Got asked, "Why does there 'need' to be a UFT"

[Cake]

I was working today with a mathematics grad student, and in the lull of the work he asked me about why physicists insist on there being a unified field theory that unites all four forces of the universe into a single equation. I sort of paused for a moment and thought before I answered, and I ended up hand waving a bit and said that the logic of the physicist is that since nature does seem to operate logically and predictably, and that we've defined how nature works mathematically pretty well so far, that it stands to reason that there should be some unification of all the forces that control the universe. He pointed out that didn't really answer the question as to why we think there 'needs' to be a UFT. I bowed to that and just said, no, I suppose there doesn't need to be one ultimately. The universe could just have completely separate mechanisms for gravity and the other forces. I wasn't really happy with that, but I wanted to leave and he started ranting about how he thinks physicists just made up the idea of tensors, so I just peaced out. But it got me thinking more about it and I was wondering what you guys who obviously have lived and breathed this idea of a unified field theory for years think about why there needs to be, or maybe a more reasonable way to say it would be why does it 'look' like there is a UFT. What do you think?

 

[axmls]

Many physicists don't believe a Theory of Everything is necessarily out there (or even possible). Stephen Hawking, for example. But why wouldn't we try to come up with one? I mean, why did we need to make calculus rigorous by creating mathematical analysis if calculus worked already? Because we're always striving for greater and greater accuracy in our works.

 

[ShayanJ]

he thinks physicists just made up the idea of tensors

Really strange for a math grad student. He should have been an applied math student! Otherwise he was simply not a good student.
Because mathematics itself works exactly the same way, some one just comes up with something and discusses some properties of it and later mathematicians continue the discussion. It should be more strange for him in mathematics itself because at least in physics, nature motivates the introduction of concepts but what motivates them in math? Only the imagination of the mathematican. Don't take me wrong! I'm not saying physics is better than math in this respect, I love both math and physics and one of the reasons I love math is exactly the above thing. So I think that the mentioned student neither knew enough about pure math nor enough about theoretical physics.
Also, mathematicians first came up with tensors, not physicists!

 

[sophiecentaur]

The fact that many of the relationships between everyday variables can be expressed in very simple linear terms seems to lead people to believe that there is no limit to this very simple modelling - i.e. we can use square laws, exponential laws, convolution, transforms and will eventually get complicated enough to describe 'everything'. That is an extremely naive suggestion and based on faith rather than experience. In a way Maths is to blame for this assumption about 'Laws' being there to be discovered but Maths is not the real World. It is far more accurate to say that we can get better and better approximations in our models of the World - and that's all.
It is a very human trait (a flaw, even) to expect a TOE to exist because it gives a much more cosy feeling about things than to acknowledge that we will never get there.

 

[Cake]

The fact that many of the relationships between everyday variables can be expressed in very simple linear terms seems to lead people to believe that there is no limit to this very simple modelling - i.e. we can use square laws, exponential laws, convolution, transforms and will eventually get complicated enough to describe 'everything'. That is an extremely naive suggestion and based on faith rather than experience. In a way Maths is to blame for this assumption about 'Laws' being there to be discovered but Maths is not the real World. It is far more accurate to say that we can get better and better approximations in our models of the World - and that's all.
It is a very human trait (a flaw, even) to expect a TOE to exist because it gives a much more cosy feeling about things than to acknowledge that we will never get there.

So would you say there's no hole in our description of the universe that a UFT would fill? Because that's what pop-science has led a lot of people to believe.

 

[ShayanJ]

So would you say there's no hole in our description of the universe that a UFT would fill? Because that's what pop-science has led a lot of people to believe.

The hole we need to fill, is finding a quantum theory for gravitation. There are several candidate theories which only one of them is a candidate for being a TOE, string theory.(And its the only candidate) But a TOE is not needed nor there are strong indications for the existence of one. its just that by the introduction of string theory, people realized its possible to have a single theory that includes all interactions. So its wrong to say that a goal of modern physics is unification of fundamental interactions. Its not a goal, its only a possible future of theoretical physics which may turn out to be only a speculation.

 

[axmls]

If all the pop-sci I've read is to be believed, a quantum theory of gravitation is important for understanding the real nature of black holes. I'm unable to comment on the validity of this, though.

