Re: could this be possible
From: J.J. Simplicio (abc_at_nospam.com)
Date: 07/05/04
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Date: Mon, 05 Jul 2004 14:09:22 GMT
"Bill Hobba" <bhobba@rubbish.net.au> wrote in message
news:hX7Gc.79046$sj4.22799@news-server.bigpond.net.au...
>
> "J.J. Simplicio" <abc@nospam.com> wrote in message
> news:ibWFc.23448$XM6.14786@attbi_s53...
> >
> > "Bill Hobba" <bhobba@rubbish.net.au> wrote in message
> > news:Q7PFc.77717$sj4.15190@news-server.bigpond.net.au...
> > >
> > > "Simplicio" <abc@nospam.com> wrote in message
> > > news:esJFc.19664$%_6.19465@attbi_s01...
> > > >
> > > > "Bill Hobba" <bhobba@rubbish.net.au> wrote in message
> > > > news:swIFc.77281$sj4.75258@news-server.bigpond.net.au...
> > > > >
> > > > > "Simplicio" <abc@nospam.com> wrote in message
> > > > > news:G7pFc.16750$Oq2.14014@attbi_s52...
> > > > > >
> > > > > > Just for fun, consider the following.
> > > > > >
> > > > > > Suppose you had a hollow tube bent into a circle with a
> > circumference
> > > of
> > > > > 100
> > > > > > cm. Inside the tube are 100 small beads at rest and equally
> spaced
> > at
> > > 1
> > > > > cm
> > > > > > intervals around the circle. The beads have equal mass and
equal
> > > amount
> > > > > of
> > > > > > positive charge. Assume there is no friction between the beads
> and
> > > the
> > > > > > tube.
> > > > > >
> > > > > > Also suppose a bar magnet is aligned along the axis of the ring
> and
> > is
> > > > > > initially at rest at a large distance from the tube with the
north
> > > pole
> > > > of
> > > > > > the magnet pointing toward the tube. Now let the bar magnet be
> > moved
> > > > > along
> > > > > > the axis of the ring until the north pole is at the center of
the
> > ring
> > > > > while
> > > > > > the tube is held at rest.
> > > > > >
> > > > > > While the magnet is moving there will be an induced emf in the
> ring
> > > and
> > > > > the
> > > > > > little beads will start moving through the tube. By the time the
> > > magnet
> > > > > > stops, the beads will have reached some final speed. It should
be
> > > clear
> > > > > > that in this case, the spacing of the beads must remain the
same.
> > > > >
> > > > > It is not clear at all. The spacing between the beads must
contract
> > > > except
> > > > > when the motion is normal to the coordinate system as it travells
> > around
> > > > the
> > > > > ring.
> > > > >
> > > >
> > > > How can the spacing between the beads contract while the
circumference
> > of
> > > > the ring (tube) remains the same?
> > >
> > > Because the measured spacing between the beads is not dependant on
> changes
> > > in the circumference of the ring. Remember this is a relativistic
> effect
> > > independent of it being charges or beads - any particles circulating
in
> a
> > > ring will experience the same effect eg the particles of a fluid
> > circulating
> > > in the ring. Imagine a little cube going around the ring - it will
> always
> > > have the side in the direction of motion shortened by relativistic
> length
> > > contraction - no inconsistency with the ring not changing - it is
simply
> a
> > > flattened cube that travels around. Of course if you add up the sum
of
> > all
> > > the little cubes it will be less than the circumference of the ring -
> but
> > > that is the well known sort of thing you get with relativistic
> > > circulations - remember the turntable thought experiment from GR It
> > really
> > > is an effect of space-time geometry. Now as the speed increases the
> > > circumference of the circle will get smaller so an interesting
question
> is
> > > what constrains it to stay inside the tube? Small changes at
realistic
> > > drift velocities are easily accommodated by a bit of give in the
ring -
> > but
> > > there would in principle seem to be no limit. I must admit I have
never
> > > thought about this before - I will have a little think and do another
> post
> > > if nothing occurs. Inserting question. Perhaps the centrifugal
forces
> > > would tear it apart before any problem arises.
> > >
> >
> > Note that the circular tube remains motionless. So, its circumference
> does
> > not change relative to the original 'lab' reference frame. The beads
are
> > equally spaced around the tube before they start moving. They then
> undergo
> > identical accelerations relative to the lab frame until they reach their
> > final speed. You end up with the same number of beads occupying the
same
> > circumference. Therefore, the spacing between the beads (in the lab
> frame)
> > must be the same as before they started their motion.
>
> The issue is that as they rotate they in fact do not occupy the same
> circumference according to SR. Imagine the tube with a line of what is
> moving inside. The circumference of what is inside can decrease and still
> remain in the tube - it just can not do so indefinitely.
I don't follow this. How can a circle of smaller circumference fit inside a
tube of larger circumference? Why should there be a time element regarding
how long the smaller circle can fit inside the larger circle tube?
Maybe it's the hollow cross-section of the tube that is a confusing factor.
If so, we can go to a slightly different model. Consider 100 beads that can
slide on a thin wire that is bent into a circle of circumference 100 cm.
Initially the beads and wire are at rest with the beads equally spaced.
Then, as the wire remains at rest, all the beads begin to accelerate around
the ring in the same direction with the same acceleration relative to the
wire. They begin accelerating at the same instant relative to the lab
frame, they all undergo the same acceleration as a function of lab time, and
they stop accelerating at the same time according to the lab frame. We
imagine that they end up with near light speed relative to the wire (lab
frame). What will be the spacing of the beads according to the lab frame
now? Will the spacing be greater, less, or the same?
> But for normal
> velocities it is doubtful if this will cause a problem - it would only
seem
> to be in issue - in principle. But other factors will also come into play
> such as whatever is circulating will exert a centripetal force that would
> tend to throw its constituent particles outward and counter the effect.
> Thus I see no contradiction.
>
We can assume that something provides a sufficient centripetal force without
any problem arising. We can suppose that the wire is strong enough to
provide the centripetal force, that the beads have extremely small mass,
etc. I don't see how these centripetal forces would 'counter the effect'.
> >
> > You might want to check out the following paper regarding the Bell
> spaceship
> > paradox.
> >
> > http://www.aapps.org/archive/bulletin/vol14/14_1/14_1_p03p07.pdf
> >
> > You can generalize from two spaceships to a large number of spaceships
> > equally spaced along a line. Then think of each spaceship replaced by a
> > charged particle. Thus, arrive at the possibility of a line of point
> > charges that goes from rest to some final speed without any contraction
of
> > the spacing between the particles relative to the lab frame.
>
> There are no known irresolvable paradoxes in relativity. Those that harp
on
> such are wasting their time.
>
We are definitely in agreement here. We are both trying to help abhilsah
see that there is no paradox in his setup with the cylinders. He has simply
made some inconsistent assumptions regarding charge densities as measured in
different inertial frames.
Simplicio
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