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Blogger Florin Moldoveanu wrote on Apr. 4, 2011 @ 13:20 GMT
WARNING: If algebra and geometry caused you headaches in school, this post could bring back suppressed memories.

Credit: vaXzine
According to neuroscience, the left brain is responsible for understanding algebra while geometry is a right brain pursuit. (Image right, via flickr, courtesy of vaXzine.) However, algebra and geometry represent the same math, but disguised in a different languages. Take any line in a plane, for instance: Its points obey a linear equation. Similarly, the intersection of two lines is given by solving two linear equations with two unknowns. Or any half plane can be codified as a linear inequality. And so on and so forth.

At this point, you may well be asking, who cares? I argue that it turns out that this algebraic-geometric duality is at the core of understanding quantum mechanics, the Standard Model, and even this year’s FQXi essay question: if nature is digital or analog. (I haven’t entered this year’s contest, so I am not trying to promote my entry!)

So, if you can suppress the bad memories of algebra and geometry at school, please read on:

Let’s start the story with quantum mechanics. Solving Schrödinger’s equation is a central part of any quantum mechanics introductory class. In there one learns that the wavefunction lives in a so-called Hilbert space. What is not immediately apparent is that the Hilbert space is a very simplistic mathematical object used to codify continuity and whose main characteristic is its dimensionality. Far richer mathematical objects are operator algebras. And in fact, quantum mechanics can be axiomatized in the algebraic framework of the so-called C* algebras. Then one recovers the Hilbert space by a now standard method called the GNS construction.

In technical terms, by a theorem due to Gel'fand, (the G in GNS) any compact space X can be characterized by a C* algebra C(X) of continuous functions on X. This is nothing but the generalization of the mapping between analog properties of geometry/topology and digital properties of algebra.

Credit: Simpsons contributor
It is interesting to see how the duality between geometry and algebra holds in the case of stranger geometries where notions of points, lines, and planes do not occur. Wait a minute, you may ask, what geometries are those where points, lines and planes do not make sense?

Here are some examples. I hope the reader is aware of Penrose’s non-periodic tiling of the plane. A beautiful example is a Julia set. (Image right, courtesy of Simpsons contributor.)

There are also other non-glamorous examples from quantum mechanics: Alain Connes developed an entire branch of mathematics called non-commutative geometry to solve this algebra-geometry duality mapping in the most general sense, including all pathological cases. And it turns out that the strange cases correspond to non-commutative algebras, or algebras where a*b is not equal with b*a. Therefore the geometry side was aptly named: non-commutative geometry.

Fine then, this is what mathematicians do: they unify separated areas of math in a hopelessly incomprehensible mathematical formalism which maybe our grand-grand kids will understand 300-400 years from now. (That may sound harsh, but we still have problems today with learning calculus developed by Newton and Leibniz quite a while back.)

But this is not only pure math, as it has dramatic physical consequences. So let’s go back to quantum mechanics in its C* algebraic formalism. One can further go down the algebraic road by studying physical symmetries, and a C* algebra of operators defined by symmetries is called a von Neumann algebra.  They have very useful properties and their complete classification was obtained by mathematicians, including Alain Connes. (This classification contains three basic classes, boringly named factors of Type I, II, and III.) Commutative von Neumann algebras correspond to defining a unique measure space on compact spaces. Calculus works because of this and in turn it allows us to easily compute things which we can then compare with experiments. Loosely speaking, the type I von Neumann algebras correspond to classical measure theory. Type II algebras showcase a new behavior of continuous dimension spanning a continuum of values. Gone are the geometry of lines, planes, and discrete n-dimensional subspaces. Type III is stranger still.

So now let’s go back in time a few decades ago and pretend you are Alain Connes. You know quantum mechanics very well and you also have this new non-commutative geometry tool at your disposal. From non-commutative geometry it is clear that there is an entire gamut of options between pure discrete/digital and 100% continuous/analog. Moreover the Standard Model of particle physics, while agreeing with experiments, lacked a coherent mathematical description, but the core symmetries U(1), SU(2), SU(3) have a quantum mechanical origin. What would you do at this point?

In Alain Connes’ words, the Standard Model was a “beggar” in search for mathematical “clothes”. Why not then try to get a “best fit” of non-commutative geometry objects which can recover all mathematical properties of the Standard Model? This is a mathematical rewrite in a new language. If you have a hammer, everything looks like a nail says an old adage. But it turns out that this was an inspired guess and the new language is a much more economical way of characterizing Standard Model, and the theory appears naturally in this formalism.

