Hi Peter,

As always, an impressive essay, full of relevant examples, and focused on the overview. You begin by noting that our organic computational systems have abilities different than computers and suggest that one proper use of these abilities is to

"keep looking for the boxes outside the boxes which the boxes came in."

You also note "most believe no classical...

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Hi Peter,

As always, an impressive essay, full of relevant examples, and focused on the overview. You begin by noting that our organic computational systems have abilities different than computers and suggest that one proper use of these abilities is to

"keep looking for the boxes outside the boxes which the boxes came in."

You also note "most believe no classical rationale [re Bell] is possible", and discuss the herd behavior that shuns any deviation from conventional wisdom so that few dare to break ranks.

Your '3-filter' example beautifully summarizes the nature of propagation, and is followed by Zeilinger's very important observation that:

"...Light always has the polarization state given by the last polarizer and has no memory of its earlier history."

That is essentially the insight that I employ on Stern-Gerlach, i.e., the dipole moment aligns with the field, versus the QM view that it is only "the component in the field direction" that is being measured. But the 'unaligned' initial spin possesses precession energy, and there is no precession energy when the moment is aligned with the field. Where does that energy go? Obviously it goes into the kinetic energy of the deflection from its initial momentum. Thus the energy of precession when the initial spin enters the field is exchanged from the precession mode (rotational) to the deflection mode (linear) and this determines the scattering of the particle in the inhomogeneous field as indicated by the position measurement.

Bell assumes instead that the particle simply continues to precess all the way through the apparatus and thus has no way to produce any but a constant deflection, normalized to ±1, and, as this is compatible with the basic Quantum Credo that "measurements yield eigenvalues", he imposes unwarranted constraints on the problem. Much of my essay is concerned with why he does this.

In a nutshell, he is tricked by math, assuming that, because the Dirac fundamental eigenvalue equation "looks like" the Pauli provisional eigenvalue equation, which is valid only provided a constant field is present, which it is not! You note on your page 2 Wittgenstein's analysis that "looks like" was the reason why all 'knew' the sun orbited Earth. Today it is the reason why all 'know' that no local model can produce the quantum correlations, which my local model does produce.

The whole argument is subtle, or it obviously would not have evaded physicists for 50 years, but now it is a fundamental part of the QM faith, and it is dangerous for the faithful even to discuss it, judging from comments on my thread [or lack thereof].

Anyway I know you have been concerned with this problem for years and I hope you will find the time to study it until you understand it, or will ask me questions otherwise. Last year I promised you a new approach, but it took longer than I thought to work out all the details.

My very best regards,

Edwin Eugene Klingman

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Peter, thanks for your communication. I appreciate that you are an architect with broad interest. Your suggestion that we avoid compartmentalization is easy to relate to since I am an engineer who spent many years in compartmentalized industry which probably destroyed Kodak, the place I worked. Your essay was on point regarding the FQXi question (unlike many of us that used the opportunity to...

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Peter, thanks for your communication. I appreciate that you are an architect with broad interest. Your suggestion that we avoid compartmentalization is easy to relate to since I am an engineer who spent many years in compartmentalized industry which probably destroyed Kodak, the place I worked. Your essay was on point regarding the FQXi question (unlike many of us that used the opportunity to weave our work into the FQXi theme). The examples you used to highlight the differences between math and reality were excellent. I had forgotten that polarized light acted the way you described and found it interesting that the scientific community continues to use the concept of “filter” rather than “modulator”. Filters were used extensively in photographic products but we knew there was some “unwanted absorption”. I also liked your examples that remind us that physics operates at the local level within a background and going outside the brackets can mislead us.

I was pleased to find that you also publish on academia.edu since I have found several people with similar interests on that website that say they read papers (but never interact beyond that). Your continued and deep insights into entanglement are well documented there. To me it says that nature uses complex numbers and is efficient at arriving at solutions that we can only observe as probabilities. I should probably derive more meaning from it. I do believe that every atom is identical and that they are manifestations of the physics that is everywhere and identical. As such, I am not surprised by correlations but this does not lead me to superluminal “cause and effect”.

Your quote regarding “finding new ways of thinking about [facts)” is on point. I tried to “reverse engineer” nature by creating models. My interest in information theory led me to thinking about facts as probabilities. That led to a concepts that I used to model cosmology, force unification, gravity, atomic binding energy, elemental abundance, perception, black holes, meson and baryon masses, decay times, etc. I tried to point out in my essay that it was not nature. It was a new way of correlating natural phenomenon and makes it easy to understand. This is a preliminary step to true understanding just like the simple math that Newton used to correlate gravity. People don’t get it (probably because I am not a very good communicator).

