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I'm posting this anonymously as I'm sure there's a really, really, really easy answer to this thought experiment but I'm too thick to know it.
If I had a metal rod 100 million miles long sitting in a frictionless universe, and I push one end of the rod, surely the other end moves immediately, rather than taking however long light takes to travel 100 million miles. Which means that this violates the speed of light as nowt can travel faster than that, even information. I have heard about Quantum Entanglements and homeopathic medicine but assume this is not at all related as I have no idea what a quantum is except it's probably smaller than a peanut and am not sure what memory water really has.
Now I'm 100% positive that Einstein was brighter than me, indeed suspect the vast proportion of the world will fit that large set, but nobody has explained to me why my thought experiment is wrong.
Any takers who can write in crayon and use very, very small words? Please?
that amount of metal will have some compressibility
Any rod of metal has "some compressibility". The rigidity of a solid is the result of electromagnetic interactions, which are quite willing to redistribute mechanical force orthogonally to the axis of compression. So unless your "rod" is a single layer of atoms, it can always be compressed - it will just expand to the side as necessary.
And since mechanical force travels by propagating EM interactions, it can't travel down the rod faster than EM can propagate along it. There's no need to invoke compression for this thought experiment; the OP's assumption that the far end of the rod moves immediately is simply wrong. Atoms at the near end move, which decreases their distance to their nearest neighbors, which increases the electromagnetic force between them and their neighbors. Once that force propagates to the neighbors, the neighbors are accelerated by it and move in the direction that the rod is being pushed. Nothing happens immediately.
Equally not an expert on the subject, but the first flaw I notice is that your rod (snigger) is "sitting in a frictionless universe", which is automatically not our universe and so other laws of physics are non-comparable.
Other than that, I don't think I can be of much help. I'd assume material strength/elasticity, friction, force required, etc., would be enough to make it impossible.
On the entanglement side, though, my understand is that entanglement can potentially cause a correlated effect to occur instantly at a location over a light-year away, but this (with our current understanding) couldn't be used of itself to transmit information.
The common example (which I believe I've seen repeated by other commentards) is the "two cars" thought experiment:
You have two cars (one red, one blue) hidden under sheets, and both are moved a light-year away from each other. You remove the sheet from one car and immediately know the colour of the other car. You aren't receiving this information faster-than-light, but the effect appears to be the same from your position.
IANAQM
This is better put as "you have two cars, and if you ever check, one will be red and one will be blue, but at the moment because you haven't checked it's not decided - it's not a case that one is already red and you just don't know it. It isn't. The universe hasn't decided yet. It's not red. It's not blue. No decision has been made. When you look at one, the decision is made, and if the one you looked at is red, the other one will be blue whenever someone checks, even if they check a second later a light year away, so did some kind of information travel that light year in one second?"
The key thing is that the universe doesn't decide on the colours until you check.
Where the car analogy starts getting interesting is if you could reach under the blanket with a tin of blue paint and turn one of the cars blue without ever looking at it.
If the other car must be red because the one you just painted is blue then you've got a fun toy that you won't want to think too hard about.
Okay, I'll bite...
Imagining the rod to be constructed of a non-compressible material in a frictionless universe etc etc...
Both ends of the rod move at the same speed, which is as fast as you can push one end. This must be less than the speed of light.
As for information, well, it's not made of matter... so, excuse the pun, it doesn't matter...
Information is near enough the same thing. Everything in the universe is made of information and matter (or information and energy depending how you squint). "Nothing" can move faster than light in this universe (so far as we can tell with all our observations and calculations).
This should not be a problem though. It's only humans that are concerned with the speed of travel or progress, photons, protons and information can take as long as it wants. ;)
The metal rod is not infinitely rigid. Therefore it's like a very very stiff spring. When you push one end, the atoms are momentarily compressed, and pass that force onto the next atoms as they start to move and so on down the rod. You're pushing against the inertia of the rod, making your end accelerate. That wave of compression passes along the rod at less than the speed of light until the other end starts moving too.
When you stop pushing, the atoms at your end spring back, and eventually the whole rod returns to its original shape. Now the whole rod is moving through your frictionless universe, but the whole rod (including both ends) is moving at a steady speed. There's no actual 'change' (read 'information') going on anymore.
This post has been deleted by its author
There are no stupid questions :-) But this might be a stupid answer...
Compress your thought experiment back down to a hundred meters ... You hold one end and tap it - I hold the other and listen. What you are doing is (slightly) moving the rod and transmitting a wave - this travels at the speed of sound (albeit in metal - I think that's around 10x faster than in air) but it's a lot slower than light, never mind instantaneous.
