In search of the source of mass!

Is the measurement of the mass of matter more fundamental than any religion? What does modern particle physics say?

How does classical physics depend on mass?

The way the definition of mass is given in school textbooks, many may be a bit confused, let's start the discussion from there.

"The amount of matter contained in an object is called its mass."

But how can matter be measured? Let's say, one of my school friend Democritus was asked such a question. Wise Democritus's answer is ready, 'Very simple. A substance is made up of many molecules, measure the amount of matter in one molecule. Multiply it by the number of molecules in the substance. Then mass of object = total number of molecules ⁢⨉ mass of one molecule.'

One thing is known from the words of Democritus. In classical physics the concept of mass comes somehow from the combined concepts of density (in this case the mass of a molecule) and volume (in this case how many molecules). That is, mass = density X volume.

But this concept of mass is not quite complete. For example, to arrive at the kinetic formula given by Newton we have to assume another very fundamental religion of mass. That is the permanence of mass, — mass cannot be created or destroyed. This religion is so fundamental to Newtonian mechanics that it can be called Newton's zeroth law of motion! However, it is not understood why mass will be conserved from the concept of Democritus.

We then define momentum as 'a measure of the object's speed'—mathematically written as the object's mass X velocity. Using the definition of momentum and the constancy of mass, the conservation of momentum of a particle can be easily derived from Newton's first law of motion and the concept of force from Newton's second law of motion. So you see, mass is the key concept in Newtonian mechanics around which classical physics grew. See here for a more detailed discussion on this.

In order to arrive at the kinetic formula given by Newton, we have to assume a very basic law of mass, that is the constancy of mass.

But what is the source of mass? Can we derive a measure of the mass of matter from its more fundamental religion? The biggest question is, can matter have mass in the absence of 'matter'? The last question may bring to mind the famous E=mc2 formula. It's fine to think this way but we'll go a little bit further with more logic and evidence and try to understand how most of the mass actually comes from energy. In fact, most of the mass of an atom comes from the nucleus, and the nucleus contains two very heavy particles—protons and neutrons. These two particles are actually a huge amount of energy, matter-reality is nominally there!

A few words about the nucleus

To try to understand how protons and neutrons get their mass, let's first look at these two experimental facts about atomic nuclei:

The nucleus is a very flexible thing, in which neutrons and protons are tightly bound. What force holds them together so well? It cannot be the electromagnetic force we know. Because neutrons are uncharged – they are not affected by the electromagnetic force. And the state of the proton is more sanguine. All protons are positively charged, so they repel each other by the electromagnetic force. From this it can be inferred that there is an entirely different attractive force between nucleons (protons and neutrons together) that does not depend on charge. And to hold all the nucleons together, this force must overcome the electromagnetic repulsive force between the protons. So this force is stronger than electromagnetic force.

With the discovery of neutrons by James Sadwick in 1932, another strange thing came to the attention of scientists. Both protons and neutrons behave in the same way if you forget that protons and neutrons have roughly the same mass and that protons have a positive charge. Werner Heisenberg deduced from this that protons and neutrons are inverses of the same quantum state. Just like an electron with up-spin and down-spin. 

Therefore, this strange symmetry is named 'isotopic spin' or 'isospin' in accordance with spin-symmetry. Numerically speaking, this symmetry is actually SU(2) symmetry and the electron spin has the same symmetry as the fundamental representation. However, this symmetry means that roughly the same amount of nuclear force will act between two protons or two neutrons or one proton and one neutron. In this context, physicists have a special love for such equations because they make a theory beautiful. As a result, the calculations are often quite simple.

Werner Heisenberg hypothesized that protons and neutrons are inverses of the same quantum state.

Let's fast forward forty years. It turns out that Heisenberg's conjecture is roughly correct. It was also found that protons and neutrons are not fundamental or indivisible particles. They are each made of three more elementary particles. They are named quark. Proton-neutrons are almost identical but not exactly the same because the quarks have different 'flavors'. 

Both protons and neutrons have quarks of 'up' and 'down' flavor, but protons have two up and one down and neutrons have one up and two down (see cover image). The up charge is +(2/3)e and the down charge is -(1/3)e, so the proton has a charge of +e and the neutron is neutral (-e = charge of an electron). And proton-neutron SU(2) symmetry actually comes from up and down SU(2) symmetry.

Where does the mass of the nucleon come from?

Even if these are correct, the problem is elsewhere. Two problems, and both are pretty crazy. First, lone free quarks are never observed. However, indirect experimental evidence for the existence of quarks can be obtained from the behavior of the composite particles in which these quarks are bound. Second, the mass of the up and down quarks obtained from quantum field theory calculations is about a thousand times greater than the mass of the nucleon. Meanwhile, there are only three quarks in the nucleon. 

Where does the mass of the nucleon come from, if not from quarks? To understand the two puzzles, let's start with our familiar example of electromagnetic force. Two charges exert force on each other through the exchange of photons. A photon is a carrier of electromagnetic force and has no rest mass but can have momentum according to relativism. When two charged photons are exchanged, momentum is also exchanged, which manifests as an electromagnetic force.

The repulsive force between two electrons (e-^) arises from the exchange of photons (γ) between them. Arrows indicate the direction of the two electrons. Similarly, the force between the quarks inside a proton or neutron is created by the exchange of gluons.

Interestingly, the photon itself is uncharged, that is, two photons cannot exert a force on each other1.

A generalization of these concepts also explains the force that binds the quarks inside a nucleon. The name of this force is strong force or color force. Two quarks have a color charge and momentum is exchanged between them by exchanging gluon particles, which appear as colored balls.

Like photons, gluons are massless particles. But the biggest difference between these two particles is that gluons have color, so they can interact with each other even in the absence of quarks. In this way they can also create new gluons. So if you increase the distance between two quarks, more gluons are created by the interaction of the gluons between them. This creates so much chromatic force that the quarks become completely entangled and cannot escape each other. This is why lone free quarks are never seen.

Not only that, the size of a nucleon is close to one fermi (femtometer). If the quarks are at this distance, so many gluons are created between them that the three quarks float in the sea of gluons. These gluons also cannot escape from the confinement of the nucleon because a nucleon has a collective charge of zero and wants to stay that way. Since gluons have charge, when a gluon is ejected from a nucleon, the nucleon will no longer have zero charge, which is not favorable at all. Thus a proton or neutron can hold a large amount of energy, which is expressed as their mass according to the formula E=mc2.

There is no end to the questions

Pretty nice explanation! However, some questions remain that we still don't know the answers to. Within a nucleus, the quarks are approximately the same distance apart as the nucleons themselves. So why do not these quarks together form a quark commune in the nucleus? Why are protons so stable particles? Can protons disintegrate by themselves? In fact, particle physicists don't really want the proton to be a permanent particle. 

Because if the proton is transient, we can use it to solve a bigger puzzle. That is, why is the amount of matter in this universe so much more than antimatter? (It will take another whole article to tell its story. So I'm holding back for now. You can Google Baryon asymmetry.) But it is not yet understood where the mass of particles like quarks or electrons comes from. Particle physicists have asked and answered that question. They gain mass by interacting with the Higgs boson, but how, the explanation is quite profound. We will discuss that later.


[1] One way we can learn about the nature of photons. There are two main reasons why we can see any nearby object: One, the photons coming from that object do not interact with each other. Second, photons do not interact with nitrogen or oxygen atoms either, because atoms are inert at normal temperatures. That means photons reflected from an object do not interact with anything else on their way to us.

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