Dear Dr. Crowther,
I don't mean to be picky, but on page 5 you say the Planck scale is 10^-32cm. Should it not be 10^-33cm? I'm sure you meant millimeters (I hate when that happens). If this essay wins a prize (which I think it's deserving of) and goes into a book that should probably be amended.
Cheers,
Peter
Dear Karen.
Thank you for your stimulating contribution. It's a long way to Tipperary!
My London publisher calls me a philosopher though I didn't earn this epithet formally. Neither am I a physicist. I am simply attracted to both disciplines because of their all-inclusive presumptions. So I feel quite comfortable in discussing ethereal subjects with you.
I have always loved the essay form as a means by which to clarify my thoughts on any subject that is too complex to organize clearly in my head.
While the goals of the Essay Contest are intended to 'Encourage and support rigorous, innovative, and influential thinking about foundational questions in physics and cosmology'; one cannot reasonably expect to define what constitutes a fundamental principle or part until one has clearly identified a context within which one can then proceed with the search. Understanding this contingent requirement necessarily admits the prospect of there being as many 'fundamentals' as there are contexts within which one can proceed.
We should bear in mind that theories derive from subjective points of view. When we attempt to consolidate theories into a single unifying theory-of-everything we drastically compromise the essential (i.e. fundamental) merits of contributing theories.
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'
Thus I have been led to search for a singular fundamental prerequisite that embraces all-there-is - and that is all there is to it! пЃЉ
Thanks again, and good luck with this and all your endeavours.
Gary.
Karen, Don,
I've found that if we actually get one fundamental correct (it seems none are yet) it will point to the rest. Rather like that vein of gold. My essay here describes an apparent classic derivation of QM, which emerged from trying to falsify a more coherent interpretation of SR's postulates which gave a string of top 10 scored essays from 2011.
I do hope you'll read, analyse and point out any apparent flaws. Trying to falsify using other anomalies hasn't worked as they evaporate (many other papers archived). This may be such a vein but I don't want to shout until opened up. I also haven't turned the SM on it as I'm no expert there.
You're right Don. A problem does lie in abuse of maths i.e. treating emitted sequential signals from clocks as 'time itself' as some physical entity has confounded understanding and Cartesian 'wire frame' transformation analysis. Logic clicks back into place one we start with correct assumptions and logical system. (See My 2015 'Red/Green sock trick' essay).
I'll try to get to your essay to Don as I'm sure you have insights.
But Karen I agree, no one human brain could have the capacity to comprehend it all!
Hope to hear comment on mine. Very Best
Peter
Dear Karen,
Your essay is great! You characterized perfectly the criteria that determine when we can stop digging. There is nothing to add. The essay is also excellently written, with clear explanations.
What I can say more about this may be only a matter of personal taste. I want to make some points that even if QFT and GR may not survive as they presently are in the final theory, some parts of both will, and I want to try and identify which.
QFT1. Many problems of QFT are, as you mention, because we don't have a good mathematical formulation. Maybe such formulation exists, without necessarily requiring input from GR. But even in this case, the problem with the UV limit seems to be that the only way we know how to calculate is perturbative. And maybe this can't be made mathematically rigorous even in principle (by mathematician's standard of rigor, which is the correct one). So we will need not only the true, rigorous QFT, but also the way to do the calculations in a rigorous way, which is independent of the fundamentality, it is just a translation for humans of the predictions of the theory.
QFT2. The way to obtain a QFT is tributary to history of physics. We start with a classical theory, and quantize it. This is a cooking recipe, there is no reason why the true QFT wouldn't be completely independent by the classical theories (except for the condition that they have to emerge in the classical limit). I will give an example. Schrödinger's equation is obtained by quantizing a classical theory. But Dirac's equation is not the quantization of a classical theory. Historically, it appeared because Dirac wanted to make the Pauli-Schrödinger equation relativistic, but it is only because of his genius that he arrived at something completely new. Of course, we know that his equation was not able to explain what Schrödinger's already did, so it had to be fixed by putting it in the same Procrustean bed. For example, to give it a Hamiltonian formulation, which is not friendly with Lorentz invariance, but allowed to obtain the Pauli-Schrödinger QM in nonrelativistic limit. And although Lorentz invariance is restored in the path integral formulation, that historical gene is still there and I think it obfuscates the true lesson. Another historical atavism is the so called second quantization, which is just cooking new food by an old recipe. Because this is the best we know.
QFT3. The QM measurement and emergence of classical problems. These two are really weird. You have such a good theory to describe particles, atoms, and their interactions, and they simply destroy this. I think these problems show that there's something essential we don't understand about the quantum. The theory is not complete, but I don't mean in the sense of needing some hidden variables, but we simply don't have an ontology and its dynamics. And I think all these attempts to find it, called "interpretations", are tailor-made to solve the measurement problem, ignoring much of the bigger picture, for example the lessons from GR, which is always seen as the one to be sacrificed. I think this also blocks the development.
