Kuiperbelt2003 says photons have no mass but do have momentum.?

Question

Momentum is the product of mass & velocity; therefore, photons must have mass, however minute. If there is mass to light waves, why not mass to the whole range of the electromagnetic spectrum? Could that mass result in measurements of "dark matter" which is not visible and is unknown in its nature?

Answer 1

Ah, you caught us...we physicists have no real clue what light really is. First we say it's a wave. Then we say it's a particle. Next we say it's massless. Then we say it has momentum. Argh.

The truth is that mass and energy are simply different manifestations of the same thing. That we learned from good old E = mc^2.

So at the subatomic level, things get a bit jumbled and photons with their virtual mass are a prime example of that mix of mass and energy. We know photons have momentum because we can observe electrons being knocked out of a photoelectric cell by the momentum of light particles. [By the way, Einstein won his Nobel for the photoelectric work he did, not for relativity.]

We also know they have no inertial mass. If photons had inertial mass, they could not travel at, ta da, the speed of light. Inertial mass has infinite inertia at the speed of light and it would take infinite energy plus some to attain that speed if light had inertial mass.

So we give light a virtual mass, one that does not increase its inertia with light speed. Photon energy is E = hf = hc/L; where h is Planck's constant, f is the frequency of the photon, c is light speed, and L is the wavelength, where fL = c. And then there is E = mc^2; so hf = mc^2 and m = hf/c^2 is the virtual mass of light. Also p = mc = hf/c, which is that momentum you were talking about.

Like all momentum, this one for light is also mass times velocity. But this mass is a virtual mass rather than inertial. Note that pc = mc^2 = E; so light gets its energy in part from its momentum.

Re your dark matter hypothesis, no the virtual mass of light is not dark matter. Dark matter has one major characteristic that virtual mass does not have...the ability to create a gravitational field.

One of the principle characteristics of inertial mass is its ability to attract other inertial mass by the force of gravity. And it's the need to explain why galaxies don't fling apart under their own spins that dark matter was posited. The extra gravity from dark matter keeps the galaxies together. Virtual mass could not do that because it lacks the gravity force field.

Answer 2

> Momentum is the product of mass & velocity;

That's actually a special case. For objects that have mass, momentum is indeed mass times velocity. But for photons, momentum is E/c (where "E" is the photon's energy).

Since Einstein showed that mass and energy are equivalent, you _could_ say that the photon's energy is "equivalent" to a mass of p/c (where "p" is the photon's momentum). However, physicists nowadays, when they use the term "mass," generally refer to the body's "rest mass" (i.e. the mass-energy it has when it's standing still). In the case of a photon, the rest mass is zero.

> why not mass to the whole range of the electromagnetic spectrum?

You're right; every photon of every wavelength has an energy that is equivalent to some specific rest mass.

> Could that mass result in measurements of "dark matter" which is not visible and is unknown in its nature?

Probably not. We can detect photons covering a very wide range of the spectrum, and we haven't detected any that could account for all the mass of dark matter.

Answer 3

In my own Fractal Foam Model of Universes, massive particles consist of photons in orbit around one another (due to exchange of momentum with dark energy). If the orbital speed is the speed of light, then all of the photons' energy is converted to mass, and the photons' momenta cancel each other because they are moving at the speed of light in opposite directions. Accelerating an orbiting pair of photons gives momentum to the mass because it makes the wavelenght of the photons shorter in world coordinates than it is in the particle's coordinates (because of special relativity time dilation).

In the case of a neutrino, the orbital speed of the pair of photons is less than the speed of light, and the pair follow a double helix path. The photons continue at the speed of light but the center of the pair moves slower than light, so only a small fraction of the photon energy is converted to mass.

Answer 4

You're trying to apply Newtonian physics to objects moving at the speed of light, of course there will be contradictions.

In relativity, the momentum of a photon equals Planck's constant divided by the photon's wavelength, or the energy of the photon divided by c.

Answer 5

Momentum = velocity X Mass is incorrect! it works purely for products that have mass, and for low velocities (in comparison to mild velocity). the terrific relativistic equation is this: Momentum = M0 * v / sqrt( a million - v^2 / c^2 ) the place M0 is the "relativistic mass". Photon's don't have elementary mass, yet they do have "relativistic mass". additionally they have v = 0, so the equation will become 0 / 0. meaning we ought to apply a various equation for photon momentum. That equation is p = E/c.

Answer 6

Here's a good article on photons & their momentum, etc:

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

Answer 7

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