 

[HallsofIvy]

I was working today with a mathematics grad student, and in the lull of the work he asked me about why physicists insist on there being a unified field theory that unites all four forces of the universe into a single equation. I sort of paused for a moment and thought before I answered, and I ended up hand waving a bit and said that the logic of the physicist is that since nature does seem to operate logically and predictably, and that we've defined how nature works mathematically pretty well so far, that it stands to reason that there should be some unification of all the forces that control the universe. He pointed out that didn't really answer the question as to why we think there 'needs' to be a UFT. I bowed to that and just said, no, I suppose there doesn't need to be one ultimately. The universe could just have completely separate mechanisms for gravity and the other forces. I wasn't really happy with that, but I wanted to leave and he started ranting about how he thinks physicists just made up the idea of tensors

Actually, "tensors" were invented by Levi-Civita and Ricci-Curbastro, working in differential geometry before physicists started thinking of modelling space time in terms of differential geometry. In fact, Einstein had to learn both differential geometry and tensors before he wrote his "General Theory of Relativity".

, so I just peaced out. But it got me thinking more about it and I was wondering what you guys who obviously have lived and breathed this idea of a unified field theory for years think about why there needs to be, or maybe a more reasonable way to say it would be why does it 'look' like there is a UFT. What do you think?

 

[Cake]

Actually, "tensors" were invented by Levi-Civita and Ricci-Curbastro, working in differential geometry before physicists started thinking of modelling space time in terms of differential geometry. In fact, Einstein had to learn both differential geometry and tensors before he wrote his "General Theory of Relativity".

I think as an undergrad he avoided topology and dif. geometry like the plague for some reason. Idk, that certainly wasn't MY view of it by any means. He was just kind of a prick.

Thanks though. If I have to work with him again I'll let him know he's got some reading on diff. geometry to do :D

The hole we need to fill, is finding a quantum theory for gravitation. There are several candidate theories which only one of them is a candidate for being a TOE, string theory.(And its the only candidate) But a TOE is not needed nor there are strong indications for the existence of one. its just that by the introduction of string theory, people realized its possible to have a single theory that includes all interactions. So its wrong to say that a goal of modern physics is unification of fundamental interactions. Its not a goal, its only a possible future of theoretical physics which may turn out to be only a speculation.

That's a great explanation. I think that's more or less what I was trying to get across, I just wanted to avoid invoking string theory if I could because I didn't want him to start ranting about that too. The tangents he took in this conversation were numerous as it was. But thanks. What you said, said a lot.

 

[eachus]

Actually Gδdel's proofs apply here. (That should be an umlaut over the o.) Physics is a (consistent) mathematical system of more than sufficient complexity. So there must be theorems in Physics which cannot be proven true. If a (provably) true theory of everything exists, it would only apply locally, or over some limited domain. Do the problems most mathematical physics have with singularities match this model? Or does the possibility of causality violations make and complete physics inconsistent? Very good questions, and I can only provide guesses not answers.

in other words, any theory of everything must be incomplete or inconsistent. Any theory which admits time travel, even for one nanosecond by one particle is likely to be inconsistent. In other words, any experiment can have the result of a shoe falling from nowhere to generate unexpected data. However, it is possible to ignore those possible materializing shoes and get useful results. But it is difficult to design time machines with a restricted theory, even if the theory says they can be built. Is it possible to create a physics that admits of some time travel and is still consistent? Possibly, but I wouldn't know where to begin.

 

[ShayanJ]

Actually Gδdel's proofs apply here. (That should be an umlaut over the o.) Physics is a (consistent) mathematical system of more than sufficient complexity. So there must be theorems in Physics which cannot be proven true. If a (provably) true theory of everything exists, it would only apply locally, or over some limited domain. Do the problems most mathematical physics have with singularities match this model? Or does the possibility of causality violations make and complete physics inconsistent? Very good questions, and I can only provide guesses not answers.

in other words, any theory of everything must be incomplete or inconsistent. Any theory which admits time travel, even for one nanosecond by one particle is likely to be inconsistent. In other words, any experiment can have the result of a shoe falling from nowhere to generate unexpected data. However, it is possible to ignore those possible materializing shoes and get useful results. But it is difficult to design time machines with a restricted theory, even if the theory says they can be built. Is it possible to create a physics that admits of some time travel and is still consistent? Possibly, but I wouldn't know where to begin.

This isn't an established fact, among the reasons of which, I can mention the fact that the current physics we have in hand, is not a well defined mathematical structure. Whether future physics will be different, is something we should wait and see.
I also should say that my incomplete knowledge about Godel's theorems tells me that they are not general enough to give us such conclusions. But I'm not sure about this.

 

[sophiecentaur]

So would you say there's no hole in our description of the universe that a UFT would fill? Because that's what pop-science has led a lot of people to believe.

I meant the converse. The 'everything' cannot be covered by any 'theory'. How can people imagine it can? There is no evidence to suggest that.

 

[mathman]

I am not sure it has been covered, but one major reason for a unified theory is to handle the problem that quantum theory and general relativity are incompatible where they are both need. The most revealing problem is trying to describe what happens inside a black hole.

 

[Cake]

I meant the converse. The 'everything' cannot be covered by any 'theory'. How can people imagine it can? There is no evidence to suggest that.

