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

[Careful]

So really, should we expect to get the right foundational theory by ignoring this key aspect of QM? Is it really a trivial fact about the universe that all of its parameters are physically observable?

I hope you are not implying here that every variable/parameter should have a direct operational meaning, because then I sharply disagree. For the rest, your text is beautifully written.

It is a part of the problem. But I wouldn't say we have to solve it right away, but merely that we should invent preliminary structures allowing for a genuine solution to this issue. And QM as it stands is much too simple for this.

Actually, if you think about it, you will see that the ultimate theory has to be self-dual in a sense that the equations should be defined in terms of the equations. That's precisely the kind of thing which lead to Russel's paradox. It implies we have to move beyond classical logic (denying the axiom of restricted comprehension in traditional Zermelo Freankel, which was added precisely to avoid Russel's paradox). Such extensions of logic are done by Sorkin, Isham (Topos theory) and in general in category theory. But as I said, this problem is too difficult to tackle directly, there are other pressing, more mundaine issues.

Careful

 

[Haelfix]

These are just some superficial problems, they are not the real issues. But even, if you admit these issues cannot be adressed within current framework, doesn't this logically imply that you will have new physics. You will have to give up at least one cherished assumption before you can proceed.

It is pretty clear that nature cannot just be the standard model + Einstein gravity and nothing else. Even if you assume asymptotic safety is correct, something else has to resolve the laundry list of problems (mathematical, physical and experimental) with beyond the standard model physics.

Dark matter, the hierarchy problem, the strong CP problem, matter/antimatter asymmetry, all the standard model 'why' questions (chief amongst them, why is it so arbitrary and adhoc), cosmology and structure formation issues...

And then we get into pure gravity problems perse, including the information loss paradox, the positive cosmological constant problem, the exact nature of inflation, as well as the annoying landscape issues.

New physics will have to enter the picture at some scale and in some manner.

 

[Careful]

It is pretty clear that nature cannot just be the standard model + Einstein gravity and nothing else. Even if you assume asymptotic safety is correct, something else has to resolve the laundry list of problems (mathematical, physical and experimental) with beyond the standard model physics.

Dark matter, the hierarchy problem, the strong CP problem, matter/antimatter asymmetry, all the standard model 'why' questions (chief amongst them, why is it so arbitrary and adhoc), cosmology and structure formation issues...

And then we get into pure gravity problems perse, including the information loss paradox, the positive cosmological constant problem, the exact nature of inflation, as well as the annoying landscape issues.

New physics will have to enter the picture at some scale and in some manner.

This is already a more extensive laundry list. But the question now is, in which logical order are you going to place these issues? Is even one of them a pressing issue or can they all be derived from something which is beyond imagination (in either 99,999%) of most people currently?

Especially, the strong CP problem, the CC problem and even the value of the fine structure constant are ''existential'' issues in some sense.

I don't know if the landscape is a problem, I think I have a logical way out of it, but I have no idea how to make the idea quantitative so far.

Careful

 

[qsa]

This is already a more extensive laundry list. But the question now is, in which logical order are you going to place these issues? Is even one of them a pressing issue or can they all be derived from something which is beyond imagination (in either 99,999%) of most people currently?

Especially, the strong CP problem, the CC problem and even the value of the fine structure constant are ''existential'' issues in some sense.

I don't know if the landscape is a problem, I think I have a logical way out of it, but I have no idea how to make the idea quantitative so far.

Careful

Unify EM plus gravity in a natural way and all the puzzle pieces will start fitting perfectly, that is all what is needed.

 

[Careful]

Unify EM plus gravity in a natural way and all the puzzle pieces will start fitting perfectly, that is all what is needed.

You were joking right ?

 

[arivero]

Other favorite idea of me is "Dual quark-gluon model of hadrons", by J.H. Schwarz, Phys.Lett.B37:315-319,1971. There he proposes to consider supersymmetry between quarks and the QCD string, instead of a whole set of new particles.

I don't know about this one, but how do the degrees of freedom match? You have 12 quarks (anti-quarks included), normally you have 8 gluons, so you have 4 degrees of freedom too much. What kind of new physics do these guys give?

