Maybe there is no grand unified theory?

[Warp]

This is a complete layman question because the topic goes well beyond my head, but I was thinking... There has been a quest of a "grand unified theory", a single theory of physics that would explain spacetime, gravity, quantum mechanics, and everything in between.

But what makes scientists so sure that there is such a unified theory?

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?

It's a bit like the shape and color of an object. Both are independent features of the object, and neither one defines the other, nor is there any third feature that affects both and creates a connection between them. Trying to develop a "unified theory of color and shape" is futile because they simply are not connected. An object can be of any color and any shape, completely independently of each other.

 

[mathman]

The problem that physics has to address is what happens when both quantum theory and general relativity apply, such as what happens inside a black hole or how the big bang started. The current theories are incompatable.

 

[bapowell]

Yes. For example, how does a Planck mass particle behave? Both general relativity and quantum theory are intertwined at this scale.

 

[PAllen]

Finding a sound framework for dealing with both quantum field theory and gravity when both are significant is required (else there is no theory at all to address conditions presumed to exist in the universe).

However, that is separate from a grand unified theory. It is conceivable that such framework still has a separate representation for QCD, electroweak, and gravity. A grand unification is, IMO, motivated only by aesthetics and historically informed physical intuition. Part of that intuition is that known problems in SM seem to go away in partially successful GUTs, and there is promise of M-theory. But none of that amounts to an argument that nature must be so unified.

[Edit: I see the OP wasn't necessarily asking about what is normally called grand unification. For what they were asking, I agree with the prior answers.]

 

[detective]

...warp has brought up a simple question...my simple thoughts are that gravity, being intimately related to mass, has the problem of allowing for the component of time...

...anything massive has a ''life''...and all things no matter how massive ''die'' or reduce...this exactly is the proper definition of entropy, and entropy taken to it's finality and most extreme means...nothing ...

we invoke the ''time taken'' for that to occur...cheers

 

[bapowell]

But a single electron floating in space will remain a single electron floating in space for eternity.

 

[Warp]

The problem that physics has to address is what happens when both quantum theory and general relativity apply, such as what happens inside a black hole or how the big bang started. The current theories are incompatable.

Of course, but my question was about the quest for finding the one single unifying theory that explains both at the same time. Maybe there isn't one. Instead, we have to simply find out how exactly GR and QM interact with each other.

I understand, however, the motivation behind the idea of there being one single theory that explains everything at once. After all, the history of science has consisted in big part of us discovering that phenomena that we initially thought were separate and completely independent of each other were, in fact, the one and same, and that the same laws of physics actually apply to the entirety of the Universe.

 

[friend]

Of course, but my question was about the quest for finding the one single unifying theory that explains both at the same time. Maybe there isn't one. Instead, we have to simply find out how exactly GR and QM interact with each other.

We have to keep looking for a common cause for events in the universe (for QM and GR). For if there is no common cause, then we would have to explain how two totally unrelated phenomena can fit together everywhere at all times. If there is a logical explanation for everything, then there is a common reason why the universe is both quantum mechanical and generally relativistic. The fact that the universe came from a single point in the big bang means that all reality shared everything in common at some point so that there must have been a common cause for everything in the universe.

 

[Warp]

We have to keep looking for a common cause for events in the universe (for QM and GR). For if there is no common cause, then we would have to explain how two totally unrelated phenomena can fit together everywhere at all times.

If one phenomenon applies to the whole universe, then why not two?

 

[friend]

If one phenomenon applies to the whole universe, then why not two?

What are the odds that that two arbitrary theories should be completely consistent with each other. That's probably a contradiction of terms. Can a contradiction actually exist in the universe? I think not. At some level all of physics laws are consistent with each other, which means by definition that there is a common cause. It's just a matter of finding it.

 

[marcus]

Two comments: we laypeople and non-experts should make an honest effort to use words more or less consistently with the pros, else more confusion results. I have NEVER heard someone use "GUT" the way you do. Normally a GUT does NOT include gravity. See WikiP for example:
http://en.wikipedia.org/wiki/Grand_Unified_Theory
So please to stop saying GUT when you mean unification of GR with QM.