Certainly. Just making sure I wasn't missing something :)

 

[ShayanJ]

I am not sure it has been covered, but one major reason for a unified theory is to handle the problem that quantum theory and general relativity are incompatible where they are both need. The most revealing problem is trying to describe what happens inside a black hole.

A theory of Quantum Gravity will solve the problem. It doesn't have to unify gravity with other interactions.

 

[eachus]

This isn't an established fact, among the reasons of which, I can mention the fact that the current physics we have in hand, is not a well defined mathematical structure. Whether future physics will be different, is something we should wait and see.
I also should say that my incomplete knowledge about Godel's theorems tells me that they are not general enough to give us such conclusions. But I'm not sure about this.

Um, you have to understand how Godel's Proof works. It shows that if you can embed a very simple arithmetic (Peano arithmetic, which doesn't even require integers) then the system as a whole is either incomplete (some true things are not provably true) or inconsistent (there are false things that can be proven true in that formalism). It would probably take a book--and a not very readable one--to define the standard model well enough to decide that it was incomplete. Inconsistent can be done pretty quickly. For example, almost every attempt to define physics inside a black hole ends up inconsistent, Whether that inconsistency applies outside the event horizon is model dependent.

 

[ShayanJ]

It shows that if you can embed a very simple arithmetic (Peano arithmetic, which doesn't even require integers) then the system as a whole is either incomplete (some true things are not provably true) or inconsistent (there are false things that can be proven true in that formalism).

That's what I mean...why should a TOE contain arithmetic axioms?
A TOE is a physical theory. It can be inconsistent and imprecise from a mathematical point of view but be a good physical theory! I don't think Godel's theorems apply to such a thing.

 

[sophiecentaur]

As an Atheist I have no problem with a theory of 'not everything'. People of 'faith' (admitted or not) may want to think that an ultimate truth is out there somewhere. It may be connected with the life after death thing and the notion that, when we die, everything will be revealed. Personally, again, it is no disappointment that there ain't an answer to everything. That fits with my experience so far and I have 'got over it' fine.
Just imagine that a theory of everything comes up that includes an element of chaos in it. That could spoil a lot of days for a lot of people.

 

[eachus]

That's what I mean...why should a TOE contain arithmetic axioms?
A TOE is a physical theory. It can be inconsistent and imprecise from a mathematical point of view but be a good physical theory! I don't think Godel's theorems apply to such a thing.

I can't imagine a TOE that does not use arithmetic. Even if you could come up with a TOE based on string theory that used only topology, embedding Peano arithmetic in topology is possible.. http://en.wikipedia.org/wiki/Peano_axioms will tell you much more than you want to know about Peano arithmetic and related systems. Basically what you need is the natural numbers (for example the number of holes in a topological object,), equality, a successor function (how to add a hole to an object) and induction. There are games you can play with the axiom set that result in equivalent systems.

You could argue that a finite theory of everything could avoid infinities, but that is sophistry. The integers may be unbounded, but any well formed theorem in PA does not involve infinities. For example the fairly well known diagonalization proof that the rational numbers are the same order of infinity as the integers basically shows that a map can be constructed such that for any rational number R there is a unique integer and vice-versa.

What you end up with is that if there is a consistent TOE, it can not be proved consistent inside this universe. That does not mean that the new theory is useless, just that the universe will have properties that cannot be derived from the new theory. That means the best we can get is to run experiments and not finding any contradictions. However, that shoe, or more realistically an extremely high energy cosmic ray can come along and mess up any particular experiment. In other words there will always be room to look for new physics, even if you don't find any.

 

[dx]

There is no "need" in a logical sense. It is just based on a faith in the intelligibility of the world, and past historical experience. As we discover more about fundamental physics, the whole structure seems to become more "unified", in the sense that the number of independent conceptual elements becomes smaller. Things that were previously considered separate become related or unified. Overwhelming evidence points to the existence of a kind of "final stage" or an "eschaton" in this process of unification, that is generally called "quantum gravity"

 

[mathman]

Quantum gravity and string theory are both supposed to be theories of everything. So far neither of them has produced a definitive prediction, subject to experiment.

 

[dipole]

I think a big reason, as pointed out, is that one can imagine physical circumstances where both gravitational and quantum effects are important - we currently have no good theoretical framework for handling this.

If we hope to have a complete mathematical description of nature someday, then a unified theory is probably necessary. Further, why shouldn't there be one consistent set of natural laws? How does nature decide on what scale one theory begins to apply and another doesn't? There's a lot to be reconciled with the everyday classical world, the quantum world, and the bizarre gravitational effects of the cosmic-scale world. Wouldn't it be awfully nice if there was one single theoretical framework, that within the appropriate limit, could describe accurately all three cases?

