B Unified Quantum Field: Is it Possible?

[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?

 

[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.

 

[ftr]

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?

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"

 

[PeterDonis]

the electroweak unification is a good example. It is baffling how one field became three

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.

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

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

 

[PeterDonis]

A better description would be that "one field" and "three fields" are two different ways of looking at the same underlying Lagrangian.

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.)

 

[PeterDonis]

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.)

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.

 

[ftr]

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

 

[PeterDonis]

when they were one force

Which model are you asking about? The SU5 grand unification model?

it participated in which/what force transmition/process?

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

 

[ftr]

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

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

 

[PeterDonis]

Are you saying the electroweak unification was achieved WITHOUT a full proper theory

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.

 

[ftr]

Ok, let me simplify the question(and complicate it later!). Let's 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.

 

[PeterDonis]

Lets say at some point the universe was hot enough for this force(unified) was possible to exist

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.

my question is which particles and what was the process

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.

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

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

 

[ftr]

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.

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?

 

[PeterDonis]

the moment we allude to unification then it is not the standard model, because you will need more particles

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.

is unification important to the standard model

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.)

 

[fresh_42]

This is my main point, the moment we allude to unification then it is not the standard model,

Yes, because SM doesn't include gravity.

because you will need more particles, am I correct?

That's a consequence of the exemplary assumption above, not the reason.

So, is unification important

To whom?

to the standard model in whatever sense you wish?

No, the SM doesn't have such feelings.

 

[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.

 

[jtbell]

Isn't electroweak a unification kind of scheme or not.

It is.

IF yes, what is it doing in the standard model.

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.

 

[fresh_42]

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.

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).

 

[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?

 

[Vanadium 50]

"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.

 

[PeterDonis]

Isn't electroweak a unification kind of scheme or not.

Yes, it unifies the weak and electromagnetic interactions.

IF yes, what is it doing in the standard model.

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.)

Lets say we scatter two electrons at the electroweak unification energy,
1. Is there a theory that can predict the outcome.

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

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?

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

 

[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.

 

[PeterDonis]

why they had to go for the electroweak, it is the original parity violation for the conjectured W particle

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.

 

[Vanadium 50]

Weak interactions are the ones for which parity violation occurs, yes. But when those violations were first discovered, nobody had hypothesized W particles, AFAIK.

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.

 

[dextercioby]

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 September. The unification paper came a decade later in 1967.

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

 

[Vanadium 50]

The Lee/Yang paper is rather confused. (In fact, many of the papers of that era on weak interactions are confused) The paper tries to explain what is now known to be an incorrect measurement of one of the muon Michel parameters, but in the midst of the calculation they determine that this can't explain it because the sign is in the wrong direction, and oh by the way, there might be W's. It only has 63 cites. But that's the history as it happened - progress is not the steady march from brilliant insight to brilliant insight you read about in textbooks. The real world is messier and more chaotic.

 

[ChrisisC]

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.

What do you mean a "Scheme"?

 

[Tollendal]

Dear ChrisisC,

Since gravity is not a "real" force, but relative to the observer, it seems to me dificult unifying it with the tree known real forces, already unifyed.

Tollendal

 

[PeterDonis]

gravity is not a "real" force

The "gravity" that people talk about unifying with the other "forces" is not what you are describing here. It is spacetime curvature, which is not observer-dependent.

 

[David Neves]

The U(1) in the SU(3) x SU(2) x U(1) of the Standard Model is not the same U(1) as in electromagnetism. It's a different U(1) related to hypercharge, Y. The U(1) of electromagnetism is still there. It's sitting diagonally inside SU(2).

 

[Dukon]

Wikipedia says that Glashow graduated from Cornell in 1954 (before 1957 parity violation) and received his PhD from Harvard in 1959 (after parity violation). AFAIRecall the topic for Glashow's dissertation was supplied by Schwinger to extend the then familiar U(1) gauge symmetry which generates electromagnetism to now perform the more complicated version of this calculation for SU(2) symmetry. (Motivated by the 1954 Yang-Mills models then recently proposed?) If this work was completed in 1959 it was then a few years later in 1961 when Glashow proposed SU(2)xU(1) to which Weinberg later added the Higgs mechanism (1964) to arrive at the 1967 model cited today.

Performing this same gauge symmetry calculation for the SU(3) group delivers QCD and the 8 gluon (performed by others Gell-Mann?)

 

[PeterDonis]

The U(1) of electromagnetism is still there. It's sitting diagonally inside SU(2).

I don't think this is quite correct. It is true that the U(1) in SU(2) x U(1) (the electroweak gauge group) is not the U(1) of electromagnetism, it's hypercharge. But the U(1) of electromagnetism is not "inside" the electroweak SU(2) (which is weak isospin). It's a combination of part of weak isospin and part of hypercharge.

 

[David Neves]

Peter Donis is right. That would be more accurate. I was just trying to respond to his post

https://www.physicsforums.com/threads/unified-quantum-field.911768/#post-5743470

where he wrote

"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"."

 

[PeterDonis]

I was just trying to respond to his post

Yes, you're right, I was being sloppy in that post. It should really be "SU3 is strong, SU2 is weak isospin, U1 is weak hypercharge", at least if we talk about the fundamental Lagrangian before electroweak symmetry breaking. After electroweak symmetry breaking we have a more complicated situation, where we have two charged weak gauge bosons that take up two of the SU2 degrees of freedom, and a neutral weak gauge boson and electromagnetic gauge boson (the photon) that are each linear combinations of the remaining SU2 degree of freedom and the U1 hypercharge degree of freedom.