Natural Science Forum / Physics / Relativity / September 2005

In this example the accelerating force is already there. The counter
force, provided by the string, would have to remain even after the
source of the tension is removed. Thus the inertial mass of the string
would have to be infinite for a brief period. Given the EP, this would
seem to be a bit contradictory, since during the period that the sphere
is suspended after the cut, the Earth would suffer infinite acceleration
toward the severed string.

Suppose the spheres are suspended by in equilibrium positions
electromagnetic fields whose source is some portion of the carriage. In
this case we can certainly see the restraining force continuing even
after the source of the field has shut down, since the field is a local
phenomenon, a property of space, it must radiate past the sphere before
ceasing to act on it. How, OTOH, does this principle apply to the strings?

Richard Perry

Thanks Tom. I see that you have no further insight than afforded by the
transform on a macroscopic scale. I'm looking for details. How does the
severed string manage to suspend the sphere for any interval at all?
This seems like a bootstrapping effect. The string holds itself up with
enough extra force to hold the sphere as well. Where is the reaction force?

Richard Perry

Richard Perry

That goes the wrong way, and would lead one to conclude that in the
earth frame the front weight would start falling before the lagging weight.

You must also remember that in the Earth frame the front weight is
moving away from the signal, and the lagging weight is moving toward the
signal. This is a larger difference than the anisotropy in the signal
speeds in the Earth frame.

In the Earth frame, the lagging (rear) weight starts falling before the
front (leading) weight. This, of course, is simply "length contraction"
viewed from the carriage frame (because that's the frame in which the
two events are simultaneous).

Tom Roberts    tjroberts@lucent.com

That's a different perspective for sure, and I follow what you're
saying. My only difficulty is trying to get correct advice on the
subject. And though the subject heading specified "advice requested" Tom
took that to mean "advice being offered". I even stopped to qualify my
arguments with "this is just speculation", and yet he felt he had to
flame me for presenting incorrect information as though I was proffering
it as the bottom line of reality. So in return let me flame Tom back,
and maybe you can tell me whether my arguments below are correct or
incorrect.

I understand reaction forces and quite frankly, Tom is talking bullshit.
The upward force on the sphere may instantaneously counter the force of
gravity, but will have a progressive reduction in magnitude over time,
beginning at the moment the string is cut. Here's a simple proof:
Suppose that the downward force on the sphere is provided by its
mechanical attachment to some rigid assembly (U shaped) that wraps
around with two arms, the other arm being the one that the string is
attached to. Now locate this system in free space. If both ends are
simultaneously severed then both the sphere and the far end of the
string will begin to accelerate simultaneously under the tension in the
string. That is, wrt the frame of the center of gravity of the system.
The sphere will not accelerate for any non-zero interval at a rate
determined by the initial tension, because after the first infinitesimal
instant the force will have been reduced. IOW, the entire string is
going to contract simultaneously. If it helps the argument, then simply
place an identical sphere at the other end of the string. We can imagine
that these are bound to the bracket via electromagnets that are
simultaneously switched off. There is now no severing of strings, OTOH
both spheres will simultaneously accelerate (Assuming Newton) toward
each other. We can't even talk about a sound wave propagating down the
string causing the acceleration of these two masses, because the entire
string, and the masses, are contracting simultaneously. Now if we
release only one of the spheres in this system, then we must have
exactly the same results when perceived from the accelerating frame of
the center of gravity of the system. If the center of gravity of the
system remained fixed in position wrt lab frame, as suggested by Tom,
then we would have a violation of conservation laws on our hands. The
released sphere would have accelerated while the other remained at rest.
Thus there must be an acceleration of the bound sphere, along with the
bracket to which it is bound that is simultaneous to the acceleration of
the released sphere. IOW, the string in the original gedanken will not
suspend the f.cking sphere at perfect rest at a height of h until such
time as a sound wave can reach it. That's f.cking bullshit. It will
partially counter the gravitational pull with a time-varying force, but
won't null it completely, except, as I stated, for one infinitesimal
instant at the start. Again, this is in a Newtonian context; Special
Relativity is added below.

However, in this latter experiment with two spheres at the end of the
same stretched string, when we take into account information delay (the
speed of causality), per special relativity, then the center of the
string cannot know that the electromagnets were switched off until a
time r/c later, and thus there is a wave, an *causality wave*
propagating at c, but not a sound wave. The proof is that this delay is
independent of either the material or the tension that the material is
under, and this is because the delay must precisely equal that of the
offset between the end and middle clocks on the carriage wrt Earth frame.

It is light speed delays, independently of longitudinal mechanical
compression waves that foils the gedanken. It would help greatly if the
experts would get their f.cking facts straight.

The problem with the gedanken is independent of sound waves. We could
easily adjust the elasticity of the strings to provide the desired
simultaneous fall of the spheres wrt K'. The problem then reduces to the
difference in the "apparent" speed of the sound waves horizontally and
vertically along the string, the temporal offset over distance along the
string being exactly exactly r/c. IOW, we could have used a laser at the
midpoint of the carriage to sever a vertical string at the rear of the
carriage, in which case we would have had to fire it earlier wrt K'
(r'/c) in order to provide for both rear spheres falling simultaneously.
However (r/c) the delay wrt K, is a different value, and corresponds to
the disagreement in time intervals between the two frames. The gedanken
fails, but the failure had not a god damn thing to do with sound waves,
their presence is only incidental to the argument.

Now, although I've come to value your opinions above pretty much
everyone elses around here, I wonder if you still believe, after all
this debate about LET, that the Lorentz transform cannot be derived from
Galilean relativity. This seems to be, in contrast to your sentiment,
exactly what Lorentz did, so I wonder how you justify your opinion that
it cannot be done? If you, like some of the other experts, are also
leading me astray with false claims, then I don't have a chance in hell
of getting the facts about relativity straight unless I simply derive
them on my own from the transform, which seems to be what I'm
consistently having to do anyway :)

Richard Perry