sci.physics.relativity

Rudolf Drabek skrev:
> On 13 Feb., 21:57, "Paul B. Andersen"
> <...@> wrote:
>> Rudolf Drabek wrote:
>>> ad Java applet: the distance scale is constant in "Running B's view".
>>> Is that correct?
>> You are obviously referring to the "Twins" Java :///pb_andersen/
>>
>> It depend on what you mean by "constant".
>> The distance scale in the "Run B view" is the distance in B's rest frame.
>> When B is accelerating, it is at any time the distance in the inertial
>> frame where B is instantly at rest.
>> Note that the "Speed of A measured by B" is the rate of change of the distance to A.
>> When B is accelerating towards A at turn-around, B will continuously
>> "change his opinion about the distance to A" (because he changes his opinion
>> about simultaneity), with the rather weird consequence that A seemingly
>> moves _away_ from B at several times the speed of light.
>
> It can be calculated simply with Newton, because he did'nt know about
> the axiom c=constant.

Meaning what?
This phenomenon can certainly not be calculated with Galilean
relativity. According to this, the speed of A observed by B
would always be identical to the speed of B observed by A.

But you probably meant that this speed could exceed c
if the acceleration is high enough, and is lasting long enough.
(1 c per year (~1g) for longer than one year would obviously do it)
True, but this is a fundamentally different phenomenon.

>> This illustrates that "nothing can go faster than c" isn't valid
>> in accelerated frames.
>
> I'm working on that point.

Let's say that the distance to Alpha Centauri is 4 LY, measured
in the rest frame of the Sun.
But if are moving towards AC at the speed in the Sun frame,
the distance to AC will be only 2 LY, measured in your rest frame.
So if you are accelerating towards AC, you will measure the distance
to AC to progressively shorten. If we define 'the speed of AC' as
the rate of change of the distance to AC in your rest frame, you
are measuring AC to move at high speed towards you.
There is no upper limit to this 'speed'.
It is an artefact of your accelerated frame, because you are
continuously changing your opinion of what the distance to AC is.
Speed is not well defined in accelerated frames.

>
>> Note however that the _local_ speed never exceeds c.
> Yes, clear. See just above.
>
>> The local speed is something like this:
>> The speed of A as it would be measured by an observer adjacent to A,
>> who is at rest in the inertial frame where B is instantly at rest.
>> Not easy to parse, maybe. :-)
>>
>> --
>> Paul
>>
>> http:///pb_andersen/
>
> Yes, you and I say the same, B'S view about the distance is changing
> during the trip, but the distance scale is constant in the applet, not
> reflecting that what B experiences as you write.
>
> Rudi


--
Paul

http:///pb_andersen/