Gene H Barbee

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Dear Peter,

I greatly enjoyed your essay. Its wonderful.This is one of the most relevant essays I have found here on this site.

The reasons are obvious.

As you have mentioned

("We consider mathematics as fundamentally digitised geometry, so well able to approximate natures 'non-linearity'. As Galileopointed out;

“He who undertakes to deal with questions of...

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Dear Peter,

I greatly enjoyed your essay. Its wonderful.This is one of the most relevant essays I have found here on this site.

The reasons are obvious.

As you have mentioned

("We consider mathematics as fundamentally digitised geometry, so well able to approximate natures 'non-linearity'. As Galileopointed out;

“He who undertakes to deal with questions of natural sciences without the help of geometry is attempting the infeasible.”

We cite various tricks which mislead us, not the fault of mathematics itself but of it's poor application due to our limited conceptual understanding.Reliance on mathematics as the 'language of physics' became pragmatic necessity when we were unable toclassically rationalise findings. Many now believe no classical rationale is

possible at quantum scales. John Bell describing that view as 'sleepwalking.')

I too believe that Mathematics,numbers ultimately come down to Geometry. The main reason why maths mislead us in any scenario is not the fault of mathematics but we don't understand the compatibility of mathematics with physics/natural sciences. There are certain laws of invariance behind mathematics itself,being a geometrical phenomenon and what is generally done is that we don't try to check whether its intrinsic law of invariance matches with that of the physical scenarios we are dealing with, and this leads to the mutual conflict and friction that can mislead us.

The true reason why mathematics is effective in physical scenarios : first of all we have limited physics to certain criterias to be able to explain it mathematically. Further,once we have done it, its infact the hidden laws of invariance behind the mathematical setup (geometry) which explains the laws of invariance of physical setup, even if the scientist/mathematician may not be aware of this intrinsic invariance behind the mathematics itself. This is the key point.

In context of Skolem paradox , as I have mentioned in my essay how model theory succeeds to explain some aspects of aphysical scenario while fails in other aspects. This is because of the instrinsic compatibility & incompatibility of their hidden laws of invariance.

The main focus should be to peep into that hidden laws of invariance behind the mathematical setup itself . This is greatly revealed i probably the most important problem of mathematics"Riemann Hypothesis. David Hilbert said - if he wakes up after 1000 years , the 1st question he will ask - has RH been resolved ? I personally have devised a method to attack RH that its true and the clue is to reveal the intrinsic invariance behind the mathematical geometrical setup itself.Numbers are nothing but Geometry.

As you have mentioned

(Mathematics can show that multiple inversely proportional 'complementary' sine and cosine curves naturally and physically exist for various qualities, as they do for the Dirac paired inverse spinors in so called 'unphysical' quantum mechanics.

Yet some higher order curvature is always superposed, at reducing scales but ensuring no entirely linear and precise mathematical description can be possible beyond the limits identified by Gödel. Many will find the visualisation methods revealing the relationships difficult, but they are powerful conceptual tools which

can be taught.)

You have also dealt with The Filter paradox.

The concern is paradoxes. the paradoxes reveal the fundamental discrepancy lying at the root of mathematics. They arise because of underlying structural conflicts.

I am also focusing on Godel incompleteness and Inconsistency theorems.

Now, if they arise, there are two ways.Either, considering it as the the end and accepting the limitation and secondly,trying to resolve the limitation by making some structural and fundamental change in the way way formalistic mathematics has been developed. I am concerned with this shift in the formalistic mathematics by allowing time and reference dimension to mathematics to sort out the paradoxes like physics. What we do is we take physics to be in time and reference dimension and take mathematics to be in timeless absolute dimension. This is the cause of paradoxes.If physics is in timeless , absolute, then so is mathematics and if physics is within the periphery of time and reference frame and the so is mathematics. This is because Physics and Mathematcis both are the cause of vibrations.

As you have mentioned :

(

We suggest then that 'new ways of looking' at large sectors of physics may then be

possible by using mathematics in fundamentally different ways, improving

understanding. However it seems that those 'different ways' are not visible using

just the 'lens' of current mathematics. We need formalisms to avoid the various

fallacies and hidden tricks and invalid proofs of a system which can prove 2 =1

via 'division by zero' easily disguised for instance by any term with a value of 0)

We certainly need formalistic mathematics which can sort out the fallacies,paradoxes,inconsistencies to deal with physical scenarios in a improved ways beyond conventional approaches.

