Dear Peter,

Thanks very much for reading and commenting on my essay. I usually tend to think of the standard model as a collection of theories, but since it can be written as a single Lagrangian, it seems more usual to call it a theory (even if it is non-unified and rather inelegant one!) I also explored general relativity and quantum field theory instead of special relativity and quantum mechanics, because the latter are held to be less-fundamental than the former (SR being a special case of GR, and QFT being a combination of QM and SR).

If we are talking about a TOE in the sense of a complete theory valid at the most fundamental level, as I do in the essay, then yes I think it is potentially within our power to formulate and understand such a theory. However, if you mean actually using such a theory to get results about everything (i.e., physics at all scales), then this is most certainly not possible. As you say, it would require some incredible level of computational power. In the essay, I used the assumption that it is possible "in principle" but, in honestly, I don't believe that -- in fact, I can't even make sense of such a statement.

Thanks again,

Karen

Dear Diogenes,

Thanks very much for your comments. Yes, in the essay I assume that it is possible "in principle" to derive results valid at larger length-scales from theories formulated at shorter length-scales. This is one sense of reductionism, but it is not one that necessarily conflicts with the possibly of emergent phenomena, particularly the examples you mention.

Yes, I agree that there are many ill-defined concepts in mainstream physics, and I believe that part of my job is to help clarify these where needed (though being ill-defined is not always a bad thing, nor something that can in all cases be fixed). In this essay, though, I decided to work with the mainstream perspectives (this is also why I used the reductionist assumption, in spite of finding it problematic myself) --- this was partly for reasons of simplicity and accessibility for a short essay, but also because I wanted a better understanding of them. My aim next (i.e., my current project) is to critique these conditions (particularly their motivations, and consequences for other principles) from a philosophical standpoint.

Best,

Karen

Sorry for the formatting in that post. The small "n"s that appear out of place at the start of some sentences were supposed to be new lines. I don't know why that happened, or how to fix it now!

Dear Luca,

Thanks very much for your comments! That's an interesting idea, that a fundamental theory cannot describe interactions. I will have to think about that, but there are simple systems with interactions that can be described without requiring perturbation theory.

In regards to empirical adequacy, I did not think this to be a condition of fundamentality but a requirement for a theory in order that it be considered scientific at all. And, as I mention at the top of page 8, I take it for granted in the essay that we are considering only scientific theories. This saves me from having to explore the problem of demarcation in science, which is too complicated to discuss in a short essay! As you say, too, the issue of connecting theory with observation is certainly not a straightforward one.

Best,

Karen

Sorry for the formatting in that post. The small "n"s that appear out of place at the start of some sentences were supposed to be new lines. I don't know why that happened, or how to fix it now!

Sorry for the formatting in that post. The small "n"s that appear out of place at the start of some sentences were supposed to be new lines. I don't know why that happened, or how to fix it now!

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

Dear Paul, Thanks very much! Yes, I agree the idea of naturalness is an interesting one for the reason you mention -- it may be desirable to have a theory that doesn't require fine-tuning, but we can't rule out the possibility that, at the fundamental level, we have a theory that is "unnatural". This is true of several of the requirements, including -- most obviously -- those of unification, and "no weirdness". It's very possible that, fundamentally, the world is described by an unsettling, non-unified theory. And yet, if we arrive at a theory that doesn't fulfil these conditions, then we will keep digging for a more satisfactory one. So, actually, it's possible that we have a final theory and yet continue to search in vain for something more. That's an interesting consequence of the epistemic worry that I hadn't considered, so thanks for that. Best, Karen

Dear Lawrence B. Crowell, Thanks very much. Your comments touch on several interesting issues. Yes, I wonder about the no weirdness requirement, too, and am still not certain of its inclusion or interpretation. But, the idea generally expressed is that QM is not fundamental, precisely because of its weirdness. Many people (most prominently Penrose) argue that a more fundamental theory is necessary in order to solve these issues, particularly the measurement problem. Quantum gravity, although the moniker suggests otherwise, need not -- and probably, in fact, can not -- be a quantum theory in the usual sense. One reason is because quantum theories utilise space and time, and these are to be modified in quantum gravity. So, another reason why quantum mechanics is supposed to be non-fundamental is because of the expectation of the necessity of QG. If QG contains similar weird features, then this will push people to seek a more-fundamental theory, in turn. But, that said, you are right that QG is likely to be weird! The ideas of a shortest length scale and a shortest time scale are extremely difficult ones -- as is the possibility of formulating a theory that describes a non-spatiotemporal regime. Your suggestion that QG be an EFT valid "close to" this regime, is interesting, too. We would have to think more about the issue of UV completeness in this case. Best, Karen

