Friday, November 06, 2015

Ask a Physicist: FTL Communication With a Very Long Stick

Amy from Hull, England asks:

"Imagine a tube structure stretching a large distance (say a light year) encasing a row of ballbearings that are lined up inside the full length of the tube. If I push one more ballbearing in from one end, would a ballbearing at the far end instantaneously drop out? Or for millions of years until the information is transferred would there be more ball bearings than the tube would normally fit? Or would it simply take me millions of years to push an extra ballbearing in the tube?"

Amy,
Great question!

Better than ballbearings, we can imagine the tube being filled with water—like a lightyear-long syringe, with a plunger at our end. Since water is practically incompressible, it's just as good as a solid object, here. When you push the plunger (which would be difficult—there's going to be a LOT of water in this tube, and it's got inertial mass, even in zero-gravity), the information that you pushed on the plunger is going to travel as a pressure wave—moving at the speed of sound in water—from your plunger to the distant end where, years later, a squirt of water will emerge.

If you insist upon ballbearings, you could imagine a very long Newton's Cradle. When you pull one ballbearing back and let it clack against the next one in line, it seems as though the one on the other end receives the impulse instantly, flying off.
But if you filmed it with a high-speed camera, you'd see that the process isn't quite instantaneous—once the first ballbearing hits its neighbor, the impulse of momentum travels, again as a sound wave—a tiny structural deformation—through each ballbearing in line before reaching the other end. The process appears instantaneous because the speed of sound in solid objects is very high.

Unfortunately, no matter what material we choose, its speed of sound is always going to be slower than the speed of light, because the compressions and rarefactions that create sound waves are ultimately driven by electromagnetic attraction and repulsion, mediated by electromagnetic waves.
(I should mention that, while sound would take many years to propagate a single lightyear, it wouldn't necessarily be millions of years—aluminum's speed of sound is around ~6 km/s, at which rate it'd take 50,000 years to travel one lightyear. Not a short time by any stretch of the imagination, but nothing close to a million.)

Curiously enough, a teacher once explained electric current to me in a way very reminiscent of your thought experiment, with electrons in place of ballbearings, and wires in place of the "tube". You probably know that, when you turn on a lightswitch, you're closing a circuit and allowing charge to flow through it. What you might not know is that it can take several minutes for the electrons that crossed the switch when you closed it to reach the lightbulb! In the meantime, the light is powered by electrons forced out the far end of the wire by the ones let in at the switch, much like the ballbearings in your tube! Of course, this transmission still doesn't happen instantaneously, but it does happen at a significant fraction of the speed of light.

3 comments:

  1. An interesting aspect of this thought-experiment it that for a row of ball bearings(or a tube filled with water) the compression wave that travels through it will dissipate and transform into heat energy in a relatively short distance, because of the Amplitude of the Energy dissipation Function is E(loss) as a function of time, in simplified form =Eo*EXP(-at). . . In "no time" at all the The energy E(loss) will be zero. . . .All the Kinetic Energy Eo of hitting the first ball with a hammer will be transformed into heat , and a "listener" a lightyear away will be none the wiser about the impact of the First Hit. ..

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  2. Thanks, Totally answered my question.

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  3. So water and ball bearing have a lag based on the transmission of energy through the medium, but what about a broom handle that stretches from earth for alight year. you move one end, the other end moves straight away?

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