Give me a long enough lever...

[shunn]

We're used to thinking of the movement of an object as homogeneous and instantaneous. In other words, for example, when I give a push to the fat end of my pool cue, the felted end moves at the same time to strike the cue ball.

But I have a question—and I'm asking this because I'm curious about the answer, not because I know the answer. Let's say I had a pool cue that was 186,282 miles long. In other words, light would take a full second to travel from one end of it to the other. So, if I were to give my end of this pool cue a push, would the far end move simultaneously? Or would the motion take something more than a second to propagate along the length of the cue (causing it to ripple, as it were)? Physicists, I'm talkin' to you.

Comments

[jwgh]

I believe the impulse would generally travel at the speed of sound in wood (or whatever the stick is made out of), so this would not allow you to exceed the speed of light.

[kellysarah.livejournal.com]

I think it would depend in large part on the nature of the pool cue. If the pool cue is made of perfectly rigid material, maybe it would be instantaneous. However, I doubt many materials are perfectly rigid, especially at the length you give in your example. Since I'm not a physicist, I'll give you a geology example. Earthquakes occur when pieces of the earth's crust bang together for one reason or another. The waves produced travel from the epicenter (the site of the impact) through what we generally think of as solid rock and are then sensed by seismometers around the world at different times, depending on how far away they are from the epicenter. Hope that helps at least a little!

[dustchick.livejournal.com]

In a crystal lattice, the atoms respond in vibrations known as "phonons". The speed of propagation of a phonon is equivalent to the speed of sound in the material. As Sarah mentioned seismic waves, which we see as P and S waves, the direction of the vibration is important in determining the sound speed (longitudinal vs. shear). As far as I know, the end of the long pool cue must wait its turn to move, unless the speed of sound in the material can somehow be manipulated to allow superluminal phonons.

[steelbrassnwood.livejournal.com]

Whatever you do, don't scratch with THAT cue please.

[bobhowe.livejournal.com]

This is a thought experiment, so I'm not sure the actual composition of materials is relevant. For your purposes I think we can assume a material that is perfectly rigid and that you can produce enough force to move it in a linear way, I don't think it violates any laws of physics. The cue isn't approaching the speed of light.

[frogworth.livejournal.com]

I'd say that assuming a "perfectly rigid" material in this thought experiment, as some have done, is already violating the laws of physics. If you had a perfectly rigid pool cue then the amount of energy required to push your end of it would approach infinity as the length increased.

More to the point, the end of the cue never moves instantaneously with the movement of the other end. There's always some time taken for the propagation of the energy through the substance. You can assume it's instantaneous for small values, but at even non-relativistic length/mass you'll start getting a delay.

nothing is perfectly rigid

[geoffrey-landis.livejournal.com]

Right, the various comments are mostly on the mark. When it comes to things that are so large that the speed of light delays are appreciable, perfectly rigid materials don't exist- in fact, they can't exist in the real world. When you push on one end of the stick, the stick ahead of where you are pushing compresses slightly-- the other end doesn't move until the compression wave catches up to it.

--Geoff