Is a New Principle Necessary to Resolve Quantum Gravity and Unify Interactions?

[qsa]

Holography today is - in my opinion - like scratching at the surface hiding a fundamental principle still to be fully understood; like Mach's principle was a guideline for Einstein which did not made to a fundamental principle in GR (... he must so to speak throw away the ladder, after he has climbed up on it ...); nevertheless holography is certainly some aspect of reality b/c it shows up in so different approaches so that it's hard to deny that there is something fundamental behind it.

Gravitons (including virtual particles of the gravitational field) on the other hand are mathematical artefacts of perturbation theory; of course some strong-weak dualities allow us to express certain amplitudes in certain regimes using perturbation theory but that doesn't mean that the graviton itself is a fundamental concept; there are too many scenarios where the graviton concept fails completely or is too restricted (just like the virtual gluon concept fails in non-perturbative QCD).

So for me holography is a concept or a guideline pointing towards a fundamental principle, whereas gravitons are a rather limit calculational tool valid only in a rather limited regime.

In that case I want to connect holography (which hint strongly that space-time is emergent) to that other question I had. My guess is that emergence means that space-time can be calculated from the original theory.

One more Question: the ultimate background independent theory is a theory were space and time are emergent, causal set, arkani-hamed's theory(path integral without space-time) and torstens theories come to mind. shouldn't somebody study the connection.


Q1. would you expect a theory were space-time will be emergent to automatically produce the appropriate symmetries for space time.

Q2. Since all these theories hint of space time emergence, can you see any hint of equivalence in some way.

 

[tom.stoer]

"emergence" is only a word; in the AdS/CFT scenario space-time is emergent, too, but due to a conformal, gravity-free SUSY gauge theory livig on the boundary; here "emergence" is more like"duality"; as in AdS/CFT holography is build-in, I agree that there is a connection with emergent gravity, but in that specific case NOT in the sense of Verlinde, causal sets etc.

I don't agree that all theories point towards emergent space-time; unfortunately the situation is far from clear, but looking at twistor theory, LQG like approaches and 4dim exotic smoothness it could be exactly the other way round, namely that matter does emerge from spacetime.

Perhaps these links are interesting ...
http://arxiv.org/abs/1006.2230v1
http://arxiv.org/abs/1003.5506v1

 

[arivero]

Alright, where does the top quark comes from?

Again, generically or in this setup ?

All the information we can extract from this setup is that the partners of the top quark come, jointly with the partners of the up and charm quarks all of them, from the six pairs dd,ds,db,ss,sb,bb and their antiparticles. We do not solve, neither address, the question of the top quark itself. All we know is that their superpartners are part of an intriguing SU(5) symmetry related to the charges of the two flavours of the light quarks.

Even outside of this particular setup, it is clear that whatever the top quark is about, it is related to electroweak symmetry breaking. A yukawa coupling of 0.98 is too near of 1.0 to be considered unique (and actually, 1. is still compatible with the experimental measurement).

 

[Fra]

This is a question that the rest of the public of the thread could enjoy: Are the so-called effective theories just effective, or something more important?

I wouldn't agree that effective theories are less important.

Just to throw back a reflection on this: From the inference perspective I hold, there is actually no way even in theory, to distinguish between an effective theory and fundamental theories. Or put differently, all theories are effective, and the notion of fundamental theory is just a realist remnant.

To understand effective theories as a result of inference processes, IS IMHO important, and that ANY actual theory is ALWAYS the result of an inference process and hences effective. But the saving conjecture in this thinking is that it's the effective laws, that rule the action of the system encoding the theory, not the - unkonwn fundamental theory.

Also, in my view, there is no rational ground in separating law and initial conditions, and hence not knowledge about states in a theory and knowledge of theory itself. The difference is merely that the theory is more unquestionable as it's what happens to be under our feet.

/Fredrik

 

[MTd2]

Again, generically or in this setup ?

