# Do Gödel Incompleteness theorems have any influence on the possibility of constructing / finding a "Theory of Everything" ?

We frequently see people arguing that Gödel Incompleteness theorems imply that no "Theory of Everything" could be found, because we would expect it to be complete, in the sense that it would adress (at least in principle) any question about the physical world, and consistent.

But the theorems are about mathematical theories and no existing physical theory is completely mathematical. I don't mean that their mathematical formalisms can't be made rigorous, what I mean is that they also have a conceptual background which is not included in the calculational scheme. They are not pure mathematics.

A related question that might shed some light in this issue is: there could be a complete correspondence between physical reality and mathematical objects? Notice, however, that even if this turns out to be true, the question is not settled down, since there is the possibility of our "Axiomatic Theory of Everything" not being expressive enough to formalize the natural numbers and in this case Gödel's hypothesis would not apply.

So, what do you think?

But the theorems are about mathematical theories and no existing physical theory is completely mathematical. I don't mean that their mathematical formalisms can't be made rigorous, what I mean is that they also have a conceptual background which is not included in the calculational scheme. They are not pure mathematics.

A related question that might shed some light in this issue is: there could be a complete correspondence between physical reality and mathematical objects? Notice, however, that even if this turns out to be true, the question is not settled down, since there is the possibility of our "Axiomatic Theory of Everything" not being expressive enough to formalize the natural numbers and in this case Gödel's hypothesis would not apply.

So, what do you think?

## All Answers (26)

DeletedJames LangworthyAlso perhaps it reveals the desire of a theory for everything as that of a theoretician and maybe something that a science that requires empirical agreement cannot satisfy.

Erkki J. Brändas· Uppsala UniversityThis is an interesting question, though a daunting one. Similar queries, relating to AI (Lucas, Penrose) and to biology, have been articulated in the past, see e.g. Seel and Ladik (1986) “Are we as living beings subjected to Gödel’s incompleteness theorem?”. Unfortunately such inferences mostly led to silence and perhaps even stultification.

The key, as I see it, is to come to grips with, and not to avoid, the problem of self-referentiability and furthermore to understand natural science from this point of view. My view is that this can be carried out properly; the assertion is a bit more serious than it seems here, see also my response to Rajat Pradhan: “What does it mean to say that time can be transformed away in e.g. General Relativity?”.

The crucial idea is not to fall into the Gödelian trap. To exemplify I will return to your question regarding Gödel’s influence on the possibility of having a “Theory of everything”: in string theory the vibrating string is not merely dictating the properties of its host particle – it is being the particle and this requires a “Gödelian” protection which string theory so far does not seem to have. So my answer is clearly YES!

James LangworthyErkki J. Brändas· Uppsala UniversityI think very few disagree with your statement regarding the experimental difficulties to directly verify theoretical descriptions based on string theories. However, my answer referring to the Gödelian conundrum in this connection does not depend on your testimonial at all.

To take another example: Einstein’s gravitational laws of general relativity are experimentally well accounted for – the GPS, the perihelion movement of the planet Mercury etc. Unfortunately there survives unexplained cosmological appearances, e.g. puzzles related to the questions of dark matter, dark energy, the expansion rate of the universe etc. Obviously there is something missing here, which is necessary to identify, e.g. a general (quantum) description of a black hole, which is not presently cured by branes, in order to ”vaccinate” the general theory (gravitation) against Gödel! In this connotation I find Vilson’s question meaningful.

James LangworthyErkki J. Brändas· Uppsala UniversityI agree with what you say, but I find your view a bit pessimistic. Gödel’s theorems in propositional logic can almost trivially be “translated” into mathematical form as a higher order singularity. In other words we can deal with self-references in the more precise language of “mathematics”. There is no physics here so far, however, by a simple relativistic model, using straightforward conjugate variables (operators) it is possible to map gravity to such a higher order singularity (on the second Riemann sheet), which directly leads to Einstein’s laws of relativity, including the Schwarzschild metric etc.

I have explained this in many of my research papers most recently in “Arrows of Time and Fundamental Symmetries in Chemical Physics”, International Journal of Quantum Chemistry 2013, 113, 173–184. I am not allowed to upload it on ResearchGate, but I will be happy to send it to those who want a personal copy.

Best

erkki

Steven G. Harris· Saint Louis UniversityErkki J. Brändas· Uppsala UniversityYou are in fact saying that we need to separate biological processes from being describable by physics laws. Can we really do that? Is the emergence of the genetic code such a process?

Steven G. Harris· Saint Louis UniversityErkki J. Brändas· Uppsala UniversityOK fine. In other words biological processes are commensurate with physics but not enough to define biological processes. Hence one is missing is, in the words of Ernst Mayr, so-called teleonomic processes i.e. those governed by an evolved program. Would the genetic code, how and why, be outside physics?

