Maybe there is no grand unified theory?

[lpetrich]

It isn't as magical as it might seem when one considers the Lagrangian:

L = R/(16*pi*G_N) + L(nongravitational)

The first term is the Einstein-Hilbert term.

Doing a variation by the metric gives Einstein's field equation G = 8*pi*G_N*T.


That aside, there isn't much that suggests a connection between gravity and everything else that's known, no readily-apparent pattern that the graviton fits into alongside some other elementary particles.

 

[friend]

That aside, there isn't much that suggests a connection between gravity and everything else that's known, no readily-apparent pattern that the graviton fits into alongside some other elementary particles.

Quantum theory seems to be derived from fields defined on spacetime, using derivatives of functions with respect to time and space presupposed to exist. There is already assumed a metric in spacetime that enables the ability to take derivatives wrt space and time. And it is possible to do QFT on curved spacetime by assuming in advance the metric of that curved spacetime. How then can the metric be part of the quantum formulation when the mathematics of QT requires a metric to start with in order to do the quantum differential equations? How can you solve for something that you presuppose? Can QT be formulated in a background independent way? What reasoning even suggests that this is possible?

 

[marcus]

...How then can the metric be part of the quantum formulation when the mathematics of QT requires a metric to start with in order to do the quantum differential equations? How can you solve for something that you presuppose? Can QT be formulated in a background independent way? What reasoning even suggests that this is possible?

A stronger version of your argument was already given in 2006 by Rovelli. See post #140 here:
https://www.physicsforums.com/showthread.php?p=4202874#post4202874

All your argument says is that a background independent QT (including gravity) is not likely to involve a spacetime METRIC. But the broader argument goes further and says such a theory is unlikely to involve a 4D differential manifold. The successful math model is not likely to be a spacetime continuum with matter fields defined on it.

But to have a unified quantum theory of gravity/geometry and matter one does not need that old-fashioned framework.

The approaches that people have been working on in recent years, towards a unified theory, do not involve that mathematical way of depicting the world---so your argument is not relevant to them.

==quote==
Can QT be formulated in a background independent way?
==endquote==
All the indications are to the effect that YES, it can. Rovelli's argument (and your weaker one) merely indicates the answer is not likely to involve depicting the world as a 4D differential manifold--a model invented by Riemann around 1850. Newer ways of modeling exist. E.g. see post #140 for one.
==quote==
What reasoning even suggests that this is possible?
==endquote==
The correct question is rather: What reasoning suggests it is NOT possible? You have not given any, nor has anyone else that I'm aware of.

It's an interesting research community to watch. Currently I see activity in the area of spin foams, group field theories (GFT), and star algebras. All these provide an alternative to picturing the world in the older form of a 4D spacetime continuum with fields defined on it.

 

[friend]

All your argument says is that a background independent QT (including gravity) is not likely to involve a spacetime METRIC.

That's difficult to imagine when one of the observables being derived is position.

But the broader argument goes further and says such a theory is unlikely to involve a 4D differential manifold. The successful math model is not likely to be a spacetime continuum with matter fields defined on it.

It's difficult to imagine QT without "waves", and it's difficult to imagine waves without respect to a background spacetime. Aren't particles defined as waves in QFT? Aren't waves defined as changes of some field with respect to space and time?

But to have a unified quantum theory of gravity/geometry and matter one does not need that old-fashioned framework.

The approaches that people have been working on in recent years, towards a unified theory, do not involve that mathematical way of depicting the world---so your argument is not relevant to them.

String theory is not background independent. And LQG does not account for matter. So I think the right way to go has not been determined yet.

==quote==
Can QT be formulated in a background independent way?
==endquote==
All the indications are to the effect that YES, it can. Rovelli's argument (and your weaker one) merely indicates the answer is not likely to involve depicting the world as a 4D differential manifold--a model invented by Riemann around 1850. Newer ways of modeling exist. E.g. see post #140 for one.
==quote==
What reasoning even suggests that this is possible?
==endquote==
The correct question is rather: What reasoning suggests it is NOT possible? You have not given any, nor has anyone else that I'm aware of.

It's an interesting research community to watch. Currently I see activity in the area of spin foams, group field theories (GFT), and star algebras. All these provide an alternative to picturing the world in the older form of a 4D spacetime continuum with fields defined on it.

It seems necessary that there be something physical that we are attempting to describe. And if there is any kind of distinction between physical things, then it seem natural to distinguish them with a different set of numbers, and we can call these numbers coordinates. It seems to me that the best we can start with is a collection of points. For if those points had any further structure, then we would break that structure down into points as well. That doesn't mean we know what the topology of those points are. That still remains to be calculated.

