# What makes up the mass of the universe?

Most of the known visible mass in the universe (i.e., excluding dark matter) is made up of protons and neutrons. We know that protons and neutrons are themselves made up of yet smaller particles called quarks and gluons. The gluons are massless so you would think that most of the mass of the universe would be quark mass. But that is not the case. In fact, quark masses are a small fraction of the total mass of each proton and neutron. So where does the rest of the mass come from?

To understand this we need to look at the relationship between mass and energy, first formulated by Albert Einstein in the equation that is now famously written as E=mc2, though that is not how Einstein initially formulated it. This results in the mass of a composite object not being just the sum of the masses of its component objects, because other forms of energy can contribute to the mass too.

Take for example the deuteron, a composite nucleus that we know is made up of one proton and one neutron. The mass of a free proton is 938.272 MeV/c2 and the mass of a free neutron is 939.565 MeV/c2, but the mass of the deuteron is 1875.612 MeV/c2, which is less than 1877.837 MeV/c2, the sum of the two free masses. What happened to the missing mass of 2.225 MeV/c2? When the two particles were brought close together and became bound as one entity, some of the mass was released as energy. It is this that keeps the deuteron as a single unit. To separate the deuteron into its composite parts, we need to provide from outside an amount of energy equal to that difference.

In the case of the deuteron, it is possible to separate the two components and measure their masses individually. But in the case of the quarks and gluons within the proton and neutron, we can never free them and study their properties in isolation. They are permanently confined within the protons and neutrons and that makes directly measuring their masses impossible and we have to use various theoretical techniques to estimate them. The theory that is used is called Quantum Chromodynamics (QCD) that forms part of what is called the Standard Model of particle physics. The problem is that QCD is not easy to use to do the calculation. A new paper uses what is called lattice gauge theory to obtain a more accurate estimate of where the mass of the proton lies.

The researchers rely on a powerful method known as lattice QCD, which places quarks on the sites of a lattice and gluons on the links between them. This rigorous representation of QCD can be implemented numerically, and it is the only QCD-based method that can make quantitative predictions on length scales comparable to the proton or larger. (At these scales, the interactions between quarks and gluons are so strong, they cannot be handled with Feynman diagrams and other “perturbative” methods.) However, lattice QCD is an expensive technique. The discretization creates errors, and to remove them entails taking the lattice spacing, a, to zero. This step is achieved in practice by performing multiple calculations at different values of a, at a high numerical cost that scales as a-6. Nevertheless, lattice QCD has matured significantly in recent years, allowing for the most precise determination of the quark masses and many properties of light and heavy mesons, which are comprised of a quark and an antiquark.

The mass of the composite object (the proton) is larger than the masses of its constituents, the opposite of what we saw with the deuteron. The researchers find that the quark masses make up just 9% of the proton mass. The rest of the mass of the proton comes from the quark energy (~32%), the gluonic field strength energy (∼37%), and the anomalous gluonic contribution (∼23%) .

The smallest contribution, the quark condensate, is a mixture of the up and down quarks and a “sea” of virtual strange quarks, and it is the only one that would vanish if the quark masses were zero. The other three terms are all related to the dynamics of the quarks and gluons and their confinement within the proton. The quark energy and gluonic field strength equate to the kinetic energy of the confined quarks and confined gluons, respectively. The anomalous term is a purely quantum effect. It is associated with the QCD mass scale and consists of contributions from condensates of all quark flavors, including the strange, charm, bottom, and top quarks. The calculation by Yang and colleagues shows that, if the up, down, and strange quark masses were all zero, the proton would still have more than 90% of its experimental mass. In other words, nearly all the known mass in the Universe comes from the dynamics of quarks and gluons.

So to sum up, only about 9% the mass of the visible universe is made up of the masses of the quarks that we think are its most fundamental constituents. The rest comes from various forms of energies of the quarks and gluons within the protons and neutrons. In our current models, we think that the visible matter makes up just 5% of the total mass-energy of the universe, with 26% coming from dark matter and the remaining 69% from dark energy. Hence quark masses make up just 0.45% of the total mass-energy of the universe.

1. Owlmirror says

Sorry, but this typo leaped out at me in the second sentence:

“yet smeller particles”

2. Mark Dowd says

But in the case of the quark and gluons within the proton and neutron, we can never free them and study their properties in isolation.

How can you treat them as separate when they can never be separated? Is it a theoretical never (like decreasing entropy), or a practical never (too expensive/precise/powerful to be built by humans)?

Where have these equations come from if we can’t crack a hadron? Observation of cosmic rays or something?

3. Mano Singham says

Owlmirror @#1,

Thanks! I’ve corrected it.

4. Mano Singham says

Mark Dowd,

When beams of high energy electrons are targeted at protons, they get scattered and the pattern of scattering suggests that the electrons get scattered within the proton by three smaller particles. This is the basis of the quark model.

The problem is that while we can use high energy electron beams to knock out protons and neutrons from heavy nuclei, we cannot seem to do the analogous knockout of the quarks that exist within the protons. This is what has led to the confinement property of QCD, that the forces between quarks become larger as the separation between them increases, thus preventing them from being knocked out as individual quarks. We can knock them out as combinations of quarks and anti-quarks though.

