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this post was submitted on 15 Nov 2023
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Conservation of momentum is a law of nature, making it natural to assume it would still hold even with a hypothetical power. But you do you. It's ok to be wrong sometimes.
But what if teleportation doesn't move you from A to B, but just lets you disappear and reappear while you're just standing there, so that there's no momentum at all?
No momentum at all relative to what? Relativity tells us that there is no fixed frame of reference. In practice what that means is there is no universal zero velocity. You only have velocity relative to other things. The implicit assumption in your argument is that you would have no momentum relative to the earth, which in itself is problematic. After all, the earth spins at a rate of 360 degrees per day, so not moving relative to the earth would mean moving 463.83 m/s relative to the surface of the earth at the equator, which is supersonic. But maybe you mean relative to the surface of the earth. What if you go to the moon? Or mars? Or into orbit? Maybe you mean relative to the nearest big thing. If you could somehow teleport from the ground into a plane, would the plane count as the nearest big thing? What about a bus? That's on the ground, so maybe the nearest big thing would be the ground, if the mass of the thing matters in how the nearest big thing is determined. You can see how this can quickly turn into a mess of rules and special cases.
Where does the energy go if you are already moving when you teleport? Do you somehow lose all mass for a brief second? Instant transportation from point A to point B means that there is no in-between state to change the variables of nature. Zero time passes between being here one second and there the next.
Most everything that has mass and is moving has momentum. If momentum were to somehow be cancelled, which it can't be, your body would probably just stop completely. Even electrons have mass (9.1093837 × 10-31kg) and just stopping all electrical signals in your body at the same time seems like a bad thing. (I say "most everything", because there are these strange things called photons. It doesn't have mass, but has momentum. It's also a particle (err.. "energy packet"?) and a wave, which is even weirder.)
Sure, we are taking about a completely fictional situation when it comes to teleporting so this conversation is just really just a thought experiment.
If you were granted any wish, but you only received an extremely literal version of that wish, what are the consequences? That is humorous to think about, actually.
If you are in fact moving, there'd be momentum, like you say. But if you don't? If you just sit there, and teleport from one comfy armchair into another, not changing anything about your position?
That goes back to my point about the humble electron.
There are a ton of things moving in your body all the time regardless if you are sitting still of not. The only thing that I can think of that would be drastically impacted by instant cancellation of momentum is electrical signals. I admit, that is absolutely pushing the boundaries of what I know about physics at that scale.
Stopping every electrical signal in your body simultaneously and assuming it will just resume spontaneously seems odd to me, is all.
Well you see, there’s also the problem that if you teleported and it got rid of your momentum, unless something immediately speeds you back up to the speed of the earth, it will just woosh past you. Even if something like the air sped you up, while it’s speeding you up, the friction would likely tear you apart.
conservation of momentum is only a true, when translational invariance holds. In addition, there may be a countless number of mechanisms by which teleportation changes a persons momentum. E.g. maybe the way this kind of teleportation works is Star Tek-like and your atoms get disassembled and reassembled, meaning they don't need to have the same overall momentum, when whatever is doing the dissassembly stops atoms for dissassembly.
There are a ton of conditions that are left floating, for sure. Some people here are imagining this as "instant" teleportation. As in: here one second, there the next.
If zero time passes when a person is teleported, that causes some problems. I like thinking about that one, TBH. That starts to dive into the realm of breaking space itself, which is super cool to noodle on. (Wormholes FTW!)
My own questions would be more about how disassembly and reassembly would maintain original state. If an electron is moving when it is transported, where does that momentum go and how is it reapplied.