How can photons have momentum when their mass is zero?

Question

I read it online that photons do possess momentum though their mass is literally zero. The thing that doesn't seem to be getting into my mind is how can it possess momentum if its mass is zero. I've read that momentum = Mass x Velocity.

So, to put it mathematically, if mass is null, the whole equation comes out to be zero. Is it, somehow that I don not know, related to the dual nature of particle? If it is, I'd like to know how. Thanks!

Answer 1

Things get weird when you get close to the speed of light.



Momentum = Mass x Velocity works quite well when describing a baseball or an airplane or a planet. But in Relativity the equation is actually Momentum = Mass x Velocity x Gamma.



Gamma = 1/√(1-v^2/c^2) is 1 when v = 0 but is infinite when v = c. So for a photon, momentum = 0 x infinity.

In some circumstances, 0 x infinity can turn out to be some ordinary number. We can't tell from this equation what that number will be. (It turns out that the momentum of a massless particle equals its energy in appropriate units.)

Answer 2

From relativity we have m = M sqrt(1 - (v/c)^2); where m is invariant mass, M is its inertia, and v its speed relative to a static frame K. We can multiply both sides by c^2 and define e = mc^2 and E = Mc^2.



Then by rearranging terms we find that E^2 = e^2 + k^2; where k = Mvc is the kinetic energy of the mass that has M inertia. Now the fun part.



We set v = c, making the mass m go the speed of light. Impossible you say...you're right, but continue on and see what must happen to make it possible.



We now have k = Mvc = Mcc = Mc^2 = E. In other words the total energy E is now all...entirely...kinetic energy.



Which leaves us with E^2 = e^2 + k^2 = e^2 + E^2 or, ta da, E^2 - E^2 = e^2 = 0. And e = 0 = mc^2. But as c is never zero, that means, drum roll please, m must = 0. And that makes it possible. The object cannot have invariant mass to go the speed of light, like, duh, light does.



But also note, it has energy, E = Mc^2 which is all kinetic. And look here, Mc = P is momentum. And look even further E = Mc^2 = Pc = hF so that P = hF/c where E = hF is the energy of a photon based on its frequency F.



And there you are. The theory of relativity says that photons must have momentum. And in fact, we can measure that momentum in labs; so it's not just a hypothesis, it's an engineering observation.

Answer 3

"How can photons have momentum when their mass is zero?"



Photons *do* have zero mass.

http://en.wikipedia.org/wiki/Photon#Experimental_checks_on_photon_mass



So their momentum is described thusly:

http://en.wikipedia.org/wiki/Photon#Physical_properties

... and note that mass is not part of that definition, and that describes the recoil of the atom that ejects the photon, so we know that is correct.



"I've read that momentum = Mass x Velocity."



This is correct for Newton. For massive objects travelling at much less than c.



"if mass is null, the whole equation comes out to be zero. Is it, somehow that I don not know, related to the dual nature of particle? If it is, I'd like to know how. Thanks!"



What do you think is so fundamental about "mass"? It does not exist at the quantum level, it is only meaningful in the system Universe. For subatomic particles, their mass is a quantum number times their particle's magnetic moment (the ability to store energy in a changing magnetic field). So mass is a complex property, made up of other things...

Answer 4

Momentum isn't necessarily described by the weight of an object.



Momentum is the amount of energy and speed of an object. So even if an object is massless like the proton it still has energy and still has a velocity.



momentum(p) has units: J*s = Joules*seconds



For large objects we can calculate momentum from their mass or from the base definition by their energy:

p=mv=mass*m/s=kg*m/s

The energy contained J=N*m=mass*acceleration*meters=kg*m/s^2*m=kg*m^2/s^2.

Joules/velocity=kg*m/s

p=Energy/velocity



For small objects like photons their momentum applies to energy and cannot be calculated from their mass:

p=h/lambda=Joules*seconds/meters=Energy/velocity as well.

Answer 5

the energy-mass equivalence formula is

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

if mo=0 [mass at rest]

E=pc

in other words the particle [photon]

has a reltivistic momentum equivalent to

p=E/c

Answer 6

When you get hit by a photon, you get warm. This means that the photon had energy and it transferred that to you. Your equation is related to physical objects at low speeds compared to the speed of light. The equation for a photon's momentum is p = h / lambda, see link.



http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relmom.html#c2

Answer 7

Are their mass zero or literally zero ? Big difference. . Great question though. One of the most thoughtful I've read so far.