 

[Wes Tausend]

...

There is actually a subtle difference between a classical UFT (unified field theory) and a TOE (theory of everything) as has been pointed out to me here before. Einstein, unaware of the strong and weak nuclear forces, attempted to unify just electromagnetism and GR, defining his unfulfilled quest for his Unified Field Theory. A theory of everything would also include the strong and weak forces, along with quantum theory, and has been a later query by Hawking and others.

Uniting classical electrodynamic and gravitational forces doesn't seem too hard to model in a logical thought experiment. For one thing, it is self-evident that the exertion of gravity to collapse dimension throughout the universe is observed to be precisely equal to the exertion of electromagnetic forces preventing that... equilibrium. This can be logically expanded to cover all inertial forces (including gravity) in a total equilibrium principle.

Arriving at UFT initially involves the logical process of strictly applying the Copernican principle to SR by simply reassigning energy and matter as merely relative frames of ultimate motion, instead of assigning light as a privilaged frame of ultimate motion as is conventional (arrgh, most difficult to intuitively accept). The acceleration of gravity is then also conveniently made relative, via Equivalence and a little conceptual trick from Poincaré. I don't think the rather simple idea violates the philosophy or quantities of either SR or GR, but rather completes them and opens a new door. Anyway, when I questioned the reasoning behind the seemingly arbitrary privilaged assignment of light, I immediately ran smack dab into a PhysicsForum FAQ called Rest frame of a photon. End of discussion. Rats, now I'll never know.

Wes
...

 

[mattt]

Um, you have to understand how Godel's Proof works. It shows that if you can embed a very simple arithmetic (Peano arithmetic, which doesn't even require integers) then the system as a whole is either incomplete (some true things are not provably true)

"some true things are not provably true" is not a proper way of explaining it.

If a given axiomatic theory (in the mathematical logic sense) is not complete (and so it is consistent) then there is a sentence (of the formal language) "p" such that neither "p" nor "no p" are theorems. Then there is a Model (in the mathematical logic sense) of that axiomatic theory such that "p" is true in that Model (and so "no p" is false in that model). There is also another different Model (in the mathematical logic sense) of that same axiomatic theory such that "p" is false in that Model (and so "no p" is true in this model).

or inconsistent (there are false things that can be proven true in that formalism).

Better said: inconsistent means that any formula (of the formal language) is a theorem. So any "p" is a theorem, "no p" also a theorem obviously. That is, an inconsistent axiomatic theory is totally useless (and of course it can not have a Model, in the mathematical logic sense).

It would probably take a book--and a not very readable one--to define the standard model well enough to decide that it was incomplete. Inconsistent can be done pretty quickly. For example, almost every attempt to define physics inside a black hole ends up inconsistent, Whether that inconsistency applies outside the event horizon is model dependent.

I think you are quite mixing some things here.

In Physics we use some mathematical structures + some interpretation of some of its mathematical concepts in terms of physical measurements in experiments/observations.

For example, take Semi-Riemannian Geometry (used as a mathematical structure in General Relativity). It is true that there could exist one mathematical statement (involving only geometric concepts about semi-riemannian geometry) that is undecidable (one formula "p" of its formal language such that neither "p" nor "no p" is a theorem).

That would not be a problem (for Physics) if that mathematical statement "p" does not belong to the physical interpretation of the mathematical structure.

A similar example, let M be one given 4-dimensional Connected and time-oriented Lorentz manifold (a spacetime).

The mathematical statement: "There is a set A, A\subset M, such that Aleph_0 < Card(A) < 2^(Aleph_0)".

is undecidable within ZFC (equivalently NBG) assuming consistency of ZFC, but that is irrelevant for Physics, because that fact does not affect the way we use that mathematical structure (spacetimes) to do Physics (that mathematical statement does not belong to the physical interpretation (of some mathematical concepts of that mathematical structure)).

 

[mattt]

What you end up with is that if there is a consistent TOE, it can not be proved consistent inside this universe.

Again, not to nitpick, but I quite don't like the way you state things.

First of all, what do you mean by a "Theory of Everything"?

We humans just create concepts and find relations between these very same concepts we create and then we decide about its usefulness.

What is consistent or inconsistent (in the mathematical logic sense) is a given axiomatic theory. Some parts of Physics use rigorously defined mathematical structures, and some other not (QFT, ST...).

Even if we find a way in the future to define QFT and ST (or whatever new Physics there may come) in a totally rigorous mathematical way, (let us say like Symplectic Geometry for Hamiltonian Mechanics or like SemiRiemannian Geometry for General Relativity or Functional Analysis for Non-Relativistic Quantum Mechanics), what would be consistent or not is the mathematical structure (just like those examples, that are mathematically consistent, assuming consistency of ZFC), so in that case what we will have is "X rigorous mathematical structure (that future Physics will be based on) is consistent (assuming consistency of ZFC)" just like today we can say that "Semi-Riemannian Geometry is consistent (assuming consistency of ZFC)".

