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Blackbody paradox applied to interaction of gravity with electrons

  • #1
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Homework Statement



How does the blackbody paradox argument show that the electromagnetic field cannot be classical while electrons and atoms are quantum mechanical? Should the same arguments apply to treating gravity classically and electrons quantum mechanically?

Homework Equations



The Attempt at a Solution



What is the blackbody paradox argument anyway? Is it the ultraviolet catastrosphe?

If it is the ultraviolet catastrophe, then the quantum mechanical behaviour of the electrons and atoms - the discrete spectrum of energy levels - implies that light cannot be classical. In other words, light must be absorbed or emitted by the electrons and atoms in individual units of photons. This absorption and emission of light in discrete units of photons and quanta is not a classical behaviour, but rather a quantum behaviour.

Is this what's required of the first part of the question?
 

Answers and Replies

  • #2
Simon Bridge
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Homework Helper
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The ultraviolet catastrophy is the "blackbody paradox", well done ... there is an argument about what that paradox means for quantization of the electron/atomic states in the walls of the cavity.

The question is asking for the next step: to show that it means that quantized energy for atoms cannot mean a classical electric field.
Isn't the classical EM field and discrete electron states sufficient to resolve the paradox?

Your answer just asserts that electrons must absorb and release energy in energy packets (that is what "photon" means in this context), but you don't say why this means that the light has to be divided up into photons to start with.

But I may be reading too much into the question...
https://quantiki.org/wiki/introduction-quantum-theory

The second part involves the interaction of gravity and electrons .... you are invited to see if the same arguments work in this case.
Electron energies are quantized, gravity can change the energy of electrons ...
 
  • #3
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The ultraviolet catastrophy is the "blackbody paradox", well done ... there is an argument about what that paradox means for quantization of the electron/atomic states in the walls of the cavity.

The question is asking for the next step: to show that it means that quantized energy for atoms cannot mean a classical electric field.
Isn't the classical EM field and discrete electron states sufficient to resolve the paradox?
That's what I'm worried about. If my knowledge of the history of quantum mechanics is correct, Planck thought it sufficient to consider light as a classical EM field and simply take the absorption and emission of chunks of light from or to electrons/atoms as an ad hoc hypothesis that was supposed to be explained off later by someone else. However, Einstein made a bigger leap and thought that light itself was divided up into chunks.

I don't see why this hypothesis (that light itself is divided up into chunks) is necessary in either the blackbody paradox or the photoelecrtic effect. The particulate nature of light is manifest only in interactions with matter/fields. Light itself does not need to be divided up into chunks/quanta of energy.

In fact, the very observation that light behaves like a particle in interactions with matter/fields, while it behaves like a wave while propagating freely, is a quantum behaviour. Therefore, Plank's hope that the particle nature of light in its interactions with the atoms/electrons of the walls of the blackbody cavity was an ad hoc hypothesis was not really an ad hoc hypothesis, but rather it is the first description of the quantum behaviour of light.

I guess this i why the blackbody paradox argument show that the electromagnetic field cannot be classical while electrons and atoms are quantum mechanical.

What do you think?

Your answer just asserts that electrons must absorb and release energy in energy packets (that is what "photon" means in this context), but you don't say why this means that the light has to be divided up into photons to start with.
I'm not really sure if this question has been answered by anyone at all? :frown: Is this part of the measurement problem - the fact that interactions show particle-like behaviour, while free propagation is wave-like?

The second part involves the interaction of gravity and electrons .... you are invited to see if the same arguments work in this case. Electron energies are quantized, gravity can change the energy of electrons ...
I guess we can draw an analogy, but gravity is a much much much weaker force so that the shift in the energy levels is also very tiny. I'm not really sure what this implies for the energy per graviton as compared to the energy per photon.
 
  • #4
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I interpret this problem as follows: Plank resolved the ultra-violet catastrophe by assuming that light is emitted/absorbed in discrete quanta which led to the correct spectral distribution function (quantum statistics for bosons) and the conclusion that energy states for electrons in atoms must be quantized. Gravity, however, only interacts through mass, i.e. space-time curvature. If you have an ideal gravitational wave emitter/absorber like say a wormhole will its spectral distribution function be classical or quantum mechanical? Does this imply that space-time is quantized?
 
  • #5
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I interpret this problem as follows: Plank resolved the ultra-violet catastrophe by assuming that light is emitted/absorbed in discrete quanta which led to the correct spectral distribution function (quantum statistics for bosons) and the conclusion that energy states for electrons in atoms must be quantized. Gravity, however, only interacts through mass, i.e. space-time curvature. If you have an ideal gravitational wave emitter/absorber like say a wormhole will its spectral distribution function be classical or quantum mechanical? Does this imply that space-time is quantized?
Why do you consider a wormhole to be an ideal gravtitational wave emitter/absorber?
 
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I consider a wormhole to be an ideal GW source because it's purely hypothetical, therefore ideal. Hopefully, LIGO will find a wormhole and get data on the spectral distribution of GWs.
 
  • #7
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I interpret this problem as follows: Plank resolved the ultra-violet catastrophe by assuming that light is emitted/absorbed in discrete quanta which led to the correct spectral distribution function (quantum statistics for bosons) and the conclusion that energy states for electrons in atoms must be quantized. Gravity, however, only interacts through mass, i.e. space-time curvature. If you have an ideal gravitational wave emitter/absorber like say a wormhole will its spectral distribution function be classical or quantum mechanical? Does this imply that space-time is quantized?
Well, there's no mention of the interaction of electrons with gravity in your interpretation of the problem, so I'm not really sure if the problem is being correctly interpreted?
 
  • #8
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Electrons interact with gravity through their mass.
 
  • #9
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Electrons interact with gravity through their mass.
I get it now.

This is a very nice interpretation of the problem, but I guess the problem is open-ended and can't be resolved unless we have conclusive evidence (or not) of quantum gravity. :biggrin:
 

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