Dear Terry Bollinger,

Thanks very much for taking the time to read and vote on my essay, and to provide useful feedback; I really appreciate it. I also greatly appreciate your voting pledge, and will strive to implement it myself more consistently.

Yes, the contest's question drew me in so I used it as an opportunity to explore some new ideas, and to understand issues surrounding quantum gravity from a different perspective. Writing the essay has been very beneficial for me, and I'm really glad to hear that you enjoyed it and think it useful for the community.

In regards to the first two critical comments.... aaah yeah, these are fair---the stance I adopted in the essay was, indeed, to view the question from the perspective of mainstream physics, and my aim was to distil and make palpable the conditions that are being assumed as consensus in high-energy physics. So, it is rather status quo in that respect.

However, I did not mean to sound as though I actually advocate all these conditions myself (especially without further refinement and provision of their precise definitions, as required particularly for the conditions of naturalness, unification, and no-weirdness). I certainly do not want to side with mainstream high-energy physics just because it is mainstream. Nor am I a supporter of string theory, so I'm (very! haha) sorry if the essay comes across like that. I considered string theory because it is the only approach to more-fundamental physics (that I know of) that claims to be a ``final theory'' (or, rather, final framework).

Instead, I am a philosopher, and this is just the first step of a bigger project: what I really want to do, but could not here given the time and length constraints of the essay, is to now go on and more thoroughly examine each of these conditions. I want to better understand what they each mean, what their motivations are, and especially what their implications are, particularly when combined with other theoretical desiderata. I agree completely with what you say in your second comment, and believe that progress can be made by re-examining, and perhaps giving up some of the implicit, deeply-held assumptions that turn out to be not well-founded or useful. So, I'm very glad you pointed this out, and I regret that I wasn't able to do more justice to this fact in the essay itself.

In regards to your last point, yes, I see what you mean and also agree. Given the incredible success of the standard model, together with all the difficulties in trying to fit gravity into this framework, I agree that this seems unlikely to be the right way of going about it. Both the standard model and GR might emerge from a more-fundamental theory, without having to do so in the same way (this is one reason why I'd like to more deeply question the requirement of unification). In fact, there are compelling reasons for not treating gravity as a force at all, as Maudlin says (in On the Unification of Physics), ``Objects do not couple to the gravitational field, they merely exist in space-time.''

Also worth noting that most approaches to quantum gravity (apart from string theory) don't seek to fit gravity into the framework of QFT.

Thanks again, and also for your handy summary of the conditions! Even I'm finding it useful. I particularly like the alternative titles for 6 and 7, because they're a bit more evocative.

Just a couple of notes... firstly, I realised this from other comments, as well, that there are different uses of uniqueness: the stronger one is as you state it, but it may be too strong a constraint to be realistically implemented, so I only meant to refer to the weaker notion of a theory being unique, which is just that there be only one fundamental theory we have... not that we have to rule out the possibility of there being any other theories that could do the job (in other words, I don't know how to solve the problem of underdetermination!)

And secondly, I don't know about probabilistic in requirement 4. I just meant not reliant upon approximations. But it is interesting to ask now whether being non-proababilistic is also a requirement...! It seems like it could well be, actually.

Best,

Karen

Dear Don Limuti,

Thank you! OK I will try to have a look at your essay when I can, and let you know whether or not I agree that it's easy-peasy ;)

Best,

Karen

Dear Mozibur Ullah,

Thanks very much! Yes, I agree, I love mathematics too, but an essay is an essay, and I wanted to make it as accessible as possible. I'm glad you enjoyed reading it.

Yes, you're right that it's easy sometimes for people to forget the origins of QFT. Certainly it is a very successful step towards unifying our most fundamental theories---and, indeed, the most successful framework for physics that we have! And yet it has so many conceptual and theoretical difficulties. Also, it's interesting now to explore how QFT in curved spacetime can give insight into a greater unification of QM with GR, and approximate quantum gravity.

Thanks again,

Karen

Dear Conrad,

Thanks very much! I'm really happy to hear that there are people out there finding my work useful!

Yes, thanks, I had wanted to bring in some discussion of emergence from that paper for the essay, or at least mention it, but couldn't manage it in the end. So, I'm glad you discovered the paper, as well as the book, and can advertise them here!

