Re: twin patadox question

On Thu, 01 Sep 2005 18:19:04 +0200, Harry wrote:

> But sorry, I didn't show him a good method in order to waste my time
> on arguments.

Any argument about what "the reason" is for an observed effect can end
in a semantic swamp if one isn't careful, and that's particularly true
in discussions of special relativity.

But there's actually a point to this particular semantic argument,
though it's buried rather deeply.

If we try to look at a homebody/traveler problem from the point of
view of the _traveler_, then the question of acceleration typically
becomes more interesting. One could divide these problems into two
classes. In the first class, all clocks are inertial throughout. That's
what the OP discussed.

In that case, the question "Who experienced more elapsed time?" is
really ambiguous: the answer depends on the choice of reference
frame. If you select the reference frame of some particular clock,
then all the other clocks will seem to have been running slower
throughout the problem. Since no two clocks ever meet twice, there's
no unambiguous way to resolve it.

On the other hand, if at least one clock accelerates and eventually
meets another clock for a second time, there's an unambiguous answer.
And as soon as we look at it from the point of view of the clock which
accelerated we see that acceleration does have a significant effect:
it caused the accelerating clock to frame-hop.

Whether the acceleration is instantaneous or smooth, when one views
the problem from the point of view of the accelerating clock, one
finds that the acceleration and associated frame-hopping causes all
clocks toward which the acceleration vector is directed to seem to run
fast during the acceleration.

For two clocks to meet twice, one must accelerate toward the other.

You can obtain the answer by looking only at inertial frames, but
most people are left with a nagging feeling that there was something
left out. If a clock which I see as moving is always running slower
than my clock, how can it end up showing a time ahead of my clock?
The answer is that it doesn't "always" run slower than my clock; when
my frame of reference is accelerating, clocks ahead of me "run faster"
than my clock.

That was a good part of the point I was trying to make.

[SAL:]
>> Please explain how this example, in which one clock does accelerate and
>> the other does not, supports your assertion that acceleration has
>> nothing to do with the twins paradox.
[Harald:]
> Please explain why you thought it should do so.

I believe I just did.

[Harald:]
> That was exactly my point: that indeed acceleration itself does not
> directly bring about the change of age. Don't you know how to
> distinguish between the two?

Between which two? Acceleration and speed? Something which should be
part of a complete explanation but which isn't the proximate cause?
Or some other "two"?

> According to the equations it's the difference in speed that is at
> cause, and according to you it's "the changed path of the geodesic"
> - which if you ask me, belongs to GRT.

I didn't ask you what you thought it was proper to discuss in SR, and
if you feel geometric discussions of the behavior of flat manifolds
are "improper" topics of discussion, frankly, I don't care.

As long as there is a universal frame in which the metric is Lorentzian
the model remains that of SR, regardless of the particular frame of
reference from which we choose to view it.


> Of course I have no problem with that comment if it boils down to
> the same thing as a change of speed...

You may view it that way as long as you stick to inertial frames.

--
Nospam becomes physicsinsights to fix the email

.

Relevant Pages

  • Re: Twin Paradox paper available
    ... >>use of an inhomogeneous Lorentz transform (for frame S''). ... > Acceleration breaks the symmetry of who ages faster. ... No clock anomaly is ... Acceleration defines which reference frame takes ...
    (sci.physics.research)
  • Re: Twin Paradox paper available
    ... >>use of an inhomogeneous Lorentz transform (for frame S''). ... > Acceleration breaks the symmetry of who ages faster. ... No clock anomaly is ... Acceleration defines which reference frame takes ...
    (sci.physics)
  • Re: Simple Sagnac
    ... The use I made of relativity ... we know that acceleration, ... With Einstein's SR clock syncing provides one and only one time ... coordinate for a given location in a frame. ...
    (sci.physics.relativity)
  • Re: The concept of time contractrion in special relativity
    ... >> If the frame of reference is NOT inertial, ... A's frame of reference is NOT inertial. ... A has a constant acceleration a, ... >> t be the time of clock A while t' is the time of clock B, ...
    (sci.physics.relativity)
  • Re: Uncle assAl: (SR) Lorentz t, x = Intervals
    ... > According to your argument, MCIFs are sufficient to resolve the issue, ... let's let the B clock remain at rest in lab frame ... > During acceleration from rest, clock A intercepts n waves corresponding ...
    (sci.math)