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Denton
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Suppose you have a very strong, spinning disc with a diameter of say 10 km in length. At the centre the centripetal velocity is approaching the speed of light, how would we observe the outer edge of the disc to be.
Denton said:Suppose you have a very strong, spinning disc with a diameter of say 10 km in length. At the centre the centripetal velocity is approaching the speed of light, how would we observe the outer edge of the disc to be.
Please see also the excellent book by Poisson, A Relativist's Toolkit, Cambridge University Press, the quartet of Wikipedia articles in the versions I cited, and the invaluable review paper by Oyvind Gron in the book edited by Rizzi and Ruggiero, Relativity in Rotating Frames, Kluwer, 1994.Chris Hillman said:it's not nearly that simple!
DaleSpam said:I think this question would require a relativistic version of Hooke's law in order to properly analyze
Denton said:Suppose you have a very strong, spinning disc with a diameter of say 10 km in length. At the centre the centripetal velocity is approaching the speed of light, how would we observe the outer edge of the disc to be.
That isn't a simple question at all. We have to make some assumptions to make sense of it. In particular, we have to say how the train cars are to be accelerated. These are the assumptions I've made:jimgraber said:Hi everyone, but particularly Chris:
I'd like a simple (yes-no)answer to a simple question:
Consider the circular train in the current Wikipedia article "Ehrenfest paradox".
Replace the bungee cords with rigid threads, as suggested.
Gently accelerate to 0.6 c.
Do the threads break or not?
TIA.
Jim Graber
Denton said:I do have a pre existing knowledge of relativity, however I am reaching my limit of understanding for now - I've not yet delt with the complex math of general relativity what with these 'tensors' and whatnot which is vaguely confusing, I understand in principle but not in math yet. I however hope to 'catch' up to all of this once I start University.
It is often taken for granted that on board a rotating disk it is possible to operate a global 3+1 splitting of space-time, such that both lengths and time intervals are uniquely defined in terms of measurements performed by real rods and real clocks at rest on the platform.
Comment on Klauber’s article: “Toward a Consistent Theory of Relativistic Rotation
Klauber [1] analyses rotation with relativistic velocities from several points of view. The analysis is unconventional and controversial, but not uninteresting. Klauber argues against Einstein’s conclusion that the spatial geometry in a rotating reference is not Euclidean, and claims that the conventional relativistic analysis or rotating reference frames is not consistent.
One can think of Klauber’s article as representing the point of view of “The Devil’s Advocate”, and it gives an opportunity to defend the point of view that is about to be “canonized”. In the present note I shall try to show that the relativistic analysis is indeed consistent.
Fredrik said:That isn't a simple question at all. We have to make some assumptions to make sense of it.
Each train car has its own engine, controlled by a computer in that train car, and all the computers are running the same program, at the same time, according to clocks in the the train cars that were synchronized in the stationary frame before the acceleration started.
“One can give a consistent definition of the length of the whole “circumference” relative to the rotating reference frame K as the length of the curve PP’ everywhere orthogonal to the world-lines of the reference points of K, starting from an event P and ending on an event P' on the world-line of the same particle of the edge of the disk, and winding once around the axis of rotation. Notice that such a curve is not closed in space-time, and distant events on it, such as P and P’, can in no sense be regarded as simultaneous.
You seemed to not want this topic rehashed without your mentioned conditions.Chris Hillman said:And everyone: please don't resurrect long-dormant threads, and please don't illustrate the phenomenon discussed in [thread=200063]this thread[/thread]! Thanks to all in advance for their cooperation!
"Unveiling the Observations of a Spinning Disc Approaching Light Speed" is a scientific study that explores the effects of a spinning disc as it approaches the speed of light. It aims to uncover new observations and understand the behavior of matter at such high speeds.
The study was conducted using various experiments and simulations. The spinning disc was created using advanced technology and was accelerated to different speeds, while the observations were recorded and analyzed.
The study revealed that as the disc approached the speed of light, its shape and physical properties changed significantly. The effects of time dilation and length contraction were also observed, providing further evidence for Einstein's theory of relativity.
This study is important because it contributes to our understanding of the fundamental laws of physics and how matter behaves at extremely high speeds. It also has practical applications in fields such as aerospace engineering and astrophysics.
The study could have significant implications in the future, such as the development of new technologies that can harness the effects of high-speed spinning discs. It could also lead to advancements in our understanding of the universe and its mysteries.