As far as we know right now, quarks can never be isolated as free particles.

5. Rob Grigjanis says

Mark Dowd @2: You certainly can crack a hadron, but you’ll never see free quarks in the outcome. They bind so strongly that if you try and pull two quarks apart, you just create another pair. As John Rennie says here;

A free quark is like the free end of a rubber band. If you want to make the ends of a rubber band free you have to pull them apart, however the farther apart you pull them the more energy you have to put in. If you wanted to make the ends of the rubber band truly free you’d have to make the separation between them infinite, and that would require infinite energy. What actually happens is that the rubber band snaps and you get four ends instead of the two you started with.

Now, the strong coupling does decrease with increasing energy, so in the early high temperature universe, there were free quarks.

6. Rob Grigjanis says

I like Matt Strassler‘s comparison between the simplicity of a hydrogen atom and the horrible quark-gluon mess inside a hadron;

In short, atoms are to protons as a pas de deux in a delicate ballet is to a dance floor crowded with drunk twenty-somethings bouncing and flailing to a DJ.

7. Mark Dowd says

Mano @ #4
So it’s the Rutherford experiment turned up to 11?

8. says

I kinda feel bad that my first thought when reading the headline was an obvious and not particularly funny “joke”.

9. Mano Singham says

Mark @#7,

Exactly!

10. Mano Singham says

Tabby @#8,

No obvious joke, funny or otherwise, comes to my mind.

11. Mano Singham says

Tabby,

Ah, now I get it.

12. Pierce R. Butler says

I wanted to post a quick smart-ass comment about the mass of virtual particles going untallied because they don’t hang around long enough for measurements … but then I made the mistake of trying to look that up:

A virtual particle can have any mass, including a negative mass-squared (i.e. a mass that is imaginary) by having more momentum than energy instead of the other way round.)

13. Rob Grigjanis says

Pierce @13: You should have read a bit further;

It’s a very bad idea to think about a virtual particle as being something like a particle; it’s not a particle, it’s a generalized disturbance in a field, and it doesn’t obey the rules particles obey. Energy and momentum are conserved in Feynman diagrams at each vertex in the diagram, so the combination of the virtual photon and virtual electron into which the real electron has dissociated has the same energy, momentum and invariant mass of the real electron that entered and exited the diagram.

“virtual particle” is one of many unfortunate names in physics, because it can be very misleading. And Feynman diagrams are a handy way to represent mathematical expressions in perturbation theory, but they shouldn’t be taken too seriously as depicting what’s going on physically.

14. Mano Singham says

Pierce @#13,

As an aside and to cause your head to spin even faster, when the article said ‘negative mass squared’, they did not mean (negative mass)2, they meant that (mass)2 is negative. i.e., the value of the square of the mass is negative. Since the square of any real number is always non-negative, the ‘mass’ in this case is an imaginary number.

Go easy on the Cavorite, whatever that is.

15. Rob Grigjanis says

Mano @15: As Strassler says, these “things” are not particles; they are disturbances carrying energy and momentum. To ascribe mass to them at all is grossly (one might say massively) misleading.

16. Rob Grigjanis says

Cavorite; named for Joseph Cavor, the inventor in the film First Men in the Moon. Lionel Jeffries at his best.

17. Pierce R. Butler says

Thanks to Rob Grigjanis & Mano Singham @ #s 14-16 for the clarifications (if adding to my confusion can be called that).

This at least reduces my befuddlement as to how “virtual” “particles” can, it seems, appear, collide/cancel, and disappear with 100% efficiency and without adding to entropy/heat: the only such reaction in the universe (unless I missed some more in my physics-ignorance).

Fwliw: HG Wells did publish a novel about Cavor and his ~ite well before the movie (though issues of precedence always get complicated once we factor in The Time Machine…).

18. Rob Grigjanis says

Pierce @18: Shame on me for forgetting Wells!

Yeah, it’s a mistake to think of virtual particles as “doing” anything temporally.

In quantum field theory, first comes the math. For a particular process, like a scattering of (real) particles, or a decay, it’s generally impossible to get an exact solution, but you can in some cases use perturbation theory to get approximate solutions. Contributions to these approximate solutions have a general form which can be graphically represented by Feynman diagrams, with external lines representing real particles, and internal lines representing parts of the mathematical expression.

There is no time dependence in these expressions; the only way time enters might be in the sense that some external particles may represent an initial state (say, an electron and positron about to collide), with the other external particles being the final state (whatever gets produced by the collision). But somehow these internal lines, which are just mathematical entities, got promoted to “virtual particles”, leading to a lot of pop-sci nonsense.

19. Owlmirror says

Yeah, it’s a mistake to think of virtual particles as “doing” anything temporally.

20. Rob Grigjanis says

Owlmirror @20: What about it? The vacuum energy calculation involves the zero modes of an infinite set of harmonic oscillators. There are no virtual particles anywhere in sight.

