The theory of everything

Tom Mattson

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Yes, absolutely. The reason physics will never be complete has nothing to do with Goedel. It has to do with the fact that physics is done a posteriori, as opposed to mathematics which is a priori. That means that it's always possible to do an experiment tomorrow that current theories cannot describe. That is why physics will never be complete. Although I'm loathe to use the word "complete" here for fear that it will be misunderstood as the same kind of "complete" that Goedel was talking about...
 
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A theory of everything would be inconsistent. This means that a theory could not cover everything,
Just noticed it:)
Inconsistent theory covers everything, because ANY statement is derivable there.
What you probably wanted to say, "incomplete"
 
2,460
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Yes, absolutely. The reason physics will never be complete has nothing to do with Goedel. It has to do with the fact that physics is done a posteriori, as opposed to mathematics which is a priori. That means that it's always possible to do an experiment tomorrow that current theories cannot describe. That is why physics will never be complete. Although I'm loathe to use the word "complete" here for fear that it will be misunderstood as the same kind of "complete" that Goedel was talking about...
Well, here I am not sure.
If Max Tegmark's vision of TOE is true (mathematics does not DEFINE real world, it IS real world) then there is no difference between physics and mathematics.
 

Tom Mattson

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How would one even begin to test such a hypothesis? To me that sounds like saying that a map isn't just a representation of the territory, it is the territory.
 
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How would one even begin to test such a hypothesis? To me that sounds like saying that a map isn't just a representation of the territory, it is the territory.
Piece of cake
If there is no difference between map and territory, then map IS territory
If TOE can be defined using just equations, with ZERO blah-blah (Max Tegmark calls it 'baggage') then it is true
 

Tom Mattson

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If there is no difference between map and territory,
That's a pretty big "if". How would you know if there is no difference? There's an intrinsic error associated with every measurement.
 

SixNein

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Yes, absolutely. The reason physics will never be complete has nothing to do with Goedel. It has to do with the fact that physics is done a posteriori, as opposed to mathematics which is a priori. That means that it's always possible to do an experiment tomorrow that current theories cannot describe. That is why physics will never be complete. Although I'm loathe to use the word "complete" here for fear that it will be misunderstood as the same kind of "complete" that Goedel was talking about...
"That means that it's always possible to do an experiment tomorrow that current theories cannot describe. " -tom

This is exactly what the incomplete theorem is stating.

"That is why physics will never be complete"

Physics will never be complete because math cannot be complete. You seem to want to separate the two fields, but they are joined at the hip. When a new thing is observed in physics, you usually find something in pure mathematics for it.
 

SixNein

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That's a pretty big "if". How would you know if there is no difference? There's an intrinsic error associated with every measurement.
You do know that is defined in math as well. Cantor opened that can of worms, as well as many others.

I think you just haven't seen mathematics in this kind of light. Physics has poster children like Einstein and Newton. While in the early days some names appear on both list, they are mostly remembered for work in physics. While great mathematicians are not mentioned at all, or they are just remembered for going crazy.

Example List:
Georg Cantor
Aryabhatta
Kurt Godel
Euclid of Alexandria
Carl F. Gauss
Leonhard Euler
Bernhard Riemann
Henri Poincare
Niels Abel
Evariste Galois

When a lot of mathematicians see the universe, they see numbers. It's one of the reasons some mathematicians go nuts. They get too focused on the numbers, and they don't step back and look at the big picture. You can take any number and find it everywhere.
 
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You still need to prove that Godel theorem is applicable to TOE equations.
 

SixNein

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You still need to prove that Godel theorem is applicable to TOE equations.
Perhaps you should read Stephen Hawking's page on Godel's theorem:
http://www.damtp.cam.ac.uk/strings02/dirac/hawking/

My explanation is that physical theories are mathematical models. To give you an example, Einsteins theory of relativity relies on the geometry created by Riemann (geometry of sapce). If there is some kind of mathematical extension or limitation found of Riemanns work, it will directly effect physics and it's concept of space.
 
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OMG!!! How many times should I repeat: Godels theorem IS NOT applicable to ANY mathematical axiom system (and Hawking does not try cover the applicability issues in this short article). Geometry for example is Godel-free. Even algebra - you probably think that algebra is about numbers, so Godel is applicable to algebra, BUT IT IS NOT!

So when you have some equations (TOE for example) IT DOES NOT MEAN that Godels theorem is automatically applicable.
 

SixNein

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OMG!!! How many times should I repeat: Godels theorem IS NOT applicable to ANY mathematical axiom system (and Hawking does not try cover the applicability issues in this short article). Geometry for example is Godel-free. Even algebra - you probably think that algebra is about numbers, so Godel is applicable to algebra, BUT IT IS NOT!

