# Why do we use rest mass to define restless particles?

1. Mar 10, 2014

### MacElliott

I, like many others, have always wondered whether photons truly massless or if their mass is just so small that its irrelevant? And of course, if they truly are massless, then how can black holes attract them?

http://cosmoquest.org/forum/showthread.php?98056-Upper-limit-to-photon-mass <-- states the upper limit to the mass of the photon as 10^-18 eV. Doesn't that mean it's mathematically possible to prove photons can have mass, without contradicting the behavior of our universe?

I understand that the massless notion is based off of the fact that photons are never at rest, but SINCE photons are never at rest, why do we even use rest mass to define them?

Not only that, but the fact that nothing is EVER truly at rest is a well-established concept in physics due to the fact that motion is always relative to the observer, so why is a notion that can never actually be true treated like a fundamental scientific law?

Wouldn't it make more sense if you looked at it in a way that said, yes they have a mass, but the reason they can still reach light speed without succumbing to relativistic mass is a combination of the facts that
a) they're born at light speed and therefore skip the initial process
b) their excess energy gets converted to shortening their wavelength, rather than their velocity

I'm aware that someone is inevitably going to argue that black holes don't attract photons via gravity, rather they merely bend the space that photons travel along towards them resulting in said photon being sucked in. The common analogy that usually accompanies this argument is:

"Imagine you place a bowling ball in the centre of a mattress, then, you roll a marble along the mattress. The path of the marble would be straight until in reached the indent at which point it would begin traveling towards said bowing ball."

However, that analogy seems hugely flawed to me due to the fact that it's still the gravity of the earth that causes the marble to travel down the indent, not the altered path itself

The more I think about it, the more I believe that the masslessness of photons is just an idealization of a concept that would otherwise throw our knowledge into question, and as the fear of the unknown is a fundamental human instinct, its widespread acceptance is better explained with the psychology, rather than physics.

Agree/disagree?

2. Mar 10, 2014

### vanhees71

The notion "rest mass" is a contradiction for massless particle. The correct terminus is "invariant mass" or simply "mass". Unfortunately in the popular-physics literature they often use an old-fashioned idea about a socalled "relativistic" mass which is the (kinetic) energy of a particle divided by $c^2$, but that's just the (kinetic) energy of the particle and not its mass. Nowadays, physicists use the word "mass" for a scalar quantity, while the energy is the temporal component of a four-vector (with momentum making the three spatial components of this four-vector).

That massless particles are affected by gravity is no contradiction since according to the general theory of relativity gravity acts on everything having energy and momentum. Only in the non-relativistic (Newtonian) limit, gravity becomes proportional to the (invariant) mass.

3. Mar 10, 2014

### MacElliott

Thanks, that actually cleared things up in terms of the usage of the concept, however, if its mathematically possible for a photon to have a mass thats just so small its insignificant, why does everyone assume its just massless?

Last edited: Mar 10, 2014
4. Mar 10, 2014

### TheDemx27

Well, if light had a mass, it would take infinite energy for it to move at c.

So, if I'm correct, you are essentially asking why E=mc^2 is true. As in you are asking for a derivation of it. Hit up that google.

5. Mar 10, 2014

### MacElliott

No? The idea is what if the mass of the photon is just SO SMALL that the amount of relativistic mass it would gain approaching the speed of light wouldn't slow it down in time before it reached the actual maximum speed of the universe, so that essentially, when a certain speed (OR QUANTUM) is met, a second dimension is added to its would-be linear motion as a way of dispersing the velocity
Essentially, what if wave/particle duality is a loophole around/a fail-safe for relativistic mass?
Considering its mathematically. possible. and yes, e=mc^2, AND, its been PROVEN photons are only emitted when CERTAIN energy levels are met, the idea doesn't really disagree with ANY behavior of photons, if anything, I feel that incorporating relativistic mass to such an unfathomably small particle seems to better explain them

Last edited: Mar 11, 2014
6. Mar 11, 2014

### vanhees71

In fact, there's nothing in the Standard Model of elementary particle physics that forces the photon to be massless. Ablian gauge fields can be made massive by a naive mass term without violating gauge invariance and spoil renormalizability (Stueckelberg formalism for massive Abelian gauge fields). Thus, today it's an empirical question whether photons are really massless or not. There are no hints of a photon mass. So it's commonly assumed that the photon is strictly massless.