The other thing is
1) physics is a mathematical science
2) math is a man-made human language
3) theories do not exist in nature, they are predictive testable manmade DESCRIPTIONS and they are always provisional. We use the best available description until we discover it's limitations and are forced to improve or replace.
4) we NEVER pretend that an manmade theory is 100% eternally RIGHT, and all theories are manmade.
5) human languages evolve, mathematics evolves, if our language is not good enough to describe GR and QM in the same equation-model TODAY, that does not prove anything. The language may evolve, the concepts and equations become more powerful, we might have a unified description tomorrow or in 10 years.
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.
==================

My personal view is that gravity=geometry and QG means both quantum gravity and quantum geometry. Spacetime geometry is necessarily dynamic and uncertain especially in certain regimes like the presumed BIG BOUNCE that presumably occurred at start of expansion. At least some equation models find a bounce as you go back in time to before inflation and the start of expansion---the models find a bounce due to quantum geometric effects. And other models do not, so we have to compare what they predict with observations of the most ancient light, to see which models are in closer agreement with nature. And I see that in the past 2 to 3 years certain QG research programs have made remarkable progress and have been attracting many more young researchers. The QG enterprise is certainly not STUCK but on the contrary is making rapid progress. Plus I see that interest in String program has been declining, citations are down, string jobs are down, publication has slowed, fewer gifted young people going into string. Fashions change and it's all to the good AFAICS.

 

[friend]

The other thing is
1) physics is a mathematical science
2) math is a man-made human language
3) theories do not exist in nature, they are predictive testable manmade DESCRIPTIONS and they are always provisional. We use the best available description until we discover it's limitations and are forced to improve or replace.
4) we NEVER pretend that an manmade theory is 100% eternally RIGHT, and all theories are manmade.

This kind of argues that there can never be a completion of physics, because all theories are provisional and evolving. I would take issue with this. But the only way for a theory to be absolutely true and complete is if you start your development from the concepts of true and false. If you derived a theory of everything from "pure logic alone", then it could not be argued with, and you'd know it was complete. Yet we don't know if a development from logic is even possible or not at this time.

 

[marcus]

This kind of argues that there can never be a completion of physics, because all theories are provisional and evolving. I would take issue with this. But the only way for a theory to be absolutely true and complete is if you start your development from the concepts of true and false. If you derived a theory of everything from "pure logic alone", then it could not be argued with, and you'd know it was complete. Yet we don't know if a development from logic is even possible or not at this time.

come on, friend
True and False are human words which people use in various different ways in different contexts.
What you call "pure logic alone" is a subset of human language with its own excellent rules of syntax (special high-performance rules of grammar). It is a credit to us as a species. But it is not eternal and static---what we think of as logic continues to evolve--- it was not handed to us once-and-for-all by some absolute Authority. We made it up.

AFAIK physicists are not looking for a final "completion of physics", they show every sign of being quite human and it is human to want to always go beyond, to keep on exploring. when nature does not show them something new for 20 or 30 years they get fretful and despondent, they want their (provisional evolving) theories to be defied, challenged by nature. It is naive to imagine that they want to "complete" the job of finding out how she works and what gives rise to her and why she is the terrifically beautiful way that she is. Forget completion.

 

[friend]

come on, friend
True and False are human words which people use in various different ways in different contexts.
What you call "pure logic alone" is a subset of human language with its own excellent rules of syntax (special high-performance rules of grammar). It is a credit to us as a species. But it is not eternal and static---what we think of as logic continues to evolve--- it was not handed to us once-and-for-all by some absolute Authority. We made it up.

Yes, well, I find myself asking whether your statement is "true". I don't think you can escape the relevance of true and false in debate. All theories in a sense are statements about which we ask if they are true or false representations of reality. If you can "falsify" a theory, then there must be some truth-value content to theories.

To say that logic evolves only underminds the process of reasoning. You can't argue that the principles of reason are changeable to something we don't know yet. That just negates any ability to debate or argue or investigate the truth of theories. If logic is not authoritative, then we could claim our theories are right so we must alter reason to accommodate our theories.

I think it is obvious that true and false must be relevant to theories of the universe. For we distinguish statements that represent what actually exists by saying they are "true". We even say that the existence of the universe as a whole is "true".

AFAIK physicists are not looking for a final "completion of physics", they show every sign of being quite human and it is human to want to always go beyond, to keep on exploring. when nature does not show them something new for 20 or 30 years they get fretful and despondent, they want their (provisional evolving) theories to be defied, challenged by nature. It is naive to imagine that they want to "complete" the job of finding out how she works and what gives rise to her and why she is the terrifically beautiful way that she is. Forget completion.