So when you have some equations (TOE for example) IT DOES NOT MEAN that Godels theorem is automatically applicable.
Did you even read my post?

And yes it very much applies to physics.

Another Paper:
http://pirate.shu.edu/~jakistan/JakiGodel.pdf
 
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apeiron

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Jaki writes......
"Herein lies the ultimate bearing of Gödel's theorem on physics. It
does not mean at all the end of physics. It means only the death knell on
endeavours that aim at a final theory according to which the physical
world is what it is and cannot be anything else. Gödel's theorem does not
mean that physicists cannot come up with a theory of everything or TOE
in short. They can hit upon a theory which at the moment of its formulation
would give an explanation of all known physical phenomena. But in
terms of Gödel's theorem such a theory cannot be taken for something
which is necessarily true."

I would phrase it somewhat differently.

We can have a TOE, but we can't know it to be true. We will only be able to observe that it seems true.

So the Platonic dream is dead. Maths is not special in that sense, but instead just a practical exercise in modelling, with the limitations on "truth" that are part of modelling.

The universe can still be mathematical (with a small m) because mathematics is the modelling of logical patterns, patterns which for some reason (and here we would get into self-organisation metaphysics) will emerge with high regularity.

Godel should be taken as the death knell of Platonism. But there were already many other reasons for rejecting Platonism already.

A TOE is still a plausible project. Though the requirements are very high - all variable constants would have to emerge out the modelling of the ultimate pattern.

Current approaches like strings and standard models don't even seem close to achieving this. But actually, symmetry breaking as a general story can be seen to be heading in the desired direction.

And even if the goal cannot be achieved, it does appear to proper to be orientated in its direction.

So godel rightfully kills off Platonism, but that still leaves the modelling relations approach as the valid path to knowledge. And a TOE can still stand as its ultimate goal.
 

SixNein

Gold Member
38
16
Jaki writes......
"Herein lies the ultimate bearing of Gödel's theorem on physics. It
does not mean at all the end of physics. It means only the death knell on
endeavours that aim at a final theory according to which the physical
world is what it is and cannot be anything else. Gödel's theorem does not
mean that physicists cannot come up with a theory of everything or TOE
in short. They can hit upon a theory which at the moment of its formulation
would give an explanation of all known physical phenomena. But in
terms of Gödel's theorem such a theory cannot be taken for something
which is necessarily true."

I would phrase it somewhat differently.

We can have a TOE, but we can't know it to be true. We will only be able to observe that it seems true.

So the Platonic dream is dead. Maths is not special in that sense, but instead just a practical exercise in modelling, with the limitations on "truth" that are part of modelling.

The universe can still be mathematical (with a small m) because mathematics is the modelling of logical patterns, patterns which for some reason (and here we would get into self-organisation metaphysics) will emerge with high regularity.

Godel should be taken as the death knell of Platonism. But there were already many other reasons for rejecting Platonism already.

A TOE is still a plausible project. Though the requirements are very high - all variable constants would have to emerge out the modelling of the ultimate pattern.

Current approaches like strings and standard models don't even seem close to achieving this. But actually, symmetry breaking as a general story can be seen to be heading in the desired direction.

And even if the goal cannot be achieved, it does appear to proper to be orientated in its direction.

So godel rightfully kills off Platonism, but that still leaves the modelling relations approach as the valid path to knowledge. And a TOE can still stand as its ultimate goal.
Well aim for the stars I suppose. I believe that physics will begin looking more like pure mathematics as time progresses. In fact I would go so far as to say that it will eventually become a division of it. Physicist are limited on what they can observe in the universe. They have the earth, solor system, and then light. The problem is that space is expanding rapidly and they have a limited area of what they can observe. There is a whole lot in that area, but I believe there is likely much more outside of it. Since space is expanding, what we can view is decreasing as time progresses. So eventually people will be forced to explore the universe mathematically.

Hopefully one day mankind will be able to take over evolution enough to greatly increase lifespan. Thus we can travel outside of our play-pen and begin doing some Columbus-style exploring. We may not be able to travel the speed of light, but we can figure out a way to survive the time.
 

apeiron

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Which conflicts with what I said in what way?

Except you want to oppose maths to physics which is unsophisticated epistemology.

The more useful opposition is between modeller and modelled. Then having accepted there is a modelling relation, between the formal model and its informal measurements.

If you are really interested in the proper implications of Godel for epistemology, there is a considerable literature. It is actually a very interesting subject - too rich for debate to be cut off at a binary Godelian, yes you can/no you can't, level.

Again I would urge you to seek out something like Robert Rosen's Essays on Life Itself if you want to see what came after Godel.
 
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0
SixNein said:
You do know that is defined in math as well. Cantor opened that can of worms, as well as many others.

