Re: Length definition in SR - can anyone explain

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.

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. (Also we can generate the same pulses from
a single laser so t must be the same for both pulses).
In the moving frame these pulse lengths are not the same. In the
rest frame of the lasers these pulse lengths are identical.
David

Start by drawing a little spacetime diagram.
Hint: in your equations, use the variable v in stead of the
numeric value 0.866c.

Dirk Vdm

.

Relevant Pages

  • 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 ... As I stated in the problem I have a laser pointed along the x-axis ... laser stopped firing. ...
    (sci.physics.relativity)
  • Re: Please explain SR and this property of light
    ... > pulse at time t=tA. ... > Moving Frame ... > of the rest frame experiment just described occur ...
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  • 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)