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

Karen,

My essay leads off with a discussion of causality, in which I refer to

1. J.B. Hartle, S.W. Hawking and T. Hertog, "The Classical Universes of the No-Boundary Quantum State" hep-th/0803.1663v1 March 2008. which formulates a causal particle (lacking QC/ED) and

2. N. Seiberg, L. Susskind and N. Toumbas, "Space/Time Non-Commutivity and Causality", hep-th/0005015v3, May 2000. which sets the criteria (which btw Std Model does not meet, thus the meekly stated criterion).

So yes, I very much meant a particle theory mathematically consistent with GR. Not good news for SU(3)xU(2)xU(1), since the consistency criteria makes similar stipulations on the form of the particle |H> (representation algebra).

The criteria for consistency stems from 3. G. Takeuti, Proof Theory, Dover Publications, 1975. which requires that a particle be finite, and of course that there be no infinities in the theory. The reason that we renormalize is that the point-like approximation induces an infinity/infinity (that cannot be resolved by L'Hopitals theorem), which is removed by imposing a 'fudge factor' -actually several of them. { Of course I didn't call it that to Prof Gell-Mann when he came to OSU to pitch the SSC! ;}

String theory meets the finitary criteria, has a consistent mass formulation, but can't find QC/ED without a stiffness-induced quantum state MAP. {Just had to work the word map in there ;} There are several examples of finitary representation geometries being studied... I won't trouble to list more.

As far as replicating QC/ED (QFT) and GR, the criteria place a strict caveat on that as well, so don't expect your dad's GR to emerge. GR is the least affected since all that one needs is to correctly interpret the temporal curvature term as an imaginary quantity. The particle theory folks have to convert to a cross product of two wreath products as their representation algebra, to be sure they don't like it. Although it is a remarkably simple and beautiful algebra... which can and has been taught to HS students.

So insofar as you put it "the older theories should be derivable from the new one, under some relevant conditions", yes. But sadly for nearly everyone, NOT the reverse. Here I recommend you also read Sabine Hossenfelder's essay.

I discuss and present for consideration a foundational formula at the end of my essay, so perhaps read it from the end backward. I approached the topic as sort of a "deep dive" to reach most fundamental insight toward the end, with a fairly rapid ascent to address some old questions that are very much within bounds of the contest topic.

The "relevant conditions" mostly have to do with the space-time average SCALE. {to derive GR eqn, set time to "now +/- 100 years" the foundational QC/ED state algebra averages out, as is well-known ;}

Wayne

Invite me out for a seminar? I have an hour or two of abstract formal discussion on all mathematically related topics.

p.s. Interestingly, you add "unique". Here there is strict mathematical meaning, which, when imposed, makes the need for 'several' fundamental criteria a bit of overkill. The reason being that in math, virtually all uniqueness proofs involve a cyclic variable. Euler's equation for a circle, that is e^(i theta)... in which I choose theta as thetamass-time. There is no other theory with a true cyclic variable.

Hi Eckard,

Before I retired, my work for the US DoD was almost entirely in the open, since my main role was trying to promote funding for universities and small businesses for a variety of technology areas, including quantum.

What's happened with quantum entanglement is that one use of it, entanglement for encrypting communications, is comparatively much easier (it's still very hard!). It is a sufficiently solved problem that you can now buy commercial communications encryption boxes. Look up for example the company for example Quantique, at https://www.idquantique.com/, or just do a Google search.

Quantum computing in contrast is incredibly more difficult, mostly because instead of just keeping a single pair of photons quantum, you have to keep an entire computer quantum. That is not easy!

But more importantly, because of the huge commercial potential of such devices, the commercial sector has begun investing levels of money that government research groups cannot even begin to compete with. Companies like Google and IBM are where the action is there, not in federal programs. When an area gets hot commercially, government research programs inevitably lose people. I watched that happen first hand when robotics suddenly got "interesting" to the private sector. All of our best demos, in particular Boston Robotics, disappeared!

So, I just wanted to let you know that to the absolute best of my knowledge there is nothing weird going on for quantum computing, and I say that as someone who understands the physics there pretty well. It's just really, really hard... and the solutions to it are and will continue to be far more likely to come from the enormously larger pots of money available from the private sector than from government programs.

