# Light building the standard model

1. Jul 24, 2011

### elegysix

Something has bothered me for a long time about our model of light: that it has no mass.
Just for a moment, forget what you know about light and lets call it the unknown, X, and suppose we want to model it.

Here's what we know for certain:
X has momentum, as seen by radiation pressure
X is affected by gravity, as seen by gravitational lensing
X can act as a particle and a wave

So we take something with momentum that is affected by gravity and we can easily conclude that it has mass. And since it has mass, we can easily say that it must be a particle... And systems of particles can show wave behavior.

So then we conclude that light is a particle with mass.

How exactly did we come to the conclusion that Light has no mass?

2. Jul 24, 2011

### Pengwuino

How did you come to the conclusion that light has mass?

X has momentum, which only means it obeys conservation laws. X is affected by gravity, which only means that it has energy as per general relativity. X acts as a wave/particle, how does one conclude anything about its mass from this? How do you conclude that photons have mass from ANY of those 3 criteria?

You're just taking an elementary knowledge and trying to claim it must generalize to everything else, which is wrong. What it really should be telling you is that momenta, gravity, and wave/particle duality are more complicated than you think.

3. Jul 24, 2011

### ecneicS

I guess one way of answering your question is... experimental data. Light is nothing more than a ripple in the electromagnetic field, why should that have mass?

4. Jul 24, 2011

### Staff: Mentor

5. Jul 24, 2011

### Pengwuino

6. Jul 24, 2011

### I like Serena

The mass of any object increases if its speed increases to near the speed of light.
At the speed of light an object would have infinite mass, which is not possible.
Hence a photon can not have rest mass.

However photons do have a relativistic mass given by E=mc2.
This is called the mass-energy-equivalence relation.
That is, relativistic mass is seen as equivalent to energy.

7. Jul 24, 2011

### elegysix

Because momentum has been defined as mV in classical mechanics, and only things with mass are affected by gravity, (F=GMm/R^2...). That gives you two different reasons to think it has mass.

Everything physically tangible obeys classical mechanics... but when we look at light and anything on the atomic level, we throw out the logic of classical mechanics. Applying the logic from classical mechanics, it is obvious to me that it has mass. Yet I know that this is not so. How did we decide that classical mechanics did not apply here?

I would like to get at the history of this model, how we came to this conclusion.

an upper limit on photon mass? Why would they try to measure it if they are sure it doesn't exist?

8. Jul 24, 2011

### Pengwuino

That's not exactly true. The 'universal speed limit', as one might want to put it, is the ~3x10^8m/s speed limit we know of as the speed of light. What that speed is is actually the speed of a massless particle. The photon happens to be the only massless particle we know of at this point, so people typically say speed of light when technically, you should say "speed of a massless particle". The photon could have a mass and it would be so small that the deviation from the "speed of a massless particle" would be so insignificant that it would be completely undetectable in every experiment we've ever done at this point.

9. Jul 24, 2011

### elegysix

This is a major part of what I am questioning. From classical mechanics alone, I see no reason to believe this. We know classical mechanics works. So starting with classical mechanics, How do you figure that these things happen?

10. Jul 24, 2011

### Pengwuino

No, that is not how momentum is defined in classical mechanics. That is how momentum is defined in a very specific case. Something as simple as angular momentum is not defined like that. Get into classical electrodynamics and you'll see even more complicated forms of momenta. So in general, P = mv is NOT the whole story.

We didn't just decide one day to throw out the logic of classical mechanics. Many many experiments were able to show that classical mechanics just makes no sense at what we now consider the atomic and quantum scale. For example, Rutherford (don't quote me on who actually did this, my memory of physics history is appalling) showed that the atom was in fact, a hard solid object (the proton/nucleus). So classical mechanics makes one assume that maybe electrons and protons are like planets, the electron orbits the proton in the same way the Earth orbits the Sun. Well, one of the problems with that is that accelerating charges radiate away energy. So applying classical mechanics and classical electrodynamics to the atom, the electron should radiate away all its energy and collapse into the proton within a fraction of a second.

Clearly that is not what happens. So classical mechanics is not the way to approach things at the quantum scale. Of course, there are a LOT of other ways to show classical mechanics does not work on the atomic scale, but I wouldn't want to spell them all out.

Because that's how science works. No one is sure about anything. All we can say is that "X theory holds true up to an experimental limit of Y". All our experiments show that the photon has pretty much no mass and we can build our theories safely by assuming it has no mass. If it turns out it DID have mass, the consequences would be so small that it would have almost no bearing on present day physics.

Another example is, like you mentioned, Newton's law of gravitation. We don't actually know for sure that the law goes like $F = {{GMm}\over{r^2}}$. One could say, well, what if Newton's gravitational law goes like $F = {{GMm}\over{r^{2+\epsilon}}}$ where $\epsilon$ is incredibly small. You could measure the orbits of the planets and be able to put upper or lower limits on what that $\epsilon$ could be. Obviously since we know Newton's law of gravitation works very well, we know it would have to be very close to 0 so that it wouldn't be detectable over all these centuries.

Of course, general relativity already shows us that that form of gravity is not exactly right either, but that's kind of another way of looking at how we talk about theories vs. what our experiments tell us.