It seems that the idea was abandoned next year, in favour of fundamental supersymmetry. I asked the author but he does not remember the specific arguments against; probably it was something in the line you mention. But I think this idea was the right one. The d.o.f match if you consider "terminated gluons", ie the string with two quarks attached at the end, and the same symmetrization strategy that the pion, only that in this case each pair of quarks + gluon can appear in the three colours of the SU(3) triplet, instead of the singlet of the pion.

Regretly, in 1971 only 3 quarks were known (and a 4th conjectured) and all of them were light. For this combination, the d.o.f do not match: you get (modulo colour) two anti-down "boson d.o.f." from ud and us, and three anti-up from ds, dd, ss. Plus the same with the antiparticles. So with three quarks you can only build fully one down and one up, and some degrees must be discarded even having the same charges that the ones you are pairing to. But I like to think that, with foresight, superstring theory actually had the opportunity to predict five light quarks and one massive.

 

[qsa]

You were joking right ?

No need to go hysterical on me. Just tell me your objection in as clear manner as you can, save the sarcasm.

 

[Careful]

It seems that the idea was abandoned next year, in favour of fundamental supersymmetry. I asked the author but he does not remember the specific arguments against; probably it was something in the line you mention. But I think this idea was the right one. The d.o.f match if you consider "terminated gluons", ie the string with two quarks attached at the end, and the same symmetrization strategy that the pion, only that in this case each pair of quarks + gluon can appear in the three colours of the SU(3) triplet, instead of the singlet of the pion.

Let me see if I understand what you say: (a) the gluons have to be (electric) charge neutral
(b) they have to be Lorentz vectors, so particles couple to antiparticles (c) They have to be permutation invariant if you permute over the generations (d) the strings are not oriented (so only the combination counts).

Ok, so you can subdivide the quarks in two families : (u,c,t) and (d,s,b) each of them can be considered separately.
Right, let us look at the permutation group S_3 now, we have to look for the subclasses L of permutations such that BLB = L for all B in S_3. This gives rise to two combinations
uu* + cc* + tt* , uc* + ct* + tu* + cu* + tc* + ut* for the symmetric ones,
uc* - cu* + ct* - t*c + tu* - ut* for the totally antisymmetric one and then there still is one mixed Young tableau, which gives 4 in total. 4 times 2 is eight indeed. Was this the idea? But then, what is the dynamics of the string?

Question : will you not get in trouble here with Lorentz invariance (unless you have a different quantization scheme than Fock space).

Regretly, in 1971 only 3 quarks were known (and a 4th conjectured) and all of them were light. For this combination, the d.o.f do not match: you get (modulo colour) two anti-down "boson d.o.f." from ud and us, and three anti-up from ds, dd, ss. Plus the same with the antiparticles. So with three quarks you can only build fully one down and one up, and some degrees must be discarded even having the same charges that the ones you are pairing to. But I like to think that, with foresight, superstring theory actually had the opportunity to predict five light quarks and one massive.

I will have to think about this, no time now.

Careful

 

[Careful]

No need to go hysterical on me. Just tell me your objection in as clear manner as you can, save the sarcasm.

If you were not joking, then I am not even going to try. The gaps in what you tell are too wide to be filled in one full evening and I don't have the necessary time, sorry.

Careful

 

[humanino]

No need to go hysterical on me. Just tell me your objection in as clear manner as you can, save the sarcasm.

"careful" claims that he would loose his time on you. My advice : I stopped loosing my time on him.

 

[arivero]

No, the idea is a bit [STRIKE]more complicated[/STRIKE] simpler because the gluon is electrically neutral, but the quarks are not. So we must associate terminated strings [up----down] to built the "antidown scalarfermions", and terminations [down----down] to the "antiup sfermions". The symmetrization acts in SU(3) colour to produce the colour triplet from 3x3=6+3 as usual, and then in flavour space with five light quarks we take the 15 of 5x5=15+10. This actually contains as a subgroup the 6 of the combination (d,s,b) as we could expect, and it contains the up---down pairs too. You were building the octet of 3x3, which is relevant for neutral leptons only, not for quarks.

But I am stating just the symmetrization of the final result. More verbosely, let me to show again in, with this setup, how "superstring" (dual quark/gluon) theory "predicts" the number of generations. Let n "down" and m "up" quarks to produce p "down" and q up quarks, and let's ask this production to be exact, not having "half spinors" or, worse, single bosons. Then we have two Diophantine equations.