I think you just haven't seen mathematics in this kind of light. Physics has poster children like Einstein and Newton. While in the early days some names appear on both list, they are mostly remembered for work in physics. While great mathematicians are not mentioned at all, or they are just remembered for going crazy.

Example List:
Georg Cantor
Aryabhatta
Kurt Godel
Euclid of Alexandria
Carl F. Gauss
Leonhard Euler
Bernhard Riemann
Henri Poincare
Niels Abel
Evariste Galois

When a lot of mathematicians see the universe, they see numbers. It's one of the reasons some mathematicians go nuts. They get too focused on the numbers, and they don't step back and look at the big picture. You can take any number and find it everywhere.

Maybe some aspects of the universe weren't meant to be discovered. We humans see the universe through a very tiny distorting slit. Anyone who ventures to enhance this tiny slit gets a headache. You get to ask all kinds of questions - what are we?, what is the true nature of reality?, why are there limitations on what we are allowed to know?, why do we see the world the way we do?, why does this orderly mostly electromagntic stuff seem solid?, why does maths describe the universe so well?, etc. etc.

Maybe our logic is flawed and that's the reason we can't comprehend everything. But then what kind of higher logic rules the unexplainable? (Big Bang, infinities, black holes, emergent properties, arrow and the experience of time etc.)

As scientists uncover more aspects about existence and the true nature of reality, lay people would see that the world they perceive is not the world their incredible human drama rests upon. We do create a sort of reality within the wider reality and our senses are anything but a reliable tool to describe reality.

There are no colors in the real world. That there are no textures in the real world. There are no fragrances in the real world. There is no beauty, there is no ugliness. Nothing of the sort. Out there is a chaos of energy soup and energy fields. Literally. We take that and somewhere inside ourselves we create a world. Somewhere inside ourselves it all happens.

All that we can tentatively say that exists is four basic forces: gravity, strong interaction, weak interaction and electromagnetism, that make up everything in the known universe. "Tentatively" because 'exist' is a loaded word, no one knows for sure if there is an objective reality at all. So WTF is the material world then? We are the creators of this world. Literally. The classical world is our creation. It's almost unreal.

So how can we, under the chains of limited and distorted perception, from within the experience, describe the true nature of what we experience? How could we explain ourselves? It seems you either reach a conclusion about some higher power/intelligence behind this or you acknowledge that the universe is unknowable, thus rendering a full TOE unthinkable.
 
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0
SixNein said:
Well aim for the stars I suppose. I believe that physics will begin looking more like pure mathematics as time progresses. In fact I would go so far as to say that it will eventually become a division of it. Physicist are limited on what they can observe in the universe. They have the earth, solor system, and then light. The problem is that space is expanding rapidly and they have a limited area of what they can observe. There is a whole lot in that area, but I believe there is likely much more outside of it. Since space is expanding, what we can view is decreasing as time progresses. So eventually people will be forced to explore the universe mathematically.

Einstein and his wife were invited to see the highest power telescope. As the cosmologist(friend of Einstein) was presenting to her the capabilities of the apparatus to observe the far reaches of the universe, she said "My husband uses the envelopes of the letters he receives to do that".
 

SixNein

Gold Member
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Which conflicts with what I said in what way?

Except you want to oppose maths to physics which is unsophisticated epistemology.

The more useful opposition is between modeller and modelled. Then having accepted there is a modelling relation, between the formal model and its informal measurements.

If you are really interested in the proper implications of Godel for epistemology, there is a considerable literature. It is actually a very interesting subject - too rich for debate to be cut off at a binary Godelian, yes you can/no you can't, level.

Again I would urge you to seek out something like Robert Rosen's Essays on Life Itself if you want to see what came after Godel.
You can argue for a TOE in a "Shoot for the stars" fashion, but you will never obtain it. I don't see how you think physics can escape its foundation. Just a few years ago, Stephen Hawking argued for a TOE. In fact, read his book a brief history of time. However, Hawking is starting to accept reality and more will follow in the coming years. Quite frankly it should have been realized by him and others before implications of black holes.

Philosophically there is plenty of interesting things that can be said of Godel's work. Physicist are religiously holding onto a dream of a TOE even though there is overwhelming mathematical evidence to refute it. Perhaps that shows we are incomplete and have deep desires to find something that will make us whole.
 
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SixNein

Gold Member
38
16
Maybe some aspects of the universe weren't meant to be discovered. We humans see the universe through a very tiny distorting slit. Anyone who ventures to enhance this tiny slit gets a headache. You get to ask all kinds of questions - what are we?, what is the true nature of reality?, why are there limitations on what we are allowed to know?, why do we see the world the way we do?, why does this orderly mostly electromagntic stuff seem solid?, why does maths describe the universe so well?, etc. etc.