But how can we describe nature in non-commutative geometry terms? To characterize a geometry, Connes uses a so-called spectral triple (A, H, D) where A is the algebra, H is a Hilbert space, and D is a self-adjoined operator. The way to understand it, is that the triple (A, H, D) codifies completely the geometrical distance information in an equivalent way. The details are too technical to explain in a short blog post, but the remarkable fact emerging from this work is the natural unification of the three forces and moreover unification with general relativity as well. There is also a striking similarity with string theory (although this is by no means string theory).

For the Standard Model, in the words of Alain Connes from a Fields lecture:

“I will show that the first five axioms I had given in 96 on spectral triples suffice in the commutative case to characterize smooth compact manifolds. I will also define a new invariant in Riemannian geometry, which when combined with the spectrum of the Dirac operator is a complete invariant of the geometry. It is an analogue of the CKM mixing matrix of the Standard model.”

Also: “What we find is a geometric space which is neither a continuum nor a discrete space but a mixture of both. This space is the product of the ordinary continuum by a discrete space with only two points, which, for reasons which will become clear later, we shall call L and R. […] The naive picture that emerges is that of a double space-time, i.e. the product of ordinary space-time by a very tiny discrete two-point space. By construction, purely left-handed particles such as neutrinos live on the left-handed copy XL while electrons involve both XL and XR in X = XL or  XR.”

You may now be thinking that this sounds too good to be true. At this time is worth noting that this is still a work in progress, as a recent attempt of predicting Higgs’ mass was ruled out by experiments. It still requires some “tailoring of the clothes”, and it most likely needs to incorporate supersymmetry. However, for all its successes, the non-commutative Standard Model does not have many followers. I think the reason is twofold. First, let me say that even with advanced geometry knowledge, the math there is not for the faint of heart. Second, theoretical physicists tend to view the pursuit of algebraic methods as a useless crossing of the t(s) and dotting of the i(s) exercise, removed from practical questions.

It is very unfortunate that not many physicists understand Alain Connes’ results. But this work is of the highest caliber on par with the best mathematical results from history. And the lesson for the nature of reality: analog vs. digital is clear: nature is both, and particle chirality plays a major role in the answer.

Still, there is hope for the rest of us to further contribute here. Non-commutative geometry is an excellent tool for understanding the Standard Model, but the clothes are not yet finished, and the question of why those particular A, H, D are selected by nature is not answered.

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Lev Goldfarb wrote on Apr. 4, 2011 @ 15:44 GMT
Dear Florin,

So finally we have your promised answer to the question posed by the last FQXi essay contest ;-)

However, to be frank, I don't see the answer at all. I can only see the explanation of why the non-commutative geometry is a good way to formally continue the Hilbert space approach of quantum mechanics. The real question is whether this approach to quantum mechanics is here to stay "forever".

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Florin Moldoveanu replied on Apr. 4, 2011 @ 20:43 GMT
Dear Lev,

Let me explain why I consider the problem solved by Alain Connes. First, there is a duality between the continous and the discrete and there is a complete mathematical formalism who captures it fully.

Second, in this formalism the Standard Model emerges very naturally, and this model captures all experimental results up to date. Nature is discreete mostly because of particle chirality. Chirality is currenly the major roadblock for simmulating the strong force interaction on supercomputers.So nature is both discreete and continous at the same time.

I find your question of: "whether this approach to quantum mechanics is here to stay "forever"." irrelevant because the mathematical results have an intrinsic value regardless of formalism. A complex number is still a complex number no matter how we represent it: (radius and angle), bivector, pair of real numbers, 2x2 matrix.

Can we invent/discover new formalisms for quantum mechanics? Very possible. But no amount of mathematical technical sophistication will make right handed neutrinos appear in nature. The contest question is about nature, and nature has already spoken.

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T H Ray replied on Apr. 4, 2011 @ 20:58 GMT
Well, I confess that organic continuation of the Hilbert space with physical configuration space is my preference.

Though, Lev, I think you make a good case for your own research program, too. What rich times for physics we live in! An historic crossroad.

Tom

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Dr. Cosmic Ray replied on Apr. 4, 2011 @ 21:12 GMT
Dear Florin,

I agree that chirality is important, but I think it is incorrect to assume that right-handed neutrinos do not exist. I understand that Connes developed his model in '96 - prior to Super Kamiokande's discovery of Neutrino Oscillation, and therefore his original model did not include right-handed neutrinos.