Hence,as I have mentioned that we need to restructure formalistic mathematics itself based on their intrinsic characteristics to look at physics in fundamentally different and improved way. we need to operate the laws of invariance behind mathematical(geometrical )set up itself before explaining to physical /other natural sciences.

Anyway you have written great essay.

Thanks,

Pankaj.

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(copied from my essay forum -- THR)

Peter,

Thank you, that's very kind. There's no mystery to why my score languishes below the cut -- never in my memory, from the first time I entered these competitions (which dates from the very beginning), has a fully relativistic viewpoint in foundational physics gotten due respect, while some of the fringiest views in quantum theory have won big...

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(copied from my essay forum -- THR)

Peter,

Thank you, that's very kind. There's no mystery to why my score languishes below the cut -- never in my memory, from the first time I entered these competitions (which dates from the very beginning), has a fully relativistic viewpoint in foundational physics gotten due respect, while some of the fringiest views in quantum theory have won big prizes. So I have long abandoned any illusions I might have had. It is enough that the FQXi forum gives voice to a minority viewpoint that it de facto opposes, and I am grateful to the Institute for that, even when I think it could do more.

There is an even lower score than mine, given for a far better essay by Vesselin Petkov, and -- I expect -- is low for the same reasons. I am going to do a lazy thing, and quote Vesselin's reply to a recent forum participant, because it matches my opinion: " ... if Minkowski had lived to see the advent of general relativity, he would have realized, as a mathematician, that the mathematical formalism of general relativity implies that gravitational phenomena are merely manifestation of the non-Euclidean geometry of spacetime (not an interaction). Einstein made a gigantic step by linking gravity with spacetime geometry, but even he was unable to overcome the seemingly self-evident 'fact' that gravitational phenomena are caused by gravitational interaction (which, unfortunately, is still the accepted view in physics)."

Things are changing. I got an Email from The Minkowski Institute Press just a few days ago that they are publishing Cristi Stoica's PhD thesis (congratulations, Cristi!) , which is relativity-based, with a perturbative path to quantum gravity (my own solution is non-perturbative, but we are pretty close).

In regard to your own defense of conventional quantum theory in the Bertlmann's Socks analogy, I applaud your expansion of the pedagogy, and give high marks for that. It is deservedly among the best of Bell's output (and your own, for that matter).

If you don't mind, I am going to do another lazy thing, and reproduce this reply in your forum.

All best,

Tom

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Dear Peter, thanks for getting in touch via my Essay Forum. In reply:

The remarkably broad sweep of your latest ideas, coupled with your new ideas re the details (eg, Jackson & Minkowski (2014)),* is mostly moving beyond me! Dare I say, leaving me behind. I might even say that our approaches are diverging to the extent that we are moving to be polar opposites in...

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Dear Peter, thanks for getting in touch via my Essay Forum. In reply:

The remarkably broad sweep of your latest ideas, coupled with your new ideas re the details (eg, Jackson & Minkowski (2014)),* is mostly moving beyond me! Dare I say, leaving me behind. I might even say that our approaches are diverging to the extent that we are moving to be polar opposites in approach.

Fortunately, I still understand you to be a local realist to the point (as spelt out in my essay) of being an Einstein-local and a Gisin-realist.

To be clear re our differing methodologies: For my part, I am investigating a very small part of physical reality: one where, like a stone in my shoe, most interpretations contradict my basic understandings of that reality; at the same time aggravating my fundamental sense of comfort -- as a successful engineer -- with my intuitions re such.

That small part, as you know, relates to the many and varied interpretations of many and varied Bell-tests: whose results I accept without question, since they are exactly the results that my own views endorse.

But I reject the common interpretation that local realists like us must give up Einstein-locality (for nonlocality) or Gisin-realism (for un-realism): and, in that regard, I happily note the increasing trend of old foes to be moving to my position (which is, hopefully, still our position).

In particular, my small corner of the business holds out hope for a new quantum theory: one devoid of Hilbert space (since spacetime appears to be sufficient) and certainly absent nonlocality (since, to be blunt, how on Earth could any such thing be possible). For a very simple critique of the mainstream view, just skim paragraph #6.1 of my essay.

