units. ...
    (sci.physics.relativity)
  • Are SR effects real or not? Simplified case.
    ... Imagine two rocket ships at rest, one behind the other at a distance ... Let's tie a light string between the two ... ships -- so light that it cannot affect the motion of the ships. ... acceleration is given by x=t*t in some units. ...
    (sci.physics.relativity)
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