 

[lpetrich]

So space-time could originate from some other effect?


However, that does not address the question of what shared patterns there might be between gravity and other known particles/effects.

Shared patterns like:

• The Periodic Table of Elements.
• Atomic nuclei having masses that are approximate integer multiples of the proton's mass, even if they don't have enough electric charge for that.
• Approximate flavor symmetry of the light hadrons.
• My weak-hypercharge equation for Standard-Model particles.

 

[sshai45]

6) Nothing is gained by asking a question like you do which is essentially a speculation about human impotence: "What if our species is incapable of evolving an adequate conceptual quantitative language?" "What if we are so lame and weak we cannot do this?" What if what if what if.
That is the logical content of the question you are asking. It is about the future evolution of the human mind and it is uselessly defeatist, or so it seems to me.

To me, it doesn't seem that way. It seems they're asking a question about nature, not about what we are capable of knowing:

"I mean, couldn't it be that gravity (ie. spacetime geometry) and quantum effects are two completely separate and disconnected features of our universe? They are not related, they are independent of each other, they exist as completely separate phenomena, and there is no underlying common ground between them, and trying to search for a unified theory is a completely futile endeavor because there isn't one?"

In other words, he's asking "what if Nature simply is not unified, and we were wrong to assume it is?" If that were the case, then we could never find a (valid) unified theory, not because of a lack of capacity of our species, but rather because that simply wouldn't be how things are. Kind of like how we will never find a valid description of the Moon in terms of green cheese -- because the Moon simply is not made of green cheese. It would have nothing to do with "human impotence" or any other human-based failing.

 

[friend]

So space-time could originate from some other effect?


However, that does not address the question of what shared patterns there might be between gravity and other known particles/effects.

It's probably the case that the particles of QT and the spacetime GR are different aspects of some common formulation. The trick will be to reduce these constructions as much as possible and find out what is common to both.

 

[marcus]

"I mean, couldn't it be that gravity (ie. spacetime geometry) and quantum effects are two completely separate and disconnected features of our universe? They are not related, they are independent of each other,..?"
...

AFAICS no, it could not be that way. I thought this was already answered way back earlier in the thread. Nature obviously has a combined integrated treatment. Because matter is intimately connected with geometry. Matter bends geometry, and it knows to follow the shortest distance tracks.
If matter obeys quantum mechanics, so must geometry. They are like, in each other's pants, intimately and actively connected. Eventually we will most likely understand them as different aspects of the same mathematical model. I.e. essentially just different aspects of the same thing.

Your example of "color" and "shape" serves to illustrate the fundamental connectedness. they are human concepts (unrelated as human concepts) which correspond things closely connected down at molecular level (wavelengths, bonds). What we call color results from behavior (which wavelengths are absorbed and which reflected) related to the bonds and internal structure which also maintain shape. Nature does not distinguish these various aspects of matter interacting with light. She connects them. They arise from a common ground--and you make the disconnection in your head.

====
Besides there is already an "effective" unified theory---a effective quantum version GR---meaning good up to some energy cutoff, as a low energy approximation. When you have a quantum GR, a QG, you can put that together with matter QFT. Admittedly that doesn't prove anything---we still don't have a fundamental unified theory good all the way to Planck scale--but it sure is suggestive! You may be familiar with that. John Donoghue is someone who works on that.
http://arxiv.org/abs/1209.3511
====

There has been a lot of research activity recently, making what looks to me like real progress. In the direction of a fundamental unified theory of matter and geometry.
People who don't know much about it will tell you that the two approaches are "string and LQG" and they may have some naive stereotype idea of what these things are about, that they learned some years back. It may even not be clear what they are talking about.

If you actually watch the field you realize that the Loop community is not working on the stereotype idea of "LQG" that many people have---that was current, say, in 2005. The approaches I'm seeing in the recent papers have abbreviations like HSF, GFT (holonomy spin foam, group field theory) or they employ a so called C* algebra. I give some links to recent papers in the Reformulation thread. I'm following the star algebra approach with considerable interest. It seems to be a framework where you can put quantum matter and quantum geometry together with a general covariant quantum thermodynamics/statistical mechanics.

I think it's absurd to offer philosophical or logical "reasons" why what people are actively trying to do, and work that is going ahead is somehow "impossible".
It's a misconception that could possibly be based on STEREOTYPE thinking. Like: geometry has to be done with a metric on a manifold So therefore blahblahblah. But the main direction in QG research for over 10 years has been on doing geometry NOT with a metric and in some cases not even with a manifold. That is what spin networks, spin foams, lattice gauge methods, star algebra methods...are about. But in spite of the past 10 years you might still hear someone say that it is difficult for them to understand how anybody can do quantum geometry without a metric on a manifold.

