# B Unified Quantum field?

1. Apr 18, 2017

### ChrisisC

If all of the known forces that we know today were unified into one force before the Planck Epoch, does that mean there was just one field in which the forces acted? Is it mathematically and logically possible for all of the fields in QFT to have been united into one field?

2. Apr 18, 2017

### dextercioby

We don't know the answer to your second question. There's no field-like prolongation of the Standard Model which makes quantum gravity a powerful, finite, mathematically sound theory capable of testable predictions. So let's aknowledge the current (actually since forever) gap of knowledge and not speculate.

3. Apr 18, 2017

### ftr

Good question. I have been mulling a similar question for days now. Well you do not have to go to Planck Epoch, the electroweak unification is a good example. It is baffling how one field became three, the standard argument is "spontaneous symmetry breaking".

http://hyperphysics.phy-astr.gsu.edu/hbase/Forces/unify.html

quote"The question of how the W and Z got so much mass in the spontaneous symmetry breaking is still a perplexing one"

4. Apr 18, 2017

### Staff: Mentor

That's not a good description. A better description would be that "one field" and "three fields" are two different ways of looking at the same underlying Lagrangian. The first way works better at high energies, the second at low energies.

Not since we have actually observed the Higgs boson. AFAIK he page you linked to dates from well before that.

5. Apr 18, 2017

### Staff: Mentor

Also, if we're talking about electroweak theory, we actually have four fields in the low energy phase: W+, W-, Z, and photon.

(What's more, we can also view things as four fields in the high energy phase: W1, W2, W3, and B.)

6. Apr 18, 2017

### Staff: Mentor

I should probably clarify something else here as well. "Number of fields" and "number of forces" are not the same thing. Also, grand unification is not really the same kind of thing as electroweak unification; and any hypothetical unification with gravity would be different again.

The Standard Model is based on the gauge group SU3 x SU2 x U1. Thinking of three "forces" identifies each term in this tensor product as a "force": SU3 is "strong", SU2 is "weak", U1 is "electromagnetic".

However, the number of "fields" (or better, "gauge bosons") for a given force depends on the dimension of the group (more precisely, the number of generators in the adjoint representation of the group). U1 is a one-dimensional group, so there is one electromagnetic gauge boson (the photon), hence one field. SU2 is a three-dimensional group, so there are three weak gauge bosons (W+, W-, and Z in the low energy phase), hence three fields. SU3 is an eight-dimensional group, so there are eight strong gauge bosons (the gluons), hence eight fields. So there are a total of twelve fields for these three interactions.

Electroweak unification does not change any of these counts. All it does is take SU2 x U1 and look at it a different way, by choosing a different set of four generators for this combined group and calling those the four "gauge bosons" of the "electroweak force" in the high energy phase (before spontaneous symmetry breaking). These four gauge boson fields are usually called W1, W2, W3, and B. But all this amounts to is choosing a different basis for the group, so we can express the low energy fields, W+, W-, Z, and A (the photon), as linear combinations of W1, W2, W3, and B, or vice versa. So we haven't changed the number of fields. Whether we have changed the number of "forces" depends on how you want to choose terminology: have we "unified" the weak and electromagnetic forces (since we aren't separating the group SU2 x U1 the same way), or have we just relabeled them but still have two "forces" (since we still have two terms in our tensor product group SU2 x U1)?

Grand unification--unifying all three of the Standard Model interactions--is something different (and we don't currently have a good theory of it, we just have various models that have been constructed and then found to not agree with experiment--the model I'll describe is just one of the simplest of these). It involves finding some simple group (in the simplest case, SU5) that has the Standard Model gauge group as a subgroup. Then we can express the SM gauge bosons in terms of the gauge bosons of the simple group. But there will also be additional gauge bosons in the simple group that do not correspond to any of the SM ones (in the SU5 case, there are 24 gauge bosons total, only 12 of which correspond to SM gauge bosons).

Since we now have a single, simple group, we can think of the grand unified theory as having one "force" instead of three. But it has a much larger number of "fields" (in the SU5 case, 24). So even though we are decreasing the number of forces, we are increasing the number of fields.

7. Apr 18, 2017

### ftr

OK, Thanks peterDonis. One question though,when they were one force it participated in which/what force transmition/process?

Last edited: Apr 18, 2017
8. Apr 19, 2017

### Staff: Mentor

If you mean the SU5 model, the SU5 "force". This is not the same as any of the Standard Model forces.

9. Apr 19, 2017

### ftr

Are you saying the electroweak unification was achieved WITHOUT a full proper theory, yet it is part of the standard model.

10. Apr 19, 2017

### Staff: Mentor

What do you consider "a full proper theory"?

QED is a full, proper theory of the U1 gauge group. Electroweak unification provided a full, proper theory of the SU2 x U1 gauge group. The Standard Model provides a full, proper theory of the SU3 x SU2 x U1 gauge group. We don't have a full, proper theory for any larger gauge group that contains these; but we also don't have any evidence for the extra fields that would be present in such a gauge group. Grand unification is proposed for theoretical reasons, not experimental ones. The same is true for quantum gravity: nobody has ever done an experiment that requires quantum gravity to interpret.

11. Apr 19, 2017

### ftr

Ok, let me simplify the question(and complicate it later!). Lets say at some point the universe was hot enough for this force(unified) was possible to exist, my question is which particles and what was the process. second choice, would be high energy collisions(same question as first case). Third, naturally occurring(same question as first case). FOURTH, there is no chance in the universe for such energies to happen, hence the unification is truly pseudo-theoretical.

12. Apr 19, 2017

### Staff: Mentor

I think you're misunderstanding how this kind of model works. Let's suppose the SU5 grand unification turns out to be correct. Then the SU5 "force" always exists--it exists now. It's just that now, at low energy, the SU5 force looks like the Standard Model forces: the SU5 gauge group is not directly observable at low energy, only the SU3 x SU2 x U1 subgroup of that gauge group is.

