Can Leptons and Quarks Lead to a Theory of Everything?

[Dmitry67]

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]

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

 

[apeiron]

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]

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]

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 modeled. 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.

 

[WaveJumper]

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.

 

[WaveJumper]

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]

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 modeled. 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.

 

[SixNein]

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.

 

[Dmitry67]

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 don't 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?

 

[SixNein]

Yes, I read your post and the article.

I repeat, Godel theorem may be or may be not applicable to TOE. You don't 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.

 

[Dmitry67]

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]

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"

This is what I'm sayin'. Is this not https://www.physicsforums.com/showpost.php?p=2113879&postcount=8"?


The TOE merely reconciles the 4 fundamental forces, no more.

 

[Gear300]

"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]

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.

 

[Dmitry67]

1. 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,

2. and any attempts to lay a finite TOE definition down will result in failure.

3. 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.

1. True. There are plenty of things which are too difficult to derive directly from the first principles. Take organic chemistry for example.

2. False, if by TOE we mean "the most deep (fundamental) theory"

3. You logic is wrong.

Finite set of Peano axioms defines a world of number theory - you can study all the consequences of these few axioms for, as you say, trillions years.

You can explain the rules of Chess game on a small piece of paper, and it keeps so many people occupied for so many years.

If you remember, there is even simpler thing, the "LIFE" game on an infinite board, simple rules, infinity of possibilities.

So an infinite complexiness of our world can be a result of a small set of TOE equations.

 

[WaveJumper]

So an infinite complexiness of our world can be a result of a small set of TOE equations.

This flies directly in the face of Goedel's incompleteness theorem. A mathematical equation that describes a complete and final theory. When you see that(as opposed to just musing over it), let me know.

 

[WaveJumper]

This is what I'm sayin'. Is this not https://www.physicsforums.com/showpost.php?p=2113879&postcount=8"?


The TOE merely reconciles the 4 fundamental forces, no more.

...and those 4 forces give rise and constitute everything that was or ever will be in what we perceive as 'universe'. In principle, we should be able to derive and mathematically 'reconstruct' all the known phenomena if we have the solid basis of having a unified field. But i don't believe this, there are too many limitations and obscurities on the way. How can we find consciousness when an individual changes 98% of the atoms of his body in a year? The atoms in the molecules of the brain are said to change even sooner - every 6 months and the perception of preservation of the self in this process is astonishingly convincing.

It's amazing how arrogant humans can be - just 140 years ago our great grandparents didn't have electricity and were using candles and rode horses and carts and today we are already confident that we have the power to know all there is to know about the universe. I think we need to calm down and see if we can make it through to the next century first. As Michio Kaku says - the transition between type 0 civilisation and type 1 is the most perilous and the biggest challenge.

 

[SixNein]

It's amazing how arrogant humans can be - just 140 years ago our great grandparents didn't have electricity and were using candles and rode horses and carts and today we are already confident that we have the power to know all there is to know about the universe. I think we need to calm down and see if we can make it through to the next century first. As Michio Kaku says - the transition between type 0 civilisation and type 1 is the most perilous and the biggest challenge.

I think the limitations of physics is misunderstood by most people. We know almost nothing about our universe; however, people think they are so close to "reading the mind of God". While I find it comical sometimes, it's a very dangerous mindset for people to have. In many ways, science has made mankind weaker. Modern man is very depending on technology, and the technology is very fragile.

"I think we need to calm down and see if we can make it through to the next century first"

You have no idea how much I agree with this statement. This century has the appearance and feel of being dangerous. It's almost like a modern day version of 1348 is around the corner.

 

[baywax]

Does not the idea of "uncertainty" do away with the idea of a "theory of everything"?

What I mean is, isn't it uncertain whether or not there is consistency throughout the universe? How could a theory encompass the unknown? Wouldn't it be the "theory of the unknown"?

 

[apeiron]

It is a good point that our laws are likely to be local. Even in the history of our own universe they may have evolved to their present apparently stable state. And multiverse thinking is now standard, so how can you have a TOE that stands behind everything possible rather than just a TOE that is for our particular observable universe.

