# Understanding the Photon.

1. Jan 17, 2010

### thefifthlord

Anything that has energy must have some form of mass. Photons have both energy and momentum (Just because we chose to measure their momentum in terms of their wavelength doesn't mean they don't have mass!). It may be so small as to be immeasurable, but it does have mass. (I'm still new to this so i beg you're pardon if there is some undeniable proof that says that photons can't have mass(Please post a complete explanation).)

p = mv for pretty much everything that isn't moving at the speed of light.

But suppose if p = mv does indeed work for light

that would mean that

mv = h/lambda (possibly for all particles, light or otherwise).

in this case the velocity is the speed of light so,

mc = h/lambda
m = (h/lambda)/c

Which would mean that as the wavelength of the light decreases, the mass of the photon is increased. We know for a fact that light of a lower wavelength is of a higher frequency, and we know that higher frequency light is higher energy light. If the speed of light is indeed constant regardless of its frequency this is consistent with E = mc^2 (as E goes up so must m).

This means that either c isn't constant for all light particles, or that light does have increases in mass.

We know that all particles that move at a constant speed exhibit wave like motion, this motion becomes more apparent at the speeds of light but even if i were to throw a tennis ball in a straight line in a free-gravity vacuum, it would exhibit wave like motion. If one were to measure the wavelength and the frequency of the tennis ball i am almost 100% sure that they would get the same value for its momentum using the equation p = h/lambda as p=mv.

So can someone please explain to me thoroughly why photons don't have mass.

Thanks,

2. Jan 17, 2010

### diazona

Nope
The relativistic energy-momentum relation
$$E^2 = m^2c^4 + p^2c^4$$
describes photons perfectly when $m = 0$. Thus we conclude that photons have no mass. (The fact that the electromagnetic force has infinite range also demonstrates that photons have zero mass. There have been experiments done to test for the possibility that the photon does have some tiny mass, but so far, no evidence of a photon mass has been found.)

No, actually that's just an approximation. As you get closer to the speed of light, it gets gradually more and more inaccurate. The true expression is
$$p = \frac{mv}{\sqrt{1 - v^2/c^2}}$$

But it doesn't.

Ohhhkay... you're confusing mass with energy. In all the statements above, if you said "energy" instead of "mass" then what you're saying would be more or less correct. The problem arises when you start insisting that energy and mass must be proportional. This is a common mistake made by people who don't know that $E = mc^2$ is only part of a larger equation (which I wrote above), and that it only applies to particles which are not moving.

Back in the day when relativity was new, many prominent physicists thought the same way you did. They wound up defining two kinds of mass: one, the "relativistic mass", is what you've been thinking of as mass. It was defined as
$$m_\text{rel} = \frac{E}{c^2}$$
so that it always satisfied $E = mc^2$, and it would increase with increased velocity. The other mass, "rest mass", is the one that goes into
$$E^2 = m^2c^4 + p^2c^2$$
It is a constant for any given particle, so it doesn't change with velocity. After a while, people realized that these two definitions of mass were producing nothing but confusion, and that the relativistic mass was kind of a useless concept anyway because it's merely the energy multiplied by a constant conversion factor. So we've dispensed with the idea of relativistic mass, and these days, "mass" always means the rest mass.

Yeah, you would, but try calculating the wavelength of a tennis ball. It's extremely tiny, far smaller than the ball itself, and I can't imagine how you could possibly measure it.

3. Jan 17, 2010

### Altabeh

If you had only searched throughout Physicsforums prior posting on this subject, you would have found a lot of threads either abandoned or locked for the overlapping beliefs all going definitely to nowhere because this stuff is by no means self-consistent; if you take into account the concept of "mass" for a photon, then some big controversial repugnances arise which destroy many other things. For example, if photons were massless, then the theory of quantum electrodynamics would be in a serious trouble of losing gauge invariance which in turn would cause the loss of a guaranteed charge conservation and this means that the whole physics of quantum fields must be re-constructed. But regardless of the troubles, I have your side on this and physicists have actually not carried out a very convincing experiment or have not provided a practical evidence for the answer to the question of why a photon must not have mass.

All experiments known to pointing at this stuff are not so well-established as they all just "predict" that the rest mass of photon is zero by putting an upper limit to the mass of photon from a 'zero' lower bound so they say, in the best stance, 3 × 10-27 eV (*) is said to be a limit of photon mass while this has been controversial as some believe the method used to obtain such limit is not that much valid. So we have to come to the old estimates of approximately 10 times smaller, 7 × 10-17 eV (**), which by itself does not guarantee a vanishing mass.

Now what about a massless photon? It is all a consensus that one has to consider that photons are massless and I think we shouldn't be afraid of SR if this is not true, because then we just need to modify slightly the first law of Relativity as "the speed c is the highest of all that any object would attain in spacetime". But as I said earlier, this then would make so disastrous troubles costing lives of thousands of physicists who died of spending a lot of time and energy on formulating most of modern physical laws.

(*) E. Fischbach et al., Physical Review Letters 73, 514-517 25 July 1994.
(**) Chibisov et al., Sov. Ph. Usp. 19, 624 (1976).

