Waste less time on Facebook — follow Brilliant.

Quantization of mass?

We know there is quantization of charge, quantization of angular momentum in atoms (nh/2pi). I was wondering if there is anything as quantization of mass. Like electrons and protons are fundamental charge carriers (Actually the more fundamental carriers are quarks), are there any fundamental mass "Carriers"?.What do you think?

Note by Saurabh Dubey
4 years, 3 months ago

No vote yet
2 votes


Sort by:

Top Newest

The reason charge and mass behave differently (one being quantized and one not) is due to the geometrical nature of how we describe our physical world. Now, I'm going to let go with some math, so for those of you who don't like math you can stop here. For those math lovers (wait, isn't that all of us?) charge is the result of a symmetry that our physical theories have, called U(1) symmetry. U(1) is a group, specifically a Lie group, the elements of which are just complex numbers with unit norm, i.e. those numbers of the form \(e^{ix}\). If you think about the set of these numbers in the complex plane, you can see that they form a circle with unit radius. The charge on an object geometrically is the 'generator' of the rotations on this circle, i.e. the elements of the group are naturally expressed as \(e^{iQ\phi}\) where \(\phi\) runs from 0 to \(2 \pi\) and Q is the charge of the object in question (in units of some fundamental charge).

Now since we have continuous functions in physics, and the circle is compact (very important), we see immediately that the only allowed values for Q are integers, i.e. charge is quantized.

What about mass? Well, mass (technically) energy are also the generators of motion in some space. Just as momentum generates motion in space, energy generates motion in time. But, our time dimension is just like the real line, it goes on forever. Hence time is NON-compact and there is nothing that requires the energy/mass to be quantized! If you had a space and time where time actually was compact so that if you went far enough into the future you came back to the present, energy and mass would be quantized. The same reasoning applies to momenta as well. Finally, in scenarios with extra dimensions that are rolled up to small circles like in string theory, the momenta of particles that move in these extra dimensions are actually quantized and the masses of particles can also take quantized values.

It's all in the geometry...

Sorry for going all mathy, let me know if you like these kinds of explanations or if they are too much. If you want more of an explanation of these things pop up some threads and ask. David Mattingly Staff · 4 years, 3 months ago

Log in to reply

@David Mattingly The reason i read for quantization of charge was that as the basic charge carriers are electrons and protons, hence bodies can have charge only in integral multiples of e. Hence the charge remains quantised. Can quantization of mass be explained so easily?. Basically I'am looking for basic simple reasoning. I'am not denying your explanation just can it be more simple?something for a 17 year old basic physics knower? Saurabh Dubey · 4 years, 3 months ago

Log in to reply

@Saurabh Dubey Actually, quarks (which are part of protons) have fractional electric charges, i.e. less than e. It's a little easier to talk about energy than mass as all particles have energy, whereas only some have mass. So think about if energy can be quantized (i.e. come in discrete chunks). The answer is no, energy is not quantized. A photon has energy \(E=hf\) where f is the frequency. Since space and time is infinite (or at least very, very large) there is no limit on how small f can be and hence no limit on the lowest energy of a photon. Therefore energy doesn't come in discrete chunks, if you wait long enough you can get as small an energy added to your system as you want.

This would all change if space and time were not infinite, but instead were finite, i.e. 'compact'. This gets back into the geometry argument above.

Better? David Mattingly Staff · 4 years, 3 months ago

Log in to reply

Scientist said that mass is originated from gauge boson that called Higgs Boson. It creates higgs field that make everything has mass. Massive object interacts more with higgs field, while lighter particle interact less on it. But this particle is tentatively discovered at CERN in 2012. Mass is different with weight. Hammam Muhamad · 4 years, 3 months ago

Log in to reply

Also adding to what I said

If angular momentum is quantised then as angular momentum=mvr

The 3 quantities m,v and r should be quantised

(as even if 1 of these were to take all the values from 0 to infinity,and not just take discrete values this would make angular momentum take all values from 0 to infinity .thus we have a contradiction.hence reinstating my earlier hypothesis that mass should be quantised.) Pranav Chakravarthy · 4 years, 3 months ago

Log in to reply

Just a theory.dunno if its true

Since energy is quantised and E=mc^2

Hence the smallest packet of energy(1 quantum) corresponds to a mass of 1quantum of energy/c^2

Hence my hypothesis is mass should be quantised.

But on the other hand I am not able to guess as to what should be the most fundamental carrier of mass. Pranav Chakravarthy · 4 years, 3 months ago

Log in to reply

@Pranav Chakravarthy Energy is not quantised in every form. What you said about quantization of energy is only a special case of photon quantisation. Other forms of energy (like kinetic or potential ) are not quantized. Saurabh Dubey · 4 years, 3 months ago

Log in to reply


Problem Loading...

Note Loading...

Set Loading...