Energy of photons vs classical physics energy

In summary, Relativity says photons have energy E=pc and classical physics says E=1/2 pv. The relationship between energy and momentum for massive and massless particles is E = √(p2c2 + m2c4). For a massive particle at rest, the equation reduces to E = mc2 and for a massless particle, it reduces to E = pc. The energy of a proton can be calculated using this equation as it is accelerated to almost the speed of light.
  • #1
PBTR3
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Relativity says photons have energy E=pc. Classical physics says E=1/2 pv. There seems to be a factor of 2 missing in one case or the other or does the energy formula change as the speed of light is reached? There must be a simple explanation but I have not found it yet. I did not know where to put this question-under classical physics of quantum physics. Thanks for any help.

hjr
 
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  • #2
Classical physics says E=1/2 pv
There are no photons in classical physics, so classical physics cannot say anything about them.

With the Maxwell equations and classical physics, you can derive E=pc for electromagnetic waves. There is no factor of 2.
 
  • #3
The single relationship between energy and momentum that applies to both massive and massless particles is E = √(p2c2 + m2c4). For a massless particle, set m = 0 and it reduces to E = pc. For a massive particle at rest, set p = 0 and it reduces to E = mc2.

For a massive particle that's slowly moving, keep both terms and expand in a power series in p. The first two terms give you the usual Newonian expression, E = mc2 + p2/2m.
 
  • #4
Energy of photon vs classical physics energy

Thanks for the replys. I was trying to understand what happens to energy of a proton as a proton is accelerated from rest to almost the speed of light as in the LHA. I think I can calculate that now.

hjr
 

1. What is the difference between energy of photons and classical physics energy?

The main difference between the energy of photons and classical physics energy is the way in which they are quantized. Photons, which are particles of light, have discrete units of energy known as quanta. This means that the energy of a photon can only exist in specific amounts, while classical physics energy can vary continuously.

2. How is the energy of a photon calculated?

The energy of a photon is calculated using the equation E=hf, where E is the energy, h is Planck's constant, and f is the frequency of the photon. This equation is known as the Planck-Einstein relation and it shows that the energy of a photon is directly proportional to its frequency.

3. Can the energy of photons be converted into other forms of energy?

Yes, the energy of photons can be converted into other forms of energy through a process called photoelectric effect. This is when photons transfer their energy to electrons in a material, causing them to be emitted as electricity or heat.

4. How does the energy of photons relate to the electromagnetic spectrum?

The energy of photons is directly related to their position on the electromagnetic spectrum. Electromagnetic radiation with higher frequencies, such as gamma rays and x-rays, have higher energy photons, while radiation with lower frequencies, such as radio waves, have lower energy photons.

5. Can the energy of photons be measured?

Yes, the energy of photons can be measured using specialized tools such as spectrometers or detectors. These instruments can detect the frequency and intensity of photons and calculate their energy using the Planck-Einstein relation.

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