That does not mean that the new theory is useless, just that the universe will have properties that cannot be derived from the new theory.

Again, I don't get what you are trying to say with this: "the universe will have properties that cannot be derived from the (new) theory".

First of all, we can only talk about concepts we ourselves create. That is to say, the mathematical structure used, has an infinite number of theorems, and SOME of them we have given a physical interpretation in terms of measurements in experiments and observations. The mathematical structure + physical interpretation, is more useful or less useful, and that is something we have to decide (with experiments and consensus).

It seems you are trying to say that if the mathematical structure (what you call TOE) is mathematically incomplete (in the mathematical logic sense) then the "Universe" will have some "properties" that are not "expressable in the formal language" or just "expressable but will not be theorems".

There would be mathematical statements (formulas of its formal language) "p" such that neither "p" nor "no p" are theorems (given that that axiomatic theory (TOE) is consistent and incomplete) and so there will exist one Model (in the mathematical logic sense) of that TOE in which "p" is true and ALSO another Model (in the mathematical logic sense) of that TOE in which "p" is false.

Those "undecidable statements "p" of that consistent and incomplete axiomatic theory" could or could not be interpretable in terms of measurements (belong or not belong to the physical interpretation of the mathematical structure), i.e. it could have nothing to do with "physics".

That means the best we can get is to run experiments and not finding any contradictions. However, that shoe, or more realistically an extremely high energy cosmic ray can come along and mess up any particular experiment. In other words there will always be room to look for new physics, even if you don't find any.

I don't understand what you say here.

 

[eachus]

People seem to be getting wrapped around the wrong axle here. Let me take a real example which (astro)physicists would to solve. Take a solar system with multiple planets. For simplicity we will put the system in inter(galactic)cluster space, with no nearby masses. If there will be a collision between planets in the near future, you can compute the orbits and predict when that will happen. What if you can't predict any collisions? Does that mean there will be none? No.* This is the Halting Problem from computability theory applied to a large analog computer.

Many physicists are willing to accept that there is no closed form solution to three or more body problems (other than Lagrange points). That's fine, they are willing to work with an incomplete theory. In fact, every serious physicist tends to make that decision. Inconsistent physical theories exist, and some of them are useful, but only because we don't have anything better. General Relativity is inconsistent (very) near black holes, but is useful elsewhere. Well, time-travel demons could arrive at your experiment at any arbitrary time, unannounced. But we as a community tend to ignore those unrepeatable, unexplainable events.

So what am I really trying to communicate here? That it is useless to try merging GR and QM. You get a UFT which is both incomplete, and inconsistent. Some physicists have developed consistent versions of GR, but they are hard to test outside of event horizons. Merging a singularity free theory with QM might result in a more useful theory, even if it is hard to test.

*Yes, I know that the system will emit gravitational radiation, and eventually collapse from that..Here I am talking about tens of orders of magnitude of time before then, where the uncertainty principle prevents you from measuring the state of the system with sufficient accuracy to get the correct answer. But even if you strip that away, by insisting that your (digital) computer model is the one that matters,, you still can't get an answer in all cases.

 

[rootone]

What you are saying seems to me to be that there always will be unfathomable mysteries.
I guess in a way that's how science progresses though.
Who knows, it could happen tomorrow that somebody announces a discovery that confirms string theory is correct..
That having been established, we then are compelled to go asking what the hell are these goddam strings things though?
Where do they come from?

 

[eachus]

What you are saying seems to me to be that there always will be unfathomable mysteries.

Exactly. If we insist on consistent theories, there will always be some things which we can't know. Doesn't mean there isn't a more complete theory than the one we have today, just that there is a limit, and probably a limit we can't know.

Of course, Godel's theorem is a wonderful answer to those who say there are things that man is not meant to know. Okay, if we are not meant to know it, we can't know it. It would be nice if that would end the discussion, but there are a lot of people who don't quite understand things like diagonalization proofs.

Who knows, it could happen tomorrow that somebody announces a discovery that confirms string theory is correct.. That having been established, we then are compelled to go asking what the hell are these goddam strings things though? Where do they come from?

Or the LHC could discover super-symmetric particles this year. (If they do it would be nice if they explain dark matter.) But proving string theory or super symmetry would not be a proof that there are no particles remaining to be found.

 

[mattt]

People seem to be getting wrapped around the wrong axle here. Let me take a real example which (astro)physicists would to solve. Take a solar system with multiple planets. For simplicity we will put the system in inter(galactic)cluster space, with no nearby masses. If there will be a collision between planets in the near future, you can compute the orbits and predict when that will happen. What if you can't predict any collisions? Does that mean there will be none? No.* This is the Halting Problem from computability theory applied to a large analog computer.