11. Jul 24, 2011

### Staff: Mentor

That is not even true in classical Newtonian mechanics. Only test particles with mass have a force on them, but classically it doesn't take any force to accelerate a massless particle. The acceleration due to gravity is independent of the mass of the test particle.

That's the scientific method. You have a theory, the theory makes some prediction, so you perform an experiment to test the hypothesis.

So we have measured it over and over with increasing precision, and to the best precision possible it is 0.

12. Jul 24, 2011

### DeG

"X has momentum, which only means it obeys conservation laws. X is affected by gravity, which only means that it has energy as per general relativity." - Pengwuino
"However photons do have a relativistic mass given by E=mc2." - I Like Serena
If it's true we measure the momentum of light via radiation pressure, does this pressure increase with the energy/ frequency of light? Since light (affected by gravity) has energy as per general relativity, a relativistic mass given by E=mc^2, and energy given by E=hf, could you say that light has a mass proportional to it's frequency given by m=hf/c^2?

13. Jul 24, 2011

### Drakkith

Staff Emeritus
Don't think of relativistic mass as actual mass. The momentum of an object increases as it's velocity increases, but its mass (IE it's rest and gravitational mass) do not increase to my knowledge. I believe it is part of how people tend to explain the fact that you can't get to c, because your mass increases. However I think this is inaccurate. If I'm incorrect someone let me know please.

14. Jul 24, 2011

### Pengwuino

No. Photons (assumed to be massles) do not have relativistic masses either, contrary to what I Like Serena stated. The relativistic mass of a particle is given by $m = \gamma m_0$ where $m_0$ is the rest mass of the particle and $\gamma = {{1}\over{\sqrt{1-{{v^2}\over{c^2}}}}}$. Photons do not have a rest mass and their velocity is equal to c, so this equation is clearly ill-defined.

The momentum of light is given by the full relativistic energy equation, $E^2 = p^2c^2 + m_0^2c^4$. Light has no rest mass so the second term on the right hand side is 0 and solving for the momentum, you find it is given by $p = {{E}\over{c}}$. The energy of a photon is given by $E = \hbar \omega$ where $\omega$ is the angular frequency. So the momenta is propotional to the frequency, but there is no mass to speak of.

15. Jul 24, 2011

### elegysix

Here's what I'd like to see...

solve for the mass by calculating the momentum from radiation pressure.

Take that mass at the speed of light and solve for the trajectory in the vicinity of a planet (non-relativistically, through classical mechanics).

Then check the trajectory against that of current model.

If it doesn't match up, clearly we'd be wrong about assigning a mass to a photon...

If you've got the time and the curiosity, I'd really like to see this done. I've tried over and over again, but I always get stuck on some of the math... :(

16. Jul 25, 2011

### Char. Limit

Of course we'd be wrong about assigning a mass to a photon. That's why we DON'T. We instead say that a photon is massless. This happens to be consistent with all known experiments to all known precisions.

17. Jul 25, 2011

### Pengwuino

That's probably already been done. The easiest comparison would be to compare against the deflection of light given GR's calculation. This is common enough knowledge. Then do the calculation of a massive particle being deflected by the Sun in some 1/r potential.

There are some fairly simple reasons why I expect this won't even accidentally be right considering GRs calculation is independent of the photon's momentum whereas the deflection in this "classical mechanics" calculation would have to depend on the momentum. Of course, GR has been confirmed experimentally.

18. Jul 25, 2011

### I like Serena

So how do you calculate the momentum p of an object then?

I thought you calculate p from $E^2=p^2 c^2 + m_0^2 c^4$ by combining it with $E=m c^2$ and $m = \gamma m_0$.
For low speeds this can be approximated with p=mv.

Since the rest mass of a photon is zero (or insignificant ), the formula $m = \gamma m_0$ breaks down, giving an indeterminate result.
However, for a photon you can calculate the energy from the formula $E = \hbar \omega$.

Afaik, the mass-energy-equivalence relation does not break down.
So a photon has a relativistic mass of m=p/c (classically speaking).
And yes, a photon has to have equivalent mass (classically speaking) for gravity to act on it.

Last edited: Jul 25, 2011
19. Jul 25, 2011

### Pengwuino

Yes, that's how you calculate the momentum of a particle with some rest mass $m_0$. It's just instead of the energy given by $E = mc^2 = \gamma m_0 c^2$, the energy is given by $E = \hbar \omega$. $E = \gamma m_0 c^2$ only works for massive particles. The right hand side of the relativistic energy equation is fine, the left side is the one you tweak for photons (or equivalently you can define the momenta of a photon as $\hbar \omega /c$).

And yes, you can calculate an "equivalent classical mass", but it's meaningless beyond the one scenario of gravitational pull. Hell, I don't even think it says anything about the actual mass of a photon beyond that because the photon's mass might be irrelevant due to Equivalence.

You can do a quick calculation and find any normal photon has a "mass" 20 orders magnitude higher than the current experimental upper limit.

Last edited: Jul 25, 2011
20. Jul 25, 2011

### Staff: Mentor

This wouldn't tell you anything about the mass. Remember, gravitational acceleration is independent of the mass. The trajectory depends only on the initial velocity, not the mass. This experiment would allow you to distinguish between different models of gravity, but not different masses of the test particle.

In any case, since we have measured it's mass to be 0, then clearly we would be wrong about assigning a mass to a photon in any case.

Last edited: Jul 25, 2011