 

[friend]

I think it's absurd to offer philosophical or logical "reasons" why what people are actively trying to do, and work that is going ahead is somehow "impossible".
It's a misconception that could possibly be based on STEREOTYPE thinking. Like: geometry has to be done with a metric on a manifold So therefore blahblahblah. But the main direction in QG research for over 10 years has been on doing geometry NOT with a metric and in some cases not even with a manifold. That is what spin networks, spin foams, lattice gauge methods, star algebra methods...are about. But in spite of the past 10 years you might still hear someone say that it is difficult for them to understand how anybody can do quantum geometry without a metric on a manifold.

I wonder what happens to diffeomorphism invariance wrt changes in frames of reference if there is no background manifold on which to put possible different coordinates/frames.

 

[lpetrich]

There are lots of loose ends, both in the Standard Model and elsewhere (The Reference Frame: Why the Standard Model isn't the whole story).

Standard Model
It has lots of free parameters.
Gauge: 3
EF masses (Higgs-coupling eigenvalues): 9
EF mixing angles (Higgs-coupling eigenvector parameters): 4
Higgs mass and self-coupling: 2
Strong CP-violation phase: 1
Total: 19

Neutrino masses
Parameters:
Masses: 3
Mixing angle: 4
Total: 7, giving 26

If they are produced by Higgs interactions, they would require teeny-tiny ones, much smaller than the electron, up, and down ones. That's led to the "seesaw model", where neutrinos get their masses from both Higgs interactions and something that gives right-handed neutrinos masses near GUT masses. That gives estimates of neutrino masses that are fairly close to their observed values.

Supersymmetry
No direct evidence, but a lot of theoretical attractiveness. The easiest supersymmetry partners for the LHC to distinguish are the squarks and gluinos, but LHC observations have pushed lower limits on their masses up to about a TeV.

The Minimal Supersymmetric Standard Model has about 100 free parameters in addition to the Standard-Model ones, but many of them can be set to zero with bounds on Flavor Changing Neutral Currents and hypotheses like flavor independence. One can get as few as 5, as in the Constrained MSSM (CMSSM).

Despite the lack of direct evidence, there is indirect evidence in the form of the Higgs mass. It is about what one would predict from the CMSSM and similar models.

Higgs instability
A problem with the Standard Model at very high energies. A Higgs parameter would reverse sign, making the Higgs particle unstable. Supersymmetry would keep it from happening.

Gauge unification
This is from extrapolating the gauge coupling constants upward in energy. They converge, and the SM and various extensions of it have various amounts of convergence. The best is with the MSSM, at energies around 10¹⁶ GeV, with only a few percent discrepancy:
Backreaction: Running Coupling Constants
[hep-ph/0012288] Beyond the Standard Model (In Search of Supersymmetry )
[1207.1435] Precision Unification in \lambda SUSY with a 125 GeV Higgs
SOFTSUSY Homepage – Hepforge: http://softsusy.hepforge.org/gaugeRun.eps (EPS), http://softsusy.hepforge.org/gaugeRunZoom.eps (EPS)

Some GUT's also predict mass unification of various particles at GUT energies, like for the bottom quark and the tau lepton.

Axion
This particle would suppress strong CP violation. Parameters:
Mass: 1
Interactions: 1 if universal, 3 if one for each SM gauge field

Proton decay
Isolated-proton decay, that is. Also includes decay of both protons and neutrons in nuclei. It has yet to be observed, but lifetime lower bounds approach what one would expect from MSSM gauge unification.

GUT nucleon decay has numerous possible channels, and observation of some of them can provide several constraints on GUT models.

Baryon asymmetry
Baryogenesis has 1 parameter, the baryon-to-photon or baryon-to-entropy ratio, around 10^-9, with no prospect of finding others. However, it is evidence of C and CP violation coupled with baryon-number violation.

It could have been generated at any time between GUT temperatures and electroweak symmetry-breaking temperatures, according to several theoretical models. Some predict GUT temperatures, some predict electroweak temperatures, and some predict somewhere in between.

Lepton asymmetry
Leptogenesis had contributed to the cosmic neutrino background, something that has yet to be detected. Ordinary neutrinos and antineutrinos in it would have abundances differing by about 10^-9, which seems VERY difficult to detect.

Dark matter
Only 1 parameter is well-established for it: its average density.