Cheers,

Terry

Dear Terry,

Thank you for your (almost) convincing arguments. Kadin and McEachern/Traill might deal with them. Let me just briefly reveal my reasons to be unsure:

It begun with Pauli's statement that QM is the first disciplin that cannot replace the imaginary unit. I found a strange change in the 1920 decade. They suddenly dropped the Re( ) operation without giving an explanation. Schrödinger had revealed (in the 4rd communication) how he heuristically arrived at his complex wave equation. For a while I was puzzled why Heisenberg/Born's Hermitical square matrices are identical to Schrödinger's picture.

This essay contest provided two insights to me:

- The implicite assumption of a phase relative to the chosen reference point t=0 was made about a decade before Heisenberg and Schrödinger. They just herited it.

- Watson pointed me to a paper by Fröhner on a theorem by Riesz-Fejér that links probability theory and quantum mechanics.

I do neither see me a Sherlock Holmes nor able to investigate further. I am just a bit pedantic when it comes to the correct use and interpretation of complex calculus.

May someone else question the superposition principle, i.e. the need to work with interfering wave functions, the absolute squares of which are probabilities? Shut up and calculate? OK, as soon as the fundamentals are safe.

Cheers,

Eckard

Dear Karen,

Thank you very much for the answers and comments, and for the references, which I didn't know and I think are relevant.

You said "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?"

Yes. I think we should extract the true lessons and to rethink the assumptions we made. We understood physics in a certain historical path, and we used what we knew at that time to formulate and develop it. This may introduce problems and limitations. So if we extract the essence of each principle, we can generalize it. Then we can intersect the generalizations of different principles, e.g. distilled from GR and QM, and find the class of theories where they both apply. This may lead to an exhaustive search, but it is possible that once we get them better many options will be eliminated. For example, no-go theorems like Bell's eliminate a large class of models.

Another way to reduce the possibilities is to look for rigid models, which don't have replaceable parts. For example Clifford algebras are associated to the metric, and there's a Clifford algebra which includes a typical generation of leptons and quarks, with their exact symmetries. Because it is a simple algebra, it is difficult to change it. Without such a structure (although maybe not this one) there's too much freedom to choose the symmetry groups and the representations, hence the matter fields.

To accomplish this generalization, a very general framework may help. I think the most natural and general common framework for all theories in physics is a sheaf theoretic formulation. The sheaf framework applies to relativistic and nonrelativistic, continuous and discrete, classical and quantum, and in fact can go much beyond these options allowing us to use locales and topoi. All theories in physics can be cast in this framework and allow generalization, and generic proofs similar to those in category theory, which may allow discussions at a metaphysical and metatheoretical level without being committed to a particular model. At the same time, sheaves emphasize the need to take into account global and topological properties of the solutions, which I think is essential for the problems of quantum mechanics (one major interest I have in exploring the possibility of a single world no collapse quantum mechanics, the obstruction being that quantum measurements seem to impose inconsistent constraints on the solutions of the Schrödinger equation. Sheaves provide powerful tools to study the obstructions to extending the local solutions to global ones). I started developing this 10 years ago, and I wrote something. I didn't submit it to a journal because I wanted to develop it more, but then I moved to other things. One reason is that I think sheaf theory is too general and allows too many options for one person to explore, so I decided to try more direct ways while keeping the framework as a tool for thinking about those.

You said "it would seem to turn everything around and go in from the opposite direction". Yes, for example it is thought that QG will resolve the singularities, but the opposite is possible too, my (purely GR) treatment of singularities gave automatically several types of dimensional reduction proposed in other approaches in a rather ad-hoc way with the purpose to make quantum gravity renormalizable. So it was as you said, going in the opposite direction. But I am not satisfied enough with this, because I think it doesn't say what's the real theory behind. Every time there was real progress in fundamental physics, it was because of better understanding, better mathematics was revealed, a more rigid one, unifying different aspects.

I think much can be learned from researching the various mathematical structures involved. I think topology is essential (e.g. Wheeler's geometrodynamics, in particular "charge without charge", and even if spacetime is topologically trivial topology is relevant in many other ways). (topology may lead to the impression that we focus on the continuum and ignore the option that spacetime is discrete, but in fact the topology of manifolds was understood starting from Euler's polyhedral formula, and the simplicial complex approach to manifolds is still essential in the study of their topology.) The differential structure also may be important, see the work of Torsten Asselmeyer-Maluga. The causal (or conformal) structure is also essential, in particular the Standard Model without the Higgs has conformal symmetry. Topology revealed connections between topological properties and curvature, I think this is a place to understand how matter unifies with gravity to see what's beyond the Einstein equation.