This setup! Always this one! :)

 

[arivero]

I wouldn't agree that effective theories are less important.

Just to throw back a reflection on this: From the inference perspective I hold, there is actually no way even in theory, to distinguish between an effective theory and fundamental theories. Or put differently, all theories are effective, and the notion of fundamental theory is just a realist remnant.

To understand effective theories as a result of inference processes, IS IMHO important

I think that a valuable point is the number of free parameters in a theory. We could say that a fundamental theory is what happens in an effective theory when the free parameter disappears.

The gauge bosons in the SM are the prototypical effects. You can see them as effective, with the mass being a free parameter (and the model does not need higgs), or you can see it as fundamental theory, when the mass is generated by the Higgs.

In fact I think that when experimentalists refer to the SM, they still refer to the inferred, effective theory. It is only the theory front, and perhaps even more the science journalist front, who see the SM as the one with the Higgs. It should really be called MSM, in the same way that we call MSSM to the SSM with two higgses.

 

[arivero]

This setup! Always this one! :)

Well, what we have got -besides uniqueness- is to obtain, from this hidden SU(5) symmetry, all the non-gauge bosons of the Superymmetric Standard Model.

Of these, the ones related to the electroweak scale are the partners of the top, and the scalar partners of the W+, W- and Z bosons (more precisely, the scalar partners of the chiral fermion that is absorbed by the gauge bosons to get mass).

All of them come in different ways from the 15 + 15 representation of SU(5), which in turn is extracted from 5x5=15+10. In plain words, they are the set of different pairs you can do with u,d,c,s,b, plus the different pairs you can do with u,d,c,s,b

Of these, six plus six do the partners of Dirac up quarks:

dd,ds,db,ss,sb,bb,dd,ds,db,ss,sb,bb​

six plus six do the partners of Dirac down quarks:

du,dc,su,sc,bu,bc,du,dc,su,sc,bu,bc​

and three plus three do the partners of the Chiral (Weyl?) w+,w+,z companions:

uu,uc,cc,uu,uc,cc​

The Dirac fermions can see colour, so they triplicate for each colour. The Chiral fermions can not see colour (and they can see electroweak charge, but not pure electromagnetic charge), so their partners do not triplicate neither (the mechanism for it, I do not known yet, it implies to use Super-QCD, surely).

All we can expect is that two special combinations of the first (bi)sextet are related to the top, and then its mass before susy breaking is related to the mass of the chiral companions. Within this setup, I do not see any other exploitable feature, and even this one is unclear, as I do not see what combinations we should select. We could put some more group theory into, namely the decomposition of SU(5) into the subgroup SU(3) x SU(2), and we could also pay attention the left and right chiralities.

 

[MTd2]

Even outside of this particular setup, it is clear that whatever the top quark is about, it is related to electroweak symmetry breaking. A yukawa coupling of 0.98 is too near of 1.0 to be considered unique (and actually, 1. is still compatible with the experimental measurement).

So, top=higgs for you, that is, top condensate instead of higgs?

 

[arivero]

So, top=higgs for you, that is, top condensate instead of higgs?

I am agnostic.

If you had some condensation theory predicting also the same sQCD results that post 41 (say, 14 families with a condensate of 7 tops and 10 bottom, or 33 families with a condensate of 22 top and ...) then I would say that top condensation is the way to go

 

[Fra]

I think that a valuable point is the number of free parameters in a theory. We could say that a fundamental theory is what happens in an effective theory when the free parameter disappears.

I see that point, but what you describe is to me more the let's say condensation process where expectations are sufficiently confidence to get turned into unquestionable non-variable elements.

But I think the logic whereby a parameter disappears, and also reappears is itself a physical process. And it's this I seek to understand. It also relates as I see it to the origina of degrees of freedom. I do not personally like when all this is is spoken of as some mathematical renormalization as if it's just a mathematical scaling. The "scaling" here is truly physical and must take the form of an expectations itself, so that it takes another observer to describe the "theory of scaling" - ie. renormalization.

