The hypothetical Higgs boson has a spin of zero. Electrons have a spin of 1/2. Our friendly photons have a spin of 1. I hear it told that the graviton, should it exist, would have a spin of 2.
This got me wondering. Can we tell anything about a particle from its spin? What would a spin 3 particle be like? Could it exist?
I can give a partial answer.
We can tell something about a particle’s ability to interact by its spin.
For example electrons are spin 1/2 particles and are part of a family called fermions(as are all spin 1/2 particles, named after Fermi) and these are bound by the rules that govern these particles called Fermi-Dirac statistics.
This effectively states that fermions cannot have the same quantum state and this determines things like the structure of electron shells of atoms and the like.
Bosons are force carriers and include both the hypothetical Higgs and photons and have integer spins they are governed by Bose-Einstein statistics and can all have the same quantum state.
Whether you can have a spin 3 particle, I’m not sure, but I see no reason why you couldn’t. With an integer spin it would be a boson and therefore a force carrier of some kind.
Incidentally, just to confuse things it is possible for a system of fermions to act in a bosonic manner if the spins add up to integers. For example one system of an electron and a hole (essentially a positive charge) is called an exciton and due to the fact that the electron and hole can have either the same or opposite spins can have a spin of 0 or +/- 1 and therfore acts as a boson.
Besides the consequences of the spin-statistics theorem mentioned by Walker in Eternity above, the spin of a charged particle also determines its magnetic (dipole) moment, i.e. how strongly it’s affected by surrounding magnetic fields, broadly.
Spin is also significant for polarization states. If you take a stream of, say, spin-1 photons (AKA a light wave) coming out of the page at you, then you have two possible independent polarization states: The electric fields could be vertical, or they could be horizontal (you could also have them diagonal, but that’s actually just a combination of vertical and horizontal-- The important thing is that vertical and horizontal represent a basis set). If I start with a vertically-polarized light beam, and rotate it 90 degrees, then I have a horizontally-polarized light beam, so the two polarization states are 90 degrees apart.
If I have a beam of spin-1/2 electrons, by contrast, I can also have polarization states, but now, the states are 180 degrees apart: I could have them spin-up or spin-down, for instance.
What about spin-2 gravitons? In the same way that a stream of photons is an electromagnetic wave, a stream of gravitons is a gravitational wave (note that although we’re within a few years of detecting gravitational waves, we won’t be able to detect individual gravitons, just a whole bunch of them together). A gravitational wave coming out of the page can be detected by its effect on a ring of masses in the plane of the page: If you start with a circle, it’ll be distorted into an oval first one way, and then the other. There are two independent ways you can do this: You have what’s called the “plus polarization”, which goes something like
o – o | o – o |
etc., or you can have what’s called the “cross polarization” (“cross”, to physicists, means an X shape), which goes something like
o \ o / o \ o /
etc. Again, as with light, there are polarizations in between, but they’re just combinations of these two. Now, if we start with a beam of plus-polarized gravitons, and rotate the beam by 45 degrees, we’ll have a beam of cross-polarized gravitons. So for gravitational waves, the two polarizations are 45 degrees apart.
In other words, if a particle has spin s, then the polarization states of a beam of them will be (90 degrees / s) apart. And if we ever discovered a spin-3 particle, its polarizations would be 30 degrees apart.
I’d forgotten about that, but thanks for reminding me, there’s also the Zeeman effect which results in the splitting of the spectral lines due to spin orbital coupling.
The big difference with spin-3 and above bosons as force carriers is that massless particles with such spins don’t give rise to long-range forces. Unlike with the spin-1 (electromagnetism) and the spin-2 (gravity) cases.
I definitely recall the argument having been made that everything screws up and it becomes very difficult, perhaps impossible, to construct consistent models using them as fundamental force carriers. But I neither remember the details, nor is a quick rummage throwing anything up.
Interesting. So it’d only be short range, like the strong force? But wait. Gluons mediate the strong force, don’t they? They’re spin-1.
Interesting! I’ll be on the lookout myself. Thanks for the tidbit.
But the forces are short-range for a different reason in that case: the gluons carry colour charge. Similarly for massive spin-1 bosons.
I thought of forcing in the caviat, but decided not to: as I recall, the arguments don’t imply that you can’t have higher-spin composite objects. Or massive ones.
More precisely, one might say that gluons mediate the color force, which would indeed be long range if you could ever get two colored particles far enough apart from each other (so far as anyone can tell, you can’t, except possibly in a cosmological Big Rip). What we know as the “Strong Force” is just a sort of residual effect from the color forces on composite objects not quite exactly canceling out. If you were to describe the Strong Force as being (approximately) mediated by some force carrier, that carrier would be the pion, which is short-ranged because it’s massive (see the Yukawa potential).
I’m not a particle physicist, but there are nuclei with spin 3, as well as a whole host of wacky values, ranging up to… well, some quick googling reveals that 176Lu has a nuclear spin of 7, and that seems to be the highest.
I realize this isn’t truly the same, as we’re talking about an aggregate of protons rather than a single particle, but since I’m not a particle physicist, I can squint and say that I know something with a spin of SEVEN, and its existence hasn’t yet unraveled the universe.
Elaborating on this a little: The Pauli Exclusion Principle says that if you swap two identical fermions (for instance, two electrons) the total state changes by a minus sign (i.e., it’s antisymmetric).