Super Kamiokande's results imply that neutrinos have mass - however negligible. If we have a left-handed neutrino travelling at, say, 0.99999 c, and we Lorentz transform ahead of it at a speed of, say, 0.999999 c, and look back at the neutrino, then we will observe an opposite spin (a right-handed neutrino). I agree that this neutrino is sterile to Weak (,Strong and Electric) interactions, but not to gravitational interactions. We can ignore the right-handed neutrino at the LHC, but we should not ignore it in general. Remember that the Baryonic matter with which we are so familiar may only be 5% of our Observable Universe.

I asked Lubos Motl this question on his blog site, and he was concerned that we can't properly define weak isospin charges for a right-handed neutrino (all known Electroweak quantum charges should be zero - and therefore the right-handed neutrino becomes non-existant or irrelevant). However, if you study my Hyperflavor-Electroweak, you will see that I have introduced two new "charges" to properly place the right-handed neutrino in the same particle multiplet as the left-handed electron, the left-handed neutrino, the right-handed electron, the right-handed neutrino, and the electron-neutrino tachyon. This 5-fold "pentality" symmetry is the origin of fermionic masses - similar to Coldea et al's magnetic Ising quasiparticle masses near criticality. Please see Table 3 in my 2009 FQXi essay.

Yes - it isn't trivially obvious because my ideas also use geometry and algebra.

Have Fun!

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John Merryman wrote on Apr. 4, 2011 @ 17:45 GMT
It is a dialectic and the synthesis is wholistic, not reductionistic, because the thesis and antithesis are reductionistic.

The question is how do you reconstruct the physical dynamic from the mathematically continuous?

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Florin Moldoveanu replied on Apr. 4, 2011 @ 20:47 GMT
"The question is how do you reconstruct the physical dynamic from the mathematically continuous?"

Maybe I don't understand the question, but at face value, the answer is very easy. Forget fancy formalisms or even quantum mechanics. Consider the simple second law of motion from Newton: F=ma. This gives the dynamics, and most of the time it deals with continous quantities.

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John Merryman replied on Apr. 4, 2011 @ 21:03 GMT
Florin,

That's the mathematically continuous from the physically dynamic. My problem is when the dynamic gets mapped as some continuous dimension and then in trying to pull the dynamic back out it ends up in multiwords, because the dimension is static and can't incorporate probabilities.

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John Merryman replied on Apr. 5, 2011 @ 02:20 GMT
F=ma describes force, but dynamic implies both force and change.

Relativity is continuous and deterministic, while Quantum Mechanics is discrete and probabilistic. The determinism is a consequence of the continuity and the statistical nature of QM is a function of its discreteness.

So how is it that we have a reality which is both continuous and statistically nondeterministic?

The right brain processes spatial geometry, but that fourth dimension of time is a serial function, not a static dimension. It belongs on the left side.

The right brain is a thermostat. The left brain is a clock.

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Xiang He wrote on Apr. 4, 2011 @ 21:08 GMT
Before s/he asks for mathematical clothes, the Standard Model Beggar must beg for physical existence first. What if such a beggar does not exist? The Standard Model imagines a beggar standing still in the cold (even worse, in the "void") while mysteriously growing fatter and fatter without visibly taking any food -- what if the actual entity is a goddess performing beautiful rotations endlessly in the wind? What kind of clothes would we need when the nature of reality (as far as our finite cosmos is concerned) is nothing but rotational energy?

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Lawrence B. Crowell wrote on Apr. 5, 2011 @ 02:21 GMT
Noncommutative geometry in general has the Usp(n) groups, A simplectic group with z_i = (q_i, p_i} (index notation implied) obeys dz_i/dt = Ω_{ij}z_j. In quantum mechanics this is generalized to a commutation system, and the symplectic 2-form implies an operator valued Hamiltonian. However, this is not the most general system possible. A unitary Lie structure can give rise to commutators [q_i, q_j] = ħω_{ij}, which are necessary in string theory with uncertainty principles involving transverse and longitudinal string modes ΔX^+ΔX^- ~ L_s = 4πsqrt{α’}, α’ = string parameter and L_s the string length. Noncommutative geometry is then a setting for complementarity principles.