Thanks for your reply - I completely agree with what you've said here! Best, Paul

Dear Karen

Its nice to read an essay about physics that explores the issues without dragging in mathematics - not that I have anything against mathematics - I trained as one. But I do feel the essay ought to be about words and a pleasure to read and I very much enjoyed reading your essay. I'm glad that you pointed out that QFT = QM relativity as that particular point is not made often enough and it does show that progress has been made in integrating our two most fundamental physical theories. Congratulations on an informative essay!

Best Wishes

Mozibur Ullah

    It seems that the site slightly mangles up the formatting of posts by removing linebreaks for some reason.

    Hi Karen,

    I do not think, that a fundamental theory cannot describe interactions. On the contrary. But fundamental concept like mass, spin, momentum etc. are only defined in the free theory. Only if the meaning/definitions of these concepts are given, one can define, what interaction is. For instance force is something, that changes the momentum. I think that was Poincaré's view. Then whether given specific initial conditions, there exist a non perdurbative solution of the equations depends on the symmetry of that configuration. But I do not think that whether such a solution exists or not can be a criteria for a theory to be fundamental. But that might not be, what you intended to say.

    By the way I would be glad, if you could find the time to read and comment on my essay: The quantum sheep - in defense of a positivist view on physics

    Best regards,

    Luca

    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.

    Hi Karen,

    I like very much your formalism for determining whether a theory is fundamental. It is a high gate to jump over. I believe modern physics does not clear it.

    I have a theory of quantum gravity that I believe is easy-peasy. Would you take a look at my theory and see if it clears the gate? I have looked at your credentials and think you can easily "grok" what I propose.

    Visit my essay "The thing that is space-time" and give me your opinion on if it clear the gate. I'm interested in what you really think (or feel)...not looking for mutual admiration :)

    It was refreshing to read a practical approach to fundamentality.

    Thanks,

    Don Limuti

      Hi Karen & Wolfgang,

      It is interesting to consider if physical theories are susceptible to limits in Logic - such as Godel Incompleteness. If physical theories are based upon logic, then they may also be limited as to their ability to provide a complete logical explanation.

      Don

      Dear Karen & Peter,

      How could a TOE, that could not present all levels of scale be considered a TOE? Physics seems to have so constricted it's area of applicability, to this or that level, as to no longer cover what a TOE should.

      A Theory of Everything should be of Everything, no matter the scale or arena of applicability. Physics appears to no longer strive for such a theory - since it would "require some incredible level of computational power."

      Maybe the limitations physics is hitting are not philosophical or experimental, but mathematical. Maybe we do not have the tools needed to cover casual affects that cross between all levels of scale. Maybe this is where further investigation in needed.

      Don

      Professor Crowther,

      First, my essay contestant pledge: goo.gl/KCCujt

      I thoroughly enjoyed reading your essay! Positive aspects include:

      -- Your razor-sharp focus on answering the FQXi essay question, as opposed to simply using the contest an excuse to propose a personal pet theory of physics. I note with admiration that since with Dean Rickles you have in the past written an introduction to a special issue on quantum gravity and clearly are deeply familiar with that particular theory domain, keeping focused on the question rather than on a theory must have required some conscious restraint on your part.

      -- Your superb, well-argued list of nine attributes of a truly fundamental theory. It is cogent and comprehensive, and something that I think every theorist should read. Since in your essay the list is broken into two parts and so is a bit hard to extract, I have consolidated and to some degree rephrased your list below [1] in hopes that others will be encouraged to read it.

      -- Overall quality and insightfulness. You nailed a lot of important issues in this essay!

      Negative aspects of your essay, all relatively minor, include:

      -- Alas, I was genuinely disappointed when after such an insightful analysis you ended up mostly advocating more of the same 40 years in the wilderness that everyone has been tromping around in ever since the amazing consolidation of the Standard Model in the early 1970s: Quantum gravity and its wiggly offshoot, string theory. Every time I walk through NSF with its indoor palm trees (the metro path goes right through it), I think wow, why can't NSF be a bit more diverse in their research agenda for physics? Groups like DARPA utterly ignored them, since there is no experimental side to string theory.