Sadly, they’re brought up in a lot of contexts. Like Hawking radiation. In his original paper, about 22-23 pages long, the “virtual pair” picture occupies two or three paragraphs, ending with Hawking telling us that this is a heuristic explanation only, and shouldn’t be taken “too seriously”, and that the actual explanation was in the mathematics that followed. FWIW, I saw nothing in his math that even vaguely resembled the virtual pair picture.

You’ll see the same sort of nonsense in “explanations” of vacuum polarization (another horrible name, IMO).

21. Mano Singham says

As I understand it, the term ‘virtual’ particle applies to an entity that has the properties of known entities but is ‘off the energy shell’ in that E2 is NOT equal to (pc)2 + (mc2)2.

22. Mano Singham says

Rob,

Yes, of course!

23. Owlmirror says

@Rob and Mano: I don’t understand either of your responses. I’m not even sure what to start reading that might clarify my misapprehensions, let alone correct them.

24. consciousness razor says

Owlmirror, at this point, about the only thing everybody can agree on is that we have some math which is very useful for giving approximate results, to represent stuff that happens in the physical world.

Sometimes, there are real physical things which are being represented mathematically. We should be realists about real things, whatever those might be. Presumably, everyone should agree on that too.

But other times, it’s more like telling a fable, so that the audience can understand the moral of the story, whatever it might be, not to make claims that the things in the story all exist. If you start asking more penetrating questions about the talking animals or what have you (do they wear pants? how did things get to be that way? if there were talking unicorns, would they wear pants too? Etc.), then you’ll get a mix of strange and unsupported answers, or else some other kind of response that isn’t attempting to give a direct answer, depending on who you ask and how willing they are to have that kind of discussion at the moment.

A less exotic example would be the center of mass of some object. That is at a definite location and perhaps some stuff happens to be there. But it’s nothing particularly special or unusual, there’s no real need to include it as one more item that belongs in your comprehensive picture of the world, etc. It’s just useful for making certain kinds of calculations, that’s all. Talking about such things very well could make life a lot easier for physicists, but physics could still be formulated without it.

25. Mano Singham says

Owlmirror @#25,

Let take another shot at it, and Rob may also chime in.

For any ‘real’ particle (i.e., a particle that exists freely and is not bound to another particle or particles to form a combined state) its mass m, energy E, and momentum p are related by the equation E2 = (pc)2 + (mc2)2. This is what is meant by the particle ‘being on the mass shell’. The mass is one of the identifying characteristics of a particle because it remains unchanging.

But if the particle interacts with another particle in a collision, then its energy and momentum will change but if it remains a free particle after the collision, the new energy E’ and momentum p’ will still satisfy the relationship E’2 = (p’c)2 + (mc2)2 with the same mass.

But in certain collisions, the particle can acquire new values of energy and momentum so that that relationship is no longer satisfied for that value of mass. The particle is then said to be ‘off the mass shell’ and referred to as being in a virtual state. Such a state is short-lived, in that the virtual particle will soon interact with another particle and acquire new values of energy and momentum that satisfy the relationship for that particle’s mass.

As a concrete example, consider a free proton that collides with another free proton and they bounce off each other but remain free particles. All four proton states (two before and two after) consist of real particles and are on the mass shell. But on a microscopic level , what we say happens is that during the collision, one proton emits a neutral pion that is absorbed by the second proton, and this exchange is what causes the two protons to scatter off each other. It is like one person throwing a ball to another where the pion plays the role of the ball.

At each of the two stages (where the first proton emits a pion and the second proton absorbs that pion, energy and momentum are conserved. But during the short time when the pion is being exchanged, it will be ‘off the mass shell’.

26. Rob Grigjanis says

Owlmirror @25: As cr wrote @26:

But other times, it’s more like telling a fable, so that the audience can understand the moral of the story

The problem is that too often the audience comes away thinking the fable is the reality. Particular culprit: you’ll often come across stuff about electron-positron pairs popping out of the vacuum and then annihilating, and that the vacuum is a seething hotbed of these “fluctuations”. Often accompanied by other stuff about “borrowing energy from the vacuum”. All nonsense. There is no theoretical basis for this picture. It’s all short for “sorry, the math is too complicated”.

Where virtual particles tell a real story is in examples like Mano‘s @27. Even there, I’m really not fond of expressing these interactions as emission and absorption of “off-shell particles” (which puts me in a minority!), but at least there’s a solid link to the underlying theory.

I’m not even sure what to start reading that might clarify my misapprehensions, let alone correct them.

The best I can offer is that you read physicist bloggers like Sabine Hossenfelder and Matt Strassler. Non-physicist friendly, and reliably nonsense-free, IMO.

27. Owlmirror says

@Rob and Mano: Thanks, but it is still a little beyond me.

I’m trying to reword what you wrote in approximate English terms, and the best I can do so far is something like this:

When particles interact, mass-energy and momentum are conserved. But the momentum of both particles can change during the interaction, and what mediates that change are also particles. The particle system gets slightly out of balance in opposing ways, and then everything “resets” to the new conserved normal. The particles that are involved when the system is out of balance are called virtual.

Is that even close?

28. Rob Grigjanis says

Owlmirror @29: Sounds good.

29. Mano Singham says

Owlmirror @#29,

Close enough!