Cheers LC

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Florin Moldoveanu replied on Apr. 5, 2011 @ 02:56 GMT
Lawrence,

In going from symplectic to unitary (classical to quantum), there is an additional metric structure which together with the symplectic structure gives rise to a Kahler manifold. Sqrt(-1) on the Kahler manifold is a map between observables and generators, and time evolution is given by a Killing flow which preserves the metric structure. The meaning of this flow is that time evolution does not break the uncertanty principle, meaning that each observable commutes at any time with sqrt(-1). There are many kinds of Kahler manifolds, but projective Hilbert space is singled out by the requirement of invariance of physics laws to arbitrary composition (any by demanding that any curve in this space can be shrunken to a point).

Non-commutative geometry is based on completing the spectral information to recover the metric information in a spectral A,H,D triple. There are usual quantum fluctuations of the metric in addition to internal degrees of freedom fluctuations in the A,H,D triple. The dimensionality of the "space" of the internal degree of freedom is 8, just like in string theory.

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Lawrence B. Crowell replied on Apr. 5, 2011 @ 21:15 GMT
I might have jumped the gun a bit with Usp. Quantization is a generalization of symplectic structure with a Kahler one. My point is that in general physics is noncommutative everywhere! The generalized uncertainty principle, or the complementarity principle with strings ΔX^+ΔX^- ~ L_s indicates that all coordinates, or degrees of freedom have commutators. In the Algebra-Hilbert space-self adjoint (AHD) scheme the metric fluctuations reflect how there are general Lie symmetries on the symplectic structure, of which the Kahler (geometric quantization etc) scheme is the standard quantization we know.

Cheers LC

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Dr. Cosmic Ray replied on Apr. 5, 2011 @ 21:40 GMT
Hi Florin,

Lawrence said "My point is that in general physics is noncommutative everywhere!"

EXACTLY!

Quaternions are noncommutative. Maxwell's Equations can be written as a single Quaternion Equation. And the Dirac Matrices have the same noncommutative properties as Quaternions. You can't expect any kind of TOE or TONE without this property of noncommutativity, and this is not a unique discovery by Connes. All of my TOE models include Quaternions, and most include Octonions - if you want to take it to the next level of screwball noncommutivity!

Where are H and D hiding? If H (Hilbert Space) is an 8-D E8 Gosset lattice hiding in Hyperspace (similar to Lisi's TOE), and D (self-adjoined operator) is a reciprocal lattice hiding in another Scale (similar to my latest FQXi essay), then Connes' ideas and conclusions regarding continuous vs. discrete have general similarities with mine.

Have Fun!

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Steve Dufourny wrote on Apr. 5, 2011 @ 09:30 GMT
:) it was time Florin.

You have your maths friends(Tom,Lawrence and Ray) Interesting all that....beautifull team lol

ps be rational please!!!

Steve

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Xiang He wrote on Apr. 5, 2011 @ 15:32 GMT
The Standard Model does not and cannot explain why every system within the finite universe is rotating. The Standard Model fails to see how the entity that holds all its internal rotating systems together, i.e. the whole finite universe, is rotating on its own and thereby is the universe that unifies all the galaxies and stars (rather than just a name we give to the collection of celestial bodies). Without any physical evidence, without any conceptual clarity, and without any serious debate, the Standard Model has mistakenly accepted "the nature of a non-rotating reality" as the nature of reality with as much confidence as the world used to see when the Earth was believed to be the centre of the universe. Clothed or not, the Standard Model cannot stand. Yes, please be rational -- and we have to be rational from the very beginning, at the level of fundamental concepts on which all scientific theories must rest. No conceptual errors can be corrected by a mathematical trick, no matter how ingenious the latter is.

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Lev Goldfarb replied on Apr. 5, 2011 @ 17:15 GMT
"Yes, please be rational -- and we have to be rational from the very beginning, at the level of fundamental concepts on which all scientific theories must rest. No conceptual errors can be corrected by a mathematical trick, no matter how ingenious the latter is."

I agree!

This is the key, which I also have been emphasizing: if the chosen form of *data representation* does not capture the key features of "reality", it is highly unlikely that some "powerful" math machinery can recover the information that was not present in the original data representation in the first place.

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Lev Goldfarb replied on Apr. 5, 2011 @ 18:46 GMT
By the way a number of years ago I wrote several papers explaining the limitations of the basic mathematical form of representation, the vector space.

