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

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

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[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

p.s. The simple answer to your question "When do we stop digging?" has more to do with the cost-benefit of experiments. In particular, I note that the discovery of Higgs at SM mass has excluded ALL other fundamental particles from consideration to -5.5 sigma. If CERN/LHC were to collect more detailed data about Higgs, they could achieve -6 sigma, reaching their own criteria to stop searching. At least 'stop digging' in the high-enefrgy direction... some claim that high-luminosity e-,e LINACs have more to reveal.

I have also long used the words "beneath" the Std Model, rather than "beyond" because it is the foundation upon which it is built which needs work.

Wayne

Hi Karen:

I agree with your statement_ "More generally, if a theory is not internally consistent, or relies on approximations, physicists tend to believe that this is a symptom of there being something missing--some physics that the theory fails to take into account."

I would like to draw your attention to the missing fundamental physics governing - "What causes a photon to accelerate to the speed of light?" I would like to invite you to look into my paper - "What is Fundamental - Is C the Speed of Light". that describes the fundamental physics of antigravity missing from the widely-accepted mainstream physics and cosmology theories resolving their current inconsistencies and paradoxes. The missing physics depicts a spontaneous relativistic mass creation/dilation photon model that explains the yet unknown dark energy, inner workings of quantum mechanics, and bridges the gaps among relativity and Maxwell's theories. The model also provides field equations governing the spontaneous wave-particle complimentarity or mass-energy equivalence. The key significance or contribution of the proposed work is to enhance fundamental understanding of C, commonly known as the speed of light, and Cosmological Constant, commonly known as the dark energy.

The manuscript not only provides comparisons against existing empirical observations but also forwards testable predictions for future falsification of the proposed model.

Best Regards

Avtar Singh

Karen,

I'd posted earlier, was hoping for a reply before commenting further, but unfortunately no further replies have appeared, starting with my post.

So here's my take on your nine requirements as viewed from the perspective of the geometric wavefunction interactions GWI model Michaele and I present in our essay, with details there if you're interested:

1. Unified - yes. Four fundamental forces are seen as one in the GWI model

2. Unique - uniqueness proofs are difficult. How does one show that the same physics cannot be described by a different model?

3. UV complete (nothing beyond" formally) - The model appears valid at the Planck length, and beyond to the singularity.

4. Non-perturbative (exactly solvable) - yes

5. Internally consistent (well-dened formally, with no problematic singularities) - yes

6. Level comprehensive (no gaps and no overlap" in description at the scales that the theory is required in order to describe) - In QFT one is permitted (and required) to define but one fundamental length. In the GWI model that length is take to be the Compton wavelength. It appears that the model is valid at all length scales.

7. Background independent (no fixed structures across all models of the theory) - yes. GWI model is background independent.

8. Natural (no ne-tuning" of parameters) - yes. Requires only five fundamental constants input by hand (one of which is electron Compton wavelength), no free parameters.

9. Not weird - durn. Ya got me on this one. What's the fun of that? How about if it is the dual of not weird, plus the inversion. Very very weird.

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,

Cristi Stoica, Indra's net

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

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