What is meant by no complete TOE ?

[curtdbz]

What is meant by "no complete TOE"?

What does it mean exactly when people say "there is currently no complete quantum theory of the remaining fundamental force, gravity" for a Theory of Everything.

I know there are a few competing theories. Spin Foam, String Theory, etc... Are those not "complete"? What do you mean when you say it's not complete? What's missing? Sorry for the basic questions!

 

[TheTechNoir]

Yes, theories of quantum gravity such as loop quantum gravity/spinfoam, and string theory/m-theory, etc. are all far from 'complete'.

They are incomplete for lots of reasons depending on how exactly you are defining the term, I'm thinking the number one reason to be aware of is the fact that as of now we are using approximate equations with which to make predictions or try and build models, etc. It is impossible to describe everything in the universe, which these theories strive for when you don't know the full equations you are working with to begin with. I imagine that when you see a quote along those lines they are more or less specifically addressing this key point of these 'theories' (it is a little difficult in some ways to truly consider them full theories due to this incomplete nature).

Also keep in mind, even if we were to discover the true equations there is still the matter of unlocking secrets using them, testing predictions, and inferring new information about the universe. It won't just be a matter of one afternoon "There we go! We have it, we now know everything."

Though important to note is that while I am positive of what I said as it pretains to string theory/m-theory, I cannot say with 100% certainty that loop quantum gravity/spin foam do not have full equations. I strongly disbelieve that they would, but you may want to try researching that or waiting for another poster to confirm/deny or further explain. I simply don't know enough of it to say so as fact.

 

[marcus]

It's a good question and that's a helpful reply. Thanks to Curt and Tech! I've nothing important to add but will just amplify what Tech said.

We've heard so much in the popular media about "TOE" as a goal that there is a widepread impression that "final theory" is the overriding goal of today's physics.
TOE and Final Theory might actually be reasonable and relevant program goals or they might be buzzwords. Same with "unification of forces". I'll try to say something about that later.

The most important thing to get across, though, is that the Loop program's goal is different.
It is more like "First let's get the geometry right!"
For many years physics has been done on fixed geometry. Quantum field theory is usually constructed on flat 4D spacetime (of special relativity).

Another common statement of the program's goal is to learn how to construct a "background independent QFT". In Loop context, background independent means "no prior geometry". So the idea is to be able to do Quantum Field Theory with no prior geometry specified.

One way that might be realized is to replace the spacetime continuum by a cell-complex or foam (the analogous thing to a graph in one higher dimension) and label the foam with both geometric information and matterfield quantum numbers. The graph or cell-complex is a way of representing the FINITE measurements we can imagine making which nail down the finite number of (geometry and matter) degrees of freedom which are in principle controllable, or that we can say something about, as in an experiment. Our information is finite so we truncate to a finite number of degrees of freedom in the way we represent it mathematically.

Such a thing can be thought of as a geometry+matter Feynman diagram. Where not only particles interact but also geometry interacts. Loop geometry can be formulated as a handful of Feynman rules for calculating amplitudes, and these rules then boil down to some integrals
( http://arxiv.org/abs/1010.1939 )
So far the Feynman rules involve geometry only. The program is incomplete in that sense. Last year a preliminary paper on putting fermions into the spinfoam picture appeared but there is still a ways to go in that direction.

The best overall presentation of the current status of Loop program is a February 2011 paper http://arxiv.org/abs/1102.3660
It has an abbreviated treatment of the 1010.1939 stuff in an appendix---the interpretation of spinfoam as Feynman diagram.
Actually 1102.3660 is remarkably complete. It does a good job of describing and motivating and summarizing results so far in only about 20 pages. Plus a few pages of appendix.

The most interesting thing to me (as retired mathematician turned physics-watcher) is the potentially revolutionary impact of replacing the manifold with a different representation of spacetime. For roughly 200 years physics has been done on manifolds with fixed geometry.
Very often the geometry was flat. Or if not flat it was at least a prior fixed curvature setup.

But GR says that the geometry is live and interactive. It takes part in the action.
And QM says we can't say anything about geometry beyond what we can imagine measuring. Reality responds to measurement. And there are tradeoffs. Areas, angles and volumes may resist being once-for-all determined just like position momentum and spin do.
A manifold is uniformly the same down to infinitesimal scale and that might be wrong. If we cannot measure geometry past some point then we should not presume continuity past that point. The mathematical representation of spacetime should reflect what we measure or at least in principle infer and say something about.

So to me it seems that the Loop program is not even in the "TOE" ballpark. It is groping for a new idea of spacetime!