For down quarks, 2 p = n*m while
For up quarks, 2 q = n*(n+1)/2

In 1971, as said above, n=2 (down and strange) and m=1 (the up), so p=1 and q=1.5, and the attempt is doomed to fail: because p<n and because q is not integer.

Note that the second equation tells us that either n or n+1 must be a multiple of 4. If n+1 is multiple of 4, the first equation only works has solutions for even m.

So, here you can see the table of first p,q pairs for each n,m:

p,q    3     4      7       8   ...
1     --   2,5     --     4,18   ...
2    3,3   4,5    7,14    8,18   ...
3     --   6,5     --    12,18   ...
4    6,3   8,5   14,14   16,18   ...
5     --  10,5     --    20,18   ...
6    9,3  12,5   21,14   24,18   33,33    ...
...

And two observations follow:
- the case m=1 actually implies p<n, so that the number of "down" type quarks we can produce in this case is less than the input we started from.
- the simplest case is p=q=3 from n=3,m=2. This is the standard model quark content.

 

[Careful]

"careful" claims that he would loose his time on you. My advice : I stopped loosing my time on him.

The feelings are entirely mutual At last a sociological issue we agree upon. But if you feel like having the time to explain to qsa why his claim is ''not so well considered'' to use a euphemism, be my guest.

Careful

 

[Haelfix]

This is already a more extensive laundry list. But the question now is, in which logical order are you going to place these issues? Is even one of them a pressing issue or can they all be derived from something which is beyond imagination (in either 99,999%) of most people currently?

Obviously I am biased, since it has to do with my own speciality, but I would say dark matter is the most obvious 'pressing' issue, since it is by now pretty airtight experimentally and in clear conflict with the standard story. Further, you can run 'what else can it be' arguments at length and pretty much arive at the conclusion that it must be either something highly exotic, or basically just another particle.

If the latter, on dimensional grounds, in order to have evaded detection such an object either has to be very light or basically in the nearby energy range that the LHC is going to probe.

In any event, it is almost certainly guarenteed to be an extension of the standard model.

 

[arivero]

(b) they have to be Lorentz vectors, so particles couple to antiparticles

I think I see the problem, but I think that the issue is solved by the gluon itself, which provides some indexes to couple to the quarks where it "terminates", so the whole object should be a Lorentz scalar, shouldn't it? Or should actually this way drive us to the topic of the anomalies of the quantum string and the infamous D=10 prediction?

 

[Careful]

No, the idea is a bit [STRIKE]more complicated[/STRIKE] simpler because the gluon is electrically neutral, but the quarks are not.

Everything I wrote down is electrically neutral.

So we must associate terminated strings [up----down] to built the "antidown scalarfermions", and terminations [down----down] to the "antiup sfermions".

None of those are electrically neutral so they cannot gluons, You said the point was to construct gluons from quarks attached to a string and now you are constructing something else.

The symmetrization acts in SU(3) colour to produce the colour triplet from 3x3=6+3 as usual, and then in flavour space with five light quarks we take the 15 of 5x5=15+10.

I didn't think about these issues, but which ones are the five light quarks? I know the top quark is 40 times heavier than the bottom quark, but 40 is still a small number. And flavour is supposed to be just a quantum number, so I don't know what flavour space is supposed to mean.

You were building the octet of 3x3, which is relevant for neutral leptons only, not for quarks.

I can build whatever I want to, if you claim to have an alternative theory for the gluons then you will have to explain why the very legitimate representation I constructed is not allowed. Building a theory does not only consist into playing with representations.

So, I constructed 8 bosonic particles from quarks, nothing you wrote suggests you do the same. You seem to introduce moreover some new continuous group SU(5) (?) without any motivation where it comes from (SU(3) has no 5 dimensional representation).

Careful

 

[Careful]

I think I see the problem, but I think that the issue is solved by the gluon itself

I thought gauge particles were supposed to be Lorentz vectors. Normally you need the gamma matrices for that if you write them as composite particles.

