Why is Photon Energy Quantized in Terms of Sine Wave Frequency?

[hutchphd]

Neither of these are "the energy of a photon".

But they are the energies to which Planck was referring in the quantum relation Planck compounded for a cavity black box which was the original question. Semantics, see.

 

[PeterDonis]

they are the energy Planck was referring to

"They" doesn't make sense. Planck wasn't referring to a "they". He was referring to a single thing, not multiple things. Unfortunately there is no single thing that has the properties Planck originally assumed. The fact that Planck proposed his relation with some idea in mind does not mean that idea is still considered to be valid.

the relation Planck compounded, which was the original question

I do not read the OP's question as being about Planck's original proposal, but about our best current understanding of what the Planck relation means--or doesn't mean, which is more to the point.

 

[hutchphd]

They: more than one individual energy.

 

[PeterDonis]

They: more than one individual energy.

More than one individual energy of what? And don't answer "a photon", because the whole point is that there is no such thing as "a photon" in the states that are relevant for black-body radiation (i.e., coherent states), which is the scenario that Planck's proposal was intended to apply to.

 

[hutchphd]

Please see #69 . Semantics I fear.

 

[PeterDonis]

Perhaps an alternate response to the OP question will help: the actual physical law that Planck proposed was not $E = h \nu$, it was his black-body radiation law:

$$
B_\nu(\nu, T) = \frac{2 h \nu^3}{c^2} \frac{1}{\exp \left( \frac{h \nu}{k T} \right) - 1}
$$

(Note that we now understand this law as the law for bosons; for fermions the last term in the denominator on the RHS is $+1$ instead of $-1$.)

Planck proposed the formula $E = h \nu$ as a heuristic justification for the above law, but the actual physics is the above law, and even though we now do not think Planck's original heuristic justification was valid, the above law is still valid (we just derive it now using different reasoning from the reasoning Planck originally used).

 

[hutchphd]

Yes but the fundamental Ansatz was regarding the counting.

 

[PeterDonis]

Thread closed for moderation.

 

[PeterDonis]

The OP question has been addressed. Thread will remain closed. Thanks to all who participated!