I think it's a bit misguided to suggest there are no all encompassing principles to guide us into what is actually the case about reality. Experiment is one way to determine if a theory is a correct statement about reality. Logical consistency of a theory is another, assuming that the logic of true and false is even relevant to the investigation of physical theories.friend

 

[marcus]

...I think it's a bit misguided to suggest there are no all encompassing principles to guide us into what is actually the case about reality. Experiment is one way to determine...

Who says there are no all encompassing principles? We have all encompassing principles which guide us, and they change. What underlies/selects/redefines them is the COMMUNITY and the TRADITION that it maintains. People.

The empirical Baconian tradition goes back 400 years to the time of Sir Francis Bacon, contemporary of Shakespeare.

Until not so long ago EUCLIDEAN GEOMETRY was an "all encompassing principle" just like the principles of Aristotelian LOGIC.

The community of scholars--nature-philosophers, etc.--redefines its tradition and by a kind of restless argumentative CONSENSUS chooses what are to be the "all encompassing guiding principles" for that generation.

There will always be persons so anxious to have certainty, or so mistrustful of the community consensus, that they cling to the floating debris from that previous shipwreck.

The rest of us just use what we collectively think are the best guiding principles we have so far.

 

[Chronos]

Perhaps science is inherently limited to compiling ever more accurate, but, never quite perfect approximations of nature. An interesting discussion is here http://arxiv.org/abs/physics/0510188.

 

[friend]

Who says there are no all encompassing principles? We have all encompassing principles which guide us, and they change. What underlies/selects/redefines them is the COMMUNITY and the TRADITION that it maintains. People.

Is that true? Yes, of course I think people can refine their theories and beliefs. To think otherwise would be another argument stopper. I'm not a religious fanatic.

 

[VantagePoint72]

If one phenomenon applies to the whole universe, then why not two?

As others have already said, the issue is that the two models are incompatible when applied at the same time (in certain circumstances). There's no reason you can't have two separate models needed to explain physical reality, but they must be consistent with each other. There are physical questions, answerable—in principle, at least—by an experiment which quantum theory gives one answer to while GR gives a different answer to. Thus, it's just a logical fact that one or both of them cannot be completely correct in its current form. So, it may not be the case that there is a theory of everything, but it is certainly the case that our current understanding through GR and quantum theory is not the whole story.

 

[julian]

Einstein's equation

R_{\mu \nu} - {1 \over 2} g_{\mu \nu} R = T_{\mu \nu}

tells us how geometry is coupled to matter. Since matter is in a quantum superposition, isn't geometry as well?

 

[VantagePoint72]

Whom is your question directed to, julian? That is in fact one the points of tension between QM and GR. The curvature tensor is purely classical and we don't have a well-defined notion for a 'superposition of curvature'. However, QM says it should be coupled to something that is in a superposition. Hence, one of the incompatibilities between QM and GR is the question of what the gravitational field looks like for a particle small enough to have quantum effects dominate.

 

[bapowell]

Einstein's equation

R_{\mu \nu} - {1 \over 2} g_{\mu \nu} R = T_{\mu \nu}

tells us how geometry is coupled to matter. Since matter is in a quantum superposition, isn't geometry as well?

This is the motivation behind so-called semi-classical treatments of gravitational phenomena, in which the stress-energy tensor is replaced by its quantum expectation value, \langle T_{\mu \nu} \rangle, but the geometric side of the Einstein Equations remain classical. This approach, while only approximating the full quantum theory of gravitation, is quite powerful. Hawking used it to discover that black holes radiate, and it is central to the derivation of the temperature anisotropies in the CMB.

 

[julian]

The origin question was can GR and QM be independent theories...and I'm saying they are incompatible.

 

[julian]

This is the motivation behind so-called semi-classical treatments of gravitational phenomena, in which the stress-energy tensor is replaced by its quantum expectation value, \langle T_{\mu \nu} \rangle, but the geometric side of the Einstein Equations remain classical. This approach, while only approximating the full quantum theory of gravitation, is quite powerful. Hawking used it to discover that black holes radiate, and it is central to the derivation of the temperature anisotropies in the CMB.

Really the right hand side is an operator. Attempts are made to replace the right hand side by an expectation value but an iterative procedure must be implemented to define the expectation values. It has been shown that the iteration does not converge in general, whence we must quantise the gravitational field...see p.g. 5-6 of Thiemann's book.