So I still do not think there is a proper distinction between fundamental and effective, because what as you defined "fundamental theory" effectively just means that we "truncate" expectations to become facts. But this doesn't mean they ARE. It just means the doubts are not distinguishable.

I expect the entire RG stuff to alsos be revised (in some way) with a new future understanding.

/Fredrik

 

[arivero]

I expect the entire RG stuff to alsos be revised (in some way) with a new future understanding.

Sometimes, the effective theory seems as fundamental as its high energy theory.

Think in the electroweak part of the SM. The effective theory have three parameters, alpha, MW and MZ. In the RG above the critical point, the masses become zero, and that is all. But as a consequence of it, the effective theory is instead written as a function of g, g' and <v> So Ok, when <v> is zero, we lost a parameter, as said before. But we really need to predict the value of <v> if we want to claim that we have produced a more fundamental theory.

 

[arivero]

Alright, where does the top quark comes from?

By now, I am exhausted and I am sure I have lost any audience left. But I have been thinking hard about an answer to your question, and I could have an sketch of a possibility.

Look to the SU(3) flavour sextet dd,ss,bb,ds,sb,bd.

There is actually only a way to separate this sextet in pairs so that every pair can move to another by a simultaneus action of flavour on a single quark of each component. The pairs are.

dd,sb
ss,bd
bb,ds

And we could thing that these pairs are the partners of the U family.

On other hand, they are three ways to put a SU(2) triplet in this sextet
dd,ds,ss; ss,sb,bb; bb,bd,dd.

You can notice that each of the triplets contains one of the components of the pairs.

But more important, the first of the triples is a mirror of our misterius "electroweak breaking" triplet uu,uc,cc

So I feel inclined to believe that the partner of the top quark is the pair ds,bb. In some way, the breaking of electroweak symmetry puts mass into this ds but it does not put mass to cc nor dd.

Thanks for your attention.

 

[MTd2]

Of these, six plus six do the partners of Dirac up quarks:

dd,ds,db,ss,sb,bb,dd,ds,db,ss,sb,bb​

six plus six do the partners of Dirac down quarks:

du,dc,su,sc,bu,bc,du,dc,su,sc,bu,bc​

So, the partners for the up quark are the dual combinations among d,s,b and its antiparticles
The partners for the down quark are the dual combinations of d,s,b with u,c and its antiparticles.

So, the difference between the partners of up and down, it is that the up is more internal and the down is more external.

Is that it?

 

[arivero]

I have no idea what "external" and "internal" mean. Technically, we are decomposing SU(5) flavour in SU(3) "downflavour" and SU(2) "upflavour". Standard group theory tell us that
5x5=15+10
and that
15= (6,1) + (3,2) + (1,3).

The up partners are in the 6,1: sextet of SU(3) but singlet of SU(2)
The down partners are in 3,2. You can call it "external" but it is just representation theory.

What is important is that inside a SU(3) sextet you can represent a SU(2) triplet, this is the point of #132.

 

[MTd2]

Internal, means you are just dealing with (d,s,b), external means that you are opertating out of this set, to the remaining quarks (u,c).

Oh, why up in SU(3) and down in SU(2)? This is getting confusing, since when you say up and down quarks, I imagine that they don`t have anything special between them. So, what about the companions of the 3 other quarks?

 

[arivero]

Hmm, sorry, I was not willing to add more confusion, I was just pointing out that there is a standard way to name this decomposition of SU(5) into SU(3) and SU(2). SU(5)_flavour is the group that allows to exchange any of the five quarks. SU(3)_"downflavour" is the subgroup that allows to exchange all the s,b,d quarks, and SU(2)_"upflavour" is the group that allows to exchange the u,d quarks. It is pretty obvious notation, but if you are unfamiliar with group theory, just dispose of it.