I'm intrigued by your arguments regarding unification and naturalness, especially since I'm very interested in better understanding the definitions of each, their motivations and implications myself (I'm quite suspicious of them, in spite of their apparently being so central to the business of physics!), so I'll certainly take a look at your essay when I can.

Thanks again,

Karen

Dear Branko,

Thank you! OK, I am interested in the heuristic role of the Planck units, so I will try to have a look at your essay. But what do you think, does your approach satisfy these conditions?

Best,

Karen

Dear Adel,

Thank you!

I think your quote here captures the requirements that a fundamental theory be simple and that it be explanatory (additionally, the quote suggests how the theory should be explanatory), maybe also the requirement that the theory be self-consistent. I did not explicitly have the requirements of 'being simple' and 'being explanatory' as criteria in my list, although several of the criteria may be related to simplicity (e.g., unification, uniqueness, no-weirdness), and all of them are based on the principle that a fundamental theory not leave anything that apparently requires explanation.

I like your idea that a fundamental theory should explain current physics, I think that is certainly desirable, and unfortunately not something that I discussed enough in my essay.

There are also criteria on my list that I think are not captured by your quote here, though. I will have to read the rest of your essay.

Best,

Karen

Hi Peter,

Thanks very much! I'm embarrassed to say that I had not heard of Hestenes before, so I'm glad you mentioned his work, it indeed seems very interesting. I'll read up more and see how it can apply to my work, as you suggest. Sorry I'm not sure how to answer your question, though. Will reply to your other post now, too.

Best,

Karen

Thanks again, and sorry for the delayed response. Haven't yet read the essay, but this sounds good to me!

In regards to uniqueness... I knew I picked the wrong word here, because of its different uses, but struggled to think of a better one! But, the idea is supposed to be that we have just a single theory, as in alone -- rather than being the only possible theory. So, your model may satisfy this criterion, after all, I think.

As you say, it's difficult to see how we could establish that a given model is the only possible one able to describe the physics. I'm not sure if the problem of underdetermination can be solved -- however, Dawid's book is an extensive argument trying to demonstrate the limitations on theoretical underdetermination (I am still trying to work through his arguments, though).

In regards to "not weird" haha! well, this is the one I am not so sure of myself. I was mainly thinking of it as a response to the general frustration surrounding the measurement problem.... but now I realise that may have more to do with how the theory links back to observations, rather than the weirdness apparently described by QM. Maybe we can be OK with fundamental weirdness if everything else is satisfied, and the weirdness is inherent? I guess it depends on how otherwise happy people are with the approach, whether they'll tolerate some weirdness for its other virtues, or whether they'll keep searching for something else (even if in vain).

Dear Peter,

Thanks very much!

ooops!10 ^- 33 cm yes you're right, thanks for pointing it out!

Best,

Karen

Dear Wayne,

Thanks very much!

In regards to your mathematically formal criteria, I'm interested in what you mean by causality and how you define it? (If you're importing the notion from GR, you mean that you have a spacetime, and that it shares the same topological and metrical structure as GR spacetime? Or something less than this?)

Also, I'm assuming by "non-renormalisable" as a criterion, you mean a theory that doesn't require regularisation, rather than that it actually be non-renormalisaable (because that would mean it has infinities)?

But I'm most interested in what you mean by when you say that the theory must "replicate [older theory] when evaluated at [relevant length scale]", because this is a large part of my own research (which I regret that I didn't have opportunity to include in my essay, due to the various constraints on it). You mean that the older theories should be derivable from the new one, under some relevant conditions, I gather?

And yes, agree with your practical point, that we may stop digging when the cost (whether in terms of energy, time, or money, etc.) is estimated to be greater than the anticipated rewards of continuing beyond a certain point. But of course that's a response to a different interpretation of the question (or perhaps under different assumptions) than what I adopted here.

Best,

Karen

Dear Avtar,

Thank you. Your paper sounds interesting, particularly the potentially empirical aspects.

Best,

Karen

Dear Gary,

Thank you!

I am similar, I find I can only fully understand things, or work out my own arguments, by writing (though it's not always essay form!)

