# Relativity and very long sticks.

So, you take a stick, and you use it to poke things with. Move the end in your hand, and the far end moves apparently at the same time. You can use a long stick to tap out a message, eg on a high window.

Now just suppose you had a very long stick. One end is on Earth, the other end is at Proxima Centuri, 4.22 light years away. It is, of course, made of that wonderful substance unobtanium which has the properties of being super light, so the entire stick only weighs 1 kg and super strong, so the stick dfoesn’t bend or break. So, you push and pull the near end of the stick, tapping out a message in Morse Code. What happens to the far end? Since we know that information cannot travel faster than light, the far end can’t move, can it? Or does it?

So, what exactly happens to the stick during those years? does the stick compress, then expand 4.22 years later? Does the stick stay still when you push it, then move 4.22 years later, or what?

The morse code propagates through at the speed of sound, actually, so your information gets there much, much later than 4.22LY. The stick compresses just like it always does, sending a compression down the line until it reaches the end.

I think it is more interesting to think about what happens if two people (or a a person and an alien…) start to pull in opposite directions. You can pull on the stick for many, many years until you realize someone is pulling on the other end (and likewise on the other end). Your “super strong” stick would break somewhere in the middle, after stretching for a while, I’m sure. Or, the stick would just stretch a LOT.

-Tofer

Why the speed of sound? AIUI that is caused by molecules of Nitrogen, Oxygen and CO2 bumping into each other. Why would it proipogate along thge hypothetical stick at the same rate?

Variation of the question: what if the stick has a pivot in the middle, 2.11 LY away. You move the near end up, and the far end moves down, and vice versa.

When you tap on anything, the molecules bump into the next molecules over, this repeats, and that’s called “sound.” Sound travels much faster in solids than in gasses, as the molecules are packed pretty close together (and it travels medium-fast through liquids), but sound still only travels at about 13,000mph through steel (quick, but still 50,000 times slower than the speed of light).

-Tofer

Perhaps I’m reading the OP differently. I took it that the stick-holder was moving the stick forward and backward in a Morse code pattern, rather than tapping a message on the stick.

Ah – doesn’t matter. A push and a pull will do the same thing – the molecules in the stick have to communicate with neighboring molecules, and they do this at the speed of sound. They have to physically move through space, and when you push on the end molecule, it moves to the next one over at the speed of sound in that material. The process repeats all the way to the other end of the stick.

-Tofer
p.s. I’m assuming that unobtanium, despite its super qualities, is still matter as we know it and not some sort of incompressible theoretical non-mass substance.

Not to mention the Earth is rotating and also moving in relation to Proxima Centuri.

There cannot be an incompressible anything. Relativity precludes the existance of any such animal.

correct, that’s exactly what I was intending.

It also precludes the existence of any such animal.

It’s another one of those “let’s suspend half the laws of physics, and examine the results” type of problem.

The object (stick) cannot have mass, or it collapses instantly under its own gravity. The stick must have infinite tensile strength, or be instantly wrenched into pieces by gravity, impacts with other objects, and solar winds. It has to have a non orbital motion and somehow remain inside the orbits of two unrelated systems without moving with respect to either of them, and somehow remain the same size and shape while it does it. It must have no interactions with magnetic or electrical fields.

Unobtainium certainly has some interesting properties. Why not assume that it also magically transmits information at infinite speeds as well? That, it seems to me is no less reasonable than its existence.

Tris

I don’t know about that, Triskadecamus. Just today, I went hiking with a stick that had mass, finite tensile strength, and electromagnetic interactions, and it didn’t collapse under its own weight, be wrenched into pieces, or impact with anything I didn’t want it to impact with. Does oak qualify as unobtainium now? The effect we’re talking about here is most dramatic with a stick light-years long, but with sensitive enough instruments, there’s no reason you can’t do the same experiment with a stick light-nanoseconds long like my hiking staff.

It should be noted that in the OP’s experiment, the signals travel at whatever the speed of sound is in the material of the stick, which might be significantly faster than in steel. Sound travels through a neutron star at speeds very close to that of light, for instance. But the speed of sound can still never exceed that of light, in any real (or even theoretical) material.