Nevertheless I see a growing trend to go for the Full Monty here; and though I'm not in favour, it's good to see that trend reflected in the very high standing of your essay.

However, from my own broad experience (and for those who are aware of it), the Full Monty does not quite measure up against what I have to offer!

With best regards, and hoping to keep in touch; Gordon Watson: Essay Forum. Essay Only.

* Jackson, P. A., Minkowski, J.S. Quasi-classical Entanglement, Superposition and Bell Inequalities. Academia.edu 9th Nov 2014.

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I love the polarizer/analyzer game, but you have set up a fixed game with your absorbing polarizer paradox. A polarizer actually works for even a single photon and not just for ensembles of photons.

A single photon is always in a superposition of polarization states and a linearly polarized photon is a sum of a right and left circularly polarized states. A circularly (or helically as...

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I love the polarizer/analyzer game, but you have set up a fixed game with your absorbing polarizer paradox. A polarizer actually works for even a single photon and not just for ensembles of photons.

A single photon is always in a superposition of polarization states and a linearly polarized photon is a sum of a right and left circularly polarized states. A circularly (or helically as you like to say) polarized photon is a superposition of two linear polarizations with a pi/2 phase shift.

A linear polarizer prepares a photon in two circularly polarized states and a circular polarizer prepares a photon in two linear polarized states. There is no paradox therefore in how this game works.

A photon or indeed any particle also exists as a superposition of polarizations or spins or two paths with a beam splitter or a dual slit or any number of similar techniques. The basic issue with quantum effects for civilians is that phase and amplitude and interference and coherence are simply not yet part of our gravity reality. We think that the incoherent reality that we normally experience with macroscopic objects is how all the universe works.

This is not how the universe works, but it is close.

I actually do get a lot out of your intuitive grasp of reality because your eliptical plasmas do seem to represent superpositions of coherent matter states, you just do not have the math to make it work. The superpositions of coherent matter states are at the root of quantum action, but are not yet a part of gravity action.

Your DFM plasma refracts light just like any dielectric medium and my quadrupole gravity photon field seems to behave just like your DFM plasma. A quadrupole photon field surrounds all matter objects and derives from the photon emission for each object over the history of the universe. Photon waves emitted from an object matter in the past result in the quadrupole photon field around each object that we call gravity. In effect, each photon wave emitted from a matter object is equivalent to a photon wave coming back to the object attenuated by the size of the universe.

The quadrupole photon field that we call gravity deflects or delays a single photon at twice the Newton deflection or delay of an MEE equivalent particle. This as it turns out is due to the additional dielectric effect that a photon dipole has in quadrupole gravity. An equivalent oscillating matter dipole will then show the same deflection as light does in a quadrupole gravity field.

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Peter:

A very interesting essay with evidence for the need to open one’s mind. Thank you.

I do have one concern with your essay (being educated as a mathematician) - that maths “doesn’t do ‘imagination’.” And I agree with your statement that any “solution is unlikely to emerge just from maths”.

Consider the number of squared quantities in physical theories...

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Peter:

A very interesting essay with evidence for the need to open one’s mind. Thank you.

I do have one concern with your essay (being educated as a mathematician) - that maths “doesn’t do ‘imagination’.” And I agree with your statement that any “solution is unlikely to emerge just from maths”.

Consider the number of squared quantities in physical theories along with the connection to complex numbers. If we have a squared value, then the ‘real’ (un-squared) value can be either positive or negative. Since we cannot know which it is, from only the squared value, there are two paths by which the squared result can be obtained. We cannot know which ‘path was taken’, so long as we live in a ‘real’ world constructed with Real numbers. In this world, there are always two paths. This is not the case if we use all complex numbers, in which case the path can be known.

Integers, Rationals, Reals, Complex, Quaternion are all ‘bracketed’ levels of mathematical knowledge with specific mathematical contexts that present a multitude of mathematical spaces. Algebraic equations with integer coefficients, rational coefficients, real coefficients are examples. Also equations with integer exponents and rational exponents bring us into much more complex mathematical spaces. We can consider algebraic equations with real coefficients and integer exponents or rational exponents. What about such equations with complex coefficients and complex exponents? Can we even do this?

Are we using the correct spaces to understand our physical world? (I will suggest we are using one layer of your hierarchical relationships) Do we have the correct tools to make use of certain mathematical spaces? It would appear we do not, since we cannot represent a complex number in the same way as we represent real, rational, and integer numbers - as completed values without unknowns (complex values today always have the unknown ‘i’). If this is true (we don’t have the correct tools), then we would be forced into ‘heuristic necessity’ in order to address situations that require math tools that we do not have.

