It’s like the earth spinning on its own axis and going around the sun. imagine, the earth keeps spinning at the same rate (0nce every 24 hours), but is accelerated to go around faster around the sun (I.e. the year gets shorter).
Ah - nicely explained! Thanks - I can follow this thread now…
Maxwell’s equations are the relativistic equations for electromagnetism. Without relativity, all you have is electric fields and Coulomb’s law. There is no non-relativistic magnetism, at all.
Maxwell’s equations are also the classical equations for electromagnetism, because “classical” means “not quantum”. QED is the quantum explanation for electromagnetism.
In fact, even if you’re doing electromagnetism near a black hole, so you have to use general relativity (which is also classical), you still use Maxwell’s equations. You just have to be a little bit more careful about how you take your derivatives.
The term for “not classical and not relativistic” is Newtonian, but Newton didn’t do anything with electromagnetism. I suppose that you could go with the spirit of the term and call Coulomb’s Law “Newtonian” (especially since it’s so similar to Newton’s law of gravity), but that’s as far as you can go.
In Newtonian mechanics if an accelerating force is distributed equally throughout an extended body than that body will not deform, but that is not the case in special relativity. Further, in some cases of non-inertial motion of an extended body in relativity, no distribution of force will prevent the body from deforming. Also in relativity, time (and hence RPM) and angular momentum are frame dependent. So to have any hope answering the question firstly the distribution of the acceleration and then the frame must be specified.
In this case (but as mentioned above, not all cases) we can assume that the acceleration is Born-rigid, which means the distribution is such that the body does not deform. As long as the acceleration is low enough this is a good approximation how we would expect the internal forces in a reasonably rigid disk to behave. This means that for an observer moving with the centre of mass the RPM doesn’t change. The question about angular momentum isn’t really answerable as it requires an extended accelerated frame, which means there isn’t a fixed definition of angular momentum.
Thanks @Asympotically_fat and @Chronos for explaining this.
So if I understand this correctly, :
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The concept of relativistic mass is antiquated. It’s not like a free spinning potters wheel where you throw some clay and it starts spinning slower to conserve angular momentum.
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The concept of Lorentz contraction is also antiquated. It’s not like a spinning ballerina who draws her arms in and thus starts spinning faster. Lorentz contraction does not result in changing the rpm of the disk.
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A single relativistic mass does not fully describe a body’s resistance to change of state in motion like mass in Newtonian physics does. To do that you need two frame-dependnent relativistic masses (longitudinal an transverse), which you could combine as a single frame-dependent 3x3 “mass matrix”. But describing mass using frame-independent rest mass is much more straightforward, so the concept of relativistic mass is indeed antiquated.
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Lorentz contradiction is not antiquated, but as mentioned when we look at the effects of acceleration on an extended bodies we must consider how the force is distirbuted throughout the body. In this case we’re just choosing the distribution so that the shape and RPM are unchanged in the centre of mass frame as that is what we’d approximatley expect with small enough acceleration, so it doesn’t illustrate much.
Note there will be a size limit to the disk which will depend on both its period of rotation and its linear acceleration, but assuming both are small then the size limit will be very large.