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Assuming it's possible to vibrate a human at near light speed without harming him, would a few minutes of this from his point of view be much longer from a stationary observer's point of view?

In other words do vibrations work the same as normal movement with regards to time dilation?

So a person could walk into such a machine, and walk out hundreds of years in the future, even though a much smaller amount of time would have passed from their perspective?

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    $\begingroup$ Somebody should make an anime which has a goofy character who can vibrate his hands so fast that he can grab objects out of the future and pull them into the present. $\endgroup$ – DumpsterDoofus Dec 29 '13 at 2:03
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There's two kinds of vibration that would make this "work": thermal vibration and actual shaking. Actual shaking is out of the question because that would involve pushing and pulling a person back and forth such that their average velocity was near-light speed. The "back and forth" part of this would involve way more acceleration, hence force, than the human body could handle.

To have a look at thermal vibration, i.e. heating, we use the following formula for the average velocity of molecules in a body of temperature $T$ (see below for note):

$$v = \sqrt{\frac {3kT}{M}}$$

and in so doing make the assumptions that the body is made up of molecules with the same mass $M$ with uniform temperature $T$. Let's take a human made entirely of carbon-12 for which $M$ is 12 kilograms divided by Avogadro's number. For $v \approx c$,

$$T \approx \frac {Mc^2}{3k} \approx \frac {2*3^2}{3*1.38}*10^{-23+2*8-(-23)} \approx 4.4*10^{16}K$$

which is pretty hot.

So I'm not really answering your question.

Do vibrations work the same as normal movement with regards to time dilation?

Yes.

So a person could walk into such a machine, and walk out hundreds of years in the future, even though a much smaller amount of time would have passed from their perspective?

Well you could do it in principle, and the particles you started with would have travelled into the future, but it would be a stretch to say that the thing you end up with in the future is the person you started with in either method of vibration.

Note: This formula only holds for ideal gases, which a relativistically heated gas is not. But it gives an estimate of the ballpark of temperatures we're working in. If someone has the expression for the hyper-relativistic thermal velocity I'd appreciate a comment or edit :)

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  • $\begingroup$ The equation you have for $v$ comes from the equipartition theorem, and is strictly speaking true only for an ideal gas or perhaps a lattice of springs. Also, is your temperature supposed to be in Kelvin? $\endgroup$ – lionelbrits Dec 29 '13 at 0:34
  • $\begingroup$ @lionelbrits Thanks for catching the J. As for the formula, I know there exists a hyper-relativistic expression for the thermal velocity but I couldn't find it after some searching so used this one to give an estimate. I should mention that though. $\endgroup$ – Andrew Odesky Dec 29 '13 at 0:42
  • $\begingroup$ I'm hesitant to conclude anything about the reference frame of the person from the reference frames of it's particles. While the particles indeed have a greater proper time, and somehow the average proper time has been increased, (stable) particles don't have any notion of time, so there is no a priori reason to transfer this time dilation to the centre of mass reference frame. More likely, once you have cooked the OP in this fashion, you have increased his mass-energy, curving the space around him, thereby causing time dilation. $\endgroup$ – lionelbrits Dec 29 '13 at 0:49
  • $\begingroup$ What about an artificial time varying gravity field that is flat enough over a human sized volume that the tidal forces are bearable? The proposed time traveller then "free-falls" in the field for a while whilst we all age on the outside. The generator for such a thing would be one hell of a complicated beast though and probably would need a star to power it. We could radiate "hello World" gravitational wave announcements at the same time! Actually, even a Newtonian interpretation shows this is OK: you need all the atoms in your body to undergo the same acceleration, then there is no stress. $\endgroup$ – WetSavannaAnimal Dec 29 '13 at 0:55
  • $\begingroup$ I don't have anything useful to contribute here, except to say that this has to be one of the most made-you-smile questions and answers I've read so far on se. "but it would be a stretch to say that the thing you end up with in the future is the person you started with in either method of vibration"... LOL! $\endgroup$ – user1459524 Dec 29 '13 at 2:20
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In principle, yes, it would work. However, there are two huge practical issues that would probably make it much easier to just fly to a distant star and then come back, or go and orbit a black hole for a bit.

The first has already been mentioned: it would be very difficult to apply the vibrations in such a way that the person isn't immediately liquidized. Under normal circumstances a human being can't take more than a few $g$'s of acceleration, even with a G-suit, and this is nowhere near enough to accelerate them to near the speed of light in a fraction of a second, which is what you'd need to do repeatedly in order to do what you're suggesting.

As Rod Vance says in a comment, it could in principle be done with a time-varying gravitational field, which would apply exactly the same acceleration to every part of the body, so there wouldn't be any stress. However, then you'd run into the second issue: the energy it would take.

Accelerating a person up to $0.99c$ means changing their kinetic energy by $$ \Delta E = \frac{mc^2}{\sqrt{1-v^2/c^2}}-mc^2 \approx 4\times 10^{19}\:\mathrm{J}. $$ (calculation). You'd need to do this many times a second (if you did it only once per second the person would be flying almost to the moon and back on every vibration) so you'd need a total power of at least, let's say, $10^{24}\:\mathrm{W}$. The curent total power generated by humans on Earth is around $2\times 10^{12}\:\mathrm{W}$, which is nowhere near enough. The sun puts out around $4\times 10^{26}\:\mathrm{W}$, so I guess it might be possible using a Dyson sphere, but this would take a huge fraction of an advanced space-faring civilisation's power output just to send one person forward in time. It's difficult to imagine how you could dispose of the waste heat this would generate.

In principle you don't need to use all this energy, because you could recover the person's kinetic energy on every stroke, store it, and then turn it back into kinetic energy going the other way. But again it's very difficult to imagine how to do this. Though in a sense, this is what happens when you orbit a heavy object, so maybe orbiting a small black hole is the best way to do this after all.

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protected by ACuriousMind Jan 10 '17 at 18:31

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