Thanks again for the discussion, and for the references. I also looked into your book's summary, I think it is great!

Best wishes,

Cristi Stoica, Indra's net

Dear Karen,

I read your paper and found it very interesting in many ways. If taken strictly as presented the nine conditions could possibly identify a most fundamental theory depending on how they are interpreted. As an example, since the universe is constructed as a structural substance hierarchy, although it is possible to generate a complete theory that covers all of the structuring of all of those structural levels, it could be somewhat difficult to work with. It might be easier to still compartmentalize the total theory into parts that specifically deal with each hierarchical level or the interactions between two levels, etc. as needed to minimize the amount of work that would be required to implement it at specific levels. At the same time the overall theory could describe the overall material structural generations, their actions, and their interactions throughout the total complex structure of the universe. Also since some structures, such as energy photons and field structures remain essentially the same throughout all of the hierarchical levels of structure, these entities and their structures and functioning could be considered background fixed structures, but they are existent parts of the universe that would necessarily be a part of any truly fundamental theory.

The most interesting part of your paper to me is your description of the hierarchical tower of theories at different size scales of the universe. You do not mention that there are different hierarchical structural levels of the universe in which basic substance(s) of one level is used in that level to construct what is then the basic substances of the next larger level, etc. At the lowest structural level that man has currently gained an understanding, matter particles are the level's basic substances and are structured together with field structures to form all of the atoms. At the atomic level, the substances of the atoms are structured together with field structures to form the molecules and at the molecular level the substances of the molecules are structured together to form the substances of the large scale objects that we generally work with at our hierarchical level, etc. As you progress up the hierarchical chain, the number of different structures that are produced within each level increases. The lower the level is, therefore, the simpler or more fundamental it is than those levels above it. Any truly fundamental theory would, therefore, need to be able to explain the complete construction of all of the structures at all of the levels in the total structure and the complete progression of substance production from the first level through the last level. One reason that currently accepted theories such as QFT and GR, etc. can't be truly fundamental is that they do not address the substance or the structuring of that substance that produces the the basic entities of matter particles, energy photons, and fields, which make up the currently known lowest hierarchical level of the universe. This is very odd, since there is now (and has been for some time) adequate information in both observational information and also within the mathematical constructions of current theories to allow these things to be extrapolated and understood. It appears that this area has been purposely avoided. I can see reasons why that may be the case, but it is holding back man's progression because hidden within the internal structure of matter particles is the key that can free man from the limited scale problems that you mention. When these things are understood by man, some of the parts of both QFT and GR that man currently considers to be important will be seen to be in error. This will simplify the remaining parts and allow a complete workable theory to be developed. The real question is how long will man hold back this development for what amounts to petty reasons?

Sincerely,

Paul

Awaiting response of Author, Jaren to xomments of mine and Paul !

Dear Karen,

Good to see that your Aussie connections have done no harm: for your excellent essay hits the spot as I work on "wholistic mechanics" (WM), a classical/deterministic reformulation of physics in spacetime. WM = {CM, SR, QM, GR, QFT, QG, EFT, ...|TLR}, my essay being an introduction.

Identifying your nine conditions as KC-1 to KC-9, it was the last -- no weirdness -- that got me started; ie, I studied EPRB, the experiment analysed in famous Bell (1964), not accepting that the assumptions behind Bell's theorem (BT) were valid in that setting, and rejecting nonlocality.

My starting premiss (my classical boundary condition) is true local realism (TLR): the union of true locality (no influence propagates superluminally, after Einstein) and true realism (some existents may change interactively, after Bohr).

Revising EPR's naive definition of "elements of physical reality", I find determinism in play, refute Bell's theorem, and (from first principles, in spacetime) find the Laws of Malus, Bayes and Born validated. Born's law (an effective field theory, in my terms; in the space of probability amplitudes) can then be tested by confirming the correct result for the EPRB expectation; then the correct DSE results; then onward to the stars.

In thus eliminating "wavefunction collapse" and nonlocality from QM, it follows that such weirdness need no longer trouble the foundations of QFT; etc. And since my calculations are conducted in spacetime (not Hilbert space), I'm thinking QG is covered automatically.

Enough: such is my long way of saying that I will welcome your comments at any time.

With thanks for your stimulating essay, and with best regards from down-under,

Gordon Watson (determined and free-willed)

Dear Karin,

Yes, for the reason that physics has taken to predicting pointer positions from which it conjures up sociologically desirable 'worlds'. Your essay reminds me of the trend in many sciences to deal with secondaries like methodology and the definition of what would count as progress and what it is supposed to look like.