Yes, I agree that there may be many different conceptions of fundamentality, depending on different contexts. For this exercise, I explicitly chose to write from the perspective of high-energy physics, and certainly do not mean to imply that such an account is appropriate for other contexts, or that it is the only perspective on offer. In fact, I am more inclined towards "emergentist" accounts (e.g., those offered by condensed matter theorists), where what is fundamental is scale-dependent, so I agree that much is lost when we consider only a single fundamental "theory of everything" (you may like to see some of my published work on emergence).

However, the FQXi question: What is "Fundamental?" invites a singular response; otherwise the question would be framed: What are "Fundamental?" The only exception to that interpretation is to respond to the FQXi question with the answer: 'Yes'

I'm sorry, but I don't really understand what you're saying here. I read the question as asking about the meaning of the word "fundamental", as in, what it means for something to be fundamental. I don't see how that requires just a one-condition answer? It's just that they are only asking about one word. And what is the interpretation of the question that could be answered by "Yes"?

Best regards, and good luck to you too,

Karen

Dear Karen,

you've produced an interesting list of conditions for fundamentality (fundamentalness?). Your argumentation is exceptionally clear and down to the point, and you present your points in an enormously comprehensible way that nevertheless never runs the danger of leaving out something important.

I have one question, though, regarding the need for unification: it seems possible to imagine a universe ruled by Newtonian mechanics, or a universe ruled by Maxwellian electrodynamics. But it's also possible to combine the two: adding charge to a massive ball and putting it into an electromagnetic field means that its behavior is no longer solely governed by Newtonian gravitation, but that additional effects due to electromagnetism play a role; but both theories seem to be well capable of existing side by side. Furthermore, they seem to do well with respect to the other criteria you mention. So isn't it possible to have a universe with several equally fundamental theories?

It would certainly be aesthetically dissatisfying if the universe were like that, but well, the universe probably isn't under any obligation to appear pleasing to us.

You seem to be dissatisfied with the fact that in such a case, there's something 'left open' to explain; but then, isn't that also true if there is a single fundamental theory? Are we not always left with an ultimate, 'but why this?'

Additionally, your dictum that 'physics does and must, by its nature, assume that we are able to formulate a physical description of all phenomena' strikes me very much like Hilbert's declaration that there can be no 'ignorabimus' in mathematics, and his search of a single, unified axiom system that underlies all of mathematics---which, of course, was shown to be impossible by Gödel.

In my essay, I argue that similar restrictions may well be true of physics---and furthermore, that it's not any more of a problem than Gödel's results have been for mathematics. I would be very interested in hearing your thoughts!

    Karen,

    Thank you for your most gracious and informative response! I would have added this reply earlier, but I don't seem to get any kind of notification from FQXi when someone replies on anything except my own essay thread. I had to search manually for my own name, essay by essay to find responses. Argh! I must be missing something?

    You are very generous about my critique points, and I deeply appreciate that you used them as an opportunity to make positive, constructive suggestions. That to me is the heart of good science! I note that some of my favorite comments from one fellow essayists were the ones in which he did his best to point out holes in my argument. Delightful! The points were valid and made me both think carefully and explain myself better.

    I'm glad you liked my two title suggestions, and that they were constructive.

    Regarding your number 4 non-perturbative criterion, I must confess that was the only one I wasn't quite sure of. Why? Well, there seems to be a deep "lumpiness" to both physics and our universe in general that lurks behind such powerful mathematical concepts as renormalization. Renormalization is not really as exotic or even as mathematical is it is in, say, Feynman's QED theory. What it really amounts to is an assertion that our universe is, at many levels, "lumpy enough" that many objects (and processes) within it can be approximated when viewed from a distance. That "distance" may be real space or some other more abstract space, but the bottom line is that this sort of approximation option is a deep component of whatever is going on. I say that in part because we are ourselves as discrete, independently mobile entities are very much part of this lumpiness, as are the large, complex molecules that make up our bodies... as are the atoms that enable molecules... as are the nucleons that enable atoms... and as are the fundamental fermions that make up nucleons.

    This approximation-at-a-distance even shows up in everyday life and cognition. For example, let's say you need an AA battery. What do you think first? Probably you think "I need to go to the room where I keep my batteries." But your navigation to that room begins as a room to room navigation. You don't worry yet about exactly where in that room the batteries are, because that has no effect on how you navigate to the room. In short, you will approximate the location of the battery until you navigate closer to it.