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Wolfgang Pauli replied on Apr. 6, 2011 @ 17:42 GMT
"The Standard Model does not and cannot explain why every system within the finite universe is rotating"

I heard that too !

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T H Ray wrote on Apr. 5, 2011 @ 18:08 GMT
I've been ridiculed by mathematicians for making what I think is a trivial but true statement: "Content does not recapitulate meaning."

That's why, though, that I lean toward Lev's research program. One wants a representation that in some manner of speaking, interprets itself, with itself.

Tom

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James Putnam replied on Apr. 5, 2011 @ 18:18 GMT
Tom,

Could you please expand on your message? I know it was clear to you. Some more detail might make it clear to me. I probably missed out on some messages, but, these two statements are not clear enough for me. I apologize for not being up to date on this. Can you please say more about these two statements?

"Content does not recapitulate meaning."

"One wants a representation that in some manner of speaking, interprets itself, with itself."

James

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T H Ray replied on Apr. 5, 2011 @ 23:11 GMT
Well, let's take an example of what is probably the most famous equation in the world: E = mc^2. The mathematical content is extremely simple, yet the meaning in terms of energy content of an actual quantity of mass could not be determined without a measurement that accounts for atomic binding energy, and that could not have been predicted within the classical boundary of special relativity. Yet the meaning is right there in the equation, with no extra assumptions required. The equation therefore contains more meaning than the theory it was written for, predicts.

Let's get more abstract. Euler's also famous equation, e^i*pi = - 1. This is a geometric interpretation of the complex plane, giving us an exponential function using transcendental numbers and an imaginary number that results in a real and finite quantity. Meaning is still being extracted from this relationship yet today, including Schanuel's Conjecture, whose proof would tell us that this is the _only_ algebraic relation among these constants, which automatically proves a number of other conjectures.

I've been into Lev Goldfarb's idea of "structs" for quite a while, wondering whether it's possible to bridge the gap between language and meaning such that unambiguous representations combine in novel ways to produce metaphysically real and computable results outside the boundaries of language.

Tom

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Lev Goldfarb replied on Apr. 6, 2011 @ 00:25 GMT
James,

With apology to Tom, I also would like to take an initial crack at the reply.

The idea of an adequate structural language is following.

I believe we have to look for a formal languages for which syntax and semantics "coincide" (which has never happened before). It means that a structural analogue of an "equation" should be a structure that is a direct copy of the real thing.

In the numeric formalism, the equation a2 plus b2 = 1 doesn't exist in nature, mainly because none of its ingredients exists out-there.

While, for example, in the ETS formalism that we propose every entity (e.g. a struct) is supposed to be a copy of an actual thing.

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Lev Goldfarb wrote on Apr. 5, 2011 @ 20:50 GMT
In light of the increasing number of more and more esoteric attempts to improve the situation in physics, I would like to suggest why the crisis in physics cannot be resolved "peacefully", by improving the "standard" machinery.

I suggest that the crisis has to do with the numeric form of representation, which is not capable of capturing the structural side of "reality".

First, it is quite natural to assume that, as everything else in this world, any "particle", for example, must also have the (internal) *structure*. Which formal means do we have to encapsulate such structure? Well, the immediate answer I can hear is via various groups. But who said that such means are adequate at all?

Let's look at some natural (but not man-made) "objects". Foe example, a stone, a tree, etc. It is critical to understand that they have *generative" structures that are not adequately captured by groups. This is the key to fundamental crisis we are facing now.

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James Putnam replied on Apr. 5, 2011 @ 21:01 GMT
Dear Lev Goldfarb,

You are getting my attention for what that is worth. Please include more detail in your future posts.

James

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John Merryman replied on Apr. 5, 2011 @ 23:38 GMT
Lev,

Your post reminds me of something I wrote on Thomas McFarlane's thread, as a response to his philosophical approach to a discrete reality. It might not apply, but it might another perspective on the situation:

"You make a good argument for why reality can only be understood in terms of its discrete relationships, but it's wrong. With your last paragraph, it's clear you understand your point has its limits, but relegate the wholistic view to mystery. It isn't mysterious at all. It's overlooked because it's so basic. Math says that if you add two things together, they equal two. Well, if that's the case, you haven't actually added them together. Necessarily actually adding things together means you have one of something larger. In basic terms, it's like adding two piles of sand together and having one larger pile, but in reality it's more like components combining to create a larger whole. Whether physics, or biology, we like to take things apart to see how they work, but the fact is that they work together. Much like all the parts of your body add up to a larger whole, or all the components of an atom add up to an atom, not to mention all the various levels between, above and below the atom and the person.

