Sean, You asked "Is it meaningful to speak of "resonance" when something is rotating in only one direction?"
Consider a car engine. Ignoring any internal resonances, it has a max-power point at some frequency. If you add a muffler, you have modified the external environment to the engine (most strongly at a given frequency). The engine+ muffler now has a resonant frequency that may differ from that of the muffler alone (e.g. with a different source). The muffler+engine resonance can be "tuned" to alter the max-power point (increase power at a given frequency or spread the max-power point to a larger frequency range). To address the issue of resonance of bodies at the sub-micron scale: Both classical and quantum physicists get fixed within their own framework. "To a hammer, everything looks like a nail." To consider an electron to be a rotating rigid body creates problems with experimental evidence. Relativity changes the shape of the electron *E*-field and thus creates a magnetic field. The electron, being an EM creature, thus changes its shape and properties with velocity. *Spin is one of those properties.* It does not change in magnitude (except under extreme conditions - e.g., annihilation or combination); but, it does change direction. When an electron is accelerated, its spin axis nutates ( https://en.wikipedia.org/wiki/Nutation) and precesses about the velocity vector. When at high velocities (but w/o acceleration), its nutation will be "pure" (nodding, but with no precession). This precession and nutation exists at all v > 0. The nutation can be considered to be the basis of the deBroglie wavelength, where the wavelength is determined by the distance traveled in a single nutation cycle (my own definition). For a bound electron, which is accelerating all of the time, precession of the spin axis about the axis of rotation is a given. For a closed path in a conservative potential, an electron's total energy is conserved and is constant at the resonance point(s) of the orbit and precession. Thus, relativity, which also causes the magnetic field of a moving charge at v>0, is the "exterior" environment that produces the resonance for a stable orbit. The resonance is between the orbital frequency and the frequency of precession (causing the deBroglie wavelength). This resonance establishes the constant-total-energy orbits of atomic electrons. Understanding this and the resonances leading to photons and leptons provides a basis for gravitation and the possibility of null-gravity (as in photons), even if anti-gravity cannot be attained. Andrew _ _ _ On Sat, Jul 16, 2022 at 9:57 PM Sean Logan <paco66...@gmail.com> wrote: > I have a question about things that rotate: Is it meaningful to speak of > "resonance" when something is rotating in only one direction (Clockwise, > for example)? When I think of "resonance", I think of a guitar string > vibrating back and forth, or a parallel LC circuit, with the current > flowing back and forth. In both cases, the stuff is moving first one way, > then the other. We can talk about how many "back and forths" it makes in a > given amount of time. But what if you are spinning a flywheel in just one > direction? Is there some particular angular frequency which is > special, based upon other parameters of the system (maybe the flywheel's > mass)? I don't think I'd call it a "resonant frequency", but I would call > it something. I mean, is there a particular diameter or rate of rotation > at which a tornado can form and be stable -- any slower or faster and it > would fly apart? It sounds like that is what you are getting at with the > electron, Andrew. > > An old mechanic I used to live with said something to me once to this > effect: That there was a particular RPM of the flywheel in an engine at > which it was "resonant". That the engine and transmission worked best and > were happiest when the flywheel was rotating around this particular RPM. > > > > On Sat, Jul 16, 2022 at 5:01 AM Andrew Meulenberg <mules...@gmail.com> > wrote: > >> I like your derivation. It appears to be another indication of the >> resonance giving stability to the electron at a specific "size". A similar >> >
