The "scientific" dream of a "theory of everything".

[jeremyjr]

If you have some background in physics or you read with some frequency popular scientific articles you sure had hear about a so called "Theory of Everything"(http://en.wikipedia.org/wiki/Theory_of_everything), some physicist think that a set of equations, beautiful equations, can describe "in principle" all fundamental forces in nature, some even try to write equations that describe the "Universe" as a whole, equations that pretend to give an idea of the evolution past, present and future of the real world where we live.

 

Let me point out that I am not against the never ending struggle to fully understand in its fine details each natural phenomenon that is relevant to us in any way, many marvelous results we already have that fully justify that. This is about the impossibility in principle of the so called "theories of everything" or the extremely speculative nature of theories that pretend to describe the Universe as a whole.

 

It is a well known mathematical result that relatively simple axiomatic theories are always "incomplete"( see the Gödel's incompleteness theorems: http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems), this means in simple terms that any attempt to describe completely a relatively complex model axiomatically is bound to fail because always there are going to be true, or false statements about that model that can not be described by that axiomatic model, and no matter how many times we "extend" the axiomatic model with new axioms but the resulting axiomatic system will be still "incomplete".

 

When you read some physics articles and/or writings many times you get the feeling that the author do not make a distinction between the real world and the model used to describe the real world, many implicit assumptions about the real world are never fully disclosed. For example many models of the Universe assume that the Universe is homogeneous, or that the speed of light is a constant all over the Universe, etc. All of this implicitly is making an identification of the Universe with some ideal, platonic model of the real Universe. Then "theories" are build not of the real Universe but of the ideal, platonic model of the Universe that we have identified with the real Universe. Then we start talking about "Universal Physical Laws" pretending that these laws are true in the real Universe, but really these are laws for an ideal model of the real Universe.

 

Our experience, all our scientific confirmed results are eminently "local" in space and time, the Universe is vast in dimensions and time, expanding this "local" experience beyond its confirmed applicability is in essence speculation, we could be lucky and get some remarkable results, but as any person that had done any numeric extrapolations knows as we go far beyond the points of references we should expect deviations from the forecast and the real values. One "classic" example of that could be "inferring" the existence of "dark matter" from the observational results of very far galaxies.

[Strange]

 

Our experience, all our scientific confirmed results are eminently "local" in space and time, the Universe is vast in dimensions and time, expanding this "local" experience beyond its confirmed applicability is in essence speculation

 

Observations of distant phenomena appear, so far, to be consistent with the physics we know locally being the same everywhere. So I wouldn't say it is speculation, just a working assumption that hasn't yet been shown to be wrong.

 

People are constantly looking for exceptions to that (because "new phsyics" is always exciting) but so far ... nothing.

 

 

One "classic" example of that could be "inferring" the existence of "dark matter" from the observational results of very far galaxies.

 

However, as there are certainly observations of (near and far) galaxies and galaxy clusters which do not behave as predicted from their inferred mass, then something is needed to explain this phenomenon.

 

This "something" is labelled "dark matter" as a placeholder. It could be a difference in the laws of gravity on large scales, it could be some non-visible matter, it could be something else (do you have a specific suggestion?). Of course, that isn't the only evidence for dark matter and as more evidence is collected it looks more and more likely that some form of non-baryonic matter is the main explanation for dark matter.

[ajb]

When you read some physics articles and/or writings many times you get the feeling that the author do not make a distinction between the real world and the model used to describe the real world, many implicit assumptions about the real world are never fully disclosed.

It is for sure true that most theoretical physics papers do not make a very clear distinction between the mathematical constructs and what one could in principal observe. Because one is thinking mathematically from the start in terms of a model it is not easy to disentangle all the concepts.

[John Cuthber]

What Goedel showed is that in any sufficiently complex system of axioms there are theorems that can neither be proven true nor proven false.

However those unprovable systems may not be ones with a physical meaning.

It's possible that a finite set of axioms may provide a basis for proving all the things that matter, even though there will still be unprovable theorems.

 

So Goedel's work does not rule out the idea of a "Theory of Everything".

It doesn't matter if the ToE can't tell us what colour unicorns are.

 

It's also fair to say that most scientists who are seriously working on a ToE are aware of the incompleteness theorem; yet they carry on.

Does the OP somehow think he knows more about it than they do?

[Strange]

I'm not sure many scientists are really working on a "theory of everything", anyway(1). Unless that is limited to mean creating a theory which successfully merges GR and quantum theory.