Peter Morris, you thievin’ rascal, I posed this exact same question (really, almost word-for-word exact – long perfectly rigid stick from here to Proxima Centauri, push the stick forward an inch, when does it move at the other end?) in my high school physics class. Would the stick move at the same time? Or would the movement propagate at the speed of light? Or some other speed? I posed it during a discussion with my friend Lu, who’s pretty good at math, and he asked his dad, who’s a civil engineer.

Lu came back the next day and told me what his dad said. The movement will propagate at the speed of sound in the stick, but if the stick is really perfectly rigid, it would have to be infinitely dense, and “speed of sound” would equal “speed of light,” so the movement would propagate at the speed of light in that case. Of course, he pointed out that something with infinite density would either have to be infinitely massive, in which case you wouldn’t be able to move it at all, or would have to be a singularity, in which case you wouldn’t want to get near enough to poke it.

I said “Well, let’s just suppose it achieves its rigidity by being like the blade of a Slaver variable sword: a wire encased in a stasis field so it can’t bend at all.” We were big fans of Larry Niven back then, you see. Some of us still are[sup]1[/sup].

His dad’s reply was that if I brought him the stasis-field-encased wire, he’d study it and give me the answer then.

The whole thing still confuses me.

[sup]1[/sup]Okay, just me.

Chronos I don’t understand why the information is limited to the speed of sound. For example, you could take your oaken hiking stick and attach it to the nose of a supersonic jet. Give the handle a mach-5 push, the tip also moves at mach-5, doesn’t it? So, in the case of the super-long stick, why can’t you move the entire stick faster than sound?

Not that I think you’re wrong, you understand these things better than me, I just don’t follow your answer.

Here’s an article by an intersting character that touches on the point that back-and-forth motion in a lage body is really just vibration (ie sound) at a very low frequency.

He takes some getting used to, and this article seems kinda crazy unless you’ve read more of his (fascinating) site. He used to be a SDMBer as well, but I haven’t seen a post of his in years.

http://www.amasci.com/miscon/a-rant.txt

What you’re missing is, when you shove one end of a stick, any stick, the other end doesn’t begin to move instantaneously. The impulse to move is transmitted along the stick via a compression wave at the speed of sound in that stick. Even when tapping on someone’s window with a broom handle! You just don’t notice it because the speed of sound in a broom handle is very high compared with its length.

In fact your broom handle acts like a stretched-out slinky toy - shove one end towards the other and a wave of movement travels along it, eventually inducing the other end to move. For a tiny instant, as you accelerate one end of the stick, the other end stays still and the stick gets shorter.

A stick on the end of a supersonic jet, or inside of it, is already moving at mach 5 - every bit of it, along its length. And your broom handle that you tap on the window with is moving around the sun at 60,000 mph, as are you. This isn’t relevant - if everything is moving along together at the same velocity, you can treat it as if you’re standing still.

Matt, that’s somewhat clearer.

So, when I give the stick a shove, I compress it at this end. The stick gets shorter. Then many years later it expands again at the other end. Is that right?

Maybe it would help to think of a very long freight train instead.

When the engine starts moving the first car jumps forward, then transmits the motion through the coupler to the second car, and so on until the caboose finally moves some time later. (It works the same way if the engine goes into reverse. and bumps into the first car which bumps into the second and so on. One way is in tension, the other compression, but the principal is the same.) The wave of motion propagates through the train.

There is no way that the caboose could move at the same time at the engine without infinitely tensile (or compressible) material, which can’t exist in the real world. The speed of the wave depends on the materials used and the initial motive power of the engine.

The stick can be moving faster than sound, but it still can’t transmit information from one end to the other faster than sound.

Exapno Mapcase’s analogy is very good; when a train locomotive starts moving, the “wave of motion” propagates through the train. It may propagate at 30mph, so that it takes 2 minutes (1/30 hour) for an entire 1-mile long train to start moving. That doesn’t mean the entire tran can’t eventually reach 100mph. It’s just that each time the engineer throttles up/down the locomotive, the conductor on the caboose will feel the change in speed 2 minutes later.

And please don’t ruin the analogy by pointing out that a train in motion has all its couples stretched to the max already, and therefore the “wave of motion” would propagate much faster.

Actually, that helps with the point. When a engineer has to use the emergency break there is no time for the cars to respond to the slowdown. What happens is that the train crumples into a zig-zag shape and leaves the tracks. That’s not different in principle from what earlier posters were saying about any finite stick being shattered by gravity. An instantaneous force is damaging when it exceeds the material’s limits.