Photons have relativistic mass. While the photon itself doesn’t have mass in the conventional sense, it does have energy, and remember that E=mc^2; energy is mass and mass is energy. This means that a photon has a kind of ‘virtual’ mass. A photon can push on something like a solar sail by hitting the sail and imparting momentum, causing the reflected photon to have less momentum, and therefore less mass/energy (a longer wavelength).

It’s a very commonly asked question.

Einstein’s mass energy equivalence formula that’s commonly used (E = mc^2) is incomplete. The full formula is:

E^2 = m^2 c^4 + p^2 c^2

Matter hardly ever gets to relativistic speeds, so we simplify the equation and only show the rest mass part.

But photons and other force carriers travel at the speed of causality, and while they have zero mass, they still have momentum.

E=mc^2 is only 1/2 the equation.

its actually E^2 = (mc^2)^2+(pc)^2

E=mc^2 is for rest mass.

E^2 = (mc^2)^2+(pc)^2 is for something in motion.

If it has no mass, mc^2 term drops out then you have E=pc for a massless object. The pc term only become relevant when the velocity of the massless thing is very high (near c), otherwise the mass term is orders of magnitude larger and dominates the equation.

If you think of a photon as a particle, it’s easy to imagine that it could hit something. If the photon hits an object, that object will recoil. Which means that the photon has imparted momentum to the object. Which means that the photon must have had some momentum to begin with.

Also, if you imagine a particle-antiparticle pair annihilating to produce photons, the total momentum of the pair has to go somewhere. If the photons couldn’t carry momentum, the annihilation would be impossible to observe in any reference frame other than the center of mass. It would be even stranger if a particle interaction was impossible just because you were moving

What it comes down to is that mass is not necessary for momentum. People are giving you equations (which are true, but don’t answer your question) or talking about relativistic mass (which is not something all physicists agree should be used.)

I find it helpful to remember that photons are literally waves of force. That force is in the electric and magnetic fields, but it is a moving packet of oomph that passes energy on to things it interacts with. That can create heat, yes, but remember that heat is just randomized kinetic energy.

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