    The point is that the room is itself lumpy in a way that enables you to do this, but the process itself is clearly approximate. You could in principle super-optimize your walking path so that it minimizes your total effort to get to the battery, but such a super-optimization would be extremely costly in terms of the thinking and calculations needed, and yet would provide very little benefit. So, when the cost-benefit ratio grows too high, we approximate rather than super-optimize, because the lumpy structure of our universe makes such approximations much more cost-beneficial overall.

    What happens after your reach the room? You change scale!

    That is, you invoke a new model that tells you how to navigate the draws or containers in which you keep the AA batteries. This scale is physically smaller, and again is approximate, enabling tolerance for example of highly variable locations of the batteries within a drawer or container.

    This works for the same reason that in Feynman's QED is incredibly accurate and efficient for modeling an electron probabilistically. The electron-at-a-distance can be safely and very efficiently modeled as a point particle with a well-defined charge, even though that is not really correct. That is the room-to-room level. As you get closer to the electron, that model must be replace by a far more complex one that involves rapid creation and annihilation of charged virtual particle pairs that "blur" the charge of the electrons in strange and peculiar ways. That is the closer, smaller, dig-around-in-the-drawers-for-a-battery level of approximation. In both cases, the overall "lumpiness" of our universe makes these special forms of approximation both very accurate and computationally efficient.

    At some deeper level, one could further postulate that this may be more than just a way to model reality. It is at least possible (I personally think it probable) that this is also how the universe actually works, even if we don't quite understand how. I say that because it is always a bit dangerous to assume that just because we like to model space as a given and particles as points within it, those are in the end just models, ones that actually violate quantum mechanics in the sense of postulating points that cannot exist in real space due the quantum energy cost involved. A real point particle would require infinite energy to isolate, so a model that invokes such particles to estimate reality really should be viewed with a bit of caution as a "final" model.

    So my bottom line: While formal formula (criterion 4) are great, our universe seems weirdly wired for at least some forms of approximation. I find that very counterintuitive, extremely fascinating, and likely important in some way that we flatly do not yet understand.

    ----------

    Enough, I'm droning on again! Thanks again for your response, and I really like what you are doing. Your broader goals are great -- please keep at them!

    Cheers,

    Terry

    Dear Karen and essay readers,

    here are some lines of thought I would like to offer as worth thinking about them, since at least for me it seems that they are part of the problem to unequivocally answer the contest's question at all.

    The demand to stop digging is of course the result of the assumption that our best theories are not considered to be fundamental. Your approach to infer from our reasons that they aren't fundamental to your list of certeria for a fundamental theory is therefore straightforward and self-confirming. The latter due to the fact that what makes our best theories appear to be not fundamental is the expectation that there should exist a unified description of physical reality.

    This is another demand, albeit an understandable one from the viewpoint of determinism and physical causality (but maybe also from the viewpoint of philosophy). I therefore value your essay as to the point answering the contest's question, since the latter is formulated within the framework of physicalism.

    Nonetheless, it is arguable that what we call "physicalism" is just a system of consistent relationships of some placeholders for phenomena we can't reduce to some more fundamental concepts by means of grasping the true reasons of why they "are what they are". All this is not too problematic, since we anyways know intuitively that at a certain point, we have to take some concepts and ideas simply as given. In a physicalistic framework, one wishes at the one hand that the placeholders I spoke of should finally considered as simply given, albeit there are other atttempts to explain them in non-classical terms as emergent properties of even more abstract entities like global wave functions or some geometrical considerations.

    All those frameworks have in common that the physical realm should be a consistent unity, ruled by the law that any contradiction is impossible within it apriori. With this we arrive at a generalization of formal logic to the realm of natural phenomena. Since the abilities of our minds can - and must - in those frameworks also be considered as natural phenomena, it is therefore natural to conclude that nature must necessarily behave strictly logical.

    Although there are many counterexamples for human behaviour not being logical, but somewhat irrational, these counterexamples may be explained by assuming that false assumptions lead to nonsensical results. So, after all, the human mind can be characterized as being governed by the laws of logics.

    With this I would point to the only criticism I would make about your attempt to answer the question "what is 'fundamental'?". Since it doesn't answer how logical behaviour of nature should accomplish to generate some processes which we label as 'consciousness' to rightfully differentiate them from dead matter which mindlessly follows (magically?) just a verdict of some laws.