When you have a new idea of spacetime, you might build a TOE in it that turns out differently from any TOE you would construct in the old version of spacetime (the continuum with fixed prior geometry that we have been assuming for 200 years).

My personal feeling is I don't want to worry about "final theories". I'm interested in this new idea of the geometry that theories can be based on. Particularly since right now quantum geometry seems to be where the rapid progress is. The Loop program even though it involves only a couple of hundred people is evolving fast. Elsewhere it looks as if much of the theory-world is stalled.
Again that article 1102.3660 gives an idea of the rate of development, and the crucial new results just in the past 2 or 3 years.

One could say that the program's underlying attitude is that rather than unifying "forces" one should get a new idea of geometry and unify geometry with matter. It is a different idea of what one should unify.

The program's target areas for new understanding of nature are
A) the big bang singularity and ensuing early universe
B) black hole singularities
C) geometry at very small scale (or maybe it is geometry at high energy density--not sure which...)

And the program is still very incomplete! Again 1102.3660 is a good source. It has a list of open problems---some 17 problems if I remember right. It also deals frankly with unresolved issues and uncertainties faced by the Loop program.

 

[dhillonv10]

There's this thing called the Godel's incompleteness theorems which simply state that within a logical system you can never have a set of axioms that describe its entirety and that's because the system itself is based on assumptions that we can't prove from within that system. Basically that means that we just don't have tools to describe everything because the methods we use to make those tools are ultimately flawed...

 

[marcus]

I agree with your point about the Goedel incompleteness of axiomatic bodies of mathematics. But I stop short of equating empirical science theories with axiomatic systems. I think of empiricism as more of a pragmatic enterprise: the simplest mathematical model that gives the best fit to the most data, and that you can predict new phenomena with. But I don't know that Nature herself is axiomatic, so I hold back on that one.

I want to say something about the term "TOE". The rest of this post is primarily responding to Curt's OP. Primarily directed towards Curt (and the friends he was talking with, whom he quotes).
The way I understand it, Curt's original question was not about a theory of literally EVERYTHING it was simply about unification of four basic forces.

As I see it, the term "TOE" is mainly just flippant slang, not meant to be taken seriously. I don't think it was never supposed to mean an actual mathematical theory of everything in existence including the platypus and James Bond movies. "TOE" hopefully is not a term that one would use seriously, but more in the spirit of youthful enthusiasm---or playful boastfulness.

Perhaps some people may have used it in a calculating way to impress a naive unsophisticated audience---which is too bad but it happens. Pop-sci hucksters promoting books, dumbed-down TV series.

Doesn't it make better sense to avoid "TOE" talk and simply say "unified theory" or "unification of (the four) forces"?

There is no a priori reason to suppose that such unification is impossible. After all electricity and magnetism were unified, and then the weak force was merged with them. Why not add the strong force and gravity?

I think this is what Curt was really asking about (others may interpret his question differently.)

What does it mean exactly when people say "there is currently no complete quantum theory of the remaining fundamental force, gravity" ...
I know there are a few competing theories. Spin Foam, String Theory, etc... Are those not "complete"? What do you mean when you say it's not complete? What's missing? ...

String is a research program---AFAIK there is no one unique theory that fits past data and that you can make predictions with. There is no one set of equations that you can point to and say "this is String Theory".

I recall David Gross, who has often given either the opening or the concluding talk at the annual Strings conferences, has repeatedly said "We don't know what String Theory is."
That pretty much sums it up.
He has also said that there is some fundamental insight that is missing (something about the nature of space and time) that the program needs in order to move ahead.
This is a leading string theorist talking to other string theorists.

So String is an ongoing research program, not a finished theory. There is no question of its being complete

Loop Gravity is incomplete in a different way, or ways. For one thing it is not a theory of electromagnetism or the strong force or particle physics. It currently has a very limited scope. The aim is simply to get a quantum theory of spacetime geometry that maybe later you can add forces and particle fields to. There is no question of it being a theory that unifies the four forces. That would be far in the future and only if the theory survives testing as a theory of quantum geometry (geometry under extreme conditions like big bang or black hole).

