Eli5: How can some particles have no mass
In: 42
To find a satisfying answer here we need to unpack two words we throw around like they have some intuitive meaning, but they don’t. “Particle” and “mass”.
So for one “particle” doesn’t mean a practice as a dust particle. If we are talking about fundamental particles the particle is just the collective name we give these little things with the lack of a better word. So these things behave in a strange way as without interacting with anything they are literally waves (waves of probability) and once interacting they resemble more classical objects. Like how light is an EM wave but when it scatters on an electron we can treat it as a litte pool ball and we call that a photon. Or rather we call the smaller indivisible amount of energy some frequency of light can have.
The other thing “mass” has a more tangible definition. We will need special relativity for this. In SR we can look at moving objects in a 4D space. So we still have a good old 3D coordinate system but we add a 0th time like component to it. So locations turn into events. In this 4-vector formalism we can reintroduce (if thats a word) quantities like momentum as a 4-vector. We basically construct how physical quantities look in our new 4D spacetime. So lets grab 4-momentum and calculate its lenght (of course lenght here is a bit abstract). Well we directly calculate the length squared and that gives us m²c².
Ok, so we introduce a quantity called 4-momentum that describes how this move in spacetime and its lenght is mass (/c). Ok so lets look at what 4-momentum is for a path that light would take! (So for the object that would move on a light-path, these paths are called null-geodesics.) We will get exactly 0 for the lenght of that vector which was our definition of mass. So objects that move on paths that light would take have 0 mass based on our definition of mass. And this has some profound consequences like how massless things can only travel on light-paths and they have no rest frame.
And the beauty of SR is that we can start form very fundamental ideas and just derive all of this. After a bit of side-talk you can formulate this definition for mass and as it turns out this is really what we would want to call mass.
We could also go with a bottom up approach and look at how things are and aren’t coupled to the Higgs field and the reasoning is the same as for charge. A particle is coupled to the EM filed so it can excite it and how much it’s coupled and what way can be described by a signed scalars we call charge. For mass is even simpler its just a scalar value we can assign to particle. Now the “real” thing here is the interactions between the fields and particles giving particle values like mass and charge is our description of the interaction.
But still I think the SR definition of mass is just less painful to go with than trying to unpack the standard model.
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