Light implying consistency between QM and SR

In summary: According to Relativity, the energy of a photon does not change with its frequency. However, there is a relativistic Doppler effect which accounts for the correct increase in the energy of photons with their frequency.
  • #1
DaTario
1,039
35
Hi All,

Let me see if I can put my doubt in words appropriately...

Imagine a source of EM radiation, say a laser beam, and suppose you are running against the laser's direction, i.e., photons go to positive x and you to negative x direction, for instance.

From the POV of SR, light does not change its velocity, but there is Doppler effect and the transfer of momentum and energy (from light to you) increases.

From the POV of QM, there is also Doppler effect and Planck's equation E = hv introduces also an increase in the energy and momentum of the photon.

I am considering that there is conservation of number of photons produced by the source in this context.

Do these two effects rest harmonically on the top of the same physicist's desk?


In other words, if photons are to be considered roughly packets of EM radiation, whose number are conserved in going from one reference frame to another, and if its velocity does not change in going from one reference frame to another so it must be that the energy ought to increase with the frequency. Does it make sense?



Best wishes

DaTario
 
Last edited:
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  • #2
Yes, it makes sense.
So what is your question?
 
  • #3
My question is:

Does Relativity in itself imply the increase of energy of radiation with its frequency ?


And perhaps we should go beyond classical Doppler effect. Does relativistic Doppler effect accounts for the correct increase (with the frequency) in the energy of photons (EM packets of radiation) ?
Best wishes

DaTario
 
Last edited:
  • #4
DaTario said:
My question is:

Does Relativity in itself imply the increase of energy of radiation with its frequency ?

yes, it does


And perhaps we should go beyond classical Doppler effect. Does relativistic Doppler effect accounts for the correct increase (with the frequency) in the energy of photons (EM packets of radiation) ?
Best wishes

DaTario

yes, it does
 
  • #5
It seems quite strange, for if Relativity could have offered support to Planck's equation, E = hv, Planck, himself, wouldn't have said that his equation was just a hint that was capable to provide an answer to the black body problem. Do you know some reference to this result ?

Thank you in advance,

Best wishes

DaTario
 

1. How does quantum mechanics explain the behavior of light?

Quantum mechanics explains that light is made up of particles called photons, which have both wave-like and particle-like properties. The wave-like behavior of light can be described by its frequency and wavelength, while the particle-like behavior can be described by its energy and momentum.

2. How does special relativity relate to the speed of light?

Special relativity states that the speed of light in a vacuum is constant, regardless of the observer's frame of reference. This means that the speed of light is the same for all observers, regardless of their relative motion. This consistency is a fundamental principle of the theory.

3. Can quantum mechanics and special relativity be reconciled?

Yes, quantum mechanics and special relativity can be reconciled through the theory of quantum field theory. This theory combines the principles of quantum mechanics and special relativity to describe the behavior of particles and fields at the subatomic level.

4. How does the wave-particle duality of light fit into the consistency between QM and SR?

The wave-particle duality of light is an example of how light exhibits both wave-like and particle-like behavior, as predicted by quantum mechanics. Special relativity then explains how the speed of light is the same for all observers, regardless of its wave or particle nature.

5. What implications does the consistency between QM and SR have in our understanding of the universe?

The consistency between quantum mechanics and special relativity has greatly enhanced our understanding of the universe, particularly at the subatomic level. It has allowed for the development of technologies such as lasers, which rely on the principles of both theories, and has also provided a deeper understanding of the fundamental laws that govern our universe.

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