This dichotomy is basic to the difference between eastern and western philosophy. In that we in the west tend to focus on objects and view their actions as emergent. While in the east, there is the contextual view and the particulars within the context are as much a part of the larger whole as your nose is part of you."

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Lev Goldfarb replied on Apr. 6, 2011 @ 00:30 GMT
John,

I'm afraid I completely failed to see any connections. ;-)

Please read more carefully the relevant posts.

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Lev Goldfarb wrote on Apr. 6, 2011 @ 05:10 GMT
"In fact, I will call that the (ETS) emperor is naked."

Florin,

Boy, I like your "boldness", but let's see what is behind it.

First, keep in mind that since the emperor has not been born yet it is too early to call him naked. ;-)

Second, from your questions on my (second contest) essay page I couldn't see you grasping even what ETS is about. Has anything changed since then, or you are becoming more comfortable at FQXi?

Sure! Here you are even prepared to give advice to the FQXi scientific panel:

----------------------------------------------

(Blog:Wh
at is Ultimately Possible in Physics: Contest Results Announced!)

By Florin Moldoveanu wrote on Jan. 24, 2010 @ 21:25 GMT

...Then the job of FQXi is greatly simplified and in my opinion they should concentrate on separating the scientific valid from the scientific invalid papers. Judging from the final results, one invalid essay got in (I will not name it)

[may your humble servant be so bold as to suggest that it is my essay you have in mind]

and two very good scientifically valid essays remained on the outside (I will not named them either). How do I know this? Because I became very familiar with all top half essays during the many months of the contest. The panel on the other hand had only a relatively small amount of time to rank a lot of finalists, and mistakes can happen.

------------------------------------------------

After all of this, how could have FQXi missed your candidature for the panel in the last essay contest? ;-)

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Lev Goldfarb wrote on Apr. 6, 2011 @ 13:29 GMT
Dear Florin,

Honestly, I would greatly appreciate *any*s scientific criticism of ETS and that is why I'm here in the first place.

But I also know full well that I cannot expect such criticism from you, since you are most likely to hide behind such standard phrases as "I will wait until some 'solid results' are obtained." Of course, by then the value of such criticisms is considerably diminished.

Also keep in mind that FQXi does not really need such self-appointed gatekeepers as you, since they undermine at lest one of its five main goals: "To forge and maintain useful collaborations between researchers working on foundational questions in physics, cosmology, and related fields".

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Lev Goldfarb replied on Apr. 6, 2011 @ 13:32 GMT
Sorry: I didn't mean to start a new thread. ;-)

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Cristinel Stoica wrote on Apr. 6, 2011 @ 14:08 GMT
Dear Lev, (Florin too),

Above, you asked Florin to read a discussion on the page of my essay. I will summarize that discussion, to save Florin's time, because we had long discussions :-)

I said to somebody else

'I think that most of us would agree with you that "There is obviously both the continuous and the discrete in reality". Probably the divergences occur when discussing what of the two features is fundamental, and what is derived.'

You claimed that my statement is self-contradictory:

'nature cannot be both discrete and continuous, simply because "discrete" means non-continuous'

To show you that there is no logical contradiction, I gave you examples of discrete emerging from continuous: modes of a wave, topological properties of spaces, and discrete spectra in Quantum Mechanics. You then said that my examples are false, because Nature is in fact discrete.

Brief: 1. I said that it is possible to have both discrete and continuous features. 2. you said that nature cannot be both. 3. I offered you self-consistent models in which my statement is true. 4. You said that my examples cannot be true because nature is not like this.

Obviously this is a vicious circle: "Nature cannot be like this because this is a contradiction because Nature is not like this."

Clearly I was in disadvantage in that discussion, because, unlike you, I don't know how Nature is b-). Do you have any proof that Nature is discrete, and that it cannot be continuous with discrete features? Please notice that in our discussion you have the burden of proof, because you said that you know how Nature is, while I always said that I don't know.

Best regards,

Cristi

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Lev Goldfarb replied on Apr. 6, 2011 @ 16:49 GMT
Dear Cristi,

Good to hear from you again!

Your summary is not quite accurate, but I'm somewhat surprised that we are not done yet (since at the end of our discussion you led me to believe otherwise). ;-)

OK, here we go again. I will address both of your messages. But the above message first.