The mathematical structures we use to create mathematical models of physical phenomena, are more useful or less useful. We have ways to decide about their usefulness.

Many physicists are willing to accept that there is no closed form solution to three or more body problems (other than Lagrange points). That's fine,

There are several mathematical theorems about that subject. "Willing to accept" seems a very odd way of saying "they know some mathematical theorems".

they are willing to work with an incomplete theory. In fact, every serious physicist tends to make that decision. Inconsistent physical theories exist, and some of them are useful, but only because we don't have anything better. General Relativity is inconsistent (very) near black holes, but is useful elsewhere

Obviously you are using the word "inconsistent" in a different way than it is used in Mathematics or even in Physics. General Relativity is, basically, Semmi-Riemannian Geometry with a given interpretation of some of its mathematical concepts. So it is mathematically consistent ( assuming consistency of ZFC ).

Another different thing (and I think this is what you are trying to point out) is that it is more useful or less useful, depending on what you want to do with it.

. Well, time-travel demons could arrive at your experiment at any arbitrary time, unannounced. But we as a community tend to ignore those unrepeatable, unexplainable events.

So what am I really trying to communicate here? That it is useless to try merging GR and QM.

What? :-(

You get a UFT which is both incomplete, and inconsistent.

What?

Trying to create a (consistent) mathematical model whose range of applicability is larger and larger is just going on with part of what Science has achieved during the last, at least, 300 years. Creating new and better models whose range of validity is larger than previous models.

Some physicists have developed consistent versions of GR, but they are hard to test outside of event horizons. Merging a singularity free theory with QM might result in a more useful theory, even if it is hard to test.

*Yes, I know that the system will emit gravitational radiation, and eventually collapse from that..Here I am talking about tens of orders of magnitude of time before then, where the uncertainty principle prevents you from measuring the state of the system with sufficient accuracy to get the correct answer. But even if you strip that away, by insisting that your (digital) computer model is the one that matters,, you still can't get an answer in all cases.

Not sure if I understand what you try to say.

If you are trying to say that there will always exist things that we can not predict or calculate with "total" accuracy, or even that there will still exist things that we can not even "explain"...well, it is probably true.

But what the heck does it have to do with us creating better and better models with larger range of validity?

I mean, it seems to me you were kind of criticizing our efforts of trying to create models of quantum gravity (or whatever we think will be the next improvement in our quest for consistent models with larger range of validity), basing your opinion in that there will always be things we, possibly, could not explain or predict.

It is that what you're trying to say?

 

[sophiecentaur]

There is no "need" in a logical sense. It is just based on a faith in the intelligibility of the world, and past historical experience. As we discover more about fundamental physics, the whole structure seems to become more "unified", in the sense that the number of independent conceptual elements becomes smaller. Things that were previously considered separate become related or unified. Overwhelming evidence points to the existence of a kind of "final stage" or an "eschaton" in this process of unification, that is generally called "quantum gravity"

But this process has been subjected to a series of significant hiccups and changes of direction. One could say that things have ended up as they are in a form of logical progression but that's more a statement of faith than evidence based. As far as I can se, all we can expect is a series of 'Theories of Most things we know about". I have no problem with accepting that we cannot expect to know it all. Indeed, it seems a ludicrous notion - bordering on religion (which is equally badly founded).
My Dad was quite knowledgeable for my purposes when I was a lad and I don't feel the need to replace him with a more and more super-Dad to explain all I would ever want to know.

 

[dx]

But this process has been subjected to a series of significant hiccups and changes of direction. One could say that things have ended up as they are in a form of logical progression but that's more a statement of faith than evidence based. As far as I can se, all we can expect is a series of 'Theories of Most things we know about". I have no problem with accepting that we cannot expect to know it all. Indeed, it seems a ludicrous notion - bordering on religion (which is equally badly founded).
My Dad was quite knowledgeable for my purposes when I was a lad and I don't feel the need to replace him with a more and more super-Dad to explain all I would ever want to know.

That is why I don't like the phrase "Theory of Everything." There are things in the world that can never be understood, like beauty, because beauty is not in the field of consciousness or within the grasp of thought. However my notion of quantum gravity is not a "theory of everything."

If theoretical physics is like a story, then quantum gravity is like the climax of the story. Or if you think of physics as sex, then quantum gravity is the orgasm. (Moderators feel free to delete that last part if you think its inappropriate)

 

[eachus]

There are several mathematical theorems about that subject. "Willing to accept" seems a very odd way of saying "they know some mathematical theorems".