 

About the only place I see "theory of everything" used is on science forums like this. But then it is usually used to describe rather incoherent rambling along the lines of(2) "something ... fractal ... energy ... circle ... nothing ... logic ... magnets ... vibrations ... existence ... + 1 ... -1 ... quantum ... vortices ... consciousness ... therefore everything" and totally devoid of any theory or evidence.

 

(1) A quick check of Arxiv produces just 16 papers with "theory of everything" in the title. About half of those seem to be general discussions of the concept, with few actually claiming to have a "theory of everything".

 

(2) A few buzz words picked from some of the "theory of everything" threads on this forum.

[jeremyjr]

The Gödel's incompleteness theorems apply to any consistent set of axioms for the Natural Numbers.

 

If the Universe is not a finite set( some models of the Universe consider the possibility of everything: space/time to be quantized at the Plank scale: see http://academics.hamilton.edu/physics/smajor/Papers/read_guide.html , if then the number of these "cells" is finite then the Universe will be a finite set) then the Universe will have a subset that can be in a one-to-one correspondence to the set of Natural Numbers, then formally there is not finite, consistent set of axioms that will allow to fully describe the formal properties of that subset of the Universe. There always be some properties that will be indescribable but any formal set of axioms.

 

My claim part also of the philosophical position that Reality can not be reduced/described completely by simplistic/ideal theories, reality is always far richer than any imagined theory. There is a fundamental/intrinsic difference between reality and its models.

 

Even when the axiomatic approach to science have been an outstanding achievement and the level of axiomatization of a given area of science is used as a measure of how advanced is that science or aspect of science, the simplistic/reductionist way of thinking in many people lead to ignore sometimes very subtle and not so subtle aspects of reality, many times these aspects of reality are almost evident but people are unable to see them because the simplistic/dogmatic/reductionist approach is deeply rooted in them.

[elfmotat]

My claim part also of the philosophical position that Reality can not be reduced/described completely by simplistic/ideal theories, reality is always far richer than any imagined theory. There is a fundamental/intrinsic difference between reality and its models.

 

Even when the axiomatic approach to science have been an outstanding achievement and the level of axiomatization of a given area of science is used as a measure of how advanced is that science or aspect of science, the simplistic/reductionist way of thinking in many people lead to ignore sometimes very subtle and not so subtle aspects of reality, many times these aspects of reality are almost evident but people are unable to see them because the simplistic/dogmatic/reductionist approach is deeply rooted in them.

 

The problem here is that physics is not axiomatic. There are often many different principles you could take as "axioms" which would physically represent the same thing. For example, I could tell you that the axioms of classical physics are Newton's laws of motion. Or, I could tell you that the fundamental axiom of classical physics is the principle of least action. Or I could tell you that the fundamental axiom is the Hamilton-Jacobi equation, or Hamilton's equations, etc., etc. They are just different ways of describing the same behavior. You can use any one as a starting point to derive the rest.

 

The same thing applies.to more fundamental physics. There are usually several different formulations of a theory that you need to keep in mind. We don't need to take any one of them as the "axiom of physics," because there are multiple equivalent ways of doing that. And even if all of physics can be boiled down to a single principle, we still would never call it "the axiom of physics." Rather, we'd say that all observable phenomena are consistent with the notion that they all behave according to some principle.

[Strange]

The Gödel's incompleteness theorems apply to any consistent set of axioms for the Natural Numbers.

 

So it isn't really relevant to physics.

 

 

My claim part also of the philosophical position that Reality can not be reduced/described completely by simplistic/ideal theories, reality is always far richer than any imagined theory

 

I doubt many people (nowadays) would disagree with that. People have moved on from thinking that science describes "reality" (whatever that means). Even if someone develops a "theory of everything" it won't be the last theory. People will continue to test it and improve it until they come up with a better theory of everything.

 

(Maybe you should ask the moderators to move this to the Philosophy section as you are not actually proposing a new theory?)

Edited October 30, 2014 by Strange

[jeremyjr]

The general tendency to "reduction to general principles", that sometimes is identified with "understanding" not always works. For example many "emergent" properties of complex systems can not be explained by "simple" principles, because like a new independent axiom in an axiomatic system these new emergent properties can not be deducted from existent simpler principles/axioms. Like for example the self-organization tendency of complex carbon based compounds or the similar self-organization tendency of complex plasmas.