GR1. Singularities are usually considered to make the major case against GR. I think the situation is not as bad as it is presented. Here are some possible answers. i) The singularity theorems rely on three conditions. The energy condition may be broken when QFT is taken into account. At least this happens for some approaches to GR. ii) Another way is that in the Einstein equation the Einstein tensor should be replaced with something else, or equivalently, the GR Lagrangian should be changed. There are various modifications of GR like this, including conformal gravity. They give similar predictions in the regimes where GR was tested, and some of them avoid singularities or give a possible answer to dark energy and dark matter. Note that such changes still keep the lessons of GR, like matter being related to spacetime curvature, the diffeomorphism invariance, and the principle of equivalence. iii) It is possible that the GR equations can be replaced by others which give the same geometry outside the singularities, but stay finite at the singularities. Something like a change of variables. This requires extending semi-Riemannian geometry to work for some relevant cases of singular metrics, and such an extension is known, and gives good results for the usual singularities. This is just standard GR, but puts the equations in a form free of infinities at singularities.
GR2. Dark matter. There are results suggesting that this doesn't require changing GR, being due to unknown forms of matter. But there are also solutions that suggest that modified gravity may solve this, see GR1 ii).
GR3. Do we need to quantize spacetime? In fact, this doesn't mean to discretize it, it means that we may need a generalization of Einstein's equation in which the matter side is quantum, leading to some quantum geometry like superpostion of different geometries or even topologies. But if QFT3 is solved in a way which is based on some ontological fields which have well defined stress-energy tensor, spacetime could remain "classical". While the most common opinion is that this is not possible, it may be. I saw a criticism you raised in a comment about this myth of the Plank scale, and I fully agree.
GR4. We need to make gravity into a gauge theory and quantize it like the other gauge fields. This is debatable. In GR, gravity is inertia on curved spacetime. It admits formulations as a gauge theory, and maybe the gauge curvature of the SM forces can be related to the spacetime curvature, but at this time is premature to say that GR has to be made like those quantum gauge theories.
I think that there is still much for us to understand about QFT and GR. But frankly, GR is much more mathematically mature and better understood than QFT, and it is strange that most approaches take QFT for granted and are eager to throw GR away before learning its lessons. I think the entire fundamental physics needs to be redone from scratch, identifying all assumptions, in particular those tied to the history, and with good mathematics.
Thanks again for your excellent essay!
Best wishes,
Dear Karen Crowther,
Sorry for misspelling your name. Hopefully you nonetheless understood my point. Let me try and say it with other words:
Let's never stop digging in the treasure of possible corrections.
Admittedly, I am not ready to expect finding any theory to be unified, unique, UV complete, etc. by means of your nine criteria as long as commonly agreed assumptions are treated like a taboo. Elapsed time is definitely more weird to physicists than to common sense.
Kadin pointed to several possibly overlooked treasures. Just a single one out of them seems to be worth digging, at least to me. What about McEachern/Traill?
Eckard
Hi Karen,
An almost encyclopedic treatment. A couple of things, though. You prescribe conditions for theories, but you left out the premise of a unified spacetime -- " ... independent in its physical properties, having a physical effect but not itself affected by physical conditions." ~ Einstein, The Meaning of Relativity .
If, as you admit space and time are fundamental, why is not spacetime more fundamental?
Nevertheless, good essay.
Mine: https://fqxi.org/community/forum/topic/3124
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
Dear Eckard,
Thanks. Yes, I'm sorry to say I don't understand what you mean. Could you perhaps elaborate a bit more on what you mean by "possible corrections" and "commonly agreed assumptions", please?
I haven't yet read Kadin's essay, and am unfamiliar with McEachern/Traill.
Best,
Karen
Dear Karen,
Klingman followed Phipps Jr. who tried to fundamentally correct Einstein and rescue ubiquitous simultaneity. I guess, the treasure of unseen alternatives might be larger. In my essay, I even questioned Maxwell's guess as the correct fundamental of gamma. Being not an etherist, I rather share Michelson's preliminary agnosticism. I feel intrigued by Foucault's pendulum which is nicely to be seen in Magdeburg and also by the late Michelson's experiment.
Kadin questions a lot of mandatory tenets, maybe too many as to get accepted. In particular, I admire his older essay "Just too many people". W"hile I don't feel myself right in political sense, I consider Kadin's judgement as alerting. The money given by "good" people like me to the exploding population in poor regions
does not solve the problem of lacking responsibility, on the contrary ...
When Kadin confronted us with the prediction that QM will never fulfill the hope for hugely improved computers, the cautious reaction here seems to confirm that he again put his finger squarely on a moot point. Szangolies could only point to a DQC1 that is not yet based on entanglement which, if I recall correctly, corresponds to the situation about two decades ago. Others said a lot by saying nothing.
The mentioned hope was theoretically confirmed by Bell. In discussions at FQXi, McEachern gave a completely documented MATLAB simulation with a result that looks at least similar to the result by Traill. McEachern was perhaps deeply disappointed because peers and admins like John Baez simply rejected it. He decided to not participate in the contest this year.
Best,
Eckard
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 Karen,
just wondering how much sense it would have made if Ptolemy had defined the conditions for a more fundamental universe...
Heinrich
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