Would time slow down tied to a nuclear-powered oscillator?

[DavidReishi]

I've always wondered this. Let's say we're not limited by the type of vibration, e.g. if choppy vibration doesn't constitute continuous movement, then some sort of oscillating vibration.

 

[Ibix]

If you are simply asking whether a clock shaken backwards and forwards would tick slowly compared to a stationary clock, then yes. Essentially all you have is a repeated twin paradox, and the traveling clock ends up younger.

I have no idea where you think the "nuclear powered" bit comes in.

 

[DavidReishi]

I included the nuclear powered factor to indicate that I'm speaking practically, not only theoretically. Years ago I asked a professor if we could travel forward in time using some kind of device rotating around an axis. He said no, because in practice the force created by such movement around an axis would destroy everything. So that led me to wonder, could we achieve practical forward time travel through vibration?

 

[PeterDonis]

Years ago I asked a professor if we could travel forward in time using some kind of device rotating around an axis. He said no, because in practice the force created by such movement around an axis would destroy everything.

And back and forth vibration, at a frequency high enough to give significant time dilation, would also create forces large enough to tear apart the device--at least if it were made of any known material. And even if the device survived, your body wouldn't, because it would be subjected to the same forces.

 

[Ibix]

You're going to run into the same issue that the energy needed to accelerate to any noticeable fraction of the speed of light is prohibitive whether you try to spin around, shake backwards and forwards, or travel to a distant star. The last one will be the least crazy because you only have to accelerate and decelerate twice.

 

[DavidReishi]

Well that blows.

 

[A.T.]

I liked the original thread title better.

 

[DavidReishi]

I liked the original thread title better.

Me too. Why'd it get changed? Is oscillation-type vibration not really vibration?

 

[PeterDonis]

Why'd it get changed?

Because of unfortunate connotations of the original word.

 

[DavidReishi]

Lol. BTW, what you said about back and forth vibration destoying the device and the poor soul in it, would you say the same about oscillatory vibration...if such a thing exists? (I'm imagining a range of motion virtually invisible to someone looking on.)

 

[PeterDonis]

would you say the same about oscillatory vibration...if such a thing exists? (I'm imagining a range of motion virtually invisible to someone looking on.)

I'm not sure what this means, but if the motion is not detectable to an onlooker, it's probably not sufficient to give you any significant time dilation relative to that onlooker. So there would be no point if your objective is to "travel forward in time".

 

[DavidReishi]

I'm not sure I follow. If the motion is motion enough to cause any time dialation, then wouldn't how much time dialates be a function of nothing other than the speed of that motion?

 

[PeterDonis]

If the motion is motion enough to cause any time dialation, then wouldn't how much time dialates be a function of nothing other than the speed of that motion?

Yes, but motion that is undetectable to an onlooker is going to have way too little speed to matter. People can detect speeds of a fraction of a meter per second, which is a time dilation factor of around one part in $10^{18}$--i.e., you would age slower than someone at rest by less than a second over the time since the Big Bang.

Also, even if time dilation itself depends only on speed, that doesn't say anything about what it takes to maintain that speed. The general scenario you are proposing is that you want to stay in one local region of space (roughly speaking, the vicinity of the Earth) while at the same time moving, with respect to people at rest in that location, at relativistic speed. The only way to do this is to subject yourself to acceleration, and the larger the speed you want to maintain, the larger the acceleration you have to withstand. The only difference between moving around a circle and moving back and forth in a straight-line oscillation is that in the former case the acceleration is constant, while in the latter case it is intermittent (when you turn around at each end of the line). But in both cases, the acceleration will be unbearably large (by many orders of magnitude) for any speed that gives any significant time dilation. Run the numbers and see.

 

[Nugatory]

I'm not sure I follow. If the motion is motion enough to cause any time dialation, then wouldn't how much time dilates be a function of nothing other than the speed of that motion?

Don't guess, calculate.
The position $x(t)$ of an object oscillating with cycle time $T$ and amplitude $A$ is given by $x(t)=A\sin\frac{2\pi}{T}t$ (because that's the definition of an oscillator). The maximum speed reached in a cycle will will be $\frac{2A\pi}{T}$ and the maximum acceleration will be $(\frac{2A\pi}{T})^2$ (because that's what you get when you differentiate the position with respect to time). Choose a value for $A$ that you would consider to be "virtually invisible" to an onlooker; then consider what value of $T$ is needed to get the speed up to an appreciable fraction of the speed of light; and see what acceleration and hence force that implies. How does your time traveller feel after a few cycles?

And while you're at it, there's another calculation that everyone should try at some point: What is the kinetic energy $E_k=(\gamma-1)m_0c^2$ of a 100kg person moving at a speed that will cause 10x time dilation? Compare with rough estimates of the total explosive energy of all the nuclear weapons on Earth and of worldwide annual power generation.