When do we stop digging? Conditions on a fundamental theory of physics by Karen Crowther

Your essay is very well written, well informed, logical and thorough. I appreciated its intelligence. A problem might be that the arena of deep fundamentals is likely well beyond our future ability to perform experiments and beyond normal science - beyond testability. How open should we be to the attempts of string theorists to "redefine science" to include their realm? I tend to be skeptical and wonder if deep theories may end up being partly "faith based."

Hello Karen

Love it. I rate it 9, only because its originality is confined to creating the list. This is not a criticism, just an observation. I hope that you may find my essay satisfies all but one of your criteria. That is, one of my conclusions is weird - even I think it is weird, like changes in time being observer dependent. I would very much value your feedback.

Stephen Anastasi

Thanks very much! Yes, I agree the current situation with quantum gravity seems quite detached from the experimental realm, and this has led to some very interesting questions regarding the status of theoretical physics as a scientific discipline, and the role of non-empirical theory assessment. This is why I wanted to leave open the possibility that what physics currently views as conditions on a fundamental theory may change in the future, due to quantum gravity research.

But I think there is hope in the future that more connections will be drawn between the various QG approaches and the empirical realm. (Remember that it was a while before GR was experimentally verified, for example, too). Rather than being sceptical, we can try to be optimistic that the theories may eventually be indirectly testable, potentially yielding some novel predictions in regimes that are accessible to us. Similarly, we may be able to put more experimental constraints on the theories "from the other direction", using observations in currently accessible regimes (constraints on violations of Lorentz invariance is a good example of work that has been done on this). "QG phenomenology" is a branch of research that aims at drawing these connections between theory and observation, from both directions, and some good people are working on this -- even "neutrally", without being tied to particular QG approaches.

Dear Karen,

congratulation for one of the few essay that deservers to be called an eassy. Quite original and well structured. I rated it very high.

Although you approach the problem from a very different perspective (you might like to have a look at my essay for comparison), I definitely like your clarity and rogour.

As a curiosity, let me mention that I am a frined of Niels Linnemann (who I also quoted in my essay as an example for proposals of emergent gravity), that I think works on similar things of yours, in Geneva. Do you know him?

Good luck, and I wish you the very best,

Flavio

Dear Dr. Crowther,

Congratulations on a clear and readable essay on the conditions for fundamental theories of physics. I agree with you that the number-one condition should be unity. But I think it is equally important that a fundamental theory be simple, in the sense of Occam's razor. It is generally believed that no simple theory is possible. In my own essay, "Fundamental Waves and the Reunification of Physics", I argue that unity and simplicity are most fundamental, although the unity of physics was broken in the early decades of the 20th century. I review the historical basis for this rupture, and go on to present the outlines of a neoclassical synthesis that should restore this unity.

In brief, the two aspects of modern physics that have defied simple unification are curved spacetime and quantum entanglement. I argue that spacetime is an unnecessary mathematical construction, and that space and time can be more naturally defined in terms of fundamental quantum waves. I further argue that quantum entanglement is entirely wrong, being a side-effect of an incorrect mathematical construction introduced to explain the exclusion principle. This predicts strong differences from orthodox quantum theory in certain regimes that have not been tested.

This is not merely a philosophical argument. There is a newly developing technology, quantum computing, which depends critically on entanglement for its computational power. Without entanglement, quantum computing will not work. There are billions of dollars being invested in this, and I expect an answer within 5 years. But when I have tried to discuss this with active participants in the field, they react as if I am killing the goose that is laying the golden eggs. No one wants to hear such a negative story, including funding agents. My prediction is that the failure of quantum computing will lead to a reassessment of the entire foundations of quantum mechanics.

Alan Kadin

Dear Karen,

I think FQXi.org might be trying to find out if there could be a Natural fundamental. I am surprised that so many of the contest's entrants do not appear to know what am fundamental to science, or mathematics, or quantum histrionics.

Joe Fisher, Realist

Dear Dr. Crowther,

In your approach, I miss the efforts of Garrett Birkhoff and John von Neumann to establish a fundament that emerges into a suitable modeling platform. In their 1936 paper, they introduced a relational structure that they called quantum logic and that mathematicians call an orthomodular lattice. It automatically emerges into a separable Hilbert space, which also introduces a selected set of number systems into the modeling platform. Hilbert spaces can only cope with division rings and separable Hilbert spaces can store discrete values but no continuums. Each infinite dimensional separable Hilbert space owns a unique non-separable Hilbert space that embeds its separable partner. In this way, the structure and the functionality of the platform grow in a restricted way. After a few steps a very powerful and flexible modeling platform evolves. This model acts as a repository for dynamic geometric data that fit in quaternionic eigenvalues of dedicated operators. The non-separable part of the model can archive continuums that are defined by quaternionic functions.

In other words, the foundation that was discovered by Birkhoff and von Neumann delivers a base model that can offer the basement of well-founded theories and that puts restrictions on the dimensions which universe can claim.

Multiple Hilbert spaces can share the same underlying vector space and form a set of platforms that float on a background platform. On those platforms can live objects that hop around in a stochastic hopping path. This adds dynamics to the model.

The orthomodular lattice acts like a seed from which a certain kind of plant grows. Here the seed turns into the physical reality that we perceive.

The Wikiversity Hilbert Book Model Project investigates this approach.

https://en.wikiversity.org/wiki/Hilbert_Book_Model_Project

http://vixra.org/author/j_a_j_van_leunen contains documents that treat some highlights of the project.

Dear Karen,

I appreciated your essay, an interesting shift in perspective. In a certain sense, it's a way to answer to a question with another question, but in a productive way, congratulations.