Since Feyerabend we know that Everything Goes (provided it goes), because otherwise we logically overdetermine the problem and thereby prevent any solution. In other words, physics got stuck in the analytical abracadabra of pseudo-empirism.

Heinrich

Dear Karen,

Your eloquently written essay provides one of the most thorough and thoughtful responses to the contest question of any of the entries, and the list of 9 criteria is a useful way to structure any approach to thinking about fundamentality in physics.

A few comments:

1. I wholeheartedly agree with the "more general principle" that a fundamental theory not leave anything apparently in need of explanation, but I would supplement it with the caveat that "questions which are apparently in need of explanation" is a strongly paradigm-dependent notion. As you surely know, to Aristotle, our description of the world would leave a whole lot of questions (particularly in regard to teleology) open. Even to some 19th century physicists, some of our current concerns might seem to miss the point. Of course, I understood that you provided an answer from a physics perspective with the implicit assumption that it is physics within the contemporary paradigm. It is fun to imagine what kind of physics questions our descendants might ask which they feel are in need of an explanation and how these differ from the questions we consider today likewise.

2. I liked your arms-length discussion of unification as an answer to what is fundamental. Often unification is presented in a quasi-dogmatic way as the future of fundamental physics, but I tend to agree that nature is not "boshaft" (malicious) in the sense that if unification were really the answer, then nature would have given us more robust hints than we have now. In the end, what seems like the most plausible approach to understanding such deeply philosophical questions strongly depend on one's worldview.

3. The maneuver at the end, that the 9 criteria are inextricably tied to the nature of physics itself (as understood within the contemporary paradigm) is a subject well worth exploring further. I understand that this is not possible under the constraints of this contest, but understanding this deeply may well shed a brighter light on the justification for each of the criteria you named.

4. My emphasis on the importance of recognizing that we operate within a a particular paradigm springs from my belief that we have already all the elements in place that are needed to transition to the next one, and that the only reason we have not done so far is that the different pieces of the puzzle which already exist have not yet been assembled into a coherent and comprehensive picture. My entry, the first of a 2-part series, is an effort to do such an assemblage for a small number of these pieces, with the second part (regrettably still unfinished) putting a much larger set of them together.

Dear Karen,

I too apologize for my previous tone. I'm very passionate on this subject.

Why argue from secondary sources, when the primary source is quite clear? Einstein objected to special relativity even being called "relativity" since it is a theory of the absolute. I.e., the absolute speed of light in vacuo.

He allowed that the "General laws of nature are covariant with respect to Lorentz transformations." Clear enough. The LT, however, is a mathematical artifact. In a note to the fifteenth edition of the very accessible Relativity, the Special and the General Theory added in 1952, "Physical objects are not in space but these objects are spatially extended. In this way the concept 'empty space' loses its meaning."

In the appendix, "In order to be able to describe at all that which fills up space and is dependent on the co-ordinates, space-time or the inertial system with its metrical properties must be thought of at once as existing, for otherwise the description of 'that which fills up space' would have no meaning. On the basis of the general theory of relativity, on the other hand, space as opposed to 'what fills space', which is dependent on the co-ordinates, has no separate existence. Thus a pure gravitational field might have been described in terms of the g_ik (as functions of the co-ordinates), by solution of the gravitational equations. If we imagine the gravitational field, i.e. the functions g_ik, to be removed, there does not remain a space of the type (1), but absolutely nothing, and also no 'topological space'. For the functions g_ik describe not only the field, but at the same time also the topological and metrical structural properties of the manifold.

A space of the type (1), judged from the standpoint of the general theory of relativity, is not a space without field, but a special case of the g_ik field, for which - for the co-ordinate system used, which in itself has no objective significance - the functions g_ik have values that do not depend on the co-ordinates. There is no such thing as an empty space, i.e. a space without field."

http://www.relativitybook.com/resources/Einstein_space.html

Einstein was quite unambiguous on the non-separability of space and time. My attempt to address the challenge reduces the observable " ... topological and metrical structural properties of the manifold" to a soliton wave.

Hi Karen...