In this notation, the partners of the dirac UP FAMILIES are named (6,1), and the partners of the diract DOWN FAMILIES are named (3,2). Note that the (6,1) are UP families, but done from pairs of dsb only, so your external and internal labeling is creating confusion too. It does not seem a good notation.

C'mon, this part is VERY elementary. Look at the electric charge of each quark, and add them. They are Dirac quarks, so chiral charges are not in play.

 

[MTd2]

The problem is not really group theory. The only way I am use of thinking of quarks going to other quarks is the CKM matrix. And when I am thinking about SU(3), it about the charges of the gauge theory, for any quark, not as something that labels different kinds of quarks

So, how to distinguish SU(3) for colors from the ones that generates fermions? Are the charges of the SU(3)XSU(2) mapped into the fermions?

 

[arivero]

Amazing. Your are not used to the flavour global symmetries?! Ok, that is a problem. We used to put subindexes to the SUx(N) thing in order to avoid the kind of confusions you have. In any case, forget about group theory.

It is very elementary:
-(-1/3-1/3)= +2/3
-(+2/3-1/3)=-1/3

I expect that at least you have noticed this point! Can you confirm that you noticed it from the start!?

 

[MTd2]

Yes, I noticed.

But the flavour global symmetries will not work here since it broken by the lack of topness.

 

[arivero]

I don't understand your goal. For me, as I have shown, they work perfectly. So you must have a different goal. Mine was just to show that the superpartners have an SU(5) symmetry, and that it is unique.

 

[MTd2]

My goal is just to understand you Seriously.

 

[MTd2]

I really wish to understand. It is interesting, something there caught my attention.

 

[arivero]

But where is the problem? Try to be longer when writting your objections, or try to go again across al my posts then. Perhaps the problem is that you kept trying to guess what I am aiming too, while I am simply pointing out a fact of the Standard Model, and keeping agnostic abut the interpretation of this fact.

So the question is, your problem is about the facts or about its interpretation?

 

[MTd2]

The problem is with both of them. What is the objective in getting scalar duals if they are not related to gauge fields?

In my mind, the patter I was seeing was that instead of supersymmetry in terms of bosons/fermions you were getting a super charge symmetry between "fermionic charges" u,d,s,c,b (like preons combining) and "bosonic charges", red,green,blue, "white"(the null color charge of the leptons),Y. I guess this is just wishful thinking, then.

 

[arivero]

I see. On one side, you kept suspecting that there is more structure involved. I suspect it too, and more now that we have involved the scalars in the gauge supermultiplets, as this is an extra condition ovedetermining the equations.

On other side, it seems you keep trying to close everything only about the udscb. This is reasonable, because our principle was that given that the yukawa coupling of these five quarks is mass-protected, we should find a symmetry between them, justifying this mass protection. But it doesn't work.

What we have found, and that is the surprising fact, is that flavour on these five quarks in fact builds again, not the original five, but all [the partners of] the six quarks, the leptons, and really all the bosons you should expect in susy. So perhaps we have failed in our try of mass protecting "universidad de california, santa barbara", but we have found a strange beast.

 

[arivero]

I suspect it too, and more now that we have involved the scalars in the gauge supermultiplets, as this is an extra condition overdetermining the equations.

Let me clarify this statement with a minimum of group theory. Giving g generations with r+s massless (or light, or mass-protected) quarks, of those r are of type up and s are of type down, we ask:

2 g = s s(+1) / 2 matching of ups
2 g = 2 r s matching of downs

and we have two extra
4 g = (r+s)(r+s+1)/2 (matching of all the leptons wit all the "pions")
3 = r (r+1) /2 chiral matching of the W and Z scalar partners.

So we have four independent equations and only three unknowns. The last one is the one we have discovered during this thread.

 

[MTd2]

What we have found, and that is the surprising fact, is that flavour on these five quarks in fact builds again, not the original five, but all [the partners of] the six quarks, the leptons, and really all the bosons you should expect in susy.