    If nature is logical as reflected in our ability to think logically and nature is assumed to be a coherent unity, then it follows that there has to be a logical answer to the question why nature can at all at some point of its state of affairs become conscious about its own fundamental logicism. Albeit such a logical answer may not be within the reach of human beings, it would be somewhat surprising and illogical if it where so, since logical answers are defined as being principally graspable by logically functioning beings. The only way to avoid the demand that logical beings should be able in principle to find out such a logical answer to the fundamental question about the existence of consciousness may be that the logical network governing the fact that consciousness is indeed possible would be to deep and complex for human beings to grasp it without some help of computer analysis.

    Since computer are bound to mathematics and data processing, it all would boil down to the answer that consciousness is a special kind of data processing. Since Gödel's result allow one to extend a system that is subject to Gödelian limits by a choice of whether or not one adds a new axiom p or its negation (not p), all boils down again to a choice between two mutually exclusive 'givens', two mutually exclusive logical options. If there is a reason for a certain kind of data processing becoming conscious at some point of its state of affairs, Gödel's results seem to imply for me that these reasons must reside beyond what we call the 'landscape of mathematics'. This landscape does only insofar make a real difference between consistent and inconsistent relationships as there are observers that make that difference. Hence, one could say that consciousness is fundamentally driven by a natural distinction between consistent and inconsistent mathematical relationships - what immediately contradicts that this distinction should be existent independent of some observers.

    At this point I conclude that either the existence of consciousness is merely possible, or it is a fundamental necessity in the overall state of affairs we are trying to figure out as scientists or philosophers. In fact, there is a huge tension between a logico-phyiscalist's demand that nature should be overall logical (consistent) and the claim that consciousness is merely possible, but in no way necessary to occur at some time in the overall state of affairs.

    I think that this tension cannot be resolved by defining a 'mathematical landscape' as the most fundamental level of ultimate reality, since in that case, mathematics should have the ability to distinguish between consistent and inconsistent relationships. If the latter would be true, there must be a kind of reason within that mathematical landscape, but according to the orthodox definition of mathematics, this reason can only be there in the form of some mathematical relationships, pointing to the whole class of consistent mathematical relationships.

    Since such a pointer-relationship within the mathematical landscape must necessarily be itself a consistent one, we again end up with a self-referential truth about the superiority of consistent mathematical relationships that should be responsible for conscious beings to exist at all. By re-defining the consistent part of mathematics as physical worlds with observers in it, one ends up where this comment initially began, namely with the initial question how to justify physicalism as a logical unity, able to facilitate observers that are able to grasp such an assumed truth.

    Could it be that, albeit the formal demand for ultimate reality being a logical unity is somewhat necessary to not undermine the very tool with which we come to some scientific conclusions (logic) and to not being left with fundamental contradictions (as is presently the case for the relationship of our best theories of physics), that we should suppose another "placeholder" to be existent at the very bottom / top of ultimate reality? I would characterize such a placeholder with the term 'truth', since this is what we are searching anyways. In fact, it is difficult for me to think about ultimate reality other than in terms of 'truths'.

    If physical terms like energy, mass, time and space are indeed considered as fundamentally given, and if more mathematical terms like global wave function, consistency and inconsistency are also considered as fundamentally given, I see no reason why the term truth shouldn't also be fundamentally given. Moreover, without the latter, the former can never be unequivocally considered as being fundamentally given, since in the absence of some fundamental truths, only falseness and confusion remains. If 'truth' is solely a property of exclusively some physical state of affairs (as is similarily thought of about the concept of 'information') in an orthodox sense, these affairs themselves are hard to justify objectively, even within a framework of a 'mathematical landscape' without arriving at some self-referential self-confirmation of some premises one made at the very start, not to mention or to justifiy objectively the existence of consciousness and its ability to make some inferrencing about the world and itself.

    It seriously seems to me that all we have at the end of the day is our conviction that some fundamental truth must exist as an - form the frog's view - highly abstract matter of facts. In light of a scientific as well as a common sense perspective, I would say that such a highly abstract level of reality can be justified by our hitherto gained experiences with it. However, I am perfectly aware of the fact that what is 'highly abstract' for one observer may be trivially concrete for another observer and vice versa. But I think maybe the distinction between abstract and concrete are the wrong criteria to look at what many of us consider as fundamental truths about the world. At the end of the day, such truth simply is and it is true that it simply is. This seems to me to be the only sure thing I can think of by contemplating the essay contest's question and its possible answers.