 

[bapowell]

Attempts are made to replace the right hand side by an expectation value but an iterative procedure must be implemented to calculate expectation values. It has been shown that the iteration does not coverge, whence we must quantise the gravitational field...see p.g. 5-6 of Thiemann's book.

Of course. Hence how I said that this approach approximates the full quantum theory of gravititation (but I'm unclear on the non-convergence issue. I'm not an expert on stress-tensor renormalization by any means, but I was under the impression that there were finite representations of \langle T_{\mu \nu}\rangle. In other words, aren't those dangerous UV modes Thiemann mentions integrated out?). Saying that GR and QM are incompatible isn't new -- this was recognized long ago, and forms the basis of the OP's question. It seems you already know the answer to the question you asked.

 

[julian]

People talk about singularities and how GR and QM must merge in certain circumstances. But if you take QM to apply at all levels (which I do!) then they are always incompatible.

 

[julian]

Hello Bapowell

The iteration is unstable in general. It was Robert Wald and Flanagan [gr-qc/960252] who showed this.

"In other words, aren't those dangerous UV modes Thiemann mentions integrated out?"

I'm not sure how to answer it, I'm not an expert either.

But what I do know is that Thiemann shows in his book that a canonical quantization of GR (with full backreaction of matter on the quantum gravitational field) is finite.

 

[bapowell]

Thanks for the reference julian. I'll have a look.

 

[julian]

Hi bapowell

I think people take they view that quantum mechanics stops at some length scale, beyond which matter is classical, and then put it into Einstein's equations. I'm of the opinion that there is no artificial boundary between classical and quantum...

 

[PAllen]

Hi bapowell

I think people take they view that quantum mechanics stops at some length scale, beyond which matter is classical, and then put it into Einstein's equations. I'm of the opinion that there is no artificial boundary between classical and quantum...

That may be (and I agree), but as a practical matter, there is enormous range of validity to the limits of measurement for Newtonian mechanics, Maxwell's equations, and GR. As a practical matter, one must try to understand the boundaries of when classical theories are good enough, unless you want to waste endless effort calculating trivial results.

 

[atyy]

The origin question was can GR and QM be independent theories...and I'm saying they are incompatible.

Here is a discussion of GR as a quantum theory.

http://arxiv.org/abs/1209.3511

 

[lpetrich]

So a Grand Unified Theory is one that includes all the Standard Model without including gravity, and a Theory of Everything one that also includes gravity.

I don't think that I want to split hairs over this issue.

 

[bapowell]

So a Grand Unified Theory is one that includes all the Standard Model without including gravity, and a Theory of Everything one that also includes gravity.

Traditionally, yes, that's the correct distinction. GUTs are meant to unify the strong, weak, and electromagnetic forces only.

 

[lpetrich]

I remember once discovering a pattern in the discovery of the fundamental constituents of matter, a pattern that involves several stages:

1. Discovery of a few entities. Category may be poorly defined or not even properly recognized.
2. Discovery of many entities. Well-defined category.
3. Discovery of regularities among the entities.
4. Discovery of underlying simplicity and the causes of the regularities.

These entities have gone through that cycle, with all but the Standard Model completing it:

1. Atoms and chemical elements
2. Atomic nuclei
3. Hadrons
4. Standard-Model particles

The details.

Atoms and chemical elements

The idea of chemical elements goes back to antiquity, with Greek earth, air, fire, water and Chinese earth, wood, metal, fire, water. However, chemical elements became a well-defined category with Antoine-Laurent de Lavoisier, and atomism became rigorous with John Dalton.

By the middle of the 19th cy., Dmitri Mendeleev proposed his Periodic Table of Elements, complete with predictions of missing members of that table. Those members were later found, and they had the properties that DM had predicted for them.

With the discovery of electrons, nuclei, and quantum mechanics, and the development of quantum chemistry, these entities entered the fourth stage.

Atomic nuclei

Discovered in 1909, they quickly skipped through the first stage to reach the second stage, and they entered the third stage around 1920, when Ernest Rutherford proposed the existence of a "neutral proton". This particle was discovered in 1932, and named the neutron, bringing nuclei into the fourth stage.

