Asklemmy

The problem is that when you push an object, the push happens at the speed of sound in that object. It's very fast but not anywhere near the speed of light. If you tapped one end of the stick, you would hear it on the moon after the wave had traveled the distance.

For example, the speed of sound in wood is around 3,300 m/s so 384,400/3,300 ~= 32.36 hours to see the pole move on the moon after you tap it on earth.

It would work, but only in the impossible world where you have a perfectly rigid unbreakable stick. But such an object cannot exist in this universe.

Pick up a solid rigid object near you. Anything will do, a coffee cup, a comb, a water bottle, anything. Pick it up from the top and lift it vertically. Observe it.

It seems as though the whole object moves instantaneously, does it not? It seems that the bottom of the object starts moving at the exact same instant as the top. But it is actually not the case. Every material has a certain elasticity to it. Everything deforms slightly under the tiniest of forces. Even a solid titanium rod deforms a little bit from the weight of a feather placed upon it. And this lack of perfect rigidity means that there is a very, very slight delay from when you start lifting the top of the object to when the bottom of it starts moving.

For small objects that you can manipulate with your hands, this delay is imperceptible to your senses. But if you observed an object being lifted with very precise scientific equipment, you could actually measure this delay. Motion can only transfer through objects at a finite speed. Specifically, it can only move at the speed of sound through the material. Your perfectly rigid object would have an infinite speed of sound within it. So yes, it would instantly transfer that motion. But with any real material, the delay wouldn't just be noticeable, but comically large.

Imagine this stick were made of steel. The speed of sound in steel is about 5120 m/s. The distance to the Moon is about 400,000 km. Converting and dividing shows that it would actually take about 22 hours for a pulse like that to travel through a steel pole that long. (Ignoring how the steel pole would be supported.)

So in fact, you are both right and wrong. You are correct for the object you describe. A perfectly rigid object would be usable as a tool of FTL communication. But such an object simply cannot exist in this universe.

The problem lies in what "unstretchable" and "unbendable" means. Its always molecules and your push takes time to reach the other end. You think its instantaneous because you never held such a long stick. The push signal is slower than the light

You're pushing the atoms on your end, which in turn push the next atoms, which push the next ones and so on up to the atoms at the end of the rod which push the hand of your friend on the moon.

As it so happens the way the atoms push each other is electromagnetism, in other words sending photons (same thing light is made of) to each other but these photons are not at visible wavelengths so you don't see them as light.

So pushing the rod is just sending a wave down the rod of atoms pushing each other with the gaps between atoms being bridged using photons, so it will never be faster than the speed at which photons can travel in vacuum (it's actually slower because part of the movement of that wave is not the lightspeed-travelling photons bridging the gaps between atoms but the actual atoms moving and atoms have mass so they cannot travel as fast as the speed of light).

In normal day to day life the rods are far too short for us to notice the delay between the pushing the rod on one end and the rod pushing something on the other end.

When you push something you push the atoms in the thing. This in turn pushes the adjacent atoms, when push the adjacent atoms all the way down the line. Very much like pushing water in the bathtub, it ripples down the line. The speed at which atoms propogate this ripple is the speed of sound. In air this is roughly 700mph, but as the substance gets harder* it gets faster. For example, aluminum and steel it is about 11,000mph. That's why there's a movie trope about putting your ear to the railroad line to hear the train.

If you are talking about something magically hard then I suppose the speed of sound in that material could approach the speed of light, but still not surpass it. Nothing with mass may travel the speed of light, not even an electron, let alone nuclei.

*generalizing

The compression on the end of the stick wouldn't travel faster than the speed of sound in the stick making it MUCH slower than light.

If your stick is unbreakable and unavoidable you have already broken laws of physics anyway

Even if it were perfectly rigid, supernaturally so, your push would still only transmit through the stick at the speed of light. The speed of light is the speed of time.

There's a thought experiment about this in most intro classes on relativity, talking about "length compression". To a stationary observer a fast-moving object appears shorter in its direction of travel. For example, at about 87% of the speed of light, length compression is about 50%. If you are interested in the formula look up Relativistic Length Compression. Anyway, if you are carrying a pole 20 meters long and you run past someone at that speed, to them the pole will only look 10 meters long.

In the thought experiment you run with this pole into a barn that's only 10 meters long. What happens?

The observer, seeing you bringing a 10-meter pole into a 10-meter barn, shuts the door behind you, closing it exactly at the point where you're entirely in the barn. What happens when you stop, and how does a 20-meter pole fit in a 10-meter barn in the first place?

First, when the pole gets in the barn and the door closes, the pole is no longer moving, so now to the observer it looks 20 meters long. As its speed drops to zero the pole appears to get longer, becoming 20 meters again. It either punches holes in the barn and sticks out, or it shatters if the barn is stronger.

Looking at the situation from the runner's point of view, since motion is relative you could say you're stationary and the barn is moving toward you at 87% of the speed of light. So to you the 10-meter barn only looks 5 meters long. So how does a 20-meter pole fit in?

The answer to both questions is compression - or saying it another way, information doesn't travel instantly. When the front end of the pole hits the inside of the barn and stops, it takes some time for that information to travel through the pole to the other end. Meanwhile, the rest of the pole keeps moving. By the time the back end knows it's supposed to stop, from the runner's point of view the 20-ft pole has been compressed down to 5 meters. From the runner's point of view the barn then stops moving, so it's length returns to 10 meters, but since the pole still won't fit it either punches holes in the barn or shatters.

