Re: Simple length problem - for Todd, Harald, thinkers

On Tue, 27 Jun 2006 01:48:32 GMT, David <dseppala@xxxxxxxxxxxxx>
wrote:

On Sun, 25 Jun 2006 14:42:28 -0500, "Todd" <nospam@xxxxxxxxxx> wrote:


"David" <dseppala@xxxxxxxxxxxxx> wrote in message
news:8a2t9254hsf3pkpe8hns5jtpcpnq3c7ijs@xxxxxxxxxx
On Sat, 24 Jun 2006 13:43:17 -0500, "Todd" <nospam@xxxxxxxxxx> wrote:

"David" <dseppala@xxxxxxxxxxxxx> wrote in message
news:kouq929gl810r0j66m5q379ft0tbnmerc5@xxxxxxxxxx

Todd, I have no problem whatsoever following and agreeing with your
analogous examples. That is not the problem I have. Todd, here's what
I don't understand. Why do you consider that logical and something
that supports the theory instead of a negative consequence of
relativitity?

That is what I don't understand.
David


The results found in the moving frame are certainly 'logical' in the sense
that they are logically deducible from the premises of SR. Or, by
'logical'
do you mean 'intuitive'?
In the magnet example, we measure that the field strength is strongest
very close to the magnet. When all points of the rotating wire are in
close proximity to the magnet, the magnet doesn't have enough force to
pick the wire up off the surface of the cylinder. However, when only
a very small portion of the wire is in close proximity to the magnet,
then the magnet has enough force to pick up the wire off the surface
of the cylinder. I call that illogical, not counterintuitive.
Do you see that as logical and therefore simply counterintuitive?
David


Let's simplify the scenario. We have a straight rod that is placed on a
conveyor belt that lies in the x-y plane and the belt moves in the
y-direction of the rest frame. In the rest frame the rod is oriented at
just the right angle with respect to the x-axis so that in the moving frame
the rod appears parallel to the x-axis. (The moving frame moves parallel to
the x-axis relative to the rest frame.) We assume that each element of the
rod is 'stuck' to the belt by a bit of glue or whatever. As each element
of the rod passes over the x-axis, the element experiences an impulsive
force in the z-direction (from your magnet, say) that tries to lift the rod
off the belt. From the point of view of the moving frame the forces on all
the elements occur simultaneously because each element of the rod crosses
the x-axis simultaneously in this frame. From the point of view of the rest
frame the forces do not act simultaneously because different elements of the
rod cross the x-axis at different times in this frame.

As a warm-up exercise let's assume that before beginning the experiment we
chop the rod into disconnected elements. So the ''rod'' is really just a
series of little independent blocks stuck to the conveyor belt (but not
stuck to each other). As each block passes the x-axis it feels an impulsive
force in the z-direction that we assume is barely strong enough to lift the
little block off the belt. Thus the force felt by one block would not be
sufficient to lift two or more blocks. It is easy to see what happens in
this case. Both frames agree that the entire ''rod'' is lifted off the
belt. In the moving frame the blocks are lifted off simultaneously whereas
in the rest frame each block is lifted off ''one after the other''. Note,
however, that according to the rest frame the distance between two
consecutive blocks increases *during* the process of being lifted off the
belt. (The block that lifts off first gains a z-coordinate before the next
block lifts off and gains any z-coordinate). According to the moving frame
the blocks move simultaneously in the z-direction and the distance of
separation between any two consecutive blocks remains constant during the
lifting off process.

For the next exercise we suppose that the rod is still chopped into blocks
but that this time we connect together consecutive blocks with little
springs. The springs are initially in a relaxed state before the ''rod''
on the conveyor belt passes over the x-axis. The purpose of the springs is
to introduce some elasticity into the system. For now we assume the springs
have very small spring constants so that they can stretch a lot and still
not exert very much force. Thus, we have a rod that is very elastic and
easy to stretch. It seems to me that the result here would be very similar
to the previous case of totally disconnected blocks. The springs aren't
going to have a noticeable effect if they are very puny springs. In the
rest frame, the distance between consecutive blocks increases during the
lifting so that the springs stretch and develop a small tension, but the
tension is too weak to noticeably affect the motion of the blocks. In the
moving frame, the blocks appear to maintain their separation distance.
Nevertheless, the moving frame agrees that a weak tension develops in each
spring even though the springs don't get any longer in this frame.