Hadrons

The first hadrons discovered were protons and neutrons, around 1920 and 1932. I'm counting protons by Ernest Rutherford's recognition of them; a hint of them goes back about a century more to Prout's hypothesis. When they were the only two known strongly-interacting particles, hadrons remained stuck in the first stage. That began to change in 1947 with the discovery of the pion, and by the 1950's, physicists had discovered a big zoo of strongly-interacting particles, bringing hadrons into the second stage.

But regularities soon became evident, and in 1964, Murray Gell-Mann, George Zweig, and Yuval Ne'eman proposed the quark model. It had some oddities, like quarks in baryons being symmetric despite having spin 1/2, and the non-observation of free quarks. But by the early 1970's, physicists had discovered evidence that protons are composite, and that some of the "partons" in them have the properties expected of quarks. They also developed a theory of the quark's interactions, QCD. It put quarks in baryons into an antisymmetric color state, resolving the symmetry discrepancy.

With this and other evidence, like quark and gluon jets and the success of lattice QCD, hadrons entered the fourth stage.

Standard-Model particles

The first stage can go back a long way, depending on what one wants to count as first hints of the photon and electron. Visible light? Electrostatic effects? Magnetic effects? Electric shocks from electric fish?

A complication along the way is that for some decades, hadrons seemed as elementary as electrons, muons, neutrinos, and photons. In fact, in the 1960's, a "bootstrap model" of hadrons used to be popular, depicting them all as fully elementary. But the success of the quark model made it evident that hadrons were composite and not quite elementary, and that quarks and the gluon were instead elementary.

The term "Standard Model" was coined in the early 1980's or thereabouts, but some physicists were already speculating about Grand Unified Theories.

The unbroken Standard Model has some regularities in its particles' gauge-field quantum numbers, even if not in their masses, and one can find GUT's that fit all the Standard-Model particles into a small number of multiplets. So it's still in the third stage.

 

[lpetrich]

As to Standard-Model particles, there are some interesting regularities in their gauge interactions. I'll concern myself with the unbroken SM here, since that is what we must account for. Quantum numbers:

(QCD multiplicity, weak-isospin multiplicity, weak hypercharge)

The gauge particles are all in the adjoint representations of their gauge-symmetry groups, so that does not really tell us very much.
QCD: gluon: (8,1,0)
WIS: W: (1,3,0)
WHC: B: (1,1,0)

The Higgs particle is a single doublet: (1,2,-1/2)

The left-handed and right-handed elementary fermions:
Quark: (3,2,1/6) - (3*,2,-1/6)
Up: (3*,1,-2/3) - (3,1,2/3)
Down: (3*,1,1/3) - (3,1,-1/3)
Lepton: (1,2,-1/2) - (1,2,1/2)
Neutrino: (1,1,0) - (1,1,0)
Electron: (1,1,1) - (1,1,-1)

If you are starting to suspect some patterns, you are not alone. In fact, there is an interrelationship that I rediscovered; I don't know who originally discovered it.

Weak isospin works like 3D angular momentum, with overall quantum number WIS and multiplicity 2*WIS + 1. There is a "spin parity" that is conserved in rep products. Integer spins have parity 0, half-odd spins parity 1, and they add modulo 2.

QCD has a similar quantum number, "triality". It's more complicated to calculate, so I'll give its values for the reps mentioned here:
1 (scalar) -- 0
8 (adjoint) -- 0
3 (fundamental) -- 1
3* (fund. conjugate) -- 2
Trialities add modulo 3.

With QCD triality and WIS parity:
Quark: (1,1,1/6) - (2,1,-1/6)
Up: (2,0,-2/3) - (1,0,2/3)
Down: (2,0,1/3) - (1,0,-1/3)
Lepton: (0,1,-1/2) - (0,1,1/2)
Neutrino: (0,0,0) - (0,0,0)
Electron: (0,0,1) - (0,0,-1)

Now to the weak hypercharge. After some experimenting, one finds a simple formula:

WHC = (integer) + (1/2)*(WIS parity) - (1/3)*(QCD triality)

One can use (WIS) instead of (1/2)*(WIS parity), and it will work just as well.

One can get this formula from some GUT's, like Georgi-Glashow.

 

[rodsika]

OP, the reason it should be related is very simple.

EFE simply tells how the geometry must be curved by the influence of mass/stress/energy. It doesn't show how the mass is connected to geometry... which occurs in very small scale. So without knowing how mass is connected to geometry. It's just like believing in Magic like telling children about TV getting images and not explaining how.. but only that pushing channel and volume buttons can change the images (like EFE).

 

[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.