 

[Careful]

Obviously I am biased, since it has to do with my own speciality, but I would say dark matter is the most obvious 'pressing' issue, since it is by now pretty airtight experimentally and in clear conflict with the standard story. Further, you can run 'what else can it be' arguments at length and pretty much arive at the conclusion that it must be either something highly exotic, or basically just another particle.

I think a relativistic MOND theory is by far the most reasonable explanation for dark matter. It doesn't require any exotic new physics, just a non-local deformation of gravity.

Careful

 

[Careful]

The symmetrization acts in SU(3) colour to produce

Also this I do not get, if you would have a mechanism to build gluons from quarks then of course you just cannot assume the quarks carry an SU(3) index to start with. That's basically what you would like to derive no?

 

[arivero]

None of those are electrically neutral so they cannot gluons, You said the point was to construct gluons from quarks attached to a string and now you are constructing something else.

Ah, I see now the confusion! Big one, my fault. My point was the reversal: to consider gluons as equal to the the QCD string, and attach quarks to them in order to build the susy scalars (and thus match to the d.o.f of quarks).

Indeed your construction is the right one to build 8 gluons from 3 quarks, and I keep thinking about if it has a meaning too, beyond the usual of representation theory. In my construction, symmetrization wipes the d.o.f. of gluons from 8 to 3, in your construction the pairs allow to go from 3 to 8. This is the expected working of SU(3), juggling between adjoint and fundamental representations, of course.

I didn't think about these issues, but which ones are the five light quarks? I know the top quark is 40 times heavier than the bottom quark, but 40 is still a small number.

From the mechanism I sketched, a "light" quark is a quark that you can attach at the end of the string. Somehow, Nature gets to incorporate this "ban to attachment" in the top quark, it decays faster than the theoretical half-life of a possible 'toponium' meson. From naturalness principle, these five quarks should have a hidden symmetry protecting them when, at electroweak symmetry breaking, the top gets its mass. We don't know what this symmetry is, as far as I have read.

I can build whatever I want to, if you claim to have an alternative theory for the gluons then you will have to explain why the very legitimate representation I constructed is not allowed.

But it is! When your construction is applied to SU(3) colour, it produces the colour octet. When it is applied to (u,d,s), it produces the famous flavour octet of GellMann. And when applied to families, as you did, it seems to produce again the same content that gluons, and then one is left wondering if there is a relationship between SU(3) family and SU(3) colour. I think this path was pursued in the literature in the late seventies.

So, I constructed 8 bosonic particles from quarks, nothing you wrote suggests you do the same.

What I build was different: I built 18 (=3x(3x2)) particles of charge +2/3, 18 of charge -2/3, 18 of charge -1/3 and 18 of charge +1/3 by putting quarks at the extremes of the QCD string. Again, sorry the confusion.

You seem to introduce moreover some new continuous group SU(5) (?) without any motivation where it comes from (SU(3) has no 5 dimensional representation).

Yes, I did it to illustrate the symmetrization, I called it flavour space instead of naming explicitly as SU(5). I though that it followed from my remark on five light quarks, in the typical way that flavour symmetry is always described. The only difference is that usually the SU(3) flavour inside of SU(5) flavour is built only from mass, they take the u,d,s out of the u,d,s,c,b set. I consider all the five quarks equally massless, and I try to commute with electrical charge, so I take d,s,b in my illustration.

In fact, I feel that to use SU(5) in this way is correct because besides finding six +2/3 and six -1/3 in the 15 of 5x5, you can notice that the 24 in 5x5=24+1 happens to contain 6 states of charge +1, 6 of charge -1, and 12 neutrals. That is three generations of sleptons.

 

[arivero]

Also this I do not get, if you would have a mechanism to build gluons from quarks then of course you just cannot assume the quarks carry an SU(3) index to start with. That's basically what you would like to derive no?

We misunderstood ourselves completely My point (and our common point) was that the original try was to claim that the the gluon was the superpartner of the quark, and it fails obviously. The gluon is a boson, so I noticed that by adding to the gluon a pair of quarks the statistics does not change, it is very like the Chan-Paton idea, and the resultant system has the multiplicities of three families of squarks. The mechanism you understood instead also allows to reproduce the gluons, via the mysterious colour/flavour diagonal of the late seventies, but I feel that it hides the supersymmetric aspect of the original theory.