But this what I was talking about! These guys seem to be "fermionic charges", something like preons, that build fermions and they do not seem to be like partners at all. There is supersymmetry, but it is in the equivalence of the 5 "charges" used to build the fermions and the 5 charges carried by forces (bosons).

 

[arivero]

But this what I was talking about! These guys seem to be "fermionic charges", something like preons, that build fermions and they do not seem to be like partners at all. There is supersymmetry, but it is in the equivalence of the 5 "charges" used to build the fermions and the 5 charges carried by forces (bosons).

There is a "relationship" between the need of 5 "preon charges" and the standard model bosons. But it does not coincide neither in charge nor in dof, so I am pretty sure it is a more complicated relationship, not just supersimetry. On the other hand, the composites of these "ucsdb" happen to be exactly the same number AND CHARGES that the SM.

As I see, you don't have any problem understanding what I say, you have problems interpreting it. So I have, of course so I think we can call an stop here, until new ideas come.

 

[inflector]

NOTE: I should preface all this with the caveat that I know enough only to be dangerous in discussions such as these and may have very big errors and holes in my understanding.

Addressing the original line of this thread as a newcomer to physics who does not understand the trees but has a pretty decent view of the forest—I think, only time will tell—I see two potentially interesting principles hinted at that might contribute to further progress:

1) The fundamental incompatibilities between the continuous and the discrete seems to me may be an artifact of our success hill-climbing two local peaks, neither of which represents the ultimate truth, but each of which when measured independently gives us greater insight into the mechanisms of our world than prior heights did. So I think we may have climbed as far as we can on these two peaks. This is just an impression, an intuition.

The attempts to resolve this problem also seem to me to be attempts to connect these two distant peaks directly, an attempt which bypasses the summit itself and only leads one down the ravine between the two peaks.

This is clearly a hard problem. The hardest one in physics, I believe.

This leads to the potential principle that perhaps the solution lies in a different reality, not in the EITHER OR of "discrete OR continuous" but in the AND of "discrete AND continuous" at all scales. Perhaps the apparent non-locality of QM is simply a manifestation of the continuous nature of reality at the quantum level which is not apparent at this point? Perhaps the problems with GR and cosmic-scale gravity and/or missing mass is really due to some cosmic-scale discrete effects which we don't understand at this point?

2) The holographic principle can serve as a guide to a broader principle, it seems to me, so when I see tom's comment:

Holography today is - in my opinion - like scratching at the surface hiding a fundamental principle still to be fully understood; like Mach's principle was a guideline for Einstein which did not made to a fundamental principle in GR (... he must so to speak throw away the ladder, after he has climbed up on it ...); nevertheless holography is certainly some aspect of reality b/c it shows up in so different approaches so that it's hard to deny that there is something fundamental behind it.

...

So for me holography is a concept or a guideline pointing towards a fundamental principle, whereas gravitons are a rather limit calculational tool valid only in a rather limited regime.

I can't help but agree completely. I have one idea for how this principle might be expanded to broaden the scope of potential solutions to quantum gravity issues:

In particular, the holographic principle is a mapping from a higher-dimensional representation to a lower dimensional surface, the volume of a space to its boundary, the event horizon of a black hole with the informational content of the interior, etc. It seems like physics sees this mapping in one direction only. A mapping in the other direction seems just as valid and might be more fruitful.

For instance, one could also see our perceived 3+1 dimensional world as a holographic image of a higher dimensional reality, 4+1 perhaps. Or perhaps a slice of that higher-dimensional reality. So the holographic principle maybe leads us to a broader principle that tells us to stop thinking in terms of our current dimensions, and broaden our minds a bit. Perhaps thinking of time as the 4th dimension was a great mathematical simplification but a conceptual roadblock. Perhaps the 4th spatial dimension, if it exists, is not compact or rolled up but expansive and we ourselves live in a kind of moving holographic reduction of that higher dimensional reality.