Say I denote the state of a pair of electrons as (A,B), where A is the state of one of the electrons and B is the state of the other one. E.g., (2, 1) would mean the first electron is in state number 2, and the second electron is in state number 1.
Then, we can’t have (n,n) (both particles in state number n) because in this case swapping the two changes nothing. This is the narrower statement of the Pauli principle that you often hear, and which Walker gives above.
However, we also can’t have certain superpositions of states (even if states we’re superposing don’t have the particles in the same state), such as:
(1,2) + (2,1)
Again, we can see that swapping the two particles changes nothing, since:
(2,1) + (1,2) = (1,2) + (2, 1)
In other words, this is a symmetric state, and thus, forbidden.
However, we can have:
(1,2) - (2,1)
Here, swapping the two particles introduces a minus sign:
(2,1) - (1,2) = -[(1,2) - (2,1)]
Thus, this is an allowed antisymmetric state.
As noted above, you can have composite particles with spin 3, but these wouldn’t be considered force carriers. Atoms can be both bosonic or fermionic, for instance.
Actually, I’m not really sure why it’s the case that fundamental fermions are “matter particles” while fundamental bosons are “force carriers”. Maybe it’s because all the fundamental bosons are either massless or unstable, whereas there are several stable fermions with non-zero mass. But I’m not sure this has to be the case for any future bosons we discover. For instance, I don’t think we know if dark matter is fermionic or bosonic.
Also, is the Higgs boson considered a force carrier? If so, how come we don’t hear “Higgs force” included alongside the four fundamental forces?
Furthermore, if you swap two identical bosons, the total state stays the same. This also leads to some allowed and some forbidden states, so in a sense, the Pauli Exclusion Principle applies to bosons, too, just in a different way than it applies to fermions.
The argument I’ve heard is that for bosons of spin 2 or higher, the Lagrangian has terms whose coupling constants’ dimensions are a nonpositive power of mass, which makes renormalization not work. I don’t remember more details though.
I agree: I don’t think there’s any deep truth to the identification of bosons as force carriers in the standard model, it’s mostly a matter of perspective. But even if not all bosons happen to be mediators, it’s true that fermions can’t “mediate” in the usual sense. If a particle emits or absorbs a fermion, its identity has to change (between boson and fermion), which no longer sounds like a force mediation. (On the other hand, composite bosons like pions, composed of two fermions, sometimes behave like mediators in low-energy effective theories.)
Would a valid interpretation of this mean that if there were a spin-3 force carrier, this force would have infinite energy summed up over all particles? (Or, of course, the theory would be wrong.)
First, note that the problem Omphaloskeptic is talking about applies even to spin-2 bosons (like the graviton), which is a big part of why quantum gravity is hard to figure out.
Basically what it means is the theory can’t be valid up to infinite energy. In quantum field theory you have integrals up to some upper bound in energy (sometimes denoted with a capital lambda, but here I’ll call it L.) If the theory is valid all the way up to infinite energy, then you can take L → infinity. However, if the physical quantities you’re calculating depend on L[sup]E[/sup], where E is some positive exponent, then you know you have a problem, since the thing you’re calculating will then go to infinity as L goes to infinity. In this case, there’s going to be some new physics that shows up at high energies to cut off the value of L and keep everything finite. But it’s very hard to know what this new physics will be.
The argument Omphaloskeptic is referencing basically says that with bosons of spin 2 and above, the quantities we want to calculate depend on coupling constants which have units of negative energy, and so these couplings end up needing to be multiplied by positive powers of L to make the units cancel out. This leads to the problem I described in the previous paragraph.
Oh, I see. So rather than there being infinite energy, it is simply a sign that the theory does not have the domain that we wish. Does string “theory” manage this by gravity acting in the extra dimensions? (It is my understanding that there is no renormalization problem in ST for the graviton.)
I’m no expert on string theory, but one explanation I’ve heard is basically this:
Because gravity is not renormalizable (that is, because we can’t cancel out infinities in the way that works for the other forces), if we try to do quantum field theory at higher energies we end up with a theory that depends on infinitely many parameters, rendering the theory useless for actually calculating anything. (At lower energies most of these parameters are suppressed, so we can actually do some calculations. This approach is referred to as effective field theory.) In string theory, the particles are treated as strings which vibrate in many dimensions, and the various ways these strings can vibrate impose additional constraints on the theory, fixing our problem of having too many free parameters.
That said, string theory (at its present state of development) imposes its own difficulties, not least of which is that no one is really sure what version of the theory (if any) describes quantum gravity in the real world. Many of the earlier versions of string theory are now believed to be different special cases of a single more general theory (called M-Theory), but no one has yet been able to work out the details of this theory. There’s also an issue of there being lots and lots of different ways of curling up the extra dimensions in string theory, with no one yet knowing which way occurs in the real world. If you’ve heard the claim that string theory isn’t testable, it’s because of issues like these. String theorists of course hope to eventually solve these problems.
Particle physics isn’t my thing ( I majored in astro) but as I understand it the Higgs field is responsible for mass due to some kind of drag effect, so the Higgs boson would be the carrier that transferred whatever force is responsible for mass. This is a bit vague as my understanding in this area is limited, but I hope I got the idea across.
I don’t like string theory, it fails occams razor for starters by needlessly multiplying entities, also Lee Smolin in his book the Trouble with Physics has state that there are in the region of 10^500 solutions to string theory which make finding a solution relevent to our universe more difficult.