If we do not have the appropriate tools, then what might change, if we did have the appropriate tools? A complete complex value might be capable of measuring quantities we currently do not consider measuring, since we are unable to measure them using real values. If we could represent complex values as complete, without unknowns, then we should be able to compare them (greater or lesser) and rank them along a continuum. The universe might be better represented (not ‘Finally’ represented, however) using a possible complex continuum. (The separation of the Continuum Hypothesis from current foundational mathematics should allow this without destroying current foundations).

Given your presentation of red-green spin as a spinning sphere that ‘flips’, what if this is reasonably accurate, however the spinning sphere is occurring in a geometric space with a physical dimension that we currently do not include in our models (not some tiny rolled-up invisible one)?

If our mathematical tools cannot adequately measure quantities along this dimension, then we would not have a reason to include it in our models (even though this could be leading to ‘heuristic necessities’). It could be directly in front of us and we would not see it, because we do not realize it as a measurable quantity.

One last conjecture: This dimension is scale. It is exponential in character, is not measurable by current ‘real numbers’ (decimals are limited to specific scales), and is unaccounted for in current models of space (and it is ‘right under our nose’). Our body, at each level of scale - organ, cellular, molecular, atomic - is always a 3-D volume. This 3-D volume is populated by different objects at each level. Connecting the levels at any 3-D location gives a 4-D line (a line mutually perpendicular to the other 3). Note that a complex numeric system will likely require a system of numeric representation that, beyond the addition/subtraction, multiplication/division, and exponentiation/logarithm incorporated into current ‘real numbers’ (eg. decimals), will add integration/differentiation into the operations inherent in constructing a complex value - thus requiring a complete revamp (major upgrade) of all computing systems.

Maybe this is a maths fantasy and maybe it is maths imagination, yet not maths alone as it is coupled with a significant change in physical perspective. It also follows your hierarchic boxes within boxes approach, as it simply expands current ideas and levels, not destroying existing ones.

(Mark as 'inappropariate', as appropriate.)

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Dear Peter,

I have finally had a chance to read your essay and I really enjoyed it.

You make several thought-provoking arguments, which I will have to revisit and carefully consider.

I like your assertion that specific mathematical formalisms may be limited to local domains. This is precisely why, in my essay, I discuss how one can derive the appropriate mathematical...

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Dear Peter,

I have finally had a chance to read your essay and I really enjoyed it.

You make several thought-provoking arguments, which I will have to revisit and carefully consider.

I like your assertion that specific mathematical formalisms may be limited to local domains. This is precisely why, in my essay, I discuss how one can derive the appropriate mathematical formalism from symmetries based on the concept of consistent quantification. Of course, my essay focuses on a simple case of combining objects, which obeys specific properties such as ordering, closure, commutativity and associativity. Given these properties, one can show that the numbers describing the quantities of objects must be additive. What is the local domain? Well, this is precisely the domain where you have ordering, closure, commutativity and associativity! Where you promote the general idea, I demonstrate it through practical example.

I believe that rather than assuming that some specific mathematical formalism applies, one should derive it! Only then do you really understand the foundations. I do believe that this is possible. You may enjoy two of my papers on Emergent Spacetime

http://scitation.aip.org/content/aip/journal/jmp/55
/11/10.1063/1.4899081

and on Fermion Physics

http://arxiv.org/abs/1310.1667

In these works, I derive a good number of physical laws and relations from symmetries and this idea of consistent quantification. The domain boundaries are then well-understood as they were derived!

I enjoyed your discussion of the 3-filter and the work by the Vienna group. My adviser in graduate school, John Broadhurst, often discussed this problem with me pointing out that there are important clues here that have been overlooked. He said that one cannot think of vectors as arrows with directions, but rather they are cosine distributions, which are spread out.

I believe that you mentioned Sherlock Holmes (or maybe it was a post in response to your essay), but regardless, physicists can think of themselves as detectives. As such, these little clues are critical to finding the path to understanding. In addition to the 3-filter experiment, there are serious problems with the concept of motion, energy is related to frequencies, energy and time are Fourier transforms as are space and momentum. If space-time is a physical manifold, then what is momentum-energy? These are important questions that are not considered and cannot be answered as long as these concepts are taken to be fundamental.

Thank you for an excellent and thought-provoking essay!

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