When you accept even simple mathematics (2+2=4) , you get Godel's proof along with it. Most of the time you can kick it into a corner and ignore it. Other times, it is in your face. I remember a time when studying the strong force meant dealing with infinities. Fortunately renormalization came along and pushed those infinities back into the dusty corners. But with general relativity, there are still infinities, and they are in the black holes that are all over the place. (On a stellar scale at least.) You may not be able to see into a black hole, but they are sort of tough to ignore.

Obviously you are using the word "inconsistent" in a different way than it is used in Mathematics or even in Physics. General Relativity is, basically, Semi-Riemannian Geometry with a given interpretation of some of its mathematical concepts. So it is mathematically consistent ( assuming consistency of ZFC ).

No it is not consistent, and at a very fundamental level. We talk about the Schwarzschild radius of a black hole, while ignoring the fact that GR says it is infinite. Any radius beginning at the center of a black hole is infinite in GR. That rubber sheet gets stretched to infinity. It is possible to (approximately) measure the circumference at the event horizon and divide by 2π, but that radius is not physical. Similarly, if I measure the potential energy of two particles relative to a black hole and subtract, I get garbage. The distributive law doesn't work. To be blunt, anywhere in a GR universe with at least one black hole, I can prove that 2+2=5, or 42, or whatever. Do I believe that there is a version of GR that gets rid of the infinities? Sure. It may or may not be physically correct, it is hard to take measurements inside a black hole, but it could be consistent. Hawking has recently done some work which says that the event horizon may be impossible to measure accurately. So the best we can do for now is to say that we have a (mostly) consistent physics except near black holes.

Another different thing (and I think this is what you are trying to point out) is that it is more useful or less useful, depending on what you want to do with it.

No, what I said was: "That it is useless to try merging GR and QM." Right now, absent black holes, GR is consistent, and so is QM. But wishing black holes away doesn't work. And the really nasty piece of work in GR is that it is possible for things, particles, information, anything to violate causality and do it outside the event horizon (in the ergosphere). So the problems with GR are not localized to the region of black holes like we might hope, but can spread to anywhere within the event cone of the black hole.

I would like for someone to "fix" that part of GR, but it seems impossible. You may have heard the joke: "QM, GR, and causality. Pick any two." If you try to rigorously merge QM and GR, causality seems to go out the window. Way out the window. Maybe someone can come up with a logic that works without causality, but I am not holding my breath. Until then the best choice seems to be some version of GR where the distortion of space in the area of a rotating black eliminates time-travel. Hawking seemed to be headed this way with his closed timelike loops (CTL). A true CTL outside an event horizon would contain immeasurable energy. (See Heisenberg.) If every route around a black hole that violates causality has to cross a CTL then causality is preserved. (Unfortunately, this may be true for a static rotating black hole, but throw enough mass in and you may be able to sneak through.)

If you are trying to say that there will always exist things that we can not predict or calculate with "total" accuracy, or even that there will still exist things that we can not even "explain"...well, it is probably true.

It is true, it was proved a century ago by Godel. Douglas Hofstetter's book "Godel, Escher, Bach, an Eternal Golden Braid" is probably the best book on the subject for non-specialists. The writing is excellent, but the material is very hard. What you should get out of the book is that there are true statements that cannot be proven true in any consistent formal system. (You will also understand emergent properties very well.)

But what the heck does it have to do with us creating better and better models with larger range of validity?

I mean, it seems to me you were kind of criticizing our efforts of trying to create models of quantum gravity (or whatever we think will be the next improvement in our quest for consistent models with larger range of validity), basing your opinion in that there will always be things we, possibly, could not explain or predict.

It is that what you're trying to say?

The point that (current) GR and QM cannot be usefully merged is very worth knowing. (AKA the renormalization issues are impossible.) Loop quantum gravity (LQG) and spin foams may result in a version of gravity that is consistent even inside event horizons. Then a merger with QM becomes useful.

Finally, the press may like the name theory of everything (ToE) for a unified field theory(UFT). But the distance between a UFT and a ToE is not just immense. It may be impossible to cross. (A real ToE at least has to deal with dark matter and dark energy.)

 

[rootone]

Well I certainly won't worry about the 'Press'
I have not even a theory off how all these apps I did not ask for start turning up on my new phone.

 

[mattt]

When you accept even simple mathematics (2+2=4) , you get Godel's proof along with it. Most of the time you can kick it into a corner and ignore it. Other times, it is in your face. I remember a time when studying the strong force meant dealing with infinities. Fortunately renormalization came along and pushed those infinities back into the dusty corners. But with general relativity, there are still infinities, and they are in the black holes that are all over the place. (On a stellar scale at least.) You may not be able to see into a black hole, but they are sort of tough to ignore.

Again, you are confounding things. Mathematics and Physics are different things. I tried to explain it to you in previous posts.

