Rotating disc: tidal relativity across surface of disc

[red_ed]

TL;DR

relatavistic gradient across rotating object

I've been told this is an extension of the Ehrenfest paradox, which is interesting but not explanatory.

Gedankenexperimenten: take any object and rotate it. Lets use a disc for simplicity, but by extension the question applies to any relative motion. The center of the disc is stationary (has zero translational velocity). The edge is moving relative to the center and moving relative to the environment.

In the real world the disc will come apart at some high rpm. But lets pretend it doesn't. Spin it fast. The edge approaches c. The center is still stationary. Clearly there is a relativisitic gradient from the center to the edge, with the edge doing all that fun compression-in-direction-of-motion and mass increase and time slowing. While the core tracks the ambient space-time.

Questions: what does this do to the disc? More importantly, what implications does this have for contiguity of any given object? When does an object cease to be a singular object and become a collection of separate objects? What is the granularity of such a separation?

By extension, any contiguous object (say, you hand while typing) experiences relativistic motion (one finger types a letter while the adjacent finger is hovering). Yes, these are slow enough to ignore the relativistic issues. But ignoring does not mean they are not occurring. My point is to suggest we are constantly tearing at space-time fabric by existing. Not sure what that implies, though, so I"m asking. Dont' let normalcy bias prevent insight!

Last bit of the experiment: add a second disc placed next to but not touching the first, but counter-rotate it relative to the first. Clearly the space-time gets torn a-la frame-twisting around black holes. But what else happens?

I'm a PhD but not of physics, so please act as if I were an intelligent but uneducated newbie. Explain in simple terms rather than equations...such may be useful or may simply obscure the event.

Thanks!

 

[Nugatory]

My point is to suggest we are constantly tearing at space-time fabric….

The term “fabric” is used as a metaphor in unserious descriptions of relativity to avoid the math required for a real explanation of the theory. But it is a metaphor, and will be serious misleading if taken too seriously - there is no fabric and hence nothing to “tear”. So your question is based on a mistaken premise.

For a better starting point you might try Taylor and Wheeler’s “Spacetime Physics”- the first edition is available free online.

 

[Dale]

In the real world the disc will come apart at some high rpm. But lets pretend it doesn't.

You really cannot pretend it doesn't if you want to answer the rest of your question. The important fact is that angular acceleration is non-rigid motion in relativity. You cannot logically have both relativity and a disk that does not undergo strain when it undergoes angular acceleration. (I assume that you know the technical term "strain")

what does this do to the disc?

It unavoidably mechanically strains the disk.

what implications does this have for contiguity of any given object?

Any material fails at some finite strain. As the angular acceleration continues, the strain becomes unbounded as the tangential velocity approaches $c$. So, no possible material, even "lets pretend" thought experiment unobtanium, can avoid failure. At some point it will necessarily fail and then the object will no longer be contiguous. Below the failure point the object is contiguous, although it is strained.

When does an object cease to be a singular object and become a collection of separate objects?

When it reaches the failure strain.

What is the granularity of such a separation?

That depends on the size of the post-failure fragments.

Yes, these are slow enough to ignore the relativistic issues. But ignoring does not mean they are not occurring.

The normal mechanical strains of muscle contraction and joint movement far exceed the relativistic strains. The small relativistic portion of the strain also does not, even in principle, do anything fundamentally different to the object than an ordinary strain of the same magnitude.

My point is to suggest we are constantly tearing at space-time fabric by existing.

Strain in an object doesn't imply a tear in spacetime. The former is a clear, well-defined, and experimentally measurable. The latter is more of a sci-fi trope.

Dont' let normalcy bias prevent insight!

I think that the insight is primarily from recognizing that we cannot pretend it doesn't cause arbitrarily large strain. Angular acceleration is non-rigid motion in relativity. This is a kinematic difference from Newtonian mechanics.

Last bit of the experiment: add a second disc placed next to but not touching the first, but counter-rotate it relative to the first. Clearly the space-time gets torn a-la frame-twisting around black holes. But what else happens?

It is not at all clear that spacetime gets torn. As far as I know there is no such thing outside of pop-sci or sci-fi. It is not part of the actual scientific theory of relativity.

 

[Ibix]

TL;DR: relatavistic gradient across rotating object

Clearly the space-time gets torn a-la frame-twisting around black holes

I think you are confusing the time dilation and length contraction in special relativity with the curved spacetime of general relativity. They are not the same thing, and a rotating disc does not imply any significant lack of flatness in spacetime.

IIRC from the last time this was discussed here, a lump of concrete the size of a washing machine spinning at millions of revolutions per second (if it could somehow be held together) might just produce enough frame dragging type effects to be detectable by our most sensitive equipment. The experiment would require the annual energy consumption of a small country, assuming perfect frictionless operation.