General physics question -- How can massless photons have momentum?

[spacecadet11]

TL;DR Summary

P=mv

P=mv *momentum equals mass X velocity.

Light particles or "photons" are said to be "massless". And yet they have
momentum. How is that possible? (p.s. I used to know the answer)

 

[anuttarasammyak]

The relation p=mv ( and E=1/2 mv^2 ) is renewed by SR to be
$$E^2-p^2c^2=m^2c^4$$
This equation allows m to be zero,
$$E=pc$$
where c is light speed, that means massless particle could have energy and momentum.

 

[Drakkith]

Light particles or "photons" are said to be "massless". And yet they have
momentum. How is that possible? (p.s. I used to know the answer)

Because P=MV is an incomplete relation, or one that only applies to objects with mass. As anuttarasammyak said, the more complete relation is $E^2=m^2c^4+p^2c^2$, which reduces to $E=pc$ when $m$ is zero.

 

[spacecadet11]

There is something called photon pressure. Massless photons that have momentum can impart or trade
this momentum with particles that have mass...causing them to move. Does this trading mechanism
have a name? Or how does something massless cause something with mass to move?

 

[anuttarasammyak]

Compton scattering https://en.wikipedia.org/wiki/Compton_scattering might be of your interest.
Both massive and massless particles have energy and momentum total of which are conserved.

 

[spacecadet11]

 

[Drakkith]

There is something called photon pressure. Massless photons that have momentum can impart or trade
this momentum with particles that have mass...causing them to move. Does this trading mechanism
have a name? Or how does something massless cause something with mass to move?

This is nothing special. Electrons in an antenna are moved by an incoming radio wave all the time. In general, this is simply called an 'interaction'. The exact details of the interaction depend on which two (or more) particles are interacting and how much energy they have. A gamma ray photon and a radio wave photon both interact with a radio antenna, causing electrons to accelerate and move, but the exact details are very different because the energies are very different.

 

[spacecadet11]

Thank you. It is the 'interaction' that interests & concerns me. So I will keep reading...

 

[vanhees71]

From another point of view the reason for introducing the concept of fields, as was done by Faraday mid of the 19th century and then worked out bye Maxwell in mathematical form, is to have locality and at the same time momentum conservation. In Newtonian mechanics interactions are mediated by instantaneous actions at a distance (e.g., in Newton's theory of gravitation), and there is no problem for Newton's 3rd Law to hold, and the 3rd Law leads to momentum conservation for closed systems.

In relativistic physics, which is the more comprehensive description of Nature than Newtonian physics, you cannot have the 3rd law being valid between distant bodies, because it needs at least the time to mediate the change of the location of one body relative to a distant other body that's needed for a "signal" that moves with the speed of light. Now if you have a field, which is part of the dynamical system and this field carries momentum, you can always transfer momentum between a body and the field at the location of the body, and indeed, if you evaluate the momentum balance of the electromagnetic field and the charged matter interacting with it, you get local conservation of momentum by exchanging momentum between the charged matter and the electromagnetic field.

The same holds for the other conservation laws valid for closed systems: energy, angular momentum, and the velocity of the center of energy wrt. any inertial frame of reference. These conservation laws are due to the symmetries of special-relativistic spacetime, the socalled Poincare symmetry: Homogeneity of space (the physical laws are the same everywhere; spatial translation invariance), homogeneity of time (the physical laws are the same at all times; temporal translation invariance), isotropy of space (the physical laws are the same of all orientations of an experiment in space; rotation invariance), the indistinguishability of all inertial frames of reference (the physical laws are the same in all inertial frames; invariance under Lorentz boosts). This leads to 10 conservation laws (3 momentum components, 3 angular-momentum components, 3 center-of-energy-velocity components, and energy) due to a famous theorem found by Emmy Noether in 1918.

 

[spacecadet11]