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fox26

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emitted from heated bodies only in quanta of energy E = hf, where f was the frequency

of the radiation and h was a constant now called “Planck's Constant”, in order to solve

the Ultraviolet Catastrophe problem--that classical Electromagnetic and Statistical Mechanical

theory predicted that infinite power would be radiated from a finite material body at any

finite non-zero temperature in the form of electromagnetic radiation with frequencies

above any given value, which of course was observed not to occur.

For a long time I didn't know the reason that this was supposed to occur, but it seemed

to me that classical E.M., S.M., and Atomic theory wouldn't predict this. My reasoning was

that in any finite body at a finite temperature there were only a finite number of charged

particles each moving at a finite speed relative to the others, and while the collisions

between them would cause infinite accelerations which, according maybe to some

extension of Maxwell's E.M. theory, would result in the power of the E.M. radiation

emitted by such a body being infinite, for at least an instant, if the particles were

completely rigid, such a model was unrealistic. Instead of the collisions being ones with

infinite accelerations, they would be interactions between particles caused by finite E.M.

or other forces, so the accelerations would be bounded above over time for each

particle, so the power radiated by each particle would also be bounded above, so there

would be only a finite total amount of power radiated from acceleration of charged particles

in the body. Radiation from electrons in atoms falling to lower energy orbits would also be of

finite total power at all times.

When recently I looked up the reasoning which had led to the infinite power prediction, I

found that the finite body which was supposed to radiate infinite power was modeled as

a finite amount of matter inside a cavity, supposedly to simulate a black body, and the

matter and cavity were supposed to be at thermal equilibrium! In such a cavity there are

an infinite number of E.M. modes, all but a finite number being above any finite

frequency, each of which counts as a degree of freedom of the body, and so according

to the Equipartition Theorem of Statistical Mechanics, at equilibrium at any non-zero

temperature T, each degree of freedom accounts for an equal, non-zero amount kT/2 of

energy, so there would be an infinite total amount of E.M. energy in the body, and an

infinite amount of power radiated from it, most at frequencies above any given value.

While this infinite radiated power prediction was true according to classical theory under

the assumed conditions, why the body was modeled as one inside a cavity was unclear,

and much more importantly, that the material and the cavity were at thermal equilibrium

was as unrealistic an assumption as the infinite acceleration assumption, since it

requires an infinite amount of energy to be in the matter and cavity, in the E.M. radiation

in the infinite number of E.M. modes, which energy could be supplied to the

matter-cavity, which initially upon construction would contain only a finite amount of

energy, only from the environment at a finite rate, bounded above, so it would take an

infinite amount of time for the matter-cavity to reach the assumed equilibrium.

The Quantum Mechanics which was started by Planck's quantum hypothesis has been

very successful in making true predictions about the world, and can hardly be doubted to

be in many ways correct, but the supposed Ultraviolet Catastrophe which led to Planck's

hypothesis seems to be a total fake. Does anyone have an answer opposing, or at least

explaining, this?