    Sorry Karen for such a long comment on your essay page. Simply ignore it if you cannot make sense of it. It is just the attempt to stimulate some more 'philosophical' discussion during the contest for those who like to discuss these things in more detail.

    I also apologize to those who seek some truth in a more physical description / explanation of certain physical phenomena. My comment here is not ment to undermine any such attempt, and indeed it cannot, since what finally counts is surely the truth.

    Hello dear Karen,

    I loved your relevant philosophical general essay.You have well analysed the importance for a theory of everything and the different problems to find it.

    All the best, good luck

      Dear Cristi,

      Thank you!

      Yes, for my own research on quantum gravity (which I don't necessarily interpret as a candidate final theory, though) I am very interested in understanding not just the form of the new theory (to what extent, and how, it retains features of GR and QFT), but what aspects of GR and QFT are to be ``recovered'' from it in the relevant domains, and how. So I am happy to hear your thoughts on this.

      It seems like most of your comments (except perhaps the last two) indicate how our current theories/frameworks, of QM, QFT and GR could each separately be replaced in the domains where they each currently apply. I gather then, that a more fundamental theory (in the sense of being one that describes the Planck scale), will then "recover" (reduce to) each of these (new) theories in the relevant domains (i.e., have them as approximations under the appropriate conditions). So I understand your suggestion as being that the key to finding a more fundamental theory is to first find the "true" formulations of our current theories? If so, I think it's really a groundbreaking approach. I had not considered going about it this way. It would seem to turn everything around and go in from the opposite direction, since at the moment, we tend to imagine that QG will reveal what aspects of current theories are wrong... and if my interpretation of your approach is correct, then you're saying that in order to discover QG, then its necessary to first correct what is wrong with current theories?

      I have a couple of suggestions of further literature you may be interested in, as well. Firstly, in regards to your point QFT1, have you read the papers by Fraser and Wallace where they debate the suitability of axiomatic QFT versus conventional QFT for foundational/philosophical work? The debate raises many very interesting questions, I think, including whether or not the mathematical difficulties in conventional QFT are due to the neglect of higher-energy physics, and thus are, in a way, not only unavoidable features, but also "informative" ones.

      Secondly, in regards to GR3/GR4, there is some work on this: papers by Callender & Huggett, Mattingly, and Wuthrich, that considers the necessity of quantising spacetime, with the upshot that, indeed, it is not necessary for a theory of QG. So you may be interested in reading these (particularly the Wuthrich paper, which I believe is available on his website or philsci archive).

      Thanks again,

      Karen

      Hi Thomas,

      Thanks for you comment. I'm afraid, though, that there are some misunderstandings here.

      Firstly, no, I don't actually argue that space and time are fundamental, and I'm sorry that the opening lines of my essay may give that impression. In these, where I say that QFT describes all the fundamental forces, and that space and time are surely the most fundamental entities imaginable, I am just "setting the scene", as it were. I used the word "imaginable", and that is the key qualifier here: For most people (except when on psychedelics) it is nigh impossible to imagine anything without picturing it "in" space and time. This is a problem when trying to formulate and conceptualise QG theories without spacetime, too -- because of our limitations as human beings, we still rely on spatiotemporal means of presentation, for instance.

      If you read the rest of the essay, you'd see that it presents several arguments why QFT and GR are not considered fundamental --- and, hence, why the "fundamental" forces, and spacetime, are not actually to be considered fundamental either.

      Secondly, the quote by Einstein that you cite is exactly the (or, really, one) definition of background dependence. It is not a desirable condition. Einstein did not want a spacetime like this, so I think you have misinterpreted his paper, too. It's a very well-known fact that Einstein's desire to overcome this very feature as thoroughly as possible was key to the discovery of GR, with its characteristic feature of general covariance, i.e., background independence. As you see in my own essay, I take background independence as a condition on a fundamental theory, and give arguments for this.

      Dear Heinrich,

      Do you mean that current physics is so wrong in one of its central assumptions, that any speculations about future physics, made from our current flawed perspective, are futile?

      Karen