Puzzling thing about Speed of Light/Speed of Causality

[polymath257]

So this is a perplexing thought experiment I found online.

The sun is approximately eight "light minutes" away. This means that if the sun were suddenly to go dark, we on Earth would not become aware of it until eight minutes after the fact. Most of us are familiar with this aspect of the speed of light.

Now here's the weird thing: the speed of light is also the speed of causality. And the implications of this are semi-paradoxal (at least to me). In any case, it seems to defy my intuitions about how time and causality work.

This thought experiment demonstrates the part that I consider paradoxal:

Let's say there is a light switch, floating beside the sun, that can turn the sun on and off. If somebody flips the sun off, it would take us eight minutes to realize on Earth that the sun had been turned off (just as I said in the beginning of the post). Now, suppose you had a stick that stretched all the way from the Earth to the sun and you used the stick to hit the switch and turn off the sun. From the moment you thrusted the stick to flip the switch, how long would it take for you (on Earth) to see the sun go out?

The answer is: approximately 16 minutes. Why? Because, the speed of light is the speed of causality. It takes eight minutes for a cause on Earth to become an effect on the light switch that is floating beside the sun. So it would take 8 minutes for the other end of the stick to be affected by your thrust from earth, then it would take 8 more minutes for you to realize the sun had actually gone out.

Doesn't this seem counterintuitive? It seems like it should only take eight minutes to see the sun go out because the other end of the stick would only have to travel a few centimeters. But that is not the case.

What happens when you 'use the stick to turn off the sun'? You push on it. That produces a compression wave that travels down the stick at the speed of sound in that stick. This is much, much slower than the speed of light. So, in fact, it would take much longer than 8 minutes for the compression wave from your push to get to the sun. Once it does, and the sun goes out, the effects of that move outward at the speed of light.

The point is that in relativity, there are no 'solids' that instantaneously transmit information from one end to the other. Such transmission happens as a compression wave along the solid which travels at much less than the speed of light.

[The Grand Nudger]

Doesn't this seem counterintuitive? It seems like it should only take eight minutes to see the sun go out because the other end of the stick would only have to travel a few centimeters. But that is not the case.

I think it seems counterintuitive because we're not used to dealing with distances like that...but the same thing happens here on earth, your stick centimeters away from the switch and your eyes a few feet from the lightbulb, all numbers scaled down....far too fast for you to be able to detect with the unaided eye.

You could get a stop motion camera and see the compression, though you're unlikely to notice the lag between the switch breaking the current and the light going out.

(totally off topic, but the speed of a signal over cosmic distance is one of the more amusing arguments against omniscience, too.)

[polymath257]

Good point Mat. I can understand the 16 minutes easier now.

But what if we had an entangled switch!

That won't help. Entanglement doesn't produce a causal connection between the ends: it produces a *correlation* between the ends. Both ends look random until the observations are brought together and compared.

In other words, there is no way to throw an entangled switch.

[ignoramus]

Pfft! Next you'll tell me the transporters in Star Trek aren't real!




(Also Khem, remember that most Gods live outside of our spacetime so are not bound by our universal laws! Haven't you been paying any attention to our resident theists all these years! )

[vulcanlogician]

What happens when you 'use the stick to turn off the sun'? You push on it. That produces a compression wave that travels down the stick at the speed of sound in that stick. This is much, much slower than the speed of light. So, in fact, it would take much longer than 8 minutes for the compression wave from your push to get to the sun. Once it does, and the sun goes out, the effects of that move outward at the speed of light.

The point is that in relativity, there are no 'solids' that instantaneously transmit information from one end to the other. Such transmission happens as a compression wave along the solid which travels at much less than the speed of light.

Wow. Thanks for the info. But still it seems paradoxical to me for this reason: Let's say that the side of the stick that is near the switch is only 3cm away from it, but on earth, when I thrust the stick I thrust it 10 cm forward. If it takes it so long for my thrust to "register" on the other side of the stick, will I not feel the resistance of the other end striking the switch on my end?

I suppose, for sake of this second example, we could replace the lightswitch with a brick wall. Obviously, I can't push the stick with enough force to push through a brick wall. But how does that work if the stick is only 3 cm away from the wall and I thrust the stick 10 cm?

[The Grand Nudger]

Ever seen an arrow firing? It's like that.

[polymath257]

What happens when you 'use the stick to turn off the sun'? You push on it. That produces a compression wave that travels down the stick at the speed of sound in that stick. This is much, much slower than the speed of light. So, in fact, it would take much longer than 8 minutes for the compression wave from your push to get to the sun. Once it does, and the sun goes out, the effects of that move outward at the speed of light.

The point is that in relativity, there are no 'solids' that instantaneously transmit information from one end to the other. Such transmission happens as a compression wave along the solid which travels at much less than the speed of light.

Wow. Thanks for the info. But still it seems paradoxical to me for this reason: Let's say that the side of the stick that is near the switch is only 3cm away from it, but on earth, when I thrust the stick I thrust it 10 cm forward. If it takes it so long for my thrust to "register" on the other side of the stick, will I not feel the resistance of the other end striking the switch on my end?

I suppose, for sake of this second example, we could replace the lightswitch with a brick wall. Obviously, I can't push the stick with enough force to push through a brick wall. But how does that work if the stick is only 3 cm away from the wall and I thrust the stick 10 cm?

The signal travels down the stick at the speed of sound in that stick: the speed of a compression wave. This is fast enough that for 3cm, we don't notice the difference. But if the stick was a few kilometers long, we would.

So, in your scenario, you push on the stick with a certain force. This accelerates the near end of the stick, starting a compression wave in that stick that travels down the length. Typically, for 'short' sticks in your room, the speed of that compression wave is fast enough  that it looks like the whole stick is moving as one piece, but a slow motion camera will show otherwise. When the far end of the stick hits the wall, there is a reverse wave that is created, that also travels down the stick (in the opposite direction), eventually reaching your hand, producing a force on it that you notice.

There are signals in both directions.

The amount of compression for a given force is determined by the type of material in the stick, which also determines the speed of sound in that stick.

---

You might want to look at this:

https://en.wikipedia.org/wiki/Young%27s_modulus

[vulcanlogician]

Okay, I see. I wasn't thinking of it in terms of the compression wave traveling all the way down and back. I think I understand it now.

[I_am_not_mafia]

(totally off topic, but the speed of a signal over cosmic distance is one of the more amusing arguments against omniscience, too.)

Also an argument against the idea of brains being somehow controlled or guided remotely by a soul or a god, whether that's Drich's ludicrous idea of the brain as an antennae for a soul or religionists thanking their god for enabling them to knock a ball into a net. You come across real-world consequences of this in the field of artificial intelligence when people assume that you can do the processing on a nearby PC rather than in the small on-board processor in the robot and thus bypass power and performance constraints. What happens is that you get latency. Not so important if you are cutting the wires of a bomb but particularly important if your robot is walking and trying to maintain balance.

So it's quite important to ask how far away Mr God is. If the religionists then start talking about their god being in another dimension then this means that they believe in a flat god. If they instead say that their god is everywhere then how come we can't detect it?

[Whateverist]

Okay, I see. I wasn't thinking of it in terms of the compression wave traveling all the way down and back. I think I understand it now.

My intuition was the same as yours: that the stick, being a rigid object, would transfer the motion instantaneously.  Did not think about compression waves at all.  What I did think about was how difficult it might be to actually push that stick at all.  Could I even do it? Not mention the difficulty of lining up the push given that we're standing on a fast moving planet as well as one that is rotating.