Finally, we need to consider what happens as we increase the spring constant
in each spring in order to increase the rigidity of the rod. Can the
springs become stiff enough to prevent the blocks from being lifted off the
belt? I don't think so. Let the occurrence of the impulsive force applied
to a particular block as it passes over the x-axis be thought of as an
'event' in spacetime. In the moving frame, the impulsive forces felt by all
the blocks form a set of simultaneous events. Thus, any two of these events
are 'space-like' separated in spacetime. Hence, the events are causally
disconnected.
I'm a little confused here. Let's say the magnet can pick up
individual atoms. You are saying that if the atoms are chemically
bonded to each other, they will not have any effect on whether the
magnet can pick it up or not. The effect will be the same as if they
are individual atoms. This notion conflicts to answers posted in
response to another question I had. That question was does it require
more energy to accelerate individual atoms from one inertial frame to
another than it does to accelerate atoms that have chemical bonds with
each other in the direction of the motion. The answer to that
question was that yes, it must.
I typed that backwards - it takes more energy to accelerate connected
atoms. David
In SR, the amount of energy needed
to accelerate a rod from one frame to another is not simply a function
of the mass alone, but the structure of the chemical bonds in that
mass. Very simply, this problem was just a rod placed on a moving
conveyer belt. Both frames see the rod as stretched - the chemical
bonds are different in the new frame compared to an identical rod in
its normal steady-state condition. Stretching of bonds occurred.
Whereas if individual atoms are placed on this conveyer belt, no
stretching of chemical bonds occurs. In the stretched rod case,
energy is released as the stretched rod (assuming its in its elastic
state) contracts to the same length of an identical rod in that same
frame. Whereas when atoms are accelerated, no such release of energy
occurs. Do you agree with that or is that a faulty SR notion?
David

I'm trying to visualize what happens from the point of view of the rest
frame. When the first block passes the x-axis it feels an impulsive force
which should be able to lift the block off the belt (after all, the spring
attached to it is initially unstreched and so the spring is not exerting any
force on the block to oppose the lifting force). As the first block is
lifted off the belt and moves upward in the z-direction, the spring
connecting the first and second block starts to stretch. The motion of the
first block is then affected by the tension building up in the first spring
and what happens to the first block depends on detailed assumptions about
the lifting force, etc. Nevertheless, any influence that this stretched
spring can have on the second block cannot propagate to the second block
before the second block passes the x-axis and gets lifted by the impulsive
force. This is because any such influence would have to travel faster than
the speed of light in order to connect two space-like separated events. So,
I think the second block would also be lifted off the belt. Extending this
argument all the way down the line, I think that the entire rod would get
lifted off the belt no matter how stiff the springs. The tension forces
that develop in the springs affect the motion of the blocks *after* they are
lifted off the belt. These motions will propagate as stress waves (sound
waves) through the system. Or, if the stresses are too large, the rod will
break into pieces.

It seems to me that this type of argument with blocks and springs should
extrapolate to a real solid rod.

Final note. Even though the rest frame sees only a small portion of the rod
experience a lifting force at any specific instant of time, the entire rod
nevertheless gets pulled off the belt. This is so despite the fact that the
force felt by the rod at one instant in the rest frame is not strong enough
to lift the entire rod. The force at one instant is barely strong enough to
lift one small ''block'' of the rod. It's the effect of all the forces felt
by all the blocks that accounts for the rod being lifted off the belt.

Todd
.

Relevant Pages

  • Re: Simple length problem - for Todd, Harald, thinkers
    ... The results found in the moving frame are certainly 'logical' in the sense ... conveyor belt that lies in the x-y plane and the belt moves in the ... In the rest frame the rod is oriented at ... The springs are initially in a relaxed state before the ''rod'' ...
    (sci.physics.relativity)
  • Re: Simple length problem - for Todd, Harald, thinkers
    ... We have a straight rod that is placed on a conveyor belt that lies in the x-y plane and the belt moves in the y-direction of the rest frame. ... In the rest frame the rod is oriented at just the right angle with respect to the x-axis so that in the moving frame the rod appears parallel to the x-axis. ... For the next exercise we suppose that the rod is still chopped into blocks but that this time we connect together consecutive blocks with little springs. ...
    (sci.physics.relativity)
  • Re: Simple length problem - for Todd, Harald, thinkers
    ... The results found in the moving frame are certainly 'logical' in the ... conveyor belt that lies in the x-y plane and the belt moves in the ... In the rest frame the rod is oriented at ... The springs are initially in a relaxed state before the ''rod'' ...
    (sci.physics.relativity)
  • Re: Simple length problem - for Todd, Harald, thinkers
    ... The results found in the moving frame are certainly 'logical' in the sense ... In the magnet example, we measure that the field strength is strongest ... conveyor belt that lies in the x-y plane and the belt moves in the ... In the rest frame the rod is oriented at ...
    (sci.physics.relativity)
  • Re: How can this work in relativity?
    ... there's the little problem of in which reference frame t0 is ... >> people prior to them stepping on the conveyer belt. ... jumpers readjust themselves to remove the tension in the rod ... is still 1m -- requiring a physical expansion of the rod a la ...
    (sci.physics.relativity)
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