 

There is something deeply wrong with a mind set that accept "on faith" the existence of something like ether( the 1900's luminiferous ether) and now dark matter, with only indirect evidence like the indirect evidence existent to infer the "reality" of ether, and the same mind set being unable to accept the reality of extraordinary new phenomenon like the reality of anomalies, many people in this forum are clear exponents of that mind set. I would call that mind set the simplistic/dogmatic world view. It is the world view/mind set that pretend to reduce everything that is observed to simpler principles and the mind set that is unable to see "new physics/new facts" on the result of direct observations.

[Strange]

There is something deeply wrong with a mind set that accept "on faith" the existence of something like ether( the 1900's luminiferous ether) and now dark matter, with only indirect evidence like the indirect evidence existent to infer the "reality" of ether

 

The difference is that there was never any evidence at all for the aether, direct or indirect.

 

There are multiple lines of evidence for dark matter. That cannot be just ignored. It needs to be explained.

[jeremyjr]

If an ideal system/model as the natural numbers do not have a finite complete recursive/algorithmic axiomatic system it will be very naive and simplistic to expect that the Universe/Reality that as a model is a lot more complex than the Natural Numbers will have a finite set of principles that describes it completely.

 

That is one of the more fundamental/philosophical implications that the Gödel's incompleteness theorems have from my point of view..

 

The difference is that there was never any evidence at all for the aether, direct or indirect.

 

There are multiple lines of evidence for dark matter. That cannot be just ignored. It needs to be explained.

 

Have you gathered the evidence for dark matter? If not you are taking that "evidence" on faith, how many people have really gathered that evidence? Very few really, anybody else is taking that "on faith".

 

Now I agree with you "That cannot be just ignored. It needs to be explained", but relatively many more people had gathered direct evidence for anomalies, order of magnitude more than for dark matter, and the evidence have been direct, and I am talking just about the many recorded clear footage of anomalies that already is in the number of thousands, and as for dark matter: "That cannot be just ignored. It needs to be explained".

Edited November 2, 2014 by jeremyjr

[John Cuthber]

You have yet to address my point.

It's possible that a finite set of axioms will be sufficient to address all the things that actually matter, even if it can not solve all the questions.

 

You say "it will be very naive and simplistic to expect that the Universe/Reality that as a model is a lot more complex than the Natural Numbers will have a finite set of principles that describes it completely.".

Perhaps, it's naive, but that doesn't mean it's not true.

[Strange]

Have you gathered the evidence for dark matter? If not you are taking that "evidence" on faith, how many people have really gathered that evidence? Very few really, anybody else is taking that "on faith".

 

That is a very silly argument. I have never been to America so I am only taking its existence on "faith"?

 

(And stop trying to drag your closed thread into this.)

[jeremyjr]

 

That is a very silly argument. I have never been to America so I am only taking its existence on "faith"?

 

(And stop trying to drag your closed thread into this.)

 

 

First you can not tell me what to do(I will ignore you when you do that), we can speak about dark matter because you accept that on faith, but I don't, and then we can not speak of anomalies because you do not accept that and I do ( that I do not take on faith because I had seen them with naked eye and instruments)? Symmetry is a beautiful concept and it appears that you do not have a real sense of that.

 

Anything that you have not seen with your own eyes or experienced by yourself and you accept is by definition taken on faith, just for your information, we take on faith many things at many levels, in scientific terms we strive to minimize what we take on faith.

 

If, as you do, the scientific circles have ignored an aspect of reality, that many know is there as a fact because they have experienced that personally, me included, what guaranty do we have that the scientific circles, with you included, had not ignored other aspects of reality using the same deeply wrong mentality? Is not that an indication of a systemic problem? Is not that an indication that the "scientific methods/procedures/mindset" that have been in use and have been unable to deal with one aspect of reality are wrong?

[swansont]

Anything that you have not seen with your own eyes or experienced by yourself and you accept is by definition taken on faith, just for your information, we take on faith many things at many levels, in scientific terms we strive to minimize what we take on faith.

 

Mixing up different definitions of faith (or any word) to make a point is invoking the fallacy of equivocation. It makes for a poor argument.

 

In this case, not all faith is a religious-like faith. It can also be trust, i.e. trust that some scientific work by others is sound and they aren't fabricating their result, and colluding with other researchers who have replicated the results.

[jeremyjr]

You have yet to address my point.

It's possible that a finite set of axioms will be sufficient to address all the things that actually matter, even if it can not solve all the questions.

 

You say "it will be very naive and simplistic to expect that the Universe/Reality that as a model is a lot more complex than the Natural Numbers will have a finite set of principles that describes it completely.".

Perhaps, it's naive, but that doesn't mean it's not true.