Because Loop has limited scope, it is easier for it to arrive at a single formulation in terms of a few equations and to make predictions.
Here is a description of the theory as it stands today:
http://arxiv.org/abs/1102.3660
The predictions so far are mostly about features of the Cosmic Background Radiation (the ancient light left over from the early universe).
Here is a listing of some papers, mostly by phenomenologists---people who look for ways to test theories.
http://www-library.desy.de/cgi-bin/spiface/find/hep/www?rawcmd=FIND+%28DK+QUANTUM+GRAVITY%2C+LOOP+SPACE+OR+DK+QUANTUM+COSMOLOGY%2C+LOOP+SPACE%29+AND+%28DK+POWER+SPECTRUM+or+dk+cosmic+background+radiation%29+AND+DATE+%3E+2008&FORMAT=www&SEQUENCE=citecount%28d%29
You can follow the links and look at the abstract summaries, or the papers, you will see people beginning to derive predicted "footprints" of Loop Gravity which if they don't find them in the CBR ancient light, with the next generation of instruments, would rule the theory out.

Although the theory has a limited scope (it does not cover many kinds of phenomena), it has reached the stage of being testable---it makes predictions, which traditionally is what physics theories are supposed to do.

 

[dhillonv10]

I agree with you marcus, perhaps I should refrain from making broad generalizations although I must say I don't think nature is axiomatic and that's mostly because well we have the age old problem of what consciousness and awareness are. That may perhaps be not too far, cognitive emergence will soon catch up and we will have a better description of reality.

It seems as though as soon as we understand something in nature, the next instant it gets replaced by something much more complicated and we are left with more and more questions, we seem so close yet so far :)

 

[marcus]

I'm beginning to realize that you might be a researcher while I am a retired person who loves this stuff and am simply watching from the sideline. So I want to be careful about opposing out of respect for your direct experience.
I was a bit worried by my last post, #5, which seemed to contradict in a facile manner.
What I suspect is you may have some wisdom that comes from direct confrontation with nature. Whereas I am a watcher.

However what I think is that it is all evolution. Mathematics is not a fixed entity that one can define but a language and way of thought that evolves by natural selection.
(The selfselecting elite community of mathematicians provides the selection pressure and the reproductive success when it happens).
So mathematics evolves and ordinary language evolves and concepts evolve. This I admit is exceedingly vague!

And physical theories evolve under the even heavier selection pressure of nature.

Plus we can't tell in advance what might seem simple to the next generation, or several on down the line.

So all an elderly person with imperfect eyesight can do is fight to preserve the Baconian tradition (empiricism), and watch the literature, and try to be pragmatic and reasonable about things.

You can't tell ahead of time what's going to be right. And anyway it's fun to be surprised.

 

[martinbn]

There's this thing called the Godel's incompleteness theorems which simply state that within a logical system you can never have a set of axioms that describe its entirety and that's because the system itself is based on assumptions that we can't prove from within that system. Basically that means that we just don't have tools to describe everything because the methods we use to make those tools are ultimately flawed...

I don't know how or if this applies to physics, but this is not what the theorem says. The reason for incompleteness is not because the axioms are assumed true without a proof. And moreover there are complete systems, which of course have axioms.

 

[dhillonv10]

marcus: Thanks for those kind words, I am only a student who likes to mess around with stuff and I end up learning new things by doing so and yes even though we have opinions about everything being constantly surprised is what keeps me interested in physics. I must say my knowledge is nothing compared to yours, I've seen your posts every now and then, your knowledge is encyclopedic, I only know some trivial stuff.

martinbn: Incompleteness applies to a logical system, here we are talking about mathematics. Please elaborate your point.

 

[martinbn]

What I meant was that some axiomatic systems are incomplete not because they are axiomatic. Because there are axiomatic systems which are complete. So what I am trying to say is that incompleteness is not the same as axiomatic.

The way you had it written sounded to me as if there were saying that there weren't any complete systems.

 

[chronon]

I think that Gödel incompleteness is a bit of a red herring when talking about theories of everything. OK, so a theory of everything isn't likely to give a general procedure to say whether your computer program will halt or not, but did anyone think that it would?

 

[dhillonv10]

martinbn: ahh I see your point :) sorry I wasn't able to follow along before so I asked you to elaborate. From what I see, a TOE should account for *everything* that includes a solution of some sort to the halting problem or P vs NP in general, unite all 4 forces, account for consciousness and awareness, provide explanation for what exotic matter at its fundamental level is. All that to ask of one theory is perhaps really pushing the limit, and looking at that if one tries to account for all of those or essentially axiomatize a system we can't do so, that may be a better way to put my point.

chronon: I understand but what I wanted to get across to the OP was that there can't exist a true TOE that has all the knowledge, a sort of a master equation from which everything can be derived. We will hit a roadblock sooner or later and it will require a leap of imagination to make new tools unlike never before.