Steven G. Harris· Saint Louis UniversityThe only way to define any process is to have not only the laws governing its behavior (very few), but also the exact data involved: extraordinarily--overwhelmingly super-humanly--complicated for anything like a living organism. So we can predict behavior only consonant with the level of detail we can nail down, using highly approximate "laws" for that level of detail: "laws" of ecological systems for ecology with data about ecological niches, "laws" about organs for body mechanism with data about how organs are connected, etc.

It's really all just about scale of complexity. Subatomic particles are pretty simple, atoms less so, molecules getting pretty complicated. Stars can be treated as simple objects from some purposes, but their interior organization is important for others; same with galaxies. Scale of complexity for organisms depends on the view being taken: how colonies grow, how organisms feed, how organelles deliver nutrients and wastes, how mitochondria handle energy demands, how RNA synthesizes proteins, and so on. Human ability to collect data is far more limiting than our ability to synthesize laws.

Erkki J. Brändas· Uppsala UniversityEven if I agree a lot with what you say, it sounds a bit pessimistic. The structure of the DNA packing in the cell nucleus as well as the proteins in the cell cycle are governed not only by the data involved but also by the genetic program, usually called teleonomic processes. Would it be unthinkable to also have teleonomy for higher order evolution? After all we have languages, mathematics, etc. to evolve on the social, ecological and perhaps also the cosmical level!

Steven G. Harris· Saint Louis UniversitySo, sure, teleon as thou wilt: If you can spot what appears to be a developmental agenda for, say, human societies, on the order of centuries or millennia, then that might well be a useful organizing principle that furthers the understanding of historic development and be speculatively predictive for the future.

Nothing pessimistic in my view of things: We think further than those who shoulders we stand on, observe more, and come to finer conclusions. Lookin' good, I'd say.

Arno Gorgels· Principia NaturaeSteven G. Harris· Saint Louis UniversityThe continuum isn't due to Cantor, it's Dedekind who defined it. And all it is, is a mathematically handy model for the universe. As far as scientific experiment goes, the universe might just as well be modeled by the rationals, not the reals--it's just a lot handier to have the continuum available for such things as trig functions, square roots, etc. But there's nothing truly physical about the continuum. No reason you couldn't base physics on the rationals.

Arno Gorgels· Principia NaturaeSteven G. Harris· Saint Louis UniversityIt's typical for mathematicians to assume that there is no cardinal between the size of N and the size of R; but I think that's merely because we don't seem to have any "practical" need for intermediate cardinals, so things are simpler if we just assume them away. I can't imagine how either physical observations or physical theories might influence this choice of axiomatic assumption, which seems to have only mathematical implications (and those of a highly abstruse nature, even by the standards of mathematicians).

Arno Gorgels· Principia NaturaeAs to the necessity of knowledge about the cardinal numbers I may mention my humble conviction that the natural constant of the speed of light (which is the only "big" natural constant) is related to the first cardinal number of the continuum. For this reason, I carry the opinion that the knowledge of/about cardinal numbers is crucial to understanding nature and vice versa.

Steven G. Harris· Saint Louis UniversityI don't see a connection between hypothetical cardinals intermediate between the size of the natural numbers and the size of the continuum, and anything we can observe in nature. Experiment, by its very nature, is totally insensitive to anything about the infinite, as our observations are inherently approximate. (Even the "infinite universe" models constructed in relativity theory and used as test-beds for our understanding of what observations tell us about the universe, are nothing more than highly simplified models chosen for their mathematical ease of use, not because observation could ever conceivably show us that the universe is infinite.)

Which isn't to say that it's impossible to construct models for the universe that make use of intermediate cardinals--though I've no idea what such a model would look like.

Arno Gorgels· Principia NaturaeJorge Silva Barcellos· Independent researcherI like your way of seeing the world!

I will detail some understandings that resulted from my work.

I believe this is the final theory that Einstein dreamed!

First I would like to note a few points.

What is a meter?

What is a second?

What is a pounds?

The answer to these questions is very simple, arbitrary units are chosen for humanity to relate to its surroundings.

The second aspect which is the speed, if not an arbitrary number based on these measures, which expresses a relation but this one working with a value!

Here we can observe that the invariance of the speed of light and truth to the invariance of space-time relationship in an inertial reference and nothing more than that!

And the Lorentz transform, demonstrates how these relate inertial frames between them.

Starting from the idea that the speed of light and fixing born the theory of relativity.

That is correct for a vision of the inertial frame.

However if we look at the universe from outside the speed of light and variable.

And own Lorentz transform allows you to see the variation of this speed.

If we take a privileged referecial static to measure all points within the universe the speed will always be different in all of them.

That is the speed of light and variable continues, and at the same time.

Only depending on the vantage point that is taken as a reference!

Following this line we have the quantum mechanics where time does not exist and expaso. But it is within the same universe as the theory of relativity so it has a relation with the same!

