Re: Variable speed of light

["John S. Denker" <jsd@MONMOUTH.COM>]

On 04/29/2003 04:36 AM, Mark Sylvester wrote:
> Oh I agree that SR should deal with the case you describe,

I should think so!

> it's just not so
> simple to decide which way to apply the time dilation

The way to deal with virtually all problems of this
ilk is to DRAW THE SPACETIME DIAGRAM.

PV applies time dilation correctly, as far as it goes.
The problem is, that's not a complete analysis.

> because neither time
> interval can be considered "proper".

I cannot figure out this clause.
This is a misuse of the word "proper".  Previous
notes in this thread have also misused the word.
"Proper" means something very specific in relativity.

> The proper time interval between two
> events in a given reference frame must be measured with one clock only,

Not true.
The conventional wisdom is diametrically opposite.
You want a "lattice of rods and clocks" in each
frame.  (The clocks are of course synchronized in
that frame.)  This allows the observers in that
frame to measure the time of an event _at_ that
event, using the colocated clock and no other.

> so
> the two events must occur at the same place in that reference frame.

SR must be able to handle widely separated events.

> The
> proper time will always be shorter than the delta t for the same pair of
> events measured in a different frame.

OK.  I assume this sentence uses the conventional
definition of "proper time".

> Your setting is more complicated (and
> therefore probably unsuitable as a thought experiment designed to clarify
> the situation)

More complicated than what?
The stipulated setting isn't complicated in any
absolute sense, and is 100% suitable as a thought
experiment.

There is however no notion of proper time involved.
The proper time for a photon to go from point A to
point B is zero, if the concept can be defined at all.

> but should yield to the Lorentz transformations.

I should think so!

> At 10:18 29/04/03 +0200, Pentcho Valev wrote:
> > I think the only reasonable
> > criticism of my solution should consist in offering a solution proving
> > that x/t = x'/t'.

I agree.

Originally Pentcho Valev wrote:

> > There is a version which could be a thought experiment and
> > which unequivocally shows that the speed of light is not
> > constant. In the rest (railway) frame the beam approaches
> > the train at a right angle so that, in the train frame, it
> > moves obliquely. Consider two events - the beam entering the
> > train and the beam leaving the train - registered in both
> > frames. Obviously x < x', where x is the distance the beam
> > travels between the two events in the rest frame and x' is
> > the respective distance in the moving frame.

OK down to here

>> The time
> > measured in the rest frame for the travel x is t, and that
> > measured in the moving frame for the travel x' is t'. If
> > there is time dilation, t' < t and, accordingly, c = x/t <
> > x'/t' = c'

This is an elementary illustration of the breakdown
of simultaneity at a distance.

The concept of time dilation expresses the dependence
of t' on t and vice versa.  It is not, however, the
whole story, because it utterly fails to express the
dependence of t' on x, or x' on t.

According to observers in the stationary frame,
 a) The clocks on the train run slow.  This is
    time dilation.
 b) Compared to the clocks in the nose of the train,
    the clocks in the tail of the train have a fixed
    offset.  Specifically, they show a later time.
    This is the breakdown of simultaneity at a distance.

The answer is that t' is greater than t.  For observers
aboard the train, there is nothing to explain;  they
just measure t' in the obvious way, relative to their
own lattice of rods and clocks.

If observers in the stationary frame want to explain
how the nonstationary guys obtained this t' value,
they need to notice that effect (b) is larger than
effect (a).

DRAW THE SPACETIME DIAGRAM.