Maybe our logic is flawed and that's the reason we can't comprehend everything. But then what kind of higher logic rules the unexplainable? (Big Bang, infinities, black holes, emergent properties, arrow and the experience of time etc.)

As scientists uncover more aspects about existence and the true nature of reality, lay people would see that the world they perceive is not the world their incredible human drama rests upon. We do create a sort of reality within the wider reality and our senses are anything but a reliable tool to describe reality.

There are no colors in the real world. That there are no textures in the real world. There are no fragrances in the real world. There is no beauty, there is no ugliness. Nothing of the sort. Out there is a chaos of energy soup and energy fields. Literally. We take that and somewhere inside ourselves we create a world. Somewhere inside ourselves it all happens.

All that we can tentatively say that exists is four basic forces: gravity, strong interaction, weak interaction and electromagnetism, that make up everything in the known universe. "Tentatively" because 'exist' is a loaded word, no one knows for sure if there is an objective reality at all. So WTF is the material world then? We are the creators of this world. Literally. The classical world is our creation. It's almost unreal.

So how can we, under the chains of limited and distorted perception, from within the experience, describe the true nature of what we experience? How could we explain ourselves? It seems you either reach a conclusion about some higher power/intelligence behind this or you acknowledge that the universe is unknowable, thus rendering a full TOE unthinkable.
That was very well written.
 
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Did you even read my post?

And yes it very much applies to physics.

Another Paper:
http://pirate.shu.edu/~jakistan/JakiGodel.pdf
Yes, I read your post and the article.

I repeat, Godel theorem may be or may be not applicable to TOE. You dont know utilyou see the equations.

Regarding "you can not know that it is TOE" - this is always an issue in physics: no experiment can confirm that a theory is TRUE. Experiments can only confirm that a theory is wrong. Even more, the most fundamental theories we have (GR and Standard Model) are well known to be false because they are inconsistent and both break and Planks scale

Finally, Godel (if it is applicable) means that one can not derive all consequences from the TOE equations. Again, it is always the case: can you derive when the economy will be back to normal from the Standard Model?
 
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SixNein

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Yes, I read your post and the article.

I repeat, Godel theorem may be or may be not applicable to TOE. You dont know utilyou see the equations.

Regarding "you can not know that it is TOE" - this is always an issue in physics: no experiment can confirm that a theory is TRUE. Experiments can only confirm that a theory is wrong. Even more, the most fundamental theories we have (GR and Standard Model) are well known to be false because they are inconsistent and both break and Planks scale

Finally, Godel (if it is applicable) means that one can not derive all consequences from the TOE equations. Again, it is always the case: can you derive when the economy will be back to normal from the Standard Model?
The math would have to be extremely trivial and I honestly don't believe that is going to happen. Just look at the math behind a black hole.

The purpose of a TOE is to link and fully explain ALL known physical phenomena. I think you just answered yourself of why that cannot happen. You can take a question out of mathematics like prime numbers, and make it a physical question. Physics is like pure mathematics and is inexhaustible.
 
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The purpose of a TOE is to link and fully explain ALL known physical phenomena.
Contrary to its name, Theory of Everything is not a theory of EVERYTHING: it is just a funny name given by physicists, like Higgs boson is called a "God's particle"

It must explain all fundamental experiments, but not all outcomes of all experiments.

As an example, think about the Peano axiomatics. It is a theory of natural numbers, it axioms play the same role in the theory of numbers as TOE equations will play in physics. And still, Peano axioms do not allow to prove or dissaprove ALL statements regarding natural numbers (because of Goedel)
 

DaveC426913

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"A fish cannot comprehend the existence of water. He is too deeply immersed in it."
- Sir Oliver Lodge

How would we know of our limitations when we exist within them?
 

SixNein

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Contrary to its name, Theory of Everything is not a theory of EVERYTHING: it is just a funny name given by physicists, like Higgs boson is called a "God's particle"

It must explain all fundamental experiments, but not all outcomes of all experiments.

As an example, think about the Peano axiomatics. It is a theory of natural numbers, it axioms play the same role in the theory of numbers as TOE equations will play in physics. And still, Peano axioms do not allow to prove or dissaprove ALL statements regarding natural numbers (because of Goedel)
Let me try to word this differently as this obviously isn't getting across. You could discover a new theory every single day for the next trillion years, and there will be plenty left to discover. Physics is inexhaustible, and any attempts to lay a finite TOE definition down will result in failure. It's not just the TOE that is forced to these rules, but all these physical systems. So how are you going to tie these systems together when you will never fully understand any system? You can't and that is why people like Stephen Hawking is coming across. You will never explain all of the fundamentals experiments with a TOE, ever.
 

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