how can light have mometum but no mass?

Question

if P = M x V,
and the mass of a photon is zero, then regardless of its speed it should have zero momentum, but i read that light has momentum.

Answer 1

This question is often asked by students that are grasping einsteins equations but take them at face value only...

A photon also has momentum, and momentum is related to mass by Newton’s third law, p=mv. But in this case the mass is what is now unfashionably termed ‘relativistic mass’. This is defined as energy that changes with velocity. By convention, because it mucks with equations much longer than these, mass is not defined as relativistic mass, which is really just energy, but as ‘invariant mass’. This is the mass of the particle at rest and doesn’t change.

He said that energy was related directly to mass, E=mc2. So if mass is zero, energy is zero. But clearly this is not true for photons, because light has energy.

Einstein’s energy equation can also be expressed as E=mc²=sqrt p²c²+m0²c^4 with m=relativistic mass, m0 the invariant mass, E=energy, p=momentum and c=speed of light. (Bet you wished you didn’t ask the question now.)

A particle such as a photon can have momentum and energy without mass because for massless radiation, energy is equal to momentum times the speed of light (E=pc). Plug that in above and you’ll get m=0

Answer 2

Light has both Energy and Momentum according to the equations-:

E = mc^2 (E is energy, m is mass and c is the speed of light)
and
E = h f (E is energy, h is plancks constant and f is frequency)

The higher the frequency of light, the more energy it has, thus the more momentum.

In the Photo-Electric effect, photons are directed at a piece of metal and an electrical current is induced into a circuit by the photons directly mapping one-to-one with loose electrons in the conduction band of the metal. (proving the particle bit) and aslo proving that photons must be able to transfer energy (and thus momentum) to particles. i.e. They are a carrier of energy.

Particles can also behave as waves, in something called the de Broglie wavelength, electrons and other sub-atomic particles have a wavelength which is given by the equation-:
Lambda = Planck constant / (mass x velocity)

Light can be considered as both a wave and a particle - this is known as wave-particle duality.

It is a difficult concept to understand and relies on Quantum Mechanics to explain it properly.

Answer 3

Good question. I believe that may be like asking why ice has no water and water has no ice. They are different states of matter. Einstein's celebrated formula E=mc2 indicates that mass can be converted into energy and vice versa. Light exists as tiny packets of mass-less energy or photons. A photon may be captured by an electron orbiting an atom (or molecule) and the electron is kicked up into a higher more energetic orbit (with greater momentum?). Photons strike the vanes of a radiometer and cause it to rotate (some photons absorbed and some reflected by black and silver surfaces). Photons may some day allow spacecraft to 'sail' through space near the sun. Mass may be converted to photons (energy) but momentum is not lost, it is conserved.

Answer 4

Yes, it does have 'momentum'. But you have to remember that, since mass and energy are the same thing, the 'mass' involved is the relativistic mass equivalence of the energy of the photon.

HTH ☺

Doug

Answer 5

i thought that light had a duel state it was both matter therefore has massm, and enrgy. u can blame quantum physics for that... i did. but i suppose it explains how it's bent by gravity and yet can pass through things like enrgy in waves or something.

Answer 6

It's not quite that simple ... try here

http://math.ucr.edu/home/baez/physics/Relativity/SR/light_mass.html

Answer 7

is that a real question?