Your essay definitively reflects the position taken by the majority of the essay entries... i.e. "For the time being, we have to admit that we do not possess any general theoretical basis for physics, which can be regarded as its logical foundation." ~ Albert Einstein 1940 ('Science')

REF: Peter Jackson Ridiculous Simplicity "Essay Abstract https://fqxi.org/community/forum/topic/3012

In that theory is "formulation of apparent relationships or principles of specified observed phenomena... and knowledge of it's principles and methods"~ Webster

If formulation of relationships requires a Spatial measurement, then a minimum unit of Spatial measurement is fundamental to the theory... i.e. a theory is fundamental only in that it places constraints on formulation.

In that credentialed opinion is often up for auction, or already under contract, makes theoretical validity by professional consensus and unreliable approach.

In that our "best theories" are structured on a framework that is "mathematically ill-defined", and "The idea of unification is not just that there be a single theory describing all phenomena, but that it describe all phenomena as the same as fundamentally stemming from a single origin, e.g., as manifestations of a single entity or interaction.", my approach has been to build a kinematically verifiable Spatial mathematical framework stemming from a single Origin point source, and digitally simulating Energy distribution within that environment... i.e. animate pulsed distribution of minimum units of Energy (QE) over time, as a constant pulse rate, within a CAD environment quantized by a unified field single point origin encapsulation geometry... i.e. volumetric singularity as differentiated from point singularity.

REF: UQS Consciousness Investigation Geometry http://www.uqsmatrixmechanix.com/UQSConInv.php

Although to absolutely/unarguably verify any volumetric singularity quantization CAD environment as "the" Spatial framework, will require an Energy simulated Emission in which a verifiable Hydrogen Proton QE choreography emerges, which may necessitate extensive digital resources, but the approach does yield a theoretical minimum unit of measurement for Space (QI), Energy (QI), Time (QT), and Information (QFI), and simulations out to 75 pulses already verify Entity Spin, separate interactive Inertia and Radiation distribution channels, no limit on single Energy Event Spatial effect, gravity as Mach's principle, unoccupied "dark" Spatial units, etc....i.e. clarifying "the picture of the relevant physics at the scale of interest" in terms of fundamental units of measurement, instead of obscuring.

Complexity is often a result of application of inappropriate technique.

In regard to the availability and "ability to use computational resources", in that Calculus does NOT resolve a Point Energy Source 3D Encapsulation geometry that facilitates distribution of Energy equal in all directions from a single point ... i.e. Origin Singularity ... quantized by unified minimum units of Space (QI), there is no way to know if a point Energy Event can, or cannot be, resolved to a Spatially defined object, which suggest that point-like singularities may be being generated by the use of Calculus in Energy/Space analysis... and computational analysis... e.g. determination of the Singularity Sector Differentials of any Emission Node at any specified shell radius... now looks like this:

IF EN(ENR)X0 AND ABS(EN(ENR)Y) < ABS(EN(ENR)X) AND ABS(EN(ENR)Z) < ABS(EN(ENR)X) THEN SS$= +x

IF EN(ENR)Y0 AND ABS(EN(ENR)X) < ABS(EN(ENR)Y) AND ABS(EN(ENR)Z) < ABS(EN(ENR)Y) THEN SS$= +y

IF EN(ENR)Z0 AND ABS(EN(ENR)X) < ABS(EN(ENR)Z) AND ABS(EN(ENR)Y) < ABS(EN(ENR)Z) THEN SS$= +z

,,, and as a bonus, visual 3D CAD output facilitates visual verification of the accuracy of one's mathematics.

Thanks Karen for so elegantly contributing your insights, your comments on my essay would be read with attention, and I will return to rate after I have read as many essays as time permits.

Sue Lingo

UQS Author/Logician

uqsmatrixmechanix.com

ok, think i get where you're coming from re uniqueness - as opposed to many EFTs needed to cover all length/energy scales?

a different kind of uniqueness from trying to prove no other equivalent model exists.

re weirdness, did you look at our essay yet? It might relieve some of your concerns regarding interpretations of wavefunctions and their interactions. The geometric algebra gives a wavefunction that is simple and intuitive, can be visualized. Take a look. I think you'll like it.

Karen, if/when you reply to my post, please copy it to my essay-thread so that I'm alerted to it. I'm having trouble keeping abreast of many good discussions this year.

Many thanks; Gordon More realistic fundamentals: quantum theory from one premiss.

Rhanks Karen for your detailed reponse to my queries. I feel satisfied with the response as it shows oth humility and depth of understanding you have achieved. Subjectivity and objectivity both control the growth of our understanding and most of all the consensus that results in the community helps us all grow further the professionalism demanded of us. If you can spare soem time responding to our essay here we shall feel obliged, it is ashort contribution of just 2/3 pages only!