 

[qsa]

"careful" claims that he would loose his time on you. My advice : I stopped loosing my time on him.

I have been in the management for 20 years, and I have seen all kinds. Hired and fired many, but only on the merits of their work, never their personality, since mine is not perfect either. I am here on PF to learn and I have learned much more than I hoped for. I will listen to ALL, and put up with some nuisances, that is just normal in business and life.

 

[Careful]

I have been in the management for 20 years, and I have seen all kinds. Hired and fired many, but only on the merits of their work, never their personality, since mine is not perfect either. I am here on PF to learn and I have learned much more than I hoped for. I will listen to ALL, and put up with some nuisances, that is just normal in business and life.

Since you have been in management and I know how difficult job managers have (it requires a kind of intelligence I don't possess), let me explain a bit why unifying gravitation and electromagnetism is far from sufficient. First of all, you would not have a quantum theory to start with, second since 1940 people discovered the weak and strong interactions; Einstein was completely unaware of that. I don't know what your level of technical expertise is, but there are a few good introductory papers which explain in a pretty basic way what kind of difficulties you can expect trying to wed GR and QM. Let me give a few in increasing order of technical difficulty:
http://www.phy.syr.edu/~sorkin/some.papers/82.forks.pdf
http://arxiv.org/PS_cache/gr-qc/pdf/9210/9210011v1.pdf
http://arxiv.org/PS_cache/gr-qc/pdf/0602/0602013v2.pdf
This should do, especially the second one is a deeply written survey paper.

Careful

 

[Careful]

Ah, I see now the confusion! Big one, my fault.

I will respond to you tomorrow, have work to do now.

Careful

 

[MTd2]

Arivero, I am confused by what your trying to accomplish. According to papers I could find, quark-diquark supersymmetry help in simplifying scattering calculations because it supposes that baryons on strong couple can be well approximated by a quark bound to a super symmetric parter. While the possible verification of this kind of approximation is extremely important to the study of nuclear forces, I don`t see how could that be relevant to fundamental issues that could have the label "beyond the standard model".

 

[qsa]

Since you have been in management and I know how difficult job managers have (it requires a kind of intelligence I don't possess), let me explain a bit why unifying gravitation and electromagnetism is far from sufficient. First of all, you would not have a quantum theory to start with, second since 1940 people discovered the weak and strong interactions; Einstein was completely unaware of that. I don't know what your level of technical expertise is, but there are a few good introductory papers which explain in a pretty basic way what kind of difficulties you can expect trying to wed GR and QM. Let me give a few in increasing order of technical difficulty:
http://www.phy.syr.edu/~sorkin/some.papers/82.forks.pdf
http://arxiv.org/PS_cache/gr-qc/pdf/9210/9210011v1.pdf
http://arxiv.org/PS_cache/gr-qc/pdf/0602/0602013v2.pdf
This should do, especially the second one is a deeply written survey paper.

Careful

Thank for the reply, I had a feeling that it was just some misunderstanding. I don't know about the other people on pf, but I think we see the forum as a place to learn. probably more regulars here are not really hard core physicists, but we are here to know ( and sometime fantasize about discovering) what reality is all about. So for lot of us it is not a matter of "my idea is better than yours", but I think more like "my idea is worth thinking about-could you agree -". People like tom have been instrumental in giving an overall picture for the many uninitiated, tom himself is an engineer just like me. I had to practice management and I hated it, people can be difficult, you know; I had rather be a geek.

Anyway, I think my bad wording has caused mostly the misunderstanding(twice), not to mention you jumping the gun in the heated battle. I know the unification( classical) EM with gravity has been a loosing battle (Einstein -non-symmetric) , although to this day some people are still trying. but I meant more like QED side of EM, I just used EM as generic. Of course, I don't usually shoot off my mouth without having something important to say, not my nature. Yes, I am very familiar with the problems of unifying QM and GR. My level of technical expertise is not that great I admit, but I have learned to be a good problem solver with minimum information that time and circumstances allow. I have to go now( very late at night), but you will get what I mean in the next few days in black and white.

 

[tom.stoer]

Somehow I lost track.

Did we manage to identify some new principles or indications what they could be?

I guess the last papers Careful mentioned should provide some guideline; especially Sorkin is far from mainstream and could perhaps have some reasonable ideas - besides his causal sets.

