Why would'nt this work?
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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 which 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 there's some delay since part of the movement of that wave is actual atoms moving and atoms have mass so they can't travel as fast as the speed of light).
In normal day to day life the rods are far to short for us to notice the delay between the pushing the rod on one end and the rod pushing something on the other end.
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I used wave function as a bad form of shorthand for the general properties of the photon, such as the theoretically infinitely extending magnetic and electric fields. Those associated fields stop existing when the photon is absorbed onto a screen. They collapse faster than light can travel. This doesn't ruin much of modern theories, because there doesn't seem to be a way to transfer usable information through this phenomenon.
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Best answer
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It depends on the person who's holding it and pushing it. For me it takes at least three minutes!
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I don't see this mentioned in any of the other comments: the repulsion between atoms that causes the movement to propagate through the stick is actually communicated via photons. So your push really generates the same kind of particles that your light torch is generating, and they travel at the same speed (except slowed down by repeated absorption and excitation by the electrons in the atoms of the stick).
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That's wack af
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Neither do the two gravity wells the stick spans. And the earth and moon are moving relative to each other, someone would probably get their head knocked off by that stick. Before it eventually falls to the earth with quite a bit of force because earth's gravity well will win. Then it'll eventually settle into a giant teeter totter, assuming it is rigid enough to survive the impact.
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Putting it on the moon is just a distraction. It doesn't matter if the rod is 1m long or 100,000km.
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because...
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Alas, the longer the stick is, the floppier it gets.
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I don't get it. Care to explain?
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That'll anger the universe's devs who will then bully you.
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I'm not sure.
The beam of light would bend as it travels to the moon, delaying the projected dot on the moons surface. -
Sure, the time between detections is faster than the time it takes light to travel from one detector to the other. Nothing is actually traveling faster than light and no physical laws are broken.
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this isn't at all what this example depicts, here there is actual information transfer.
this depiction is actually just false, the light would send information faster than the stick, because in the stick information only travels as fast as speed of sound in the stick, which is why completely rigid objects don't exist
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I don't think gravitational waves traveling at the speed of light is the same as the gravitational attraction being apparently felt faster than light travels. Similarly, electric attraction between + and - charges is different from electromagnetic waves being transmitted in the field. It's not light that is "communicating" that attraction.
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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.