No it is not consistent, and at a very fundamental level. We talk about the Schwarzschild radius of a black hole, while ignoring the fact that GR says it is infinite. Any radius beginning at the center of a black hole is infinite in GR. That rubber sheet gets stretched to infinity. It is possible to (approximately) measure the circumference at the event horizon and divide by 2π, but that radius is not physical. Similarly, if I measure the potential energy of two particles relative to a black hole and subtract, I get garbage. The distributive law doesn't work. To be blunt, anywhere in a GR universe with at least one black hole, I can prove that 2+2=5, or 42, or whatever. Do I believe that there is a version of GR that gets rid of the infinities? Sure. It may or may not be physically correct, it is hard to take measurements inside a black hole, but it could be consistent. Hawking has recently done some work which says that the event horizon may be impossible to measure accurately. So the best we can do for now is to say that we have a (mostly) consistent physics except near black holes.

No, what I said was: "That it is useless to try merging GR and QM." Right now, absent black holes, GR is consistent, and so is QM. But wishing black holes away doesn't work. And the really nasty piece of work in GR is that it is possible for things, particles, information, anything to violate causality and do it outside the event horizon (in the ergosphere). So the problems with GR are not localized to the region of black holes like we might hope, but can spread to anywhere within the event cone of the black hole.

I would like for someone to "fix" that part of GR, but it seems impossible. You may have heard the joke: "QM, GR, and causality. Pick any two." If you try to rigorously merge QM and GR, causality seems to go out the window. Way out the window. Maybe someone can come up with a logic that works without causality, but I am not holding my breath. Until then the best choice seems to be some version of GR where the distortion of space in the area of a rotating black eliminates time-travel. Hawking seemed to be headed this way with his closed timelike loops (CTL). A true CTL outside an event horizon would contain immeasurable energy. (See Heisenberg.) If every route around a black hole that violates causality has to cross a CTL then causality is preserved. (Unfortunately, this may be true for a static rotating black hole, but throw enough mass in and you may be able to sneak through.)It is true, it was proved a century ago by Godel. Douglas Hofstetter's book "Godel, Escher, Bach, an Eternal Golden Braid" is probably the best book on the subject for non-specialists. The writing is excellent, but the material is very hard. What you should get out of the book is that there are true statements that cannot be proven true in any consistent formal system. (You will also understand emergent properties very well.)

Again, you are confounding so many things. Some non-textbooks (or pop-science books) are entertaining, but almost always, only specialists understand what actually lies beneath.

"Godel, Escher, Bach, an Eternal Golden Braid" is a good non-rigorous book (I read it twice ten years ago, before studying Mathematics), but the things you think you understood about it, the way you state those things, clearly you didn't understand it (as I explained in previous posts).

Better start with this one: http://www.uv.es/ivorra/Libros/Logica.pdf (This is absolutely great, totally rigorous, but sadly it is in Spanish) or this other one: "Axiomatic Set Theory" (Suppes).

The point that (current) GR and QM cannot be usefully merged is very worth knowing. (AKA the renormalization issues are impossible.) Loop quantum gravity (LQG) and spin foams may result in a version of gravity that is consistent even inside event horizons. Then a merger with QM becomes useful.

Finally, the press may like the name theory of everything (ToE) for a unified field theory(UFT). But the distance between a UFT and a ToE is not just immense. It may be impossible to cross. (A real ToE at least has to deal with dark matter and dark energy.)

You mix things that has nothing to do with each other. You'll understand it all much better if you study Mathematics and Physics. Have to go back to work now, more later.

 

[matt621]

Generally the "need" comes from the desire to answer the question: Is the universe created or did it just happen. If a UFT can be found, their is a reasonable next question: Why? Pretty much everyone wants to have a firm belief system. There are atheist that are sure of their position just like there are theists that are sure of their position. Then there is everyone else. They "need" to know if God exists or not. Atheists are sure he/she/it does not exist, but their belief is not more assured than the theist that says he/she/it does exist. Everyone else just wants to know. I think that "need" comes from trying to answer the 2nd question, "Why?"

The problem is this: the universe seems to be ordered. That flys in the face of atheists. (Which many if not most scientists claim to be.) But can order really come out of chaos (or nothing) by it's own accord? Science does it's best to prove it can, but for ever "hit" there is a corresponding "miss." So the point is that it's an unanswerable question. I personally believe Pi is the answer. Pi cannot be solved. It's a never ending quest but it's ultimately unknowable. For me, that proves God does exist because it proves the unknowable in an ordered universe. If the universe really created itself, then everything should be knowable. (Hence the "need" for a UFT.) The fact that there are unknowable elements in the universe seem to indicate that it's meant to be that way. It's a paradox by design.

Twice.