Probably another dumb question but learning is fun so...

Imagine a centrifuge (like those used but the apollo astronauts) that can rotate at light speed. There is a cockpit at the end of the rotating arm that has a inwards facing window in it (so the person riding the centrifuge can see the "origin" or center of the circle made by the centrifuge)

A light is positioned in the middle of the centrifuge (at the origin) and is programmed to change color every second (lets say from red to orange to green and back to orange and then back to red).

This light is in syncrony with another light inside the cockpit that also changes color every second.

A second person stands at the origin so he can see both lights change color.

The centrifuge starts to spin and gradually approaches light speed.

What does each person see (i.e. the one riding the centrifuge and the one at the origin) as light speed is reached ?

I hope I've explained this clearly enough for an answer.

Thanks

It's hard to imagine, because you start out with an impossible premise.

OK, lets just be nice and say instead of lightspeed, 99.9% percent of lightspeed, or some similar number. Anyone willing to answer this poor poster?

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They won't see the lights change at the same time.

Your problem is in saying the lights are synchronized. Who are they synchronized for?

I can't find it elsewhere on this board, but there are plenty descriptions of what happens to viewing at near light speeds.

My guess is that this scenerio is no different (within reason) than a the straight line example of what things at the side would look like.

As you near light speed, things toward the back of you shift forward. If you think of that single photon from the center, it would be approaching you at a 90 degree angle. Because of your speed, you would see it as coming nearly from a 45 degree angle. In other words, the arm of the centrifuge would appear to bend forward.

What I don't know is if it would be red or blue shifted based on that 45 or the 90 (which would imply no shift).

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Numbers are not case sensitive. (me)

The lights won't synchronize any longer. Each observer will calculate that the other's light flashes more slowly (the "transverse Doppler" of special relativity), although each will see the other light blue-shifted and situated in their forward view, because of relativistic aberration.

Grant Hutchison

Heres a wondermant about centrifuges and near light speed. Now if a record on a recocrd player spins at 33 1/2 rpm, at the edge. However, at a spot closer to the center will be spinning faster. Now, at normal speeds this isn't that big of a deal, but what about a centrafuge spinning at say 70% the speed of light. Wouldn't that mean there are actual spots on the arm of the centrifuge spinning faster then light speed? Of course, that is rather impossible.

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Not so.
Same speed (in angular velocity) or slower (in linear velocity).
The spot near the centre has less distance to travel to make one revolution.

Grant Hutchison

What? I may be reading this wrong, but the entire record spins at the same RPM, and the spots closer are moving slower (they travel a smaller circumference in the same amount of time)

By quoting a linear speed instead of a rotational speed, the assumption is the outer circumference. So...

no

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Numbers are not case sensitive. (me)

Ok, I got that wrong, but it still doesn't invalidate my point. If you spun the hub/spindle/center of the centrifuge near lightspeed, then the pod at the end would be going faster in linear velocity.

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True, but since it's not possible, and the bonds will break down (nothing is truly rigid), then how can make any predictions or suppositions as to what would happen?

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Numbers are not case sensitive. (me)

An object spinning that fast will be severely distorted. It won't look normal to anyone. Your answer lies in this deformation of the initial object and time dilation.

By the bonds 'break down' do you mean the mechanical stress, or is something else happening here?

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Even neglecting the problem with materials science cited by NEOWatcher, it would take infinite energy to get any part of the centrifuge up to lightspeed. So it's impossible to spin the region near the hub up to any speed that requires the rim to hit lightspeed.

Grant Hutchison

Yes, we're now entering the realm of the Ehrenfest paradox, which has been discussed several times before on BAUT.

Grant Hutchison

I can only take it as far as mechanical stress.

I'm sure breaking would occur first. Maybe there is some kind of process similar to liquification.

But; maybe somebody here can answer a more specific question. When a solid something breaks, what kind of forces are overcoming what other kind of forces and how are those forces transmitted from the source?

For example: I break a pencil. Is it just a matter of all those EM fields pressing against the pencil being cascaded through the pencil until there is an area with so little EM connections that the force finally overpowers that area?

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Numbers are not case sensitive. (me)

It all comes down to chemical bonds eventually, even if they're just van der Waals forces providing a little local adhesion.
In the case of the centrifuge, it has to generate internal tension forces to maintain circular motion, because every part of a rotating system is accelerating towards the centre, and a force is required to maintain that acceleration. Even a disc of solid diamond will fail when these centripetal tension forces exceed the strength of the covalent carbon bonds.

Grant Hutchison

Could it be said that this -- the chemical bonds issue -- is another reason why a massive object can never be accelerated to light speed?

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"All your bias are belong to us." Ara Pacis
"A witty saying proves nothing." Voltaire

No. It is the reason a rotating object cannot attain very high velocities.

If we consider uniform motion, the limit is the energy requirement to accelerate further.

Well, I guess if we made if of carbon nanotubes or another nanomaterial it could remain w/o breaking even at speeds close to c.

I think not. Lightspeed would be attainable eventually at any modest acceleration we cared to choose, if it weren't for the Lorentz transformations and the associated energy considerations. So there would be no structural problems for linear acceleration.

Grant Hutchison