Ask A Scientist Physics Archive

name      Jerome G.
status     student
location   NJ
Question - There is an amusing toy which suspends a set of ball bearings
in a cradle. The end ball bearing is displaced and hits the second, which
hits the third, etc. which causes the last ball bearing to move to the
height of the original displacement.
Given a set of perfectly elastic balls, is there a limit to the speed of
the pulse; i.e. is the pulse subject to the limitation of the speed of
light?
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Yes, a relativistic "Newton's cradle" would be subject to the speed of
light. The initial ball bearing transfers momentum by the motion of the
molecules of one to the next, and this motion cannot occur faster than the
speed of light in a vacuum.

Vince Calder
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Yes, but it is the speed of sound that determines how rapidly the impulse
travels through the balls.

--
Tim Mooney
Beamline Controls and Data Acquisition Group
Advanced Photon Source, Argonne National Lab.
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Jerome: let me define your "pulse" in words:
There is a pulse-shaped pressure wave that travels down the row of 
string-suspended balls.
This wave travels at roughly the speed of sound in steel, the material of 
the balls.

The speed of sound in any material is set by the mass density and elastic 
stiffness.
Heaviness and loose-springiness makes sound slower, lightness and 
stiff-springiness makes it faster.
Actually because the balls can expand sideways into empty space as they 
are compressed
in the line of propagation (both tiny amounts),
it is not quite as stiff as the solid in the center of a huge block of 
steel, so
the speed of this wave is very roughly 2 times slower.

A material with a speed-of-sound faster than the speed of light is 
considered impossible.
Any force that communicates the pressure will itself only be travelling at 
the speed of light.

The force between contacting molecules in matter is electromagnetic
(negative electrons electrostatically repelling each other when they get 
closer to each other than to their positive nuclei).
In physics, "light" is another term for Electro-Magnetic wave.
So of course that force is communicated between impacting molecules at 
only the speed of light.
And then there is further delay while the impacted molecule drifts at 
slower speeds over to the next molecule it will hit.

The speed of sound is somewhat related to temperature.  In gasses, hotter 
is faster.
But any molecular substance with molecules drifting near the speed of light,
would be hotter than the center of the sun where nuclear fusion occurs,
and molecules would not survive a single collision.

Perhaps you should look up the speculated speed of pressure waves in a 
neutron star.
No molecules, no atoms, no electric charges,
just sub-atomic particles in close contact limited only by their own 
quantum-mechanical volume exclusion.
The force involved might be one of the nuclear forces instead of the 
electromagnetic force.
I think the neutronium is considered volume-rigid like a liquid, not 
compressible like a gas.
It would still be slower than light-speed, but it might be much faster 
than sound in any normal matter.
Or would it?

Besides, so far the "speed of light" seems to be a general limitation
on the propagation of any form of change or information,
a speed-limit of space itself, not just the speed characteristic of EM waves.
It does not matter what your pulse is made of; it will not go faster than 
that speed.
If space would allow it, electrostatic force would propagate infinitely fast,
and there would be no magnetic force, and no EM waves.
The existence of magnetic force, and EM waves, and the limited speed of 
those waves,
are all consequences of the special-relativity behavior of space-time.
With special relativity and light-waves, I think G-d tied a pretty cool 
Gordian knot.

Jim Swenson
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