 

Actually I just did with the post that you are referring to, my point is that if a very "ideal/simple" model as the Natural Number can not be described with a finite set of axioms because always there are going to be properties of the Natural Numbers that can not be deducted from any finite set of axioms for the Natural Numbers, then a more complex model as Reality is will have even stronger limitations in the possibility of describing it completely by a finite set of principles.

 

Now some aspects of Reality are evidently amenable to that "almost complete" description using a finite set of principles, and I used almost completed in quotation marks because it should be also evident that no finite set of principles will describe "completely" any aspect of Reality as the History of Science clearly shows.

[John Cuthber]

And, as the song goes, "let's go round again".

Nobody has disagreed with that assertion that " a more complex model as Reality is will have even stronger limitations in the possibility of describing it completely by a finite set of principles."

OK?

So repeating it adds nothing to the discussion.

There's no doubt that some ideas will remain unprovable in any system of maths that's even remotely complex enough to describe the universe.

 

Can you show that the things that are unprovable are important or might they all refer to things like the refractive index of a unicorn?

.

[jeremyjr]

 

Mixing up different definitions of faith (or any word) to make a point is invoking the fallacy of equivocation. It makes for a poor argument.

 

In this case, not all faith is a religious-like faith. It can also be trust, i.e. trust that some scientific work by others is sound and they aren't fabricating their result, and colluding with other researchers who have replicated the results.

 

I am using the phrase "on faith" in the correct sense: "to be willing to believe something without proof" and it is very common to be used to means that in scientific/academic discussions, so I really do not see the point of your entry.

And, as the song goes, "let's go round again".

Nobody has disagreed with that assertion that " a more complex model as Reality is will have even stronger limitations in the possibility of describing it completely by a finite set of principles."

OK?

So repeating it adds nothing to the discussion.

There's no doubt that some ideas will remain unprovable in any system of maths that's even remotely complex enough to describe the universe.

 

Can you show that the things that are unprovable are important or might they all refer to things like the refractive index of a unicorn?

.

 

What is "important" or not really is a matter of "taste" and many times of "fashion" and is really very hard to define.

[Strange]

I am using the phrase "on faith" in the correct sense: "to be willing to believe something without proof"

 

Apparently not:

 

we can speak about dark matter because you accept that on faith

 

I accept that there must be something that behaves like dark matter, because of the evidence. Currently, the evidence is pretty conclusive that "dark matter" is largely or completely some sort of matter. Explanations based entirely on modified gravity, for example, don't work.

[John Cuthber]

 

 

 

What is "important" or not really is a matter of "taste" and many times of "fashion" and is really very hard to define.

Not if it's the refractive index of a unicorn.

 

Do you plan to actually answer the question?

Can you show that the things that are unprovable are important or might they all refer to things like the refractive index of a unicorn?

[swansont]

 

I am using the phrase "on faith" in the correct sense: "to be willing to believe something without proof" and it is very common to be used to means that in scientific/academic discussions, so I really do not see the point of your entry.

 

No, that's not what you are doing. To use an example already in place, evidence of dark matter exists, regardless of whether you collected it yourself. It is not a matter of faith, using the definition you give here, to acknowledge that evidence. But you are using it to mean to believe something that you have not personally verified, which is not the same thing.

[ajb]

'Scientific faith' would be closer to trust. I tend to trust those that have made the observations, as their work has been scrutinised by experts in that field. It is professional integrity and respect, not blind faith as in a religious context.

[physica]

 

I am using the phrase "on faith" in the correct sense: "to be willing to believe something without proof" and it is very common to be used to means that in scientific/academic discussions, so I really do not see the point of your entry.

 

I think the belief term has been abused enough by religious people and outsiders with their own theories with no evidence. What people do when doing this is treat the term belief as an absolute as opposed to a term that has varying strengths and actions surrounding it. Yes theoretical physicists believe in their theories but they take steps to make the theory quantifiable so in-turn it can be verified by experimental evidence. Only when it is verified will it then be pushed onto other as accepted science in textbooks etc.

 

What religious and unconventional theorists do when they believe is to push their theory on others, they do not take steps to make it quantifiable and in-turn do not make steps to verify it.

 

Although they both have an element of belief the process, outcome and development are very different. I sometimes think there should be separate words so scientists don't have to say: we believe that this may be the outcome. It would save a lot of dishonest abuse of the term by religious/outsiders and would save us a lot of time having to constantly point out the flaw in their argument. There may be a few honest ones out there, in that case it may prevent them from becoming confused.