[hamdani yusuf (OP)]

There's no adequate justification to extrapolate it to other type of power or energy, such as gravitational potential energy.

Do you know that gravity affects photon energy?

Afaik, it changes the energy by affecting the frequency, which doesn't affect the Planck energy equation, nor it's quantization.

[Bored chemist]

Afaik, it changes the energy by affecting the frequency

The statement is meaningless.
How could it affect one but not the other?
The statement is meaningless.

[alancalverd]

Planck's energy equation E = n.h.f,

Where does the n come from? E = hf in my universe. But that doesn't mean energy is quantised. Planck's model describes the energy levels available to a particle constrained in a box. Obviously if you have two particles with the same frequency in the box, you have twice as much energy, but the box can be any size you like and a free particle can have any amount of energy you care to give it.

So haviong establioshed, for the umpteenth time, that energy is not necessarily quantised, we have reduced the question "where does the quantisation come from" tothe same level of pointlessness as "why are unicorns born feet-first?"

[hamdani yusuf (OP)]

Where does the n come from? E = hf in my universe.

Are you living in a different universe?
Some sources mention that n is the number of photons.
A universe containing only 1 photon doesn't allow anyone to exist, let alone to think.
https://www.ux1.eiu.edu/~cfadd/1160/Ch28QM/Planck.html

Planck's Hypothesis
In 1900 Max Planck proposed a formula for the intensity curve which did fit the experimental data quite well. He then set out to find a set of assumptions -- a model -- that would produce his formula. Instead of allowing energy to be continuously distributed among all frequencies, Planck's model required that the energy in the atomic vibrations of frequency f was some integer times a small, minimum, discrete energy,

E_min = hf
where h is a constant, now known as Planck's constant,

h = 6.626176 x 10-34 J s
Planck's proposal, then requires that all the energy in the atomic vibrations with frequency f can be written as

E = n h f
where n in an integer, n = 1, 2, 3, . . . No other values of the energy were allowed. The atomic oscillators could not have energy of (2.73) hf or (5/8) hf.

This idea that something -- the energy in this case -- can have only certain discrete values is called quantization. We say that the energy is quantized. This is referred to as Planck's quantum hypothesis. "Quantum" means how great or of a fixed size.

This article mentions near its end.

1 photon -> 1 electron
1 electron -> 1 photon
http://www.phys.ttu.edu/~slee/3301/2018_Fall/F18_3301_Lecture4.pdf

[hamdani yusuf (OP)]

Afaik, it changes the energy by affecting the frequency

The statement is meaningless.
How could it affect one but not the other?
The statement is meaningless.

In energy equation E=n.h.f, you can change E with constant f by changing n.
Not all form of energy involve frequency. Gravitational potential energy and electrostatic potential energy has no frequency in their equations.

[hamdani yusuf (OP)]

Where does the n come from? E = hf in my universe. But that doesn't mean energy is quantised. Planck's model describes the energy levels available to a particle constrained in a box. Obviously if you have two particles with the same frequency in the box, you have twice as much energy, but the box can be any size you like and a free particle can have any amount of energy you care to give it.

So haviong establioshed, for the umpteenth time, that energy is not necessarily quantised, we have reduced the question "where does the quantisation come from" tothe same level of pointlessness as "why are unicorns born feet-first?"

Planck hypothesized about quantization of radiation energy, that's what's being discussed here. Other types of energy can be mentioned for comparison.
You don't seem to accept currently mainstream interpretation of quantum theory. Perhaps you can share the sources that you think more representative to your thinking.

[Bored chemist]

Some sources mention that n is the number of photons.

Which sources?

A universe containing only 1 photon doesn't allow anyone to exist, let alone to think.

Nobody said it did.

[Bored chemist]

Gravitational potential energy and electrostatic potential energy has no frequency in their equations.

Nor do they refer to a single entity. You need  a "system" of at least two particles for gravitational or electrical potential to exist.

That's a separate class of problems.

[Bored chemist]

In energy equation E=n.h.f, you can change E with constant f by changing n.

Only if there's an interaction with something else.

[alancalverd]

hf is the energy of a photon. Obviously if you have more photons in a box, you have more energy in the box. That doesn't mean that energy is quantised, only that photons are.

[hamdani yusuf (OP)]

hf is the energy of a photon. Obviously if you have more photons in a box, you have more energy in the box. That doesn't mean that energy is quantised, only that photons are.

Can you add radiation energy by half a photon?

[Bored chemist]

hf is the energy of a photon. Obviously if you have more photons in a box, you have more energy in the box. That doesn't mean that energy is quantised, only that photons are.

Can you add radiation energy by half a photon?

No.
Because, as Alan said, phonons are quantised.

[alancalverd]

You could ad a photon with 0.5f to the box, but it would still be a whole photon.

[hamdani yusuf (OP)]

You could ad a photon with 0.5f to the box, but it would still be a whole photon.

It means the radiation energy in particular frequency is quantized. It can be interpreted as photon, but it's not the only possible interpretation. Planck himself didn't interpret it as such.

[alancalverd]

No. It means that a quantum of radiation has a particular energy, and that energy is directly related to the frequency of  the wave  that models the propagation of that quantum.

My car is blue. That doesn't mean that all blue cars are mine, or that all blue things are cars.

[hamdani yusuf (OP)]

No. It means that a quantum of radiation has a particular energy, and that energy is directly related to the frequency of  the wave  that models the propagation of that quantum.

The concept of quantum of radiation was created after the discovery of quantization in radiation energy.
That quantization was thought to be necessary to explain the energy distribution of black body radiation.
You are getting it reversed.

[alancalverd]

The entire history of science is essentially the history of the gradual retreat of human stupidity in the face of improving models of the universe, but it has no bearing on how the universe behaves.

