# How can photons have momentum if they have zero mass?

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I understand E = hv, but I’m not getting why photon collisions can “push” things instead of just producing heat. Thanks!

In: Physics

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.