So if I've got this right, mass shouldn't be thought of as the "bulk" of a thing, it's simply thought of as a charge within that thing. So a photon is a particle of substance that contains no mass charge on it, despite the fact that it has some amount of volume?
"Mass", as referred to by physicists is what may be known to others as "rest mass" or "invariant mass". An electron and a positron both have rest-mass. (Think of it as a fundamental property, like charge.) When they collide, the result is two photons that no longer have rest-mass.
It is important to note that gravity affects energy (mass-energy). This is why a compressed spring weighs more than the same spring uncompressed. A spinning ball weighs more than the same ball when it is stationary because there is more energy.
It's an important but subtle distinction that even a lot of physics professors don't quite grasp. Matt Strassler has some very good explanations of it on his page.
Couple of points along the same lines that I always like to explain to people.
The familiar E=mc^2 we all know - people like to say that means that the energy in a system is equal to the mass times the speed of light (squared) - if we convert between the two. Which is true..... but it's also saying something else. In this formula, energy is measured in joules, and mass in kilogams - the speed of light in meters per second. Importantly, notice the c^2 is a constant - it's there for unit conversion. What we really have is a statement that energy=mass. Energy and Mass are the same thing.
In the same line - there's no such thing as "pure energy" (if I'm wrong, someone educate me, I'm all ears) - people have a hard time with this. Energy is a property of a system that can be calculated. "pure energy" doesn't exist. Radiation is not what we mean by "energy" (though obviously it's got energy) - energy is a property that we can calculate and work with, and a rather important one at that.... but it's not a "thing" or "stuff" or "non-stuff" that moves around... it's a property of a system that can be calculated.
Yep. Energy is one of the more difficult things to explain, because it's really more of a mathematical property that results from a conservation law about symmetric transformations (Noether's theorem).
The comments by others as a response are correct in that elementary particles are dimensionless.
One interesting point to add though is that only integer spin particles (the force carrying bosons) can share quantum states, which means they can occupy the same point in space.
Another way to say that is to say the opposite, i.e. that half-integer spin particles (the fermions, which includes quarks that make protons and neutrons as well as leptons like the electron) cannot occupy the same quantum state as each other, which is manifest by them obeying the pauli exclusion principle.
So if you were to take two photons they can literally occupy the same point versus two electrons which cannot (with some exceptions noted below). They are both point particles and technically have no volume, but there is this extra rule about quantum states that prevent two electrons from sitting in precisely the same place if they share all other quantum characteristics.
Since this rule applies only if those electrons share all other quantum states, that means that if two electrons have opposite spins, they can occupy the same point in space. The first valence shell in a atom is the lowest state that an electron can have in a stable orbit (think of it as a standing wave that exactly lines up in a circle). There is 'room' for only one electron when you view the electron as a wave, but that shell can hold 2 electrons because there can be one of each spin type.
Anyway kind of long winded, but I think the exclusion principle is at the heart of what makes us intuitively think about the electron as having volume in space and a photon as not.
All this stuff is really really cool, but you can tell why physicists have that itchy sensation that there is some deeper explanation that is underneath all these rules.
Elementary particles have no volume! (think about that one, it's kinda mindblowing)
They can only have "effective size" that arises due to say, electromagnetism. The electron has an effective radius that is measured by bouncing other charged "test" particles off of it. You don't get an answer of zero only because your test particles are attracted or repelled by the electron.
Mass should be thought of as something intrinsic to a particle, just like charge or spin. There's really no good way to visualize it - it's just something different particles have in different amounts.
Might be totally wrong here - photons have no volume yet can exhibit mass. (I don't fully understand that particular one yet.. need to read more. Whether or not photons have mass is a complex question it seems - or rather, multi-faceted)
Thanks - I'll read up. I've long interpreted E=mc^2 to mean not just that energy and mass are interchangeable, that energy and mass are one and the same.
What I can't quite get my head around yet (just need to read up more) is how they figured out something about the rest mass of a photon - something about using superconducting rings or something like that.
(Because photons aren't generally at rest, and they don't accelerate, right?)
Quantum mechanically, acceleration is a rather ill-defined quantity, so I don't know how to answer the question other than through Ehrenfest's theorem - <F> = m <a> when we're talking <averages> [http://en.wikipedia.org/wiki/Ehrenfest%27s_theorem]