Nobody has given ordinary language names to the 24 gauge bosons of the SU5 model (or for any other grand unification model). But those are the particles and the gauge interactions they mediate are the process. Those 24 gauge bosons are the SU5 equivalent of photons, W and Z particles, and gluons in the Standard Model.

I don't understand what you're asking here.

13. Apr 19, 2017

### ftr

This is my main point, the moment we allude to unification then it is not the standard model, because you will need more particles, am I correct? So, is unification important to the standard model in whatever sense you wish?

14. Apr 19, 2017

### Staff: Mentor

Yes, any grand unification theory, or any theory that unifies the three SM interactions with gravity, will have to go beyond the standard model and will require more gauge bosons. (Or something else extra, such as the loops in loop quantum gravity.) But any such theory will have to have our current standard model as a low energy approximation.

Not as far as testing the accuracy of the current SM, no. We can do that, and have been, without knowing what, if any, kind of unification theory will turn out to be correct. (It is possible that none will, i.e., that there is no such unified theory. Most physicists think this is highly unlikely, but unless and until we have some experiments to guide us, we don't know for sure.)

15. Apr 19, 2017

### Staff: Mentor

Yes, because SM doesn't include gravity.
That's a consequence of the exemplary assumption above, not the reason.
To whom?
No, the SM doesn't have such feelings.

16. Apr 19, 2017

### ftr

So far I am only talking about electroweak. Isn't electroweak a unification kind of scheme or not. IF yes, what is it doing in the standard model. I think I am running out of breath trying to make my question clear.

17. Apr 19, 2017

### Staff: Mentor

It is.
It's part of the Standard Model by definition, and has been since at least c. 1980 when I was a graduate student in experimental neutrino physics.

18. Apr 19, 2017

### Staff: Mentor

electromagnetic: $U(1)$
weak: $SU(2)$
__________________________
electroweak: $U(1) \times SU(2)\, \,^*)$
strong: $SU(3)$
__________________________
SM: $SU(3) \times SU(2) \times U(1)\, \,^*)$
__________________________
Gravitation: ?
__________________________
GUT: $G_{SM} := SU(3) \times SU(2) \times U(1) \leq G_{GUT} \; ?$
$G_{SM} \lneq G_{GUT} \Longrightarrow \textrm{ more gauge bosons }\, \,^{**})$

$^*)$ Whether you call these products of groups a "unification" (usually used), a "summary", an "extension", a "common language", a "common brace", or simply the "product of gauge groups" is a matter of common language, history, viewpoint, technical perspective, intention or personal taste. It doesn't affect the physics. The various energy levels only mean that the various "group elements" manifest / can be detected / can be observed / are needed to explain at the according energies. "Existence" has nothing to do with it. And "unification" simply means "in the product group", resp. "by the representations of the product group".

$^{**})$ If the gauge group of a model, that includes all four forces, is larger than a model, which includes less forces as the three in the SM, then there must be more group elements (math) aka more symmetries (geometry) aka more invariants (Noether) aka more gauge bosons (particle physics).

19. Apr 19, 2017

### ftr

Ok, I have a bit of gasp left.

Lets say we scatter two electrons at the electroweak unification energy,
1. Is there a theory that can predict the outcome.
2. what would the potential outcome would be as they get close to each other(although the coupling is known according to the theory). definitely not coulomb potential correct?

Last edited: Apr 19, 2017
20. Apr 19, 2017

Staff Emeritus
"We don't have a theory"
"But if we did have a theory, what would it predict?"

If we knew what it predicted, then we would have a theory.

21. Apr 19, 2017

### Staff: Mentor

Yes, it unifies the weak and electromagnetic interactions.

Because the Standard Model includes everything non-gravitational in the particle physics realm for which we have experimental evidence. We have experimental evidence for electroweak unification. We don't have experimental evidence for grand unification, which is why it isn't in the Standard Model. (If we had had such evidence when the term "Standard Model" was defined, it probably would have included grand unification. But we didn't. "Standard Model" is just a term. You can't change physics by redefining terms.)

Yes, the Standard Model does. These experiments have been done (more precisely, electron-electron scattering at high enough energies to require the full electroweak theory to make good predictions instead of just QED), and have in fact helped to pin down values for some of the electroweak interaction parameters. See, for example, here:

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.081601

Correct. The outcomes at these energies cannot be described by any simple central force potential.

22. Apr 20, 2017

### ftr

After reading quite a bit I think I understand(maybe not that well) why they had to go for the electroweak, it is the original parity violation for the conjectured W particle.

23. Apr 20, 2017

### Staff: Mentor

Weak interactions are the ones for which parity violation occurs, yes. But when those violations were first discovered, nobody had hypothesized W particles, AFAIK. When the first experiments that discovered parity violation were done, the only theory known for the weak interaction was the Fermi theory, which was not a gauge boson theory at all.

AFAIK there was never a gauge boson theory developed for the weak interaction by itself; it turned out that the first gauge boson theory that was found to describe the weak interaction was electroweak theory. In other words, it turned out that explaining the parity violation led us to electroweak unification, without anyone (AFAIK) having anticipated that.

24. Apr 20, 2017

Staff Emeritus
It was almost simultaneous. The Wu experiment was performed in June, 1957 and published in September. The Lee/Yang paper hypothesizing the W ("Possible Nonlocal Effects in muon Decay" was received in August and published in December (whoops, I originally wrote September. That's wrong). The unification paper came a decade later in 1967.

Last edited: Apr 21, 2017
25. Apr 21, 2017

### dextercioby

Nice historical touch. This is useful to know for any physicist who should respect his predecessors.