The fact is that the energy of electromagnetic radiation in general can take any value (up to the mass energy equivalent of the entire universe) but the energy of a single photon (the means by which we model the interaction of em energy with matter)  is hf where f is the frequency of the wave that models that photon's propagation.

[Eternal Student]

Hi.

That quantization was thought to be necessary to explain the energy distribution of black body radiation.

   You (Hamdani) have said something like this in a few places.

If we back up to post #83 for a moment,   I think the section you had in quotations presented Planck's early assumptions and his model for Blackbody radiation much more accurately.

    Planck didn't really suggest all e-m radiation was quantised and it certainly wasn't required to explain Blackbody radiation.    Taking an extract from your quotation - he only required that the energy in the atomic vibrations of frequency f was some integer times a small, minimum, discrete energy,.   To paraphrase that -  all Planck advocated for was quantised oscillators in the walls.

   I've edited and stripped out most of what I was originally going to say.   This is a condensed version:
Blackbody radiation is usually modelled by considering radiation that can exist inside a cavity.  So Planck would only require the radiation that can be supported inside a cavity to be quantised  (have allowed energies of the form nhω  for n an integer).   There are many ways and many assumptions you can make to obtain or justify that result.   For example, you can do exactly what Planck was thought to have done originally:  Assume the radiation was generated by some sort of microscopic "oscillators" within the walls of a cavity.   If those oscillators have energy which is quantised that will be sufficient to ensure the radiation inside the cavity at every frequency will have energy that is also quantised.
   So Planck wanted quantised oscillators in his cavity walls only.   Radiation in general or that exists elsewhere in the world (not inside a cavity at thermal equilibrium with cavity walls) was under no obligation to be quantised.

   That may seem like a lot of words to point out a very small difference.   It wasn't done just to be annoying but instead just to clarify what Planck needed to assume and what was not needed.   Yes, you can derive the blackbody spectrum by assuming radiation is quantised but you just don't have to and historically it does not look like Planck made that assumption.   All he needed was quantised oscillators in the walls, the quantisation of any radiation that could be found inside the cavity would follow automatically.   This has some relevance for suggesting one reason why all bits of light you might find anywhere (e.g. not just inside a cavity) would still be quantised:   If every bit of light (anywhere) has it origin ultimately in a transition that happened in an atom, then the source of all e-m radiation is suitably quantised,  so all the radiation you will find will automatically be suitably quantised.

     To check or examine this, you'd want to try to find light that you know was not made by any transition (or quantised change) within an atom (including the nucleus for very high frequency e-m radiation) and just check if this bit of light is still quantised in the same way that we expect.   The only bit of light I can think of whose origin cannot be ultimately traced back to an atom would be light from the big bang, or from any time before we had nucleogenesis and atoms in existence.   However, until the era of recombination when atoms were formed and continuing to form, the universe remained opaque and light just did not travel through it.    So there just isn't any of that light that you can see, if indeed there was ANY light (travelling e-m waves of some frequency) as we understand it that early in the universe.   Some sources of information will just directly state that the era of recombination was the first moment of light existing:   This was the moment of first light in the universe, between 240,000 and 300,000 years after the Big Bang, known as the Era of Recombination.     [ https://phys.org/news/2016-11-universe.html ].   The existence of e-m radiation and of atoms that produce or absorb only discrete quanta of e-m radiation has been inextricably linked since the earliest of days.

Best Wishes.

[hamdani yusuf (OP)]

Planck didn't really suggest all e-m radiation was quantised and it certainly wasn't required to explain Blackbody radiation.    Taking an extract from your quotation - he only required that the energy in the atomic vibrations of frequency f was some integer times a small, minimum, discrete energy,.   To paraphrase that -  all Planck advocated for was quantised oscillators in the walls.

In 1900, the British physicist Lord Rayleigh derived the λ−4 dependence of the Rayleigh?Jeans law based on classical physical arguments, relying upon the equipartition theorem. This law predicted an energy output that diverges towards infinity as wavelength approaches zero (as frequency tends to infinity). Measurements of the spectral emission of actual black bodies revealed that the emission agreed with Rayleigh's calculation at low frequencies but diverged at high frequencies; reaching a maximum and then falling with frequency, so the total energy emitted is finite. Rayleigh recognized the unphysical behavior of his formula at high frequencies and introduced an ad hoc cutoff to correct it, but experimentalists found that his cutoff did not agree with data.[1][3] Hendrik Lorentz also presented a derivation of the wavelength dependence in 1903. More complete derivations, which included the proportionality constant, were presented in 1905 by Rayleigh and Sir James Jeans and independently by Albert Einstein.[3] Rayleigh believed that this discrepancy could be resolved by the equipartition theorem failing to be valid for high-frequency vibrations, while Jeans argued that the underlying cause was matter and luminiferous aether not being in thermal equilibrium.[3]
https://en.m.wikipedia.org/wiki/Rayleigh%E2%80%93Jeans_law

Planck's quantization was an ad hoc correction to Rayleigh's model which fortunately fit with experimental data. His argument was that it takes more energy to produce higher frequency radiation, which provides the cut off he needs to explain black body radiation curve.

[Bored chemist]

The concept of quantum of radiation was created after the discovery of quantization in radiation energy.

That's linguistically unlikely.

So Planck wanted quantised oscillators in his cavity walls only.   Radiation in general or that exists elsewhere in the world (not inside a cavity at thermal equilibrium with cavity walls) was under no obligation to be quantised.

That's impossible.
How could quantised radiation escape the box other than 1 quantum at a time?
The box isn't allowed to lose half a quantum, because that would leave and impossible "half quantum" behind.