Re: Length definition in SR - can anyone explain

On Wed, 19 Apr 2006 15:15:45 -0400, "AllYou!" <Idaman@xxxxxxxxxxxxxx>
wrote:


"David" <dseppala@xxxxxxxxxxxxx> wrote in message
news:g01d421pvrfjaj05p04f3bk0541kme3q43@xxxxxxxxxx
On Wed, 19 Apr 2006 14:29:42 -0400, "AllYou!"
<Idaman@xxxxxxxxxxxxxx>
wrote:

I think what I've posted below is correct.

"David" <dseppala@xxxxxxxxxxxxx> wrote in message
news:g6rc42logom5j8a5evesc16dttoae03rhp@xxxxxxxxxx
On Wed, 19 Apr 2006 16:09:26 GMT, "Dirk Van de moortel"
<dirkvandemoortel@xxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:


"David" <dseppala@xxxxxxxxxxxxx> wrote in message
news:v8lc42dpp731snaggm8eg2me89b5ne4q77@xxxxxxxxxx
I'm trying to understand fundamental concepts of SR like time
and
length. In my posting about clocks I got a varied opinions of
what
constitutes a clock. This posting is a question about lengths.
Can
anyone explain why this is or isn't allowed in SR?

I'm in an inertial frame. Since the speed of light is constant
I
decide to make my standard unit of length equal to one
light-second
(the distance light travels in one second as measured by
synchronized
clocks in my inertial frame).

Now let there be an inertial frame moving along the x axis with
velocity V = 0.866c relative to my frame.
At time t0 I fire two lasers for a one second burst. The length
of
each pulse is one light-second. The lasers are aligned along
the
x-axis. One points in the positive direction, the other points
in
the
negative direction.

The moving observer measures the length of one pulse to be much
less
than the length of the other pulse even though in my frame they
are
identical.

What makes you decide that?
I thought this was a simple well known result of SR so I didn't
include any explanation of how I came to this conclusion.

The whole point of SR is that both observers will measure both
pulses
to be the same length and the same velocity.

Try to explain your reasoning by defining some relevant
events and calculating the lenghts of the pulses in the
moving frame.
But if you want some details here's how I came to this
conclusion.
As I stated in the problem I have a laser pointed along the x-axis
in
the positive direction and one pointed in the negative direction.
They
each fire for one second as measured in the rest frame of the
laser.
I presume you agree that in the rest frame of the lasers both
pulses
are one light-second in length. I determined this by noting that
the
start of each pulse traveled a distance ct from each laser before
the
laser stopped firing. So the front of the pulse must be c*t away
from
the end of the pulse.

Moving Frame View
In the moving frame, observers measure the laser to be moving
at -V.
(I use V =0.866c simply because its easier to express things in
words
when length contraction and time dilation are a factor of 2 and
its
easier for me to visualize things when they are different by a
factor
of 2 than by a factor of gamma).
Let's look at the pulse from the laser that is pointing in
the
negative direction (the same direction the laser is moving). Let
the
laser start firing at x = 0. Let's say it fires for t seconds.
That
means the start of the pulse traveled from x = 0 to x = -ct while
the
laser was firing. The laser moved from x=0 to x = -Vt during this
same time. When the laser stops firing the end of the pulse is
at -Vt
(where the laser's at). So the length of this pulse is (c-V)*t.
Now
for the laser that is pointing the other direction the laser again
starts firing at x=0. Again this laser moves in the negative
direction but the emitted pulse is traveling in the positive
direction. The laser again stops firing at the position x= -Vt
(the
amount the laser moved). The same as the other laser. The start
of
the pulse began at x=0 and while the laser was firing the start of
the
pulset traveled a distance ct from x=0. So when the laser stops
firing the end of the pulse is at x=-Vt and the start of the pulse
is
at x= ct so the pulse width is (c+V)t compared to (c-V)t as noted
for
the other laser.
Both lasers start firing at a common point in space and time and
both lasers stop firing at a common point in space and time so t
is
the same for both lasers.

If I read you correctly, one laser is in one FoR (S), and the other
is
in the other FoR (S').
You didn't read me correctly. Both lasers are in the same inertial
reference frame. The lasers have zero relative velocity with
respect
to each other. They point in opposite directions, and fire for the
same length of time from the same position coordinate in that frame.
In that frame the pulse widths are measured to be the same. In a
frame moving wrt the lasers the pulse widths are not measured to be
the same (according to SR).

You are right that I misread you, but you are wrong about SR. SR
predicts that the velocity of light (c) is the same for all observers.
From your FoR (S), c has the same value as in the FoR which is moving
relative to you (S'). Therefore, to you, the leading edge of the
light pulse will travel a total distance of (c /1 sec) before it's
turned off, and to an observer in S', the leading edge of the light
pulse will travel a total distance of (c /1 sec) before it's turned
off. Now, if you were to use the length of that pulse to define the
ends of a rod in your FoR, and an observer in S' did the same for a
rod in S', then the measured length of the rod in S' would be less
than the measured length of the rod in S as measured by you, and the
measured length of the rod in S would be less than the measured length
of the rod in S' as measured by an observer in S'.

I think that's correct, but I'd like other's to weigh in.
I posted a reply to Dirk where I labeled each event and result. The
two pulses move in opposite directions so observers in the moving
frame measure the two light pulses to be of different lengths while
observers in the rest frame measure them to be the same length (that's
Einstein's theory). Read my list of events and see if there is any
event you disagree with.
David
.

Relevant Pages

  • Re: Please explain SR and this property of light
    ... > pulse at time t=tA. ... > Moving Frame ... > of the rest frame experiment just described occur ...
    (sci.physics.relativity)
  • Re: Length definition in SR - can anyone explain
    ... I'm in an inertial frame. ... The moving observer measures the length of one pulse to be much ... each fire for one second as measured in the rest frame of the laser. ... laser stopped firing. ...
    (sci.physics.relativity)
  • Re: Length definition in SR - can anyone explain
    ... I'm in an inertial frame. ... The moving observer measures the length of one pulse to be much ... each fire for one second as measured in the rest frame of the laser. ... laser stopped firing. ...
    (sci.physics.relativity)
  • Please explain SR and this property of light
    ... pulse at time t=tA. ... Moving Frame ... pulses travel at some equal and opposite angle relative to the x-axis ...
    (sci.physics.relativity)
  • Re: Length definition in SR - can anyone explain
    ... I'm in an inertial frame. ... The moving observer measures the length of one pulse to be much less ... each fire for one second as measured in the rest frame of the laser. ... laser stopped firing. ...
    (sci.physics.relativity)