My problem is that most answers seem to be in the nagative; there are indications how things will NOT work (or only to a certain approximation). But I am afraid that we here cannot be smarter than excellent thinkers out there ...

 

[arivero]

Arivero, I am confused by what your trying to accomplish. According to papers I could find, quark-diquark supersymmetry help in simplifying scattering calculations because it supposes that baryons on strong couple can be well approximated by a quark bound to a super symmetric parter. While the possible verification of this kind of approximation is extremely important to the study of nuclear forces, I don`t see how could that be relevant to fundamental issues that could have the label "beyond the standard model".

The real point in the literature are not the quark-diquark models, but the so called "dual pion quark" and "dual gluon quark" models, and similarly named schemes, that appeared during 1971-1973 after the paper of Ramond on the spin 1/2 version of the "dual model". Eventually these models dissappeared, being substituted either by fully fundamental strings (going to the actual impasse) or by simple, non fundamental at all, calculational tools as you say. BTW, these attemps actually started with work of Utiyama, predating the string discovery of susy.

What I am trying to accomplish? Well, I think was trying to address two small problems, one one side the fact that some mass relationships seem to be related to composite models, while the quarks and leptons have no structure, and in other side the fact that there are coincidences between mass scales of very different origin, the "QCD" masses and the "yukawa-electroweak" masses. There is no fundamental reason for QCD to produce masses in the same "mountain ranges" that the electroweak+yukawa. This is a kind of "fine tunning" not explained in GUT models.

What I show? That the first hunch, when supplemented with quark flavours, was better that the fully fundamental way. And that actually it predicts the generation structure of the standard model, not only the number of generations, but also the number of "massless" quarks.

Of course, but this is unimportant, my discovery process was in the reverse way, upstream. First I wondered about the mass of the muon... Why is it so near of the pion mass? If it were for SUSY, we should have the same number of fermion that bosons, hmm, let's count... three spin 1/2 negative leptons... and six different ways of making negative mesons! Shock. Then I asked, but what about quarks, and again, for +2/3 and for -1/3 the degrees of freedom match. Shocking thing. Then for neutrinos you get naively 1 degree of freedom more, telling that you mast to do SU(5) instead of U(5). Then I checked uniqueness, as described above, and yep the 3 generations is the simplest model, and it becomes unique in fact if you incorporate the requisity of building neutrinos from neutrals in SU(n+m). Only at this level I checked the literature must deeply and I found that these kind of models were the first ones in the mind of the string people, but at that time they only know 3 quarks, so even if they had got to predict the generations, it had been discarded as far-fetched.

I will respond to you tomorrow, have work to do now.

Careful

Thanks, I appreciate your interaction :-)

 

[arivero]

Did we manage to identify some new principes or indications what they could be?

I think yes. We are doing heavy use of the (′t Hooft) naturalness principle, that anything which is not massive is massless at tree level.

 

[Fra]

The causaly set ideas, at least partially clearly tangent to the direction I mentioned with inference, ordering and counting. It was some time since I look into that, can someone point towards say a current review of the state of this research program?

What I particularly found missing the last time, is the evolution (or expected dynamics) of the causal sets themselves, and how to connect matter to the causal set program. It's not hard to associate to possible ideas, but what are the concrete proposal so far from this program to these questions?

I fully share the idea that one way or the other "ordering" and "counting" are two two deep key points, that I doubt can under overstated at this point.

Anyone knows of a current revivew of the causet program?

/Fredrik

 

[arivero]

Fra, the point is that while causal set ideas seem relevant to the question of foundations of quantum mechanics, it is hard to see how they can produce the SM, not to say something BSM (and including the SM). If they can, it will be probably connected to operator theory, C* algebra approach to geometry and, at the end, Connes' theory, but I'd expect 50-75 years time of development. And it surprises me its use for gravity "a la Sorkin", but ok, they could be suitable there.

Now, when I was younger I thought that the number of generations could have a direct connection to quantization procedures. While I do not pursue more this idea, it could be a way to connect foundational arguments with actual particles.

In the last century, I read an enjoyed this one: http://jmp.aip.org/resource/1/jmapaq/v5/i4/p490_s1?isAuthorized=no