You write that "Physics does and must assume that we are able to formulate a physical description of all phenomena, and that this description is useful to us as far it can be". I wonder if the "useful" parameter should change, for questions intrinsically philosophical as "fundamentality" - but as you pointed with your paper, questions and answers often changes together.

All the bets, and thank you for sharing your interesting point of view,

Francesco D'Isa

Dear Karen,

I appreciated your essay, an interesting shift in perspective. In a certain sense, it's a way to answer to a question with another question, but in a productive way, congratulations.

You write that "Physics does and must assume that we are able to formulate a physical description of all phenomena, and that this description is useful to us as far it can be". I wonder if the "useful" parameter should change, for questions intrinsically philosophical as "fundamentality" - but as you pointed with your paper, questions and answers often changes together.

All the bets, and thank you for sharing your interesting point of view,

Francesco D'Isa

Karen--

Very nice essay, well written as well as thoughtful. I do think that some of your criteria for being fundamental are a little overly restrictive, which I think may be related to your focus on QFT and GR as the only theories worthy of attention. I was especially interested in your essay because I wrote an essay with a similar intent, and I am hoping you will take a look at it and offer some feedback. I will not try to elaborate on my observations concerning your criteria at this point because to do so would essentially just rehash what's in my essay, but perhaps we can exchange more thoughts later based on your reaction to the ideas expressed there. Meanwhile, let me just say that I enjoyed reading you essay.

Dear Karen,

congratulation for one of the few essay that deservers to be called an eassy. Quite original and well structured. I rated it very high.

Although you approach the problem from a very different perspective (you might like to have a look at my essay for comparison), I definitely like your clarity and rogour.

As a curiosity, let me mention that I am a frined of Niels Linnemann (who I also quoted in my essay as an example for proposals of emergent gravity), that I think works on similar things of yours, in Geneva. Do you know him?

Good luck, and I wish you the very best,

Flavio

Dear Karen Krowther,

Is the absence of evidence to the contrary really enough or should serious doubts also matter? In mathematics there were many proofs showing the existence of God. I also would likr to remind of G. Cantor's diagonal argument.

Do you accept for instance Klingman's argument on simultaneity as evidence?

Eckard Blumschein

dear Karen Krowther,

This is certainly a good question and I'm glad you have addressed it.

Should your criteria for fundamental not also include some measure of completeness? I mean one can certainly define a self contained mathematical structure or in the case of the Standard Model a theory that eventually explains all experimental results. However does the theory answer all questions of our human condition?

As Edington's Fish Story points out, the most fundamental will eventually be the construction and methodology of out inquiry?

Thank you for writing this essay

Wolfgang Baer

Dear Karen,

Very well done. Interesting idea, nicely framed & constructed. You soundly argued the grounds for digging and presenting the conditions to stop. But don't you think it may just be for a tea break, and we may then be back to work again on infinite time etc?

I was surprised to find the SM classified as 'a Theory'. I don't mean I'm wedded to it but not sure it qualified!) . I was also surprised to find Special Relativity and QM sidelined, but it was interesting, refreshing and educating to consider from that different viewpoint. We do all learn different physics, or learn it differently, after all (and unlike many I don't insist my own worldview is correct!)

Do you think we'll evolve the intellectual capacity to understand a complete TOE? If a computer needs to be the size of the universe to predict it's future might our brains not need to be rather larger to hold the data?

My own essay suggests that with a little more complexity some things get simpler. Two more momenta identified in OAM seem to remove weirdness (meeting one of your requirements if correct) and the bar for unity with SR. I hope you'll read and analyse (alongside Declan Trail's with the maths code.)

I think yours hit all the scoring criteria well so I have it down for a top score. We share a few concepts, neither of us propound some unfalsifiable theory, and I agree your flexible conclusions.

Very nice job.

Peter

Dear Karen;

Throughout your postulates it can be seen that you are assuming as absolutely valid the reductionist approach. From many angles (epistemologically, methodologically -Bell's theorem-, and experimentally -double slit experiment, entanglement experiments, etc.) it has been shown that this approach is not appropriate for any TOE.

I like your list of the conditions a physical theory should comply with in order to be considered fundamental; but you are only applying it to the current paradigms applied by the mains stream physics. Mainstream physics is plagued with ill defined fundamental concepts (space, distance, time, mater, etc.) and lacks epistemological and ontological foundation (it is full of contradictions and paradoxes). As a philosopher surely you are very aware of it.

I invite you to check the critique and proposed solutions I make to these problems in my essay "What is Fundamental". I hope that with your background you would make good contribution to the discussion.

Truly yours;

Diogenes

Dear Karen,

I liked your essay and I think it is a nice idea for this essay contest to make a list for of necessary conditions for a theory to be fundamental. I have some questions and remarks.

I also always thought, that a fundamental theory must be non-perturbative. But I never had a clear justification for that. And in my current essay - very implicitly - I doubt, that a fundamental theory can be non-perturbative for the following reason: fundamental concepts can only be defined in a free theory. This seems to be true for Newtons laws, where the laws are valid only if a system is moving relative to an inertial system. But the definition of the inertial system itself is only possible by postulating the force free laws for it. (This may lead to a conventionalism à la Poincaré.)

Similarly in Quantum field theory, where the fundamental concepts are the free particles, which can only be defined in a free theory. So that the theory of interaction necessarily must be perturbative. Or not?

Another obvious condition for a fundamental theory is: empirical adequacy. Why did you leave this out? To evident? To unproblematic? Or to complicated to discuss?

I think this is not simple. Can a fundamental theory define itself its observable consequences? Or must observational statements be independent of the fundamental theory in order for the for the fundamental to be falsifiable? In my essay I show that in any fundamental theory that has some realistic elements, there are conventional Elements. And that what is an empirical statement and what is a definition is not given by the theory itself.

Best regards,

Luca