However, there are several attempts to detect WIMP dark matter, though none have been convincingly successful. They use several chemical elements as detector materials, meaning that one may be able to separate out several WIMP-nucleon interaction parameters.
Single nuclide: 1
Light and heavy nuclides with spin 0 or with spin-independent effects dominant: 2
With spin-dependent effects noticeable: 4
Thus giving as many as 5 parameters.

There is also the problem of the Fermi telescope's 130-GeV gamma-ray line observed near the direction of our Galaxy's center.

Dark energy
It currently has only 1 parameter: its density. However, "tracking" theories may give it some additional parameters; these theories make its density vary.

Inflaton
No "i" -- the hypothetical particle that produced cosmological inflation. Its energy scale is about 10¹⁵ GeV, judging from the primordial-fluctuation amplitude, but additional primordial-fluctuation observations may give us additional parameters.

Gravity
Only 1 parameter: the Newtonian gravitational constant. It has the Planck energy scale, 10¹⁹ GeV.
General-relativity alternatives like the Generalized Brans-Dicke theory have more parameters; GBD itself has 2.

The hierarchy problem
Between the Standard-Model particle masses and GUT/Planck energy scales is a big gap.

Collecting the numbers:
Largest Standard-Model mass:
Higgs vacuum field value: 250 GeV

Neutrino seesaw: 10¹⁵ GeV
Inflaton: 10¹⁵ GeV
Gauge unification: 10¹⁶ GeV
Gravity (Planck): 10¹⁹ GeV

 

[RUTA]

"We haven't come to the bottom level yet, but as we approach it we pick up intimations of an underlying beautiful theory whose beauty we can only dimly see at the present time. We don't know that it's true, we don't know that there really is a beautiful underlying theory. We don't know that as a species we're smart enough to learn what it is. But we do know that if we don't assume there is a beautiful underlying theory and assume that we're smart enough to learn what it is, we never will."

Steven Weinberg, Creation of the Universe, written and directed by Timothy Ferris, Northstar Associates Production, 1985. At the 27 min mark.

This sums up nicely the attitude in physics, even today.

 

[marcus]

Nice quote from Weinberg, RUTA! It puts the whole thing in a grander perspective (one I strongly share and support) which goes beyond the immediate problem of bringing quantum fields and quantum GR together. It encompasses, I think, far more than the present unification which the signs suggest (to me) is happening now. Beyond that there will surely be other even deeper questions to address---I think both you and Weinberg would agree. One can hope it will never stop.

I wonder what happens to diffeomorphism invariance wrt changes in frames of reference if there is no background manifold on which to put possible different coordinates/frames.

It is nice you are curious and asking about this! Maybe now being motivated, you will go back and read about it in the literature. There is a big literature about this very thing going back to Regge in the 1960s
Renate Loll has discussed this. The person who has written most about it recently, I believe, is Bianca Dittrich. She has written a number of papers and given talks about how diffeo invariance carries over to discrete geometry/simplicial.
One of many possible references:
T. Regge (1961). "General relativity without coordinates". Nuovo Cim. 19 (3): 558–571

People who are impatient to see signs of unification right away might be interested in this paper that was just posted:

http://arxiv.org/abs/1212.5246
Gravitational origin of the weak interaction's chirality
Stephon Alexander, Antonino Marciano, Lee Smolin
(Submitted on 20 Dec 2012)
We present a new unification of the electro-weak and gravitational interactions based on the joining the weak SU(2) gauge fields with the left handed part of the space-time connection, into a single gauge field valued in the complexification of the local Lorentz group. Hence, the weak interactions emerge as the right handed chiral half of the space-time connection, which explains the chirality of the weak interaction. This is possible, because, as shown by Plebanski, Ashtekar, and others, the other chiral half of the space-time connection is enough to code the dynamics of the gravitational degrees of freedom.
This unification is achieved within an extension of the Plebanski action previously proposed by one of us. The theory has two phases. A parity symmetric phase yields, as shown by Speziale, a bi-metric theory with eight degrees of freedom: the massless graviton, a massive spin two field and a scalar ghost. Because of the latter this phase is unstable. Parity is broken in a stable phase where the eight degrees of freedom arrange themselves as the massless graviton coupled to an SU(2) triplet of chirally coupled Yang-Mills fields. It is also shown that under this breaking a Dirac fermion expresses itself as a chiral neutrino paired with a scalar field with the quantum numbers of the Higgs.
21 pages

 

[lpetrich]

I recall a feature of GR that I concede does make it somewhat similar to the Standard-Model interactions. GR may be interpreted as a gauge theory of space-time, where the gauge transformations are coordinate transformations.

But that's not very helpful for unifying GR and nongravitational interactions as one might hope, as far as I can tell.