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I still believe that the setting of the problem is correct and consistent with
traditional relativity analysis. Two events ("light enters train" and
"light leaves
train") happen that are identifiable in either frame (otherwise any such
analysis
should be abandoned) and we are to compare the distances between them, x
and x',
and the time intervals between them, t and t'. I think the only reasonable
criticism of my solution should consist in offering a solution proving
that x/t =
x'/t'. Einstein's theory is expected to be able to resolve problems as
simple as
this one.
Pentcho
Mark Sylvester wrote:
> No mirrors. Pentcho measures the delta between the events "light enters
> train" and "light exits train" on the other side. The events are spatially
> separated in both frames, and I cannot identify a proper time interval. I
> would be interested to learn how to analyze this in the orthodox manner.
> With the mirror it's pretty much the standard intro. textbook discussion.
>
> Mark.
>
> At 14:59 28/04/03 -0400, Ken Caviness wrote:
> >I am not sure that I understand this new thought experiment. The beam of
> >light is approaching the train perpendicularly (in the station frame)
to the
> >direction of the train's motion, correct? So the view of the station
observer
> >is that the light beam enters the train (through a window), bounces off a
> >mirror on the far wall of the train, retraces its path and exits the train
> >(through a different window, since the train has been moving in the
meantime.
> >If this is the intent, then the event of entering and leaving the
train occur
> >at the same point in the station frame. The viewpoint of the observer
on the
> >train is different: the light ray approaches at an oblique angle
> >(relativistic aberration of light) through one window, bounces off the
mirror
> >and exits at an oblique angle through another window.
> >
> >The Lorentz transformation makes several nice things occur: Although the
> >angle is different, and the components (x & y or x' & y') of the speed
differ,
> >both observers measure the speed of the light beam to be c. The time
interval
> >between entrance and exit are not the same for our two observers, the
spatial
> >separation of the events is not the same, but the space-time interval
between
> >the events is the same according to all observers.
> >
> >(Differentiating the Lorentz transformations and some algebraic
substitutions
> >gives the relationship between the components of the velocity in the
different
> >reference frames, but to get the magnitude of the velocity we must
take the
> >square root of the sum of the squares of the velocity
components. Only the
> >magnitude of the speed of light turns out to be the same according to both
> >observers, not the angle, not the individual components, not the time.)
> >
> >Ken Caviness
> >
> >
> >Michael Burns-Kaurin wrote:
> > >
> > > I would add to Bob's reply that, since the events of entering the
train and
> > > leaving the train do not occur at the same place in the train
frame, then
> > > the time dilation factor is not enough--one must also consider the
position
> > > term in the Lorentz transformation for time. When dealing with
situations
> > > such as this, one should use the transformations and not rely on length
> > > contraction and time dilation.
> > >
> > > Michael Burns-Kaurin
> > > Spelman College
> > >
> > > 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. 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'
> > > >
> > >
> > > Just for the sake of the argument, assume that the numerical value
of the
> > > speed of
> > > light is the same in the two frames. then, in the frame where the light
> > > moves
> > > obliquely, the light must travel a longer distance, x', and hence
must take
> > > a
> > > proportionately longer time, t', to travel that longer distance.
The ratio
> > > x'/t'
> > > would therefore remain the same as x/t (because x' > x and t' > t).
Time
> > > dilation
> > > really is not a consideration here, and t' is definitely not less
than t.
> > > Even if
> > > time dilation was applied (which would also require considering a
length
> > > contraction
> > > of the component of obliqueness parallel to the train's motion), t' > t
> > > still holds.
> > >
> > > Your assumption of t' < t is what's leading to the differing values
for c
> > > and c'.
> > >
> > > Bob at PC
>
> Mark Sylvester
> UWCAd
> Duino Trieste Italy