      -- I was also a bit disappointed that even though your essay and criteria are most definitely compatible with theorists taking dramatically new approaches to old issues, you never specifically addressed the dangers of refusing to examine fundamental assumptions more closely to see if they even apply. Historically, most impasses in scientific theory were linked to deeply held assumptions that people often did not even realize existed in their minds. The parallel early 1900s transformation of classical physics into both relativity (time and space assumptions had to be abandoned) and quantum mechanics (deterministic reality had to be abandoned) is a superb example of how abandoning "obvious" assumptions can be a prerequisite for progress. While you do touch lightly on such possibilities e.g. in one of your footnotes ("This arbitrarily large vacuum energy may, in fact, be interpreted as an artifact of a non-fundamental formalism"), the overall tone comes over pretty status quo in approach.

      -- Your approach to theories that are powerful but not fully comprehensive feels a bit incomplete. For example, while the Standard Model that unified three of the four forces is undeniably incomplete, it is also almost mind-bogglingly effective and predictive of reality. That seems important in some way that goes beyond just saying "it's not there yet." For example, if you assume that we are indeed looking at some of this the wrong way, it might be more powerful to stop trying to force-fit gravity into the Standard Model and instead treat it as an important but for now separate unit in some larger synthesis, one in which gravity emerges not as just another quantum force, but as something entirely unexpected.

      Overall: Great essay, one every theorist should read. Below is my summary of your excellent criteria list.

      Cheers,

      Terry Bollinger

      ---------------------------------------

      [1] Since in the essay your list of attributes of a fundamental theory is broken up into two parts on two different pages, below is my full list and interpretation of your nine criteria. I renamed (6) and (7), but my intent is for them to be exactly the same concepts you proposed, as best I understood them.

      ----- The Crowther Criteria for Fundamental Theories of Physics -----

      A fundamental theory of physics must be:

      (1) Unified: It must address all of reality using a single set of self-consistent premises.

      (2) Unique: It should be the only possible theory once its premises have been stated formally.

      (3) UV complete: There should not exist any phenomena are outside of its formal scope.

      (4) Non-perturbative: Its formalisms should be exactly solvable rather than probabilistic.

      (5) Internally self-consistent: It should be well-defined formally, and should not generate singularities.

      (6) Scale smooth: Its explanation of reality should be continuous across all scales (levels) of space and time, with no gaps, overlaps, or other discontinuities.

      (7) Fully generative: It requires no pre-existing fixed or "given" structures, such as space itself, that have complex and non-trivial properties.

      (8) Natural: It should require no arbitrary, inexplicable "fine-tuning" of numeric parameters.

      (9) Not weird: The underlying premises should be simple, easily comprehensible, and subject to Occam's razor.

        Karen, all,

        It is dangerous to use the word "completeness" in the context of Physics, since Godel proved that, per Hilbert's definition of the word, it is impossible.

        Better to seek "consistency" (her 4th condition), which can only be achieved with a finitary mathematical system (Takeuti). This of course requires that all singularities be eliminated.

        Thus begins a search for a finite representation geometry for QC/ED, which includes many ideas including a string... and eventually find that a closed band suffices.

        Wayne Lundberg

        https://fqxi.org/community/forum/topic/3092

        Dear Karen,

        Your essay, and many of the comments given, were an enjoyable read which summarizes the frustrations of modern theorists... from differing perspectives.

        Very well-written, and it provides 9 clear conditions which, when met, will convince the community of a 'theoretical discovery'. So I rated it very highly.

        But my insights and investigations indicate that there are mathematically more formal criteria, which, fully considered, yield a comprehensive theory. In fact they are fewer, as they specify that the theory replicate known successful aspects of existing theory.

        Foremost is that it be a causal theory for consistency with GR.

        It must use a finite representation geometry to be consistent (no singularities, non-renormalizeble).

        The universe is the sum of its particles, so for consistency, the form of the formulae representing each must be the same (as in NBWF).

        It must replicate QC/ED particles and interactions when evaluated at their respective space-time scales.

        It must replicate GR when evaluated at cosmological scales at the present time.

        Note the importance of "evaluated at", which means use of "|" at any physical space-time scale. In particular, an intuitive leap is REQUIRED, since information is lost about the foundational formula when either QFT or GR is derived via |.

        I look forward to your comments, best regards,

        Wayne Lundberg

        https://fqxi.org/community/forum/topic/3092