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Objects can not travel faster than the speed of light.

Angular velocity is $\omega = \frac{s \times v}{|s|^2}$

It seems to me that for infinitely small objects (like electrons) there is no limit on how fast objects can rotate.

It seems wrong to me that it is theoretically possible to generate more magnetic effects and similar by rotating than by linear movement though.

I recall that sufficiently fast rotating black holes can form naked singularities. If rotation is limited to below that amount then that might be a limit on how fast things can rotate?

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    $\begingroup$ My understanding is that point particles can't rotate as there is no extension to move relative to their center. $\endgroup$ – Virgo Jun 10 '16 at 1:52
  • $\begingroup$ @ally in quantum field theory (QFT) fundamental particles are modelled as point particles which can have mass. This is an extremely successful theory which has matched a vast array of experimental results. But QFT has not yet been successfully applied to gravity and so is thought to break down at very high energies, way beyond the reach of current particle accelerators. One attempt to incorporate gravity is string theory, which replaces particles with strings as the name implies. String theory has not yet been experimentally tested and it may never be due to the very high energies required. $\endgroup$ – Virgo Jun 10 '16 at 18:29
  • $\begingroup$ But string theory assigns to particles a well-defined size, planck's length. Talking of no-size makes no physical sense. $\endgroup$ – user104372 Jun 11 '16 at 3:36
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The underlying level of nature is quantum mechanical, all classical frameworks emerge from this underlying level. Hopefully this will be true of general relativity too. Already string theories can accommodate both quantization of gravity and the structure of the standard model of physics with no definitive model yet.

Therefore the speed at which an object can rotate will be limited by the electromagnetic forces holding the object together against the mechanical centrifugal forces, and will depend on the atomic structure of the object. No need of speed of light, already if you rotate a piece of dough the outer levels will fly away :). One would have to calculate the forces for a specific size steel ball , for example, and get a limit for that ball. It will answer how fast must it rotate for the surface atoms to split off due to centrifugal forces.

Now as far as black holes go, they are a classical construct, and singularities are a classical theory effect. Think of the 1/r^2 of the coulomb force which leads to a singularity at r=0. Quantization took care of that. When gravity will be quantized, I expect that the same will happen with its singularities.

It seems to me that for infinitely small objects (like electrons) there is no limit on how fast objects can rotate.

The electron is a quantum mechanical entity, an elementary particle in the standard model, it is a point particle, there is no extent in space to describe a rotation . The spin attributed to the electron is a quantum number necessary to describe the interaction of electrons with matter, so that angular momentum is conserved in all electron interactions with other particles. It is an observational/experimental fact.

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  • $\begingroup$ @ally The question was general. The electron is a quantum mechanical entity of zero size . Its spin is a quantum number necessary to describe the interaction of electrons with matter, so that angular momentum is conserved in all electron interactions with other particles. It is an observational fact. I have edited. $\endgroup$ – anna v Jun 10 '16 at 7:39
  • $\begingroup$ @ally, nevertheless, if you look at the tables, the electron has no extent, it is a point particle, and by definition a point has no extension. The probability if its manifesting in a volume has an extent, ( the heisenerg uncertainty) but not the electron itself. It is basic quantum mechanics $\endgroup$ – anna v Jun 10 '16 at 14:26
  • $\begingroup$ annav, I have always appreciated your down-to-earth attitude, that makes you recognize when physicists are sloppy or forget the basic principles of scientific method. A point is such by definition in math, you can't take that over to the real world. Matter, mass exists only inasmuchas if has physical extension, size, dimension and one might add that even energy, radiation etc must happen somewhere in space. How can something that has no size have a scatterig cross-section? QM like other theories, takes many 'poeticl licenses', would you agree ? $\endgroup$ – user104372 Jun 10 '16 at 14:43
  • $\begingroup$ @ally You are describing the classical model of physics, that fitted macroscopic observations. You cannot expand it to the microcosm because it has no predictive ability. The quantum mechanical model, which does allow point particles with mass or with zero mass( like the photon and the gluon), is successful BECAUSE it is predictive for new data. It is continually validated in the microcosm. Both the classical and the quantum are mathematical models valid because of their predictive ability in their area. In addition it can be shown that the classical emerges from the quantum mechanical. $\endgroup$ – anna v Jun 10 '16 at 17:19
  • $\begingroup$ @ally the standard model of particle physics, which fits practically all the numerous data of particle physics with a set of point particles , seen in the figure . en.wikipedia.org/wiki/Standard_Model $\endgroup$ – anna v Jun 11 '16 at 3:51

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