Re: twins paradox problem

On Thu, 16 Mar 2006 12:53:46 -0500, sal <pragmatist@xxxxxxxxxx> wrote:

On Thu, 16 Mar 2006 13:28:11 +0000, dseppala wrote:

On Wed, 15 Mar 2006 10:40:52 -0500, sal <pragmatist@xxxxxxxxxx> wrote:

On Wed, 15 Mar 2006 13:26:20 +0000, dseppala wrote:

On Tue, 14 Mar 2006 15:17:07 -0500, sal <pragmatist@xxxxxxxxxx>
wrote:

On Tue, 14 Mar 2006 14:11:30 +0000, dseppala wrote:

I've never seen an answer to this twins paradox question.

It is because you never looked. You close your eyes in the
presence of answers, and you never invest any effort in finding
them yourself.

You invest lots of effort in finding problems, and none in finding
solutions. So you find problems, not solutions. What a surprise.


In this problem, instead of two twins there is a battery and a
light bulb connected with a pair of wires. An ammeter at the
battery measures that one ampere (one columb per second) is
flowing there. An ammeter at the light bulb measures that one
ampere is flowing through the light bulb.

Now as in the twin's paradox we let the light bulb accelerate to
V, travel for some distance,


Here is your FIRST TASK:

Given that the current through the battery is 1 amp in the rest
frame of the BATTERY, determine the current through the bulb as
measured in the rest frame of the LIGHTBULB.

Either prove that the measured currents match, or if they don't
match, determine what the "moving" reading must be. Use numbers,
algebra, Lorentz transforms, and stuff like that, not just waving
hands.

You have _assumed_ the measured currents match. But is that
correct?

No I did not make that assumption. When the battery and light
bulb were at rest, yes each ammeter measured one ampere (the given
information). Now if both current readings remain one ampere
while they are moving, then if time isn't constant then a
different number of columbs flow from the battery than flow
through the light-bulb.

Oops! I feel a breeze! You skipped the calculation.

If the readings don't match, what is the ratio of the readings?
Display your calculation, please.

But, here's the important question which you have glossed over:
Where are the ammeters placed, and how are they wired, in order to
obtain these readings?

And, just to emphasize it: To _which_ frame of reference does each
meter belong?

Be _precise!_ You are still just waving your hands.


This implies charge builds up somewhere. However, the two frames
have a different view as to whether more current flows through the
battery or through the light-bulb,

This is all garbage. You're frame shifting without even realizing
you're doing it and you're trying to conclude something from your
vacuous handwaving. You need to _start_ by comparing meter readings
obtained within a SINGLE FRAME OF REFERENCE.

Okay, help me here. How do I compare meter readings obtained within
a single frame of reference? The display on one meter is one
ampere, and the display on the meter in the other frame is also one
ampere. Can't I have two observers in the same inertial frame at
different postions look at the two meter readings?

Yes, of course. You can have any observer look at any object.
But that doesn't mean the object is in that observer's FoR.

You need to compare the readings on meters which are at rest relative
to each other. The velocity of the person looking at the needle on
the meter is obviously not relevant! :-)

The goal is to answer this question:

For _one_ observer, how much current appears to be flowing through
two different parts of the circuit?

If that observer looks at a meter which appears (to that observer) to
be in motion, it may _OR_ _MAY_ _NOT_ give the same reading as a meter
which is stationary relative to that observer.

Let's be clearer here. "Current" is electrons per second moving past
a particular point, as viewed in some particular frame of reference.
Can you clarify your statement a little more for me. When you say
past a particular point [of space?] instead of past a particular point
of the wire, are you saying that when a battery is perpendicular to
the motion and the attached wires are parallel to the motion,
observers not in motion would say that more electrons are leaving the
battery than are going into it or vice versa? And if the battery's
orientation is parallel with the motion the same number of electrons
are going into the battery as are leaving it. Or are you saying
that when the battery is perpendicular to the motion, observers not
moving with the battery would say no current flows into or out of the
battery because the battery doesn't stay at any particular point?
I'm not certain what you are saying exactly.
David
Pretend for a moment that an observer in that frame is using a
telescope to watch the electrons and a stopwatch to count seconds, and
is actually _counting_ electrons and dividing by time that has passed
(with an appropriate allowance for blueshift/redshift if the wire is
in motion relative to the observer and so forth). That's the
"current" measured in that observer's rest frame, and _that_ is the
value you need, if you're trying to determine whether that observer
will see electrons "piling up" someplace in the circuit.

