sci.physics.relativity

Alen says...
>
>On Sep 15, 1:21 am, stevendaryl3...@ (Daryl McCullough)
>wrote:

>> No, both the moving frame and the stationary frame
>> calculate the same number T' for the time shown on
>> the observer's watch when the light signal reaches
>> him. All observers in every frame will calculate
>> the *same* answer.
>
>OK. T' is an invariant, and represents the proper time.
>Therefore the distance (1/2)gT' = D is independent of
>velocity, and is the same before and after acceleration.

I'm not sure what you are talking about here. The
distance between the rockets is, initially, D in the stationary
frame, and D/gamma in the moving frame. The distance after
acceleration is D in the stationary frame, and gamma D in the
moving frame.

>> Let's look at the scenario from the point of view of the
>> moving frame (the frame that is moving at speed v to the
>> right relative to the stationary frame).
>>
>> In the moving frame, we have the following
>> facts (according to SR):
>>
>> 1. The two rockets are each traveling at speed v to the *left*.
>
>How are the rockets traveling in the frame of
>the rockets?

The rockets don't *have* an inertial reference frame,
because they are *accelerating*. They start off at rest
in the stationary frame, and then accelerate so that they
are at rest in the moving frame.

There are two frames here. As measured in one frame,
the "stationary" frame, the rockets start off at velocity 0
and then accelerate so that they are travelling at velocity
v to the right.

As measured in the other frame, the "moving" frame, the
rockets start off at velocity v to the left and then
decelerate so that they are travelling at velocity 0.

>Is that a typo, or do I not understand
>what you mean?
>
>> 2. The distance between the rockets is D/gamma.
>
>Who says?

That's the prediction of Special Relativity. I'm not
trying to convince you that SR is true, I'm trying to
convince you that it is internally self-consistent.
Whether it is true or not is an empirical question.

>There is no possible way to set up a distance
>gD between rockets that are independently
>accelerated.

As I said, if you have two rockets initially
travelling at speed v to the left, and the rocket
on the right decelerates to v=0 *before* the rocket
on the left, then the distance between the rockets
will increase. There is no mystery here. That's
what happens, as viewed from the "moving" frame.

What's the explanation, from the point of view of
the moving frame, for why the right rocket decelerates
to v=0 before the left rocket? It's because both
observers fire their rockets at t=0 according to
their own watches, but their watches are out of
synch.

What's the explanation, from the point of view
of the moving frame, for why the watches are out
of synch? Well, you have to consider how the two
observers synchronized their watches in the first
place. There are two possible synchronization
techniques that might be used, and they both
lead to the same answer.

Technique 1: Light signal synchronization. Put a
light source half-way between the two observers.
At some predetermined time, simultaneous signals
are sent to each observer. When they receive the
signals, each sets its watch to t=0.

But from the point of view of the moving frame,
the two rockets are moving to the left at speed
v. So the signal reaches the right observer *before*
it reaches the left observer. So their watches are
not synchronized; the right observer's watch is slightly
ahead. The difference in their times is proportional
to the distance between them.

Technique 2: Slow clock transport. Both observers get together
on the right rocket. They synchronize their watches. Then the
left observer walks (possibly on a gangplank stretched between
the rockets) to his rocket.

But from the point of view of the moving frame,
the two observers are travelling to the left at speed
v. So their watches experience time dilation. During
the period that the left observer is walking to back
to his rocket, he is travelling slightly faster than
the right observer. So his watch experiences slightly
more time dilation. So when he gets to his own rocket,
his watch is slightly behind that of the right observer.
The difference in their times is proportional to the
distance traveled by the left observer.

So from the point of view of the moving frame, there
is no mystery: The distance between the rockets increased
because the right rocket slowed to a stop *before* the
left rocket. The right rocket slowed before the left
rocket because the right observer's watch was ahead of
the left observer's watch. His watch was ahead because
the synchronization procedure caused it to be ahead.

So there is no mystery about why the distance between
the rockets increased, as measured from the moving frame.

--
Daryl McCullough
Ithaca, NY