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

Karen Crowther

Essay Abstract

In seeking an answer to the question of what it means for a theory to be fundamental, it is enlightening to ask why the current best theories of physics are not generally believed to be fundamental. This reveals a set of conditions that a theory of physics must satisfy in order to be considered fundamental. Physics aspires to describe ever deeper levels of reality, which may be without end. Ultimately, at any stage we may not be able to tell whether we've reached rock bottom, or even if there is a base level - nevertheless, I draft a checklist to help us identify when to stop digging, in the case where we may have reached a candidate for a final theory. Given that the list is - according to (current) mainstream belief in high-energy physics - complete, and each criterion well-motivated, I argue that a physical theory that satisfies all the criteria can be assumed to be fundamental in the absence of evidence to the contrary (i.e., I argue that the necessary conditions are jointly sufficient for a claim of fundamentality in physics).

Author Bio

Karen Crowther is a postdoc at the University of Geneva, where she is investigating questions related to scientific theory-change. Before this, she was a postdoc at the University of Pittsburgh, and before that, she obtained her PhD in philosophy from the University of Sydney. Karen is the author of "Effective Spacetime: Understanding Emergence in Effective Field Theory and Quantum Gravity" (Springer, 2016), as well as a number of peer-reviewed journal articles. She also holds a BA (Hons.) in philosophy, and a BSc (Hons.) in physics, from Monash University, Clayton.

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Joe Fisher

Dear Dr. Karen Crowther,

In qualifying the aim of the 'What is Fundamental?' essay contest, Dr. Brendan Foster, the FQXi.org Science Projects Consultant wrote: "We invite interesting and compelling explorations, from detailed worked examples through thoughtful rumination, of the different levels at which nature can be described, and the relations between them.

Real Nature has never had any abstract finite levels.

I have concluded from my deep research that Nature must have devised the only permanent real structure of the Universe obtainable for the real Universe existed for millions of years before man and his finite complex informational systems ever appeared on earth. The real physical Universe consists only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.

Joe Fisher, ORCID ID 0000-0003-3988-8687. Unaffiliated

Marcel-Marie LeBel

Karen,

The background independence is somehow nonsensical. How can we require this of a number of events at different scales but essentially happening in the same arena?

"The idea of unification is not just that there be a single theory describing all phenomena, but that it describe all phenomena as the same--as fundamentally stemming from a single origin, e.g., as manifestations of a single entity or interaction."

In my essay I construct this background arena from a bottom-up logical approach. Logic is scale invariant! A lucid but not weird vision.

Your essay is Well written, informative, a keeper,

Thanks,

Marcel,

Karen Crowther

Dear Marcel,

Thanks very much for your comments.

Less-fundamental theories may have their arena provided by more-fundamental ones, but this cannot be the case for an absolutely fundamental theory - there is no further "background", and the theory should be self-contained. As an example, Carlo Rovelli views more-fundamental theories as tending to further relationalism: all structures within a fundamental theory are defined by reference to one another, rather than to a background arena that needs to be specified for the theory.

You view the background arena as fundamental, instead? Or is it constructed from something more fundamental?

Best regards,

Karen

Marcel-Marie LeBel

Karen,

The background is the fundamental arena for things to exist and happen. In my essay, I create such background from nothingness from the rule of non-contradiction. It is more like a form of fundamental ontology in a bottom-up mode. Please read my essay in full and tell me if asking "why" in this case is the proper question.

Thanks,

Marcel,

Edwin Klingman

Dear Karen Crowther,

It is interesting that you investigate questions related to scientific theory-change. Are you focused primarily on historical instances of such, or on practical obstacles to affecting such today?

I found your discussion of fundamental theories and related issues useful. It's always nice to see thumbnail snapshots of vast theories where it's easy to get lost in details. I believe you accurately describe the situation at hand and would not argue against your points. Rather than expound upon what you said, I will suggest that as 'scientific theory-change' goes, you might enjoy my essay. Einstein's invention of "the relativity of simultaneity" was a monstrous change, and I look at the historical aspects underlying this change. I would be very interested in any comments you might have on the changes discussed.

My best regards,

Edwin Eugene Klingman

Karen Crowther

Dear Edwin Eugene Klingman,

Thanks very much for your comments; I am glad to hear that some ideas are useful to your own work. My research is currently focused on the search for quantum gravity - the principles being used both in motivating this search, as well as those serving as constraints on the new theory. But, yes, I am also interested in looking at previous instances of theory-change in order to see what lessons we can bring to the current situation. So, I will have a look at your essay, too.

Best regards,

Karen

John Hodge

We can stop digging when we can create a universe.

Hodge

Karen Crowther

What do you mean "create a universe"? And how would that give us a fundamental theory?

John Hodge

Create as in cause to come into being like God is supposed to have done.

We would have to have a fundamental (most fundamental?) understanding about cause and effect relationships. Model comes first.

Karen Crowther

Ah yes, I see what you mean now. It would obviously be a sufficient condition, but I'd hope it's not a necessary one!

Best,

Karen

Joe Fisher

Dear Karen Crowther,

You wrote in the Abstract: "In seeking an answer to the question of what it means for a theory to be fundamental, it is enlightening to ask why the current best theories of physics are not generally believed to be fundamental."

Nature produced one single real unified VISIBLE infinite surface occurring eternally in one single dimension that am always illuminated by mostly finite non-surface light millions of years before humanly contrived finite speculation about abstract physics theories ever became evident on earth.

Joe Fisher, Realist.

David Peterson

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."

[deleted]

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.

Stephen Anastasi

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

Karen Crowther

Dear Stephen,

Thanks very much! I will also have a look at your essay.

Best,

Karen

Flavio Del Santo

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

Alan Kadin

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

Karen Crowther

Dear Dr. Kadin,

Thanks very much for your comments. Yes, I agree that a fundamental theory should be simple, too. Although I have not explicitly included it as a condition, several of the conditions that I listed are associated with simplicity, e.g., unification, uniqueness, level-comprehensiveness, no-weirdness, and background independence. It may be argued that they each point to different conceptions of simplicity, but the requirement of background independence, in particular, certainly captures the Occam's razor sense of the term.

I'm curious why you say it's generally believed that no simple theory is possible? Your essay sounds very interesting, I will try to read it soon.

Best,

Karen

Joe Fisher

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

Hans van Leunen

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.

[deleted]

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.

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

Francesco D'Isa

Karen Crowther

Dear Francesco,

Thanks very much! I'm glad you enjoyed reading it. Yes, normally in my work, I adopt a more neutral philosophical standpoint, but for this essay I decided instead to explore the question of fundamentality from the perspective of physics itself. Additionally, I have interpreted physics in a rather pragmatic way. Physics is loath to accept a theory that is not able to be used to generate predictions - and, typically, it is through a theory being applied that it is confirmed.

But, yes, just as you point out, I believe that this question of "usefulness" is open to be re-considered, or reinterpreted in quantum gravity research.

Best regards,

Karen

Francesco D'Isa

Dear Karen,

thank you for your nice reply, I wish you all the best for your essay!

Bests,

Francesco

Gregory Derry

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.

Karen Crowther

Dear Gregory,

Thanks very much! OK, I will take a look at your essay and then perhaps we can discuss more.

Best,

Karen