Q&A: How Does a Photon Have Momentum w/o Mass?

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Discussion Overview

The discussion centers around the concept of how photons, which are massless particles, can possess momentum. Participants explore the relationship between energy and momentum in the context of relativity, examining various equations and interpretations related to this phenomenon.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions how photons can have momentum without mass.
  • Another participant explains that photons have momentum through their energy, referencing the equation E^2 = m^2 c^4 + p^2 c^2 and deriving p = E/c for massless particles.
  • A different participant reiterates the relativistic mass equation, noting that for massless particles, the rest mass term disappears, leading to e^2 = p^2 * c^2.
  • Several participants inquire about the relationship between momentum (P) and energy (E), with references to previous posts for clarification.
  • One participant suggests an alternative approach using the equation E = mc^2, treating mass as "relativistic mass" and deriving p = E/c, while another participant challenges this method, asserting that the derivation is incorrect and emphasizing the validity of the approach in post 2.

Areas of Agreement / Disagreement

Participants express differing views on the derivation methods for relating energy and momentum, with some supporting the approach in post 2 and others contesting the validity of alternative methods presented. No consensus is reached regarding the best derivation.

Contextual Notes

Some participants rely on different interpretations of mass in the context of relativity, leading to varying conclusions about the derivation of momentum for massless particles. The discussion reflects ongoing debates about the definitions and implications of relativistic mass.

Ed Aboud
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Sorry if this is a ridiculous queation, but how does a photon have momentum if it hass no mass?
 
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They do it with energy! The equation for energy in relativity is:

[tex]E^2 = m^2 c^4 + p^2 c^2[/tex]

Where m is the mass, p is the momentum, and c is the speed of light. Put in [itex]m = 0[/itex] and you get E = p c, so any massless particle with energy E will have momentum p = E/c.
 
Last edited:
From the relativistic mass equation - e^2 = (pc)^2 + (mc^2)^2. Since it has no rest mass, the latter term disappears but we still have e^2 = p^2 * c^2.
 
Ah I see, thanks very much!
 
what is the relationship between P and E?
 
Crosson said:
They do it with energy! The equation for energy in relativity is:

[tex]E^2 = m^2 c^4 + p^2 c^2[/tex]

Where m is the mass, p is the momentum, and c is the speed of light. Put in [itex]m = 0[/itex] and you get E = p c, so any massless particle with energy E will have momentum p = E/c.

Another way of getting the same result is to use the more popular form

[tex]E = mc^2[/tex]

and solve for m (which can be regarded as the "relativistic mass"). Then just multiply by the velocity, which is c, and treat it like any other problem. You'll see that you get the same result, p = E/c.
 
Bright Wang said:
what is the relationship between P and E?

See post #2, if you mean P is the momentum?
 
Usaf Moji said:
Another way of getting the same result is to use the more popular form

[tex]E = mc^2[/tex]

and solve for m (which can be regarded as the "relativistic mass"). Then just multiply by the velocity, which is c, and treat it like any other problem. You'll see that you get the same result, p = E/c.

...just by chance because the derivation is wrong. Photons are massless. The correct derivation is the one already written in post 2.
 

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