To obtain an equivalent value -- equivalent to the value obtained by
using a telescope and stopwatch (and adjusting for Doppler shift) --
you need to use an ammeter whose mechanism is at rest relative to the
observer. Such an ammeter is known to measure electrons/second in
that observer's rest frame. An ammeter which is in motion relative to
that observer is _not_ known to measure electrons/second in that
observer's rest frame -- in fact, part of the problem is determining
just how a moving ammeter and a stationary ammeter relate in terms of
their readings.


I don't see what you are trying to do here.
As a moving ammeter passes each observer he reports what the moving
ammeter displays. This is the same thing that would be performed if a
moving clock passes each observer.

Yes, and either way, it's showing a measurement from the _moving_
frame, not the observer's rest frame. A moving clock doesn't show the
same elapsed time as a line of stationary clocks which it's passing;
it shows less.


If there was a clock at each ammeter, these two observers might
report something as: We recorded observations at time t0 (in our
inertial frame). At one end of the wire, the ammeter read one
ampere and the clock at that ammeter read 20 seconds. The ammeter
at the other end of the wire read one ampere and that clock read 10
seconds. We made a second observation at time t0+2, the ammeter at
one end of the wire read one ampere and the clock at that ammeter
read 22 seconds. The ammeter at the other end of the wire read one
ampere and the clock at that ammeter read 11 seconds. Aren't those
readings taken in a single frame of reference. Can you please
clarify what you mean by comparing readings obtained in a single
frame of reference?

Again, the _meters_ _themselves_ must be relatively at rest.

I'll make it as easy as I can, by actually including a tiny
calculation:

Current is _not_ invariant. It's particles/second, and elapsed time
isn't invariant: elapsed time goes as 1/gamma, where
gamma=1/sqrt(1-v^2). So current transforms as gamma (inverse of
time).

Suppose there's a wire which is stationary relative to me. If I
measure the current in that wire as "a", then someone else moving at
velocity v relative to me will measure the same current in the same
wire at the same time as being "a*gamma".

While 10 electrons traverse the wire, the moving observer will measure
1/gamma times as much _time_ going by; same number of electrons, in
1/gamma times as much time, means the current was observed to be gamma
times larger.

But this raises another question: _HOW_ do you measure current in a
_moving_ wire? It's hard to set up the problem in a way that makes
sense. Any setup that moves the ammeter with the wire results in
getting the reading from the rest frame of the wire. One possibility
might be to put some of the equipment into a centrifuge and use wires
running to sliprings on the shaft to make contact with the outside;
you then take the voltage and current measurements at the sliprings.
That's not entirely satisfactory but it's a start.

And how do you tell when electrons have traversed a wire segment? The
easiest way is to assume the wire is oriented perpendicular to the
line of motion. Otherwise you've got problems with simultaneity and
clock skew between the ends of the segment.


--
Nospam becomes physicsinsights to fix the email
I can be also contacted through http://www.physicsinsights.org


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Relevant Pages

  • Re: twins paradox problem
    ... An ammeter at the light bulb measures that one ... measured in the rest frame of the LIGHTBULB. ... You can have any observer look at any object. ... At one end of the wire, ...
    (sci.physics.relativity)
  • Re: twins paradox problem
    ... Given that the current through the battery is 1 amp in the rest ... measured in the rest frame of the LIGHTBULB. ... You can have any observer look at any object. ... "How many electrons are flowing through the wire, ...
    (sci.physics.relativity)
  • Re: twins paradox problem
    ... An ammeter at the light bulb measures that one ... measured in the rest frame of the LIGHTBULB. ... If the readings don't match, what is the ratio of the readings? ... You need to _start_ by comparing meter readings ...
    (sci.physics.relativity)
  • Re: twins paradox problem
    ... An ammeter at the light bulb measures that one ... measured in the rest frame of the LIGHTBULB. ... If the readings don't match, what is the ratio of the readings? ... You need to _start_ by comparing meter readings ...
    (sci.physics.relativity)
  • Re: twins paradox problem
    ... An ammeter at the light bulb measures that one ... measured in the rest frame of the LIGHTBULB. ... If the readings don't match, what is the ratio of the readings? ... You need to _start_ by comparing meter readings ...
    (sci.physics.relativity)