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Oldfart
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If I had a spoked disc made of unobtainium that could be spun up to .9999c outer rim speed, what would it look like as compared to the disc at rest? Assume I can photo the spinning wheel with an ultra fast camera.
bcrowell said:The locus of points that forms the circumference of the disk is a circle, regardless of whether the disk is rotating. One could ask whether an optical observation such as a camera snapshot would show the various *parts* of the disk as distorted to more or less than their normal size. But this implicitly assumes that it's possible to observe the disk first without rotation and then later after it has been spun up while maintaining its rigidity. This is impossible by the Noether-Herglotz theorem, which is essentially the resolution of the Ehrenfest paradox. (There is also a theorem in relativistic optics that says that a sphere still appears to be a sphere, regardless of the motion of the observer relative to the sphere's center. For an animation showing this, see the end of this video: http://youtube.com/watch?v=JQnHTKZBTI4 .)
bcrowell said:The locus of points that forms the circumference of the disk is a circle, regardless of whether the disk is rotating. One could ask whether an optical observation such as a camera snapshot would show the various *parts* of the disk as distorted to more or less than their normal size. But this implicitly assumes that it's possible to observe the disk first without rotation and then later after it has been spun up while maintaining its rigidity. This is impossible by the Noether-Herglotz theorem, which is essentially the resolution of the Ehrenfest paradox. (There is also a theorem in relativistic optics that says that a sphere still appears to be a sphere, regardless of the motion of the observer relative to the sphere's center. For an animation showing this, see the end of this video: http://youtube.com/watch?v=JQnHTKZBTI4 .)
pervect said:Talk about what a perfectly rigid disk would do is rightly pointed out as non-productive, as one can't ask what happens within a theory when one violates the theory without generating nonsense, and SR doesn't allow perfectly rigid materials.
bcrowell said:It isn't really relevant that SR doesn't allow perfect rigidity. Born rigidity isn't a property of a material, it's the result of external forces acting in a manner that is planned so as to produce the Born-rigid motion. The issue is kinematic, not dynamic: Born-rigid angular acceleration is impossible essentially because clock synchronization isn't transitive in a rotating frame.
Oldfart said:Thanks to all for your replies! Unfortunately, I've been trying to study the Noether-Herglotz theorem and your other comments without much luck, the math exceeds my paygrade, so to speak, I'm an ME, class of 1958. But I appreciate your efforts, really do!
For whatever it's worth, I envisioned a souped-up ultracentrifuge thingy in a lab setting, the observer is a superspeed camera.
Would it help if I change my question: Does a real-life ultra centrifuge exhibit any relativistic distortions when up to full speed, no matter how tiny those distortions might be?
Thanks again, OF
Oldfart said:Thanks. Pervect, I think I'm now starting to get it! Seems now that there are two types of distortion: (1) Everyday distortion due to centrifugal forces acting on the spinning object, something that even an old ME can understand, and (2) Distortion due to light delays like you mentioned.
Oldfart said:Thanks. Pervect, I think I'm now starting to get it! Seems now that there are two types of distortion: (1) Everyday distortion due to centrifugal forces acting on the spinning object, something that even an old ME can understand, and (2) Distortion due to light delays like you mentioned.
So to sort of answer my original question, the spocked wheel will become flower-shaped and its radius will increase due to the physical forces, and if the wheel is dish-shaped so the distance between the camera and the wheel is constant, then there will be no relativistic distortion of the wheel. That seems so simple now, assuming I'm right!
Many thanks! OF
Relativistic disc appearance is a phenomenon in astrophysics where a rapidly spinning object, such as a black hole or neutron star, distorts the surrounding space-time and creates a disc-shaped region of intense radiation and gravitational effects.
A relativistic disc forms when matter, such as gas or dust, falls towards a rapidly spinning object and begins to orbit around it. The intense gravitational pull of the object causes the matter to accelerate to very high speeds, producing strong radiation and creating a disc shape.
A relativistic disc is typically disc-shaped, with a bright inner region and a dimmer outer region. It emits high-energy radiation, such as X-rays, and can also produce jets of particles that shoot out perpendicular to the disc's plane.
Yes, we can observe relativistic discs from Earth using telescopes and other instruments that detect different forms of radiation. These observations can provide valuable information about the properties and behavior of the object creating the disc.
Relativistic discs are important because they are a key element in understanding the behavior of black holes and other rapidly spinning objects in the universe. They can also provide insights into the processes of accretion and energy production in these objects, and help us better understand the overall structure and evolution of galaxies.