So an uber-TOE seems a tall order considered like that. But does that mean it has already been ruled out a priori by Godel?

No, if you accept the modelling relations argument of those who study epistemology. Godel just separated modelling into the bit that can be formalised and the bit that must remain informal (that is, the theory bit and the measurement/observation/axiom-forming bit).

So a TOE may be impractical but not formally impossible.

Thus when it comes to Godel, really the reaction should be - what a neat result. He used paradox to defeat the dream that logic is also reality. He reminded people that logic can only model reality.

The proper consequence of that is people should have then become more open-minded and questioning about the logics they were using. Physicists employ a certain brand of logic (one that is pinned to atomism, mechanicalism, locality, monadism, etc) and continue to have religious faith in it.

Within physics, there are those like Penrose who are openly Platonist. But the more common reaction to those who heard of Godel was to say they were then just going to be hard-nosed scientific empiricists - Hawking being a prime example of this camp.

However this is also just a way to employ the old logic in an unexamined fashion. An empiricist can say well, I'm using it, but I'm not actually commited to it as it is observation which really now drives me.

Godel demands a response, but not this one. What logic should be used for formulating putative TOEs seems a metaphysical question - which it is. But empiricism has been used to drive metaphysics out of the temple, leaving amateurs, like Hawking and Penrose, in charge. Not that they aren't good at the other stuff they do.

 

[Dmitry67]

I think physicists are too afraid of the implications of the Godel's theorem. Dont overestimate the power of Godel!

We don't have TOE equations yet, so let's take as an example a world of Turing machines as example.
The 'laws' of that world are simple and even more, they are deterministic.
Still, there are some statements (would the Turing machine ever stop for that combination of a program and data?) which can not be derived from the 'laws' of such universe.

Does Godel (well, itis more related to algorithmically indecidable statements, but it is closely related to Godel) in that universe ruin everything? no. Does it make that universe non deterinistic? no. Nothing to worry about.

 

[JoeDawg]

The proper consequence of that is people should have then become more open-minded and questioning about the logics they were using. Physicists employ a certain brand of logic (one that is pinned to atomism, mechanicalism, locality, monadism, etc) and continue to have religious faith in it.

Equating the science of physics with religion is as insulting as it is inaccurate. Physicists base their beliefs about the universe on obsevable phenomena, religions are based on fantastical opinion.

If you have faith in religion, you are welcome to it, but its not the same standard as science.

 

[Dmitry67]

Equating the science of physics with religion is as insulting as it is inaccurate. Physicists base their beliefs about the universe on obsevable phenomena, religions are based on fantastical opinion.

If you have faith in religion, you are welcome to it, but its not the same standard as science.

There may be some testable things:
http://www.scimednet.org/library/articlesN75+/N76Parnia_nde.htm

 

[apeiron]

Replying to Dawg - wasn't it Hawking who spoke of knowing the mind of god, Einstein asserting that god doesn't play dice?

And if you read what I wrote, I was saying that physics too often stoops to faith-based positions, even as it adopts a holier-than-thou empiricist rhetoric.

Replying to Dmitry - I have a little inside knowledge of the NDE research as Fenwick confessed to me many years ago about the little operating room experiment he was running. Indeed, I've had the opportunity to follow psi research closely.

On the whole, you could say they do science to a higher standard than ordinary scientists. But even so, when they get results, I still put it down to artifact or fraud. And that would be an article of faith on my part as a determined sceptic! Even where I could not spot the trick, I still came away believing there must be one.

 

[JoeDawg]

Replying to Dawg - wasn't it Hawking who spoke of knowing the mind of god, Einstein asserting that god doesn't play dice?

Neither one has belief in a personal gawd, its a metaphor.

And if you read what I wrote, I was saying that physics too often stoops to faith-based positions, even as it adopts a holier-than-thou empiricist rhetoric.

I've met physics, he never stoops.

Empiricism works. When it stops working, we'll stop using it.
Faith has no predictive value. Might as well roll the dice.

 

[JoeDawg]

There may be some testable things:
http://www.scimednet.org/library/articlesN75+/N76Parnia_nde.htm

Pseudoscience.