Jack Denur

University of North Texas | UNT · Department of Physics

Noether’s Theorem associates a symmetry property with each and every conservation law. For example, according to the usual interpretation of Noether’s Theorem, the time symmetry, i.e., the temporal uniformity, of the laws of physics compels the law of conservation of energy (and vice versa), the spatial symmetry, i.e., the spatial uniformity, of the laws of physics compels the law of conservation of linear momentum (and vice versa), etc. Noether’s Theorem seems to imply that the penalty for violating energy conservation would be the breaking of the temporal uniformity of the laws of physics, that the penalty for violating linear-momentum conservation would be the breaking of the spatial uniformity of the laws of physics, etc. But can Noether’s Theorem be bought off cheaply? Suppose, if only as a thought experiment, that a book of mass m on a desk spontaneously rose through a height h to the ceiling. Not got cooler and rose to the ceiling in violation of the Second Law of Thermodynamics, but just rose to the ceiling in violation of the First Law (energy conservation), with nascent energy mgh created from nothing. Could Noether’s Theorem accept payment in the cheap currency of a new initial condition on the Universe (this additional nascent energy mgh) instead of the expensive currency of breaking of the temporal uniformity of the laws of physics — leaving the temporal uniformity of the laws of physics intact in a Universe modified only by the new initial condition of this extra nascent energy mgh? (Changing the laws of physics too much would be a death sentence!) In this regard, note that NASA considered the EM and MEGA drives, which claim to violate the law of conservation of linear momentum, seriously enough to fund testing of them. As of this writing, the EM drive seems to have been refuted but the MEGA drive still seems to be under consideration. NASA did not, and does not, seem concerned about Noether’s Theorem. Perhaps NASA’s opinion is that Noether’s Theorem can be bought off cheaply — accepting payment in the cheap currency of new initial conditions.

Dark matter interacts with ordinary matter (and ordinary energy) via gravity (G), but not via electromagnetism (E), the strong nuclear force (S), or the weak nuclear force (W). But is totally dark matter that does not interact with ordinary matter (and ordinary energy) at all, not even via gravity (G), possible or impossible? If totally dark matter is possible, could there be other Universes with their own sets of forces (G´, E´, S´, W´), (G´´, E´´, S´´, W´´), etc., coexistent with our own (G, E, S, W) Universe, with each such Universe (including our own) interacting within itself but not with the other Universes? Is this a possible or impossible aspect of the Multiverse?

Some theories of physics require (not merely allow) magnetic monopoles. [See, for example, David J. Griffiths, Introduction to Electrodynamics, Fourth (Kindle) Edition (Cambridge University Press, Cambridge, UK, 2017.] But how can a theory that requires (not merely allows) magnetic monopoles be consistent with the fact that magnets with circular magnetic fields — and hence with no poles (neither a north pole nor a south pole) — exist? Two examples: (i) A horseshoe iron, alnico, or other permanent magnet bent into a circle, with the poles cold-welded together. (Cold welding is possible in a vacuum for surfaces planed very smooth.) (ii) A toroidal-solenoid electromagnet (with or without an enclosed iron core for increased strength). The magnetic field lines in such magnets are circular — and hence with no poles — neither a north pole nor a south pole.

I have Scientific WorkPlace 5.5 from MacKichan Software. But after 40 years of providing excellent products and service, MacKichan Software is no longer in business. Are there any other companies that can provide support for Scientific WorkPlace?