Is the Energy of Gamma Rays and Radio Waves Equivalent with Equal Amplitudes?

[physics user1]

According to the old thery of light the energy carried by by a wave is proportional to the amplitude of the electric field not to the frequency as Planck proposed, so an eletromagnetic radiation in the gamma spectrum carry the same energy as a radio one if their amplitude is the same?
They only different in frequency and wave length that doesn't affect the energy

(According to the old theory, i know that energy is proportional to the frequency)

 

[Ibix]

The energy per photon depends on the wavelength. But classical EM only models situations where there are lots and lots of photon, so you have another variable in the energy carried by a wave - the number of photons in the beam. An energetic radio pulse has more photons than an equally energetic gamma pulse, basically.

Incidentally, energy is related to intensity rather than amplitude, I think.

 

[nasu]

The energy "carried by the wave" does not have a well defined meaning. It depends on how long the wave does this carrying and what is the wave's extension in space. The waves are compared usually in terms of intensity, which is energy carried in 1s through a cross section of 1m² (in SI units).
In both classic and QED models you can have waves with different frequencies and same intensity. The fact that the energy per photon at low frequency is lower does not mean you cannot have high intensity. It just takes more photons.

 

[physics user1]

The energy per photon depends on the wavelength. But classical EM only models situations where there are lots and lots of photon, so you have another variable in the energy carried by a wave - the number of photons in the beam. An energetic radio pulse has more photons than an equally energetic gamma pulse, basically.

Incidentally, energy is related to intensity rather than amplitude, I think.

But the number of photons is related to the amplitude of the wave? Since the square of amplitude in related to the intensity, right?

So then a gamma "wave" and a radio wave having same energy have different amplitude

 

[nasu]

The number of photons is proportional to intensity.

 

[Ibix]

But the number of photons is related to the amplitude of the wave? Since the square of amplitude in related to the intensity, right?

The energy in a classical EM wave is proportional to the square of the amplitude. It's also proportional to the photon count (assuming it's monochromatic). So, as nasu says, the number of photons is proportional to the intensity, not the amplitude.

So then a gamma "wave" and a radio wave having same energy have different amplitude

No. Energy is proportional to amplitude squared. So two pulses with the same intensity have the same amplitude. They may, however, contain different numbers of photons if they have different frequencies.

 

[tech99]

The energy "carried by the wave" does not have a well defined meaning. It depends on how long the wave does this carrying and what is the wave's extension in space. The waves are compared usually in terms of intensity, which is energy carried in 1s through a cross section of 1m² (in SI units).
In both classic and QED models you can have waves with different frequencies and same intensity. The fact that the energy per photon at low frequency is lower does not mean you cannot have high intensity. It just takes more photons.

For radio engineering purposes, I think Intensity may conveniently be expressed as Power Flux Density in W/sq metre.

 

[nasu]

Yes, you can call it power flux density. Is the same quantity as "intensity" with the same units. Energy per second is power.
https://en.wikipedia.org/wiki/Intensity_(physics)

 

[physics user1]

I found this: https://www.quora.com/If-you-have-t...d-that-mean-would-the-photon-have-more-energy

Can you please explain me how two waves with same amplitude can have different number of photons?
You guys said the number of photons is propotional to the intensity, and intesity is proportional to the energy, but the energy is related to the ^2 of the amplitude, then logically the number of the photons is related to the amplitude^2 , where is this chain wrong?

 

[nasu]

Who said is wrong? Amplitude squared is proportional to intensity which is proportional to number of photons.Note that "proportional" does not mean equal.

 

[physics user1]

Who said is wrong? Amplitude squared is proportional to intensity which is proportional to number of photons.Note that "proportional" does not mean equal.

Ok, thanks :)

However, getting back in time when they didn't know that light is quantised, we take a gamma ray, and a radio wave , both waves gamma and radio have same amplitude, are the energy of the two waves equal?
Supposing they carry for the same amount of time, and in the same extension of space

 

[nasu]

Do you think that the energy of the waves depends on the history of our knowledge?
And again, energy of a wave is not something well defined. What do you mean by it?

 

[physics user1]

Do you think that the energy of the waves depends on the history of our knowledge?
And again, energy of a wave is not something well defined. What do you mean by it?

I mean density of energy, 1/2 ε E^2

 

[nasu]

If E is the same for both waves, what do you think, would they have the same energy density or not?

 

[physics user1]

If E is the same for both waves, what do you think, would they have the same energy density or not?

Yes i guess, but if E is the same for both then they have also same number of photons...

 

[nasu]

You forget again that proportional is not equal. The number of photons may be proportional to E^2 but it may depend on frequency too. So your conclusion does not follow.
Actually the relation between E and photons seems to be a little tricky in QED. A wave with a well defined value of E may not have a defined number of photons but rather be a superposition of states with different number of photons. Imagining photons as well defined "particles" is not very realistic.

 

[physics user1]

I didn't know that the nuber of photons can depend also on frequency, i thought that only energy depends on frequency, however i got it, now i understand, if E is defined then the number of photons is not

 

[nasu]

If you are interested in seeing the "ugly" details of quantization of the EM field, here is an example
https://ocw.mit.edu/courses/nuclear...-fall-2012/lecture-notes/MIT22_51F12_Ch10.pdf
Right on top of page 100 they show that the expectation value of the electric field for a state with definite photon number is zero.

You may know of a somewhat similar case in quantum mechanics. For a state with definite value of momentum, the position is undefined.

 

[physics user1]

Right on top of page 100 they show that the expectation value of the electric field for a state with definite photon number is zero.

That makes sense to me :), if the position of the photons is defined then the wave nature vanish

 

[nasu]

I believe that the photons don't even "have" a position operator. So talking about the position does not make sense for photons.
The relationship between position and momentum was just an example of a similar concept, but for particles like electrons or protons.