The quantum mechanics has two possible representations.

One comes from the Schrodinger wave equation and one in Hilbert space.

In the case of the wave equation she works with complex numbers and many solutions become very complex if not unattainable to be calculated!

Since the Hilbert space where most observe the quantum mechanical calculations.

At this point and interesting to observe that the Hilbert space is infinite, complex matrix and vector extruded.

Ie it works as a support for the particles enter and analyze their relations without time or space since the matrix all the points are interrelated!

Ie quantum mechanics and the theory of finite elements of another theory!

Where details what is not and the element but only the relationship between the elements they teem!

And here comes my job demonstrating that everything originates from a very small and dense string.

This string when a lively movement that is the essence of all energies, creates the universe!

In this definition the universe and closed!

E is defined as a massively parallel quantum computer.

Where the string and the element of unitary quantum processing.

Creating interference figures is in fact a holographic film.

We call the Universe!

Finally I managed to set everything in physics with only 4 numeric values that emerge from this string and your move!

And I posted a job on how to derive the theory of relativity and other so-called constants of physics, these 4 numbers.

Well as the relationship between the theory of relativity and quantum mechanics!

Would you like your opinion of my sight!

Thank you!

Steven G. Harris· Saint Louis UniversityI have very little I can contribute to the notions of combining quantum ideas with relativity. I just note that the original quantum ideas were based in an essentially Newtonian background, totally ignoring anything about relativity; and that the only really successful mingling of that original quantum conception with relativity is in Minkowski space, i.e., totally flat: no gravity, no matter fields, no curvature. There's been an enormous amount of "quantum gravity" propounded, but absolutely none of it is well-founded; in essence, nobody knows how we can combine quantum ideas with gravity--even though a great deal of effort has gone into trying to say something about quantum processes in gravity or curved spacetime.

Hilbert space of annihilators and creators works really well for empty, flat spacetime--but otherwise? No one knows how to do it. Same with Schrödinger equation.

And I can't even say what the difficulties are; that's not within my strengths.

Jorge Silva Barcellos· Independent researcherThe problem is even deeper than the Newtonian vision .

But the problem and the source of modern physics.

All theories of physics teem based on the concept of field .

But no one can tell what a field!

And it was just that I worked on and found a model that allows to describe the construction of the space , which is the basis for the propagation of waves.

Ie the space is the field in which Maxwell's equations interact .

What I would like your opinion and expert in mathematics on the fact that this model allows algebraic equations to have all the physical constants and allow to manipulate these equations within the normal equations of physics getting simpler algebraic equations in the domain and are based on 4 values and yet be absolutely correct when compared with standard models .

The question is an algebraic equation to be simplified with another equation and the result be correct in my understanding is correct because it is the mathematical point of view.

This correct my vision ?

Please review the work that will appends the mathematical point of view like you ve ?

Thank you.

Steven G. Harris· Saint Louis UniversityJorge Silva Barcellos· Independent researcherThe model is part of a string, with a diameter and length are fixed.

This string assume different geometric shapes, as the energy it receives.

Having 5 geometric shape possible.

These 5 ways are divided into 2 forms that construct the space and time.

One form is the basis to build the cluster and sub-atomic particles.

And the remaining two forms are one occurs in situations of uniqueness and the other is a transient form that transmits waves in the fabric of space created.

In this model we have 5 dimensional.

Three spatial and two temporal.

The time are the result of the transfer of information between two points of the space created.

These waves and one transverse and understand how the speed of light.

And the other, and a longitudinal wave and understand how the speed of quantum entanglement, which is trillions of times faster, than that of light.

The overall understanding of this model and a massively parallel quantum computer that mounts alone shall.

Resulting in a fluid filled structures with uniformly distributed fluid that moves the blades as membranes spherical structure.

Where one side of the "brane" to this matter and the other antimatter.

And the movement creates interference figures that generate the apparent reality in which we live.

A holographic universe in memory of a large computer.

The string is projected this universe we live in as the magnetic permeability and electrical permittivity of space.

What are the two numbers that are the basis for all algebraic equations that result from the operation of the machine.

The other two values that are used in the equations of relativistic corrections velocity and local density.

In this model the time and only delay the transfer of information between two points in space.

And this model for all the constants of physics has an algebraic equation that uses the projection of the string to generate the values that physical measures today.

As the mass of an electron, the electric charge of the electron, the Planck constant-the constant newton and all others.

Over can be used in the normal equations of physics and subsequently manipulated algebraically and turns any physics equation and equation based only on the string and much simpler normally apply the equations that we have nowadays.

If you look at the works you will see that for example the equation of relativity Einstein although simple is further simplified with reference to this string.

I hope to give a little information about the work I did, and well he has four years of extensive equations and hundreds of pages of calculations.

Can you help by adding an answer?