One of my physics profs had double-majored in theatre, and loved to perform this demo with a telescoping pole and a cardboard barn.

The motion of the stick will actually only propagate to the other end at the speed of sound in the material the stick is made of.

You're forgetting the speed at which the shockwave from the compression travels through the stick. I guess it's around the speed of sound in that material, which might be ~2 km/s

The stick would only move at the speed of sound. Or the speed the molecules can push against each other, which is the speed of sound in that material.

Even if the stick were made of the hardest known material, the information would take about 7 hours to travel from Earth to the Moon, according to the equation relating Young's modulus and the material's density.

always had this question as a kid

And then went, draw it out, and asked.
I applaud that (and the art), good for you.

(And the good people already provided answers.)

Perhaps also worth pointing out that the speed of light is that exact speed, because light itself hits a speed limit.

As far as we know, light has no mass, so if it is accelerated in any way, it should immediately have infinite acceleration and therefore infinite speed (this is simplifying too much by using a classical physics formula, but basically it's like this: a = f/m = f/0 = ∞). And well, light doesn't go at infinite speed, presumably because it hits that speed limit, which is somehow inherent to the universe.

That speed limit is referred to as the "speed of causality" and we assume it to apply to everything. That's also why other massless things happen to travel at the speed of causality/light, too, like for example gravitational waves. Well, and it would definitely also apply to that pole.

Here's a video of someone going into much more depth on this: https://www.pbs.org/video/pbs-space-time-speed-light-not-about-light/

There's no such thing as a perfectly rigid object.

I'm not a scientist, but when I asked the same question before they said, "compression."

Like, the stick would absorb the power of your push, and it would shrink (across its length) before the other end moved. When the other end does finally move, it's actually the compression reaching it.

For anyone looking for other cool ideas or videos about speed of light etc

What Is The Speed of Dark? - Vsauce (13m:31s)

• Cool older vsauce video going over shadows and light speed etc

The Faster-Than-Light Guillotine - Because Science (w/ Kyle Hill) (14m:19s)

• Basically goes over the "FTL Scissor action" that a lot of people have covered but he does a good segment covering it.

Short version: forces applied to solid objects move at the speed of sound in that object.

Lets say your stick is made of steel. The speed of sound in steel is about 19,000 feet/second. Assuming you could push hard enough for the force to be felt on the other end, it'd take over 18 hours for your partner on Earth to feel your push from the moon.

I predict we'll have FTL travel before we can invent a stick that's "unfoldable".

I could've sworn I saw a video about this and the gist is that it's called "speed of push" and is essentially the speed of sound. When you push something, you're compressing the molecules of it and that will travel like a wave through it. Light travels faster than that wave.

I'm probably explaining wrong because it's something I'm half remembering from a video I could've seen over a decade ago, but that's the quick explanation.

Matter is made of atoms. Things are only truly rigid in the small scales we deal with usually.

So have to ask what a solid is to answer this question.

Sticks are quite complex, so lets consider a simpler solid: an elementally pure iron rod.

You can imagine said rod as if it were a fixed array of crystalline atomic cores surrounded by a jelly-like substance. In this 'jellium' model the atomic cores have a positive charge, they are the protons and neutrons, and the jelly has a negative charge. The jelly is the wavefunction that represents the electron structure in bulk. If that makes no sense, congrats on knowing your limits.

You've probably seen the more modern model of an atom where there's a nucleus and around it is an electron fuzz with discrete energy levels. Or if you've studied at uni strange geometry representing a threshold in probability of finding the electron/s there on a given measurement (if not familiar under certain conditions reality kinda unfocuses it's eyes and things that we often think of as points become volumes of possible effect). This is a good model of a single atom, but when we bring atoms together they change each other's properties and the result is that these density functions (the weird electron cloud/shape things) start to blur together.

In our iron rod the electrons delocalize sufficiently we can kinda think of it as a weird jelly. A real stick is more complex, but can kinda be thought of as a stack of smaller jelly treats packed against each other.

When you push on the rod you're mashing the jelly of your hand into the jelly of the rod, this causes a shockwave that begins to spread, it propagates like a ripple in a skipping rope or a bounce on a trampoline. But since it's moving 'amount of electron like properties here'. That makes some areas more negatively charged which drags the positively charged atom cores slowly after it. It moves much slower than the speed of light as we aren't considering individual electrons which can move energy between them via photons, but the propagation of a disturbance in the collective arrangement of many that are tightly linked (we say coupled).

We can't imagine a stick that is perfectly rigid because we would be proposing a kind of matter that does not exist, one which isn't made of a lot of fuzzy electron jelly stuff but something else entirely. We can imagine matter where the jelly is very stiff, and consequently less energy goes into wobbling it all about and the squish moves forward very fast but that speed is still much slower than light because of this collective behaviour.

Next, I suppose you'll want to know about the speed of dark 🤨

it wouldn't work, because there is no unbreakable, unfoldable stick. the stick will have flex, and the force transmitted will occur much more slowly through the molecular chain of the stick than light's travel time.

reality is much more woobly and spongy than you know.