Help with SR time dilation

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dseppala@austin.rr.com - 27 Feb 2005 19:24 GMT

Given an inertial reference frame which I'll call the rest frame.
Given a pair of wires with a light at one end, and a battery at the
other end. The light, battery and wires all have zero relative
velocity. Let's say the length of the pair of wires is such that
when the battery is attached to the wires it takes 10 seconds for the
light to turn on.

Now keep the battery and light in the rest frame as before, but let
the majority of the wire be in an inertial frame that is moving with
velocity V relative to the battery and light. As measured in the rest
frame of the battery and light, does the light still turn on 10
seconds after the battery is attached to the wires, or is it
different? If it is different, does it take a longer or a shorter
time for the light to turn on once the battery is attached?

Thanks,
David Seppala

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The Ghost In The Machine - 27 Feb 2005 23:10 GMT

In sci.physics.relativity, dseppala@austin.rr.com
<dseppala@austin.rr.com>
wrote
on Sun, 27 Feb 2005 19:24:25 GMT
<42221b3e.278849083@news-server.austin.rr.com>:

> Given an inertial reference frame which I'll call the rest frame.
> Given a pair of wires with a light at one end, and a battery at the
> other end. The light, battery and wires all have zero relative
> velocity. Let's say the length of the pair of wires is such that
> when the battery is attached to the wires it takes 10 seconds for the
> light to turn on.

An interesting requirement. Is there enough worldwide copper to
satisfy it? :-) Also, what is the inductance of a coil of wire
with an air core, 1m in diameter, and just shy of 1 billion turns?
Given this inductance, what is "on"? The current flow will not
be 0-1, but will instead vary in accordance to a exponential/asymptotic
curve (if plotted in a graph of current versus time).

Is it even possible to construct such a coil? If a winder winds the
wire at 10 m/s, it will take about 9 years -- assuming there's
enough copper available. (The exact value depends on the speed
of current flow through the wire, which is somewhat less than c.)

Fortunately, two coils can be constructed just about as easily as one,
if one has twice as much copper.

> Now keep the battery and light in the rest frame as before, but let
> the majority of the wire be in an inertial frame that is moving with
[quoted text clipped - 3 lines]
> different? If it is different, does it take a longer or a shorter
> time for the light to turn on once the battery is attached?

I can't say I know. You'd be better off hypothesizing an electron
beam with such questions -- something along the lines of a
spaceborne pair of linear accelerators to throw the current around.

> Thanks,
> David Seppala

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Natural Science Forum / Physics / Relativity / February 2005

Help with SR time dilation