4. Jan 17, 2010

### Naty1

Post #2 is correct.
"So can someone please explain to me thoroughly why photons don't have mass."

No one can do that. No one knows the actual origin of mass, nor space, nor time,etc.....lots of big prizes will be available for an appropriate proof. all existing theories are incomplete.

Last edited: Jan 17, 2010
5. Jan 17, 2010

### Naty1

From above:
"
I don't think that is accurate; in any case QED has been experimentally verified to exquisite detail, roughly 1 part in 1012....and special relativity is pretty secure so far that photons ARE massless....

6. Jan 17, 2010

### thefifthlord

Wouldn't something need to reach past absolute zero to be completely at rest. If so then how do we define rest mass seeing as everything's moving?

Also, if photons are mass-less how are they affected by gravity, which is utterly dependent on mass.

Last edited: Jan 17, 2010
7. Jan 17, 2010

### diazona

Absolute zero is a temperature, and temperature is only well-defined for reasonably large groupings of particles. It's a measure of the average kinetic energy of the particles (in their collective center-of-mass frame, I believe). A single isolated particle, on the other hand, doesn't have any temperature, and there's no problem in defining its rest mass.

You're right that a collection of particles would need to be at absolute zero to all be at rest relative to each other. Physicists sometimes talk about the rest mass of collections (i.e. macroscopic objects) like that. In that case, it's understood that the rest mass includes the thermal energy of the particles, as well as any binding energy or other energy contributions resulting from their interactions. The point is that rest mass for a composite body is not just the sum of the rest masses of the individual particles.

8. Jan 17, 2010

### diazona

Actually it's energy that responds to (and produces) gravity, not just rest mass. The photon has energy, so with respect to gravity, it behaves like a particle with the equivalent mass $m = E/c^2$. (This is part of why people thought that relativistic mass was a useful concept at first)

Keep in mind that general relativity describes gravity as a distortion of space, not a force, so in the GR description, the effect of gravity is independent of the moving body's mass. All objects traveling through space have to follow the distortion, including photons and any other massless particles that may exist.

9. Jan 17, 2010

### thefifthlord

I see,

But if i were to follow
E^2 = m^2c^4 + p^2c^2

This would mean that if the particle's wavelength is zero, then it possesses an infinite amount of energy.

10. Jan 17, 2010

Staff Emeritus
Why is that a problem?

11. Jan 17, 2010

### thefifthlord

When a particle is at rest it isn't moving, therefore its wavelength is 0. Therefore it has infinite energy, so it doesn't make sense to use the rest mass in the equation.

Unless p = h/lambda isn't universal, this equation makes absolutely no sense. If you're going to use rest mass, you must use rest momentum, which is infinite because the wavelength is zero.

Last edited: Jan 17, 2010
12. Jan 17, 2010

### vela

Staff Emeritus
Not moving = infinite wavelength.

13. Jan 17, 2010

### DaveC426913

vela has identified the misconception.

The two ends of the spectrum are:
- infinite wavelength = zero frequency = zero energy
- zero wavelength = infinite frequency = infinite energy

Remember that wavelength represents an oscillation. So if the particle oscillates with a 0 wavelength, that means its oscillation is occurring in an infinitely short length of time and distance. A particle that is not moving is taking an infinite length of time to complate one oscillation.

14. Jan 17, 2010

### thefifthlord

How could one tell the difference then between a particle that has infinite wavelength and one that has zero wavelength? With any given example one could argue either.

So you may say that not moving is infinite wavelength, but i can also say that its zero wavelength.

15. Jan 17, 2010

### DaveC426913

No. If it had zero wavelength, it would be oscillating with an infinite frequency.

16. Jan 17, 2010

### thefifthlord

Infinite Oscillation is stillness. There is no difference between a still table and a table that's oscillating back and forth with an infinite frequency

17. Jan 17, 2010

### DaveC426913

This is false.

18. Jan 17, 2010

### DaveC426913

You seem to be ignoring the fact that an oscillation involves an amplitude. You also seem to be ignoring the fact that there is no such thing as "still".

The table has a non-zero oscillation, even when it is sitting in your dining room. All massive objects do. It is on a subatomic scale.

If its amplitude were on the order of an angstrom, a zero wavelength would mean it is literally at +1angstrom and maximum -1angstrom at the same time; it would literally be in both places at once. You would have to pump an inifinite amount of energy into the table to get it to oscillate so fast that it is simultaneously here and there at the same time.

19. Jan 17, 2010

### thefifthlord

In this case the amplitude is 0.

Zero amplitude = Zero wavelength = Zero movement.. thus there is no difference between

Particle A:
Oscillating Infinitely
Wavelength of Zero

Particle B:
Infinite Wavelength
Frequency of Zero

Both have a constant position in 3d space, thus both are not moving.

Edit: If there's no such thing as still, then there is no such thing as rest mass altogether, so why use it?

20. Jan 17, 2010

### Staff: Mentor

Infinity is not a number. Something can have a frequency of 0. Something cannot have a frequency of infinity. There is just no such number.

Even in cases where it makes sense to work with the extended real numbers infinity is certainly not the same as 0.

Last edited: Jan 17, 2010