Imagine if you will the venerable Saturn V rocket on the verge of takeoff. The rockets at the bottom fire and start pushing up the bottom of the rocket. However, the top of the rocket does not react momentarily. For that instant, the rocket compresses and propagates up the height of the rocket until the top start moving.
A similar thing can be observed with the humble Slinky. There is an El Reg article about a Slinky experiment that discusses the phenomenon at length.
Basically put, nothing in the universe is perfectly rigid. Apply a force at one end of the rod and, instead of the whole rod moving at once, the rod will compress at that end, and a compression wave will run down the length of the rod at subuminar speed. The other end won't react immediately because of this.
Incidentally, this compression phenomenon exists regardless of friction, as it can also occur in space where friction is as close to zero as we can get it.
I'm afraid that's physically impossible in so many ways.
A gravitational force would act along the axis of the rod, compressing the centre until it snapped. Even a small alignment error would cause the rod to twist and buckle as the ends were attracted to the centre. Unless you got your push perfectly aligned, the same thing would happen. (I've ignored the problem of not having the rod spinning in the first place.)
If you manage those problems, then there is no perfectly rigid material you could use to manufacture the rod so the best case is your "push" travels down the rod as a compression wave (sound wave) with the other end moving many years later. But it's more likely it would behave as if one end was anchored: rebounding elastically if the push was small; snapping if it was too big.
If I had a metal rod 100 million miles long sitting in a frictionless universe
A frictionless universe won't help you here. Instead you'd need an incompressible rod... not something you can make out of normal matter (see also: black holes). You push the end of the rod, you generate a compression wave, and that will travel at a finite speed even in incredibly dense material (do a quick search for 'speed of sound in neutronium', for example).
Now, I Am Not A Theoretical Physicist, but I rather suspect that you could only manufacture the required massless and incompressible rod if you already had some sort of superluminally propagating force, making it a bit of a circular argument!
Homeopathy does not work
Well, it does, but you have to choose your victims patients carefully. As homeopathy's effectiveness is equivalent to that of a placebo, it should be administered only to hypochondriacs and other true believers in order to properly "treat" what ails them.
In fairness, placebos are very effective for pretty much everyone. Bizarrely, it doesn't even matter much if you're told that you're taking a placebo. Oh, and it helps if you're charged a lot of money. Seriously.
Anecdotally, I was given homoeopathic medicine when I was covered in very virulent mosquito bites. It worked brilliantly within minutes, and I know that stuff is a load of bollocks.
As homeopathy's effectiveness is equivalent to that of a placebo, it should be administered only to hypochondriacs and other true believers in order to properly "treat" what ails them.
Studies have shown [sic] that the placebo effect works even then the patient knows they are receiving a placebo.
Homeopathy is total bollocks though, along with beliefs in 'crystal energy', any sort of 'quantum healing' and sky fairies.
I've thought about that as well. I think the rod will compress when you push on it. Even a miniscule amount of compression adds up over 100 million miles, and you're trying to move a lot of inert mass. Eventually the rod will decompress and the far end will move, but not simultaneously with the near end.
The rod could be completely mechanically incompressible (in the sense that the inter-atomic forces were effectively infinite) and the effect would still propagate at the speed of light since everything including forces propagates at the speed of light. The lightspeed limit is implemented at layer 1 of the universe.
Propagation is not instantaneous. Each atom bears some pressure and passes it on to the closest one.
Pushing on a 100 million miles long rod would not move the other end instantaneously.
You can actually easily test this in reality.
Just take a 2 meters long spring (ok, hard to get by but you can engineer one much more easily than a 300 million miles long pole). Push on one end.
By now you are imagining what's happening and you don't need to actually test it. It probably is obvious to you that the spring will compress some on your end beforespringing on the other end (and that'd be true even without and friction).
Well, your pole is the same. It's way less compressible than a spring, but then you'd have to apply inifinitely more pressure to actually give it the same acceleration as the spring. So in the end, it'd would compress, that compression would propagate at some speed actually probably way below the speed of light, and your thought experiment problem is solved.
All along it was not a real problem but just the fact that it's not a real thought experiment but just assuming that because you don't see the delay at our scale, there isn't one. Even at our scale, there is.
See also:
Dropping a slinky
The speed of sound in a slinky is much lower than the terminal velocity of the spring, if you hold one end of the spring and drop it, the bottom of the spring will not start moving before the top reaches it, as the acceleration under gravity will quickly cause its speed to exceed the speed of sound in the spring (the speed at which the compression wave propagates).
It's a cool experiment, but here's the question - when you let go of the top of the spring, does the bottom become weightless?
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