Photon: momentum without mass?

In summary, photons have zero mass but can still have momentum and energy due to their relationship with mass, as described by the formula E^2 = m^2 c^4 + p^2 c^2. This applies to all particles, not just photons. The equation p=mv is an approximation and does not work for fast-moving objects like photons. The concept of "mass" has different meanings in different contexts and can lead to confusion.
  • #1
Gabriele Pinna
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The mass of a photon is zero but why does it have a momentum and an energy (E=mc^2=hv) ?
 
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  • #2
Gabriele Pinna said:
E=mc^2
This is only true for objects at rest, and photons are not at rest.
The more general formula is ##E^2 = m^2 c^4 + p^2 c^2##. There is nothing wrong with a massless particle having momentum and energy.
 
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  • #3
Gabriele Pinna said:
The mass of a photon is zero but why does it have a momentum and an energy (E=mc^2=hv) ?

There's nothing in the laws of physics that prevent a particle from having zero mass and nonzero momentum and energy. Mass, momentum, and energy are properties, so they are related. That relationship allows for zero mass along with nonzero energy and momentum. In fact, the same relationship asserts that if the mass is zero the energy and momentum have to equal each other.
 
  • #4
But momentum is equal to p=mv so if m=0→p=0
 
  • #5
Gabriele Pinna said:
But momentum is equal to p=mv so if m=0→p=0

No. See mfb's post #2.

I suspect you are getting confused by the so-called "relativistic mass" which almost no physicists use nowadays, but nevertheless survives in introductory (especially popular-level) treatments of relativity, versus the "invariant mass / rest mass" which Orodruin is referring to.
 
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  • #6
Gabriele Pinna said:
But momentum is equal to p=mv so if m=0→p=0

That only applies to objects with mass. For photons, the equation for momentum is p=hv/c, where h is Planck's constant, v is frequency, and c is the speed of light.
 
  • #7
jtbell said:
the "invariant mass / rest mass" which Orodruin is referring to.
It sounds like something I would have said, but I have been silent in this thread so far. :wink:

There are Insights FAQs on both relativistic mass and on photons which are relevant. I suggest OP reads them.
 
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  • #8
Drakkith said:
But momentum is equal to p=mv so if m=0→p=0
That only applies to objects with mass.
And even for those, it is just an approximation for slow speeds.

@Gabriele Pinna: Formulas from nonrelativistic mechanics are just an approximation, they are good for slow objects, but they do not work for fast objects (a large fraction of the speed of light) and they are completely meaningless for light.
 
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  • #9
Gabriele Pinna said:
But momentum is equal to p=mv so if m=0→p=0

That used to be true in Newtonian mechanics, but it's not true in special relativity. See also the various comments about the ambiguities in the word "mass".
 
  • #10
Thanks
 

1. What is a photon?

A photon is a fundamental particle that is the basic unit of light and all other forms of electromagnetic radiation. It has no mass but carries energy and momentum.

2. How can a photon have momentum without mass?

According to Einstein's theory of relativity, mass and energy are two forms of the same thing. Since a photon has energy, it also has momentum, even though it has no mass.

3. How is the momentum of a photon calculated?

The momentum of a photon can be calculated by multiplying its energy by the speed of light. This is known as the de Broglie equation, which relates the wavelength and frequency of a photon to its momentum.

4. Can the momentum of a photon change?

Yes, the momentum of a photon can change when it interacts with matter. This can happen through processes such as absorption, emission, or scattering.

5. What is the significance of photons having momentum without mass?

The fact that photons have momentum without mass is important in understanding the behavior of light and electromagnetic radiation. It also has applications in various fields such as optics, telecommunications, and quantum mechanics.

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