31st July 2005 - 02:04 AM
Hi moron and Insyght,
Other than to wonder if the experiment wouldn't somehow "tear" a small hole in spacetime -- a wormhole of some kind, perhaps. Who knows? I don't. Would such an experiment even be interesting? How would it be accomplished?
The "probe" would not be possible to build (so to many it is not "interesting") since any mechanical material structure could not sustain such forces. The radius of the system would shrink to fit the structure and visa versa. If the arms were twice the length it would approach the speed of light much sooner in angular velocity (at lower rotation rate) and length contraction (rotation) would occur there sooner at a greater radius. "Interesting" experiments are contrived to support existing theory not bring it down, this is definitely not an "interesting" place to go since direct measurement
will not be possible.
All existing experiment rely on direct measurement. There is another way to proceed but it is harder. For all that it matters it may as well be a rent in spacetime since at that point it will then be no longer possible to do measurements anyway.
You are dealing with "Schrodinger's Cat" in a box... not only is it "dead" or is it "alive" but is it licking it paws or watching TV... etc? Quantum Theory does not deal with unobserved phenomena and is a recognized difficulty called the Measurement Problem. All the interesting questions about "what happens next" are taboo to Quantum Theory and have no answers. Do your measurement and you have destroyed the quantum phenomenon. Yet he whole Universe is largely an "unobserved Phenomenon", in our inflated ego we have maintained that nothing
occurs without man's personal observation to "collapse" the state of the superimposed systems to one. . A bit much to expect from even ye "gods in the making"!
Yet this is the current theory.
The radius of the wheel would remain more or less unchanged again at the larger radius and the problems will only occur close to that radius where once again things would appear to being "wound up". The reason for this apparent compression is the optical effects of approaching the speed of light is highly skewed toward to the last couple of percent of approaching the speed of light and in this system the linear velocity is increasing rapidly for small changes in radius. For the radius inside that last critical percent spacetime will appear relatively normal all the way to the center. Internally increasing the rate of rotation would simply progress the "horizon" down along the arms
compressing the tips on to a surface along with the arms. This would follow the velocity of the specific point on the arms that was now approaching the speed of light. At no point would any part of the structure actually reach the speed of light, otherwise it would be a violation of the Special Theory. Stuff that was formerly beyond that point would now appear compressed onto the new "approaching" 2D surface, an optical effect only. It would not be "intelligible" or able to be understood by measurement or observation. It is debatable if you would see anything at all... this phenomena would probably be as invisible as normal quantum events since light will barely be able to progress to or from that region - as I said before it is undergoing "extreme" clock paradox phenomena and for photons to "work" there they need a frequency and this is something they will not have - no time and hence no frequency. I think it will be interaction-less. Events will have "ceased" on this "event horizon".
All these individual effects are able to be calculated "roughly" using Special and General Relativity and by application of be Broglie's Principle and Heisenberg's Uncertainty relationships. Will this operation have quantized spacetime? All attempts to show that it has... have resulted in failure. Quantum Gravity sucks. The attempt goes on to find this granularity, stable states that might be measured. Think about the physical situation and think again.... and again.
The interesting fact is this "probe" would be a physical object that probably does indeed have a position and momentum but is now acting beyond the predictions of Quantum Theory in a space that will not map into a flatspace (3D + T) that Quantum Theory needs for that interpretation since the theory of the Quantum does not have extra dimensions beyond 4. Naturally internally you would begin to see the effects of this General Relativistic Curvature as well. Everything 'falls" apart in this process and only "New Physics"
would allow this to be interpreted. I suggest that Special and General Theory alone are capable of handling this process since it already deals with curved spaces and the Quantum Theory does not. Ditch it!
Anybody can comment... with Insyght's permission of course. It is always a good question and it is not engraved in stone.
To me it is one of the more important thought experiments in Physics.