In short, even though photons have no mass, they still have momentum proportional to their energy, given by the formula p=E/c. Because photons have no mass, all of the momentum of a photon actually comes from its energy and frequency as described by the Planck-Einstein relation E=hf.
But how do you apply this with Lorentz’ transformation (i.e. relativistic factors)? You cannot approach the speed of light without considering relativism. It is known that p = gamma * m * v where p is momentum, gamma is the gamma factor given by sqrt(1/(1-(v^2/c^2))), m is mass and v is velocity. If you study the gamma factor, you’ll realize that it approaches infinite as v approaches c, the speed of light. Since we are actually dealing with light here, where v = c we are breaking the equation. Momentum cannot be defined for any mass which moves at the speed of light. It’s asymptotic at that speed.
Also note that the same goes for E = mc^2. At relativistic speeds, also this equation needs to consider the gamma factor. So those classical equations break down for light.
The answer is that photons don’t have mass, but they have energy. There is a good explanation a bit further up in this thread on how this is possible.
Yeah, why do masless particles have momentum? And please not because law X says so.
In short, even though photons have no mass, they still have momentum proportional to their energy, given by the formula p=E/c. Because photons have no mass, all of the momentum of a photon actually comes from its energy and frequency as described by the Planck-Einstein relation E=hf.
From here: https://profoundphysics.com/if-photons-have-no-mass-how-can-they-have-momentum/
Essentially, momentum is a function of energy, not mass. It’s just that massive objects have way more momentum than massless ones.
Thanks! That’s the critical piece of information.
Because they have mass. They don’t have “mass at rest”, but they are never at rest anyway.
Do you remember that famous
E = mc^2equation? Everything that has energy has mass.But how do you apply this with Lorentz’ transformation (i.e. relativistic factors)? You cannot approach the speed of light without considering relativism. It is known that
p = gamma * m * vwhere p is momentum, gamma is the gamma factor given bysqrt(1/(1 - (v^2/c^2))), m is mass and v is velocity. If you study the gamma factor, you’ll realize that it approaches infinite as v approaches c, the speed of light. Since we are actually dealing with light here, wherev = cwe are breaking the equation. Momentum cannot be defined for any mass which moves at the speed of light. It’s asymptotic at that speed.Also note that the same goes for
E = mc^2. At relativistic speeds, also this equation needs to consider the gamma factor. So those classical equations break down for light.The answer is that photons don’t have mass, but they have energy. There is a good explanation a bit further up in this thread on how this is possible.
The one that you multiply with gamma is the rest mass, not the total mass.
To be short,
p = m_0 * γ * v, wherem_0is the rest mass. Put that in your equation and look what happens.So photons only have no mass if they don’t move? Do they even exist if they don’t move?
No. Or, at least not from our point of view.
They only exist moving at the speed at light. All particles with no rest mass only exist moving at the speed of light.
So photons do have mass?
only as long as they exist
Else they don’t. We are talking quantum here.
Energy is mass