One of the questions I get most often from my readers is this:
- Since gravity pulls on things proportional to their mass, and since the Higgs field is responsible for giving everything its mass, there obviously must be a deep connection between the Higgs and gravity… right?
It’s a very reasonable guess, but — it turns out to be completely wrong. The problem is that this statement combines a 17th century notion of gravity, long ago revised, with an overly simplified version of a late-20th century notion of where masses of various particles comes from. I’ve finally produced the Higgs FAQ version 2.0, intended for non-experts with little background in the subject, and as part of that, I’ve answered this question. But since the question is so common, I thought I’d also put the answer in a post of its own.
As preface, let me bring out my professorial training and correct the question above with a red pen:
- Since gravity pulls on things proportional to their
massto a combination of their energy and momentum, and since the Higgs field is responsible of giving everythingnot everything, just the known elementary particles excepting the Higgs particle itself its mass, there obviously must be a deep connectionbetween the Higgs and gravity… right?wrong.
Now let me explain these corrections one by one.
When you first learn about gravity in school, you learn Newton’s law: that the force of gravity between two objects, one of mass M1 and one of mass M2, has a strength proportional to the product M1 M2.
But that was true before Einstein. It turns out that Newton’s law needs to be revised: the Einsteinian statement of the law is (roughly) that for two objects that are slow-moving (i.e. their speed relative to one another is much less than c, the speed of light) and have energy E1 and E2, the gravitational force between them has a strength proportional to the product E1 E2.
How are these two statements, the Newtonian and the Einsteinian, consistent? They are consistent because Einstein and his followers established that for any ordinary object, the relation between its energy E, momentum p and mass M [sometimes called ``rest mass'', but just called `mass' by particle physicists] is
- E2 = (p c)2 + (M c2)2
For a slow-moving object, p ≈ Mv (where v is the object’s velocity) and pc ≈ Mvc is much smaller than Mc2. And therefore
- E2 ≈ (M c2)2 (i.e., E ≈ M c2 for slow objects)
Since planets, moons, and artificial satellites all move with velocities well below 0.1% of c relative to each other and to the sun, the gravitational forces between them are proportional to
- E1 E2 ≈ M1 M2 c4
And since c is a constant, for such objects Einstein’s law of gravity and Newton’s law of gravity are completely consistent; the force law is proportional to the product of the energies and to the product of the masses, because the two are proportional to one another.
But for objects that have high speeds relative to one another, or for objects subject to extremely strong gravitational pulls (which will quickly develop high speeds if they don’t have them already), the Einsteinian law of gravity involves a complicated combination of momentum and energy, in which mass does not explicitly appear. This is why Einstein’s version of gravity even pulls on things like light, which is made from photons that have no mass at all. (And it is why gravitational waves — waves in space and time, massless just like light — can be formed by objects that are orbiting one another.) Simply put, the Einsteinian view of gravity (now reasonably well confirmed by experiment) differs significantly from the Newtonian view, and in particular, it is not mass but energy and momentum which are primary. And all objects, not matter what they are made from or how they are moving from your point of view, have energy — so everything in the universe exerts a gravitational effect on everything else. We say “gravity is a universal force” (here the term is not referring not to the universe but to the notion of universality — of complete generality.)
What about the Higgs field being the source for all mass in the universe? This statement, though you will often find it in the press or in glib articles written for the public, is false.
What is the true statement? Well, here is a list of the elementary particles that we know about so far. The massless ones are
- photons, gluons, gravitons (the latter presumed to exist)
while the ones with mass are
- W and Z particles
- quarks: top, bottom, charm, strange, up, down
- charged leptons: electrons, muons, taus
- neutrinos: three types (at least two and probably all three with small masses)
- the recently discovered new particle with a mass of 125 GeV/c2 (which I will assume for now is a Higgs particle of some type)
Now it is true that the W and Z particles, the quarks, the charged leptons and the neutrinos must get their mass from a Higgs field. It’s not possible for them to have masses any other way. But this is not true of the Higgs particle itself.
The mass of the Higgs particle does not entirely come from the Higgs field!
Where does its mass come from? Oh, that’s a long story that ends in a question rather than an answer. I will try to explain it someday. For now, suffice it to say that the mass of the Higgs particle does not have a single, simple, understood source, and the curious feature is that its mass is so small — this is one aspect of the enormous puzzle called the hierarchy problem.
But in any case, the Higgs field is not the universal giver of mass to elementary particles. The Higgs particle itself gets its mass, at least in part, from elsewhere. And it probably isn’t alone. It is very possible that dark matter is made from particles, and these too probably get at least part of their mass from another source. Dark matter is believed by most physicists and astronomers to be the majority of the matter in the universe; it is believed to provide the majority of the mass of the Milky Way Galaxy that we inhabit. The Higgs field likely provides little of that mass.
Other things get their masses from sources other than the Higgs particle. The majority of the mass of an atom is its nucleus, not its lightweight electrons on the outside. And nuclei are made from protons and neutrons — bags of imprisoned or “confined” quarks, antiquarks and gluons. These quarks, antiquarks and gluons go roaring around inside their little prison at very high speeds, and the masses of the proton and neutron are as much due to those energies, and to the energy that is needed to trap the quarks etc. inside the bag, as it is due to the masses of the quarks and antiquarks contained within the bag. So the proton’s and neutron’s masses do not come predominantly from the Higgs field. [Experts: There is a subtlety here, having to do with how the Higgs field affects the confinement scale; but even when it is accounted for, the statement remains essentially true.] So the mass of the earth, or the mass of the sun, would change, but not enormously, if there were no Higgs field… assuming they could hold together at all, which would not be true of the earth.
And black holes, which are some of the most massive objects in the universe, holding court at the centers of most galaxies, can in principle be made entirely from massless things. You can make a black hole entirely out of photons, in principle. In practise most black holes are made from ordinary matter, but ordinary matter’s mass is mostly from atomic nuclei, and as we just noted, that doesn’t come entirely from the Higgs field.
No matter how you view it, the Higgs field is not the universal giver of mass to things in the universe: not to ordinary atomic matter, not to dark matter, not to black holes. To most known fundamental particles, yes — and it is crucial in ensuring that atoms exist at all. But there would be just as much interesting gravitational physics going on in the universe if there were no Higgs field. There just wouldn’t be any atoms, or any people to study them.
Finally, you can ask more technically whether, in the equations that physicists study, there is any mathematical connection between gravity and the Higgs field. The answer is no. Gravitational fields have spin 2 and are described as part of space and time; they interact with all particles and fields in nature. The Higgs field, which has spin 0, only interacts directly with elementary particles and fields that also participate in the electromagnetic and weak nuclear forces.
So — the guess that the Higgs has something to do with gravity is natural for a non-expert, but I am afraid it is naive; it comes from misunderstanding both
- the Higgs field, which is not universal: it gives masses to most of the known elementary particles but not to the Higgs particle itself, and not to protons and neutrons, dark matter (most likely), or black holes,
- and Einstein’s gravity, which is universal and has to do with energy and momentum but not mass directly, and most certainly does pull on protons and neutrons, dark matter and black holes even though their masses don’t come entirely from the Higgs field.
It’s really true: despite appearances at first glance, the relation between gravity and the Higgs is just skin deep.