Look, I am saying something very simple. First, in our context, "discrete" means "non-continuous" (see also intro in my essay). And second, therefore from both formal and informal points of view, we do not want to have the state of affairs where the nature possess two mutually excluding features (more about it in my second post). I.e if we are relying on the (continuous) vector space formalism (e.g. Hilbert space) to model "reality", we cannot then turn around and declare that "Oh, by the way, the nature also has some important discrete features". Such state of affairs seriously undermines the quality of the vector space model in the first place.

Of course, I do believe that we should settle only on the formalism which (by itself, without hair-splitting additions) satisfactory captures the nature of reality. This is how we should evaluate the quality of our models. The present situation is such that conventional math does not have any such models, and this is the first time when we have been seriously faced with such situation. As one can see, the reaction of the vast majority of scientists is a classical case of the ostrich syndrome.

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Cristinel Stoica replied on Apr. 6, 2011 @ 18:21 GMT
Dear Lev,

What I said now is exactly what I said then, I've just made a long story short.

You say: 'if we are relying on the (continuous) vector space formalism (e.g. Hilbert space) to model "reality", we cannot then turn around and declare that "Oh, by the way, the nature also has some important discrete features".'.

This is completely wrong, and I will tell you why. When you measure an observable, the apparatus records an eigenvalue of the corresponding operator. This means that the state is an eigenvector corresponding to that eigenvalue. The eigenvector is from the (continuous) Hilbert space, and the eigenvalue is from the spectrum of the operator representing the measured property. The spectrum may have discrete parts. For example, the energy of the electron in the atom is precisely like this. All I said is true, and invalidates what you said. It is not something put by hand, the discrete values simply follow from the Hilbert space. It is proven. It is undeniable. It's a fact.

By the way, this way to obtain discrete values from continuous formalism is due to Schrödinger, and it is something you deliberately ignore, in favor of an obscure passage which has no scientific support.

The Hilbert space formalism has been accepted because it predicted accurately the spectra, and not because it was continuous.

Best regards,

Cristi

P.S. I do not claim here that the actual formalism of Quantum Mechanic is the last word, and cannot be improved or even completely replaced. I just showed that your statement that the Hilbert space cannot exhibit discrete features is simply false.

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Lev Goldfarb replied on Apr. 6, 2011 @ 18:47 GMT
Cristi,

OK. So if what I said "is completely wrong", then please tell me:

How does Hilbert space help us to understand what a photon (or electron) is?

After all, the main goal of science is understanding, isn't it?

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Cristinel Stoica wrote on Apr. 6, 2011 @ 14:34 GMT
Dear Lev,

About your favorite quote from Schrödinger:

"[...] If you envisage the development of physics in the last half-century, you get the impression that the discontinuous aspect of nature has been forced upon us very much against our will. [...] Nature herself seemed to reject continuous description ..."

Could you please explain how is this a proof that Nature cannot be continuous and it is in fact discrete? Can you tell the precise phenomena which show this?

You also said "(as was done with Einstein, let's declare Schrödinger "incompetent" to make such statements ;-) )"

This is an argument from authority.

Schrödinger was unable to construct a discrete theory, but he was able to construct a continuous theory of the quantum phenomena. According to your logic, do you declare him incompetent for the highest accomplishment of his genius?

I reassure you that I respect very much Schrödinger's work, but even his affirmations need to be proven. I'd like to see the evidence supporting the words you quote.

Best regards,

Cristi

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Florin Moldoveanu wrote on Apr. 7, 2011 @ 03:53 GMT
Dear Cristi and Lev,

In the post above I was saying: "In technical terms, by a theorem due to Gel'fand, (the G in GNS) any compact space X can be characterized by a C* algebra C(X) of continuous functions on X." For a reference see: http://mathworld.wolfram.com/GelfandTheorem.html This is the starting point of non-commutative geometry which generalizes this to the non-commutative case. One very important point is that: the norm in a C* algebra IS NOT ARBITRARY, but it is given uniquely by the square root of the spectral radius of X^* X Now spectral radius is defined as suppremmum (lambda in R such thast xx^* -lambda*lambda has no inverse). Discretness enters the formalism through the lack of an inverse and spectral theory has both continous and discrete elements in the commutative/continous/compact case.

von Neuman algebras are specializations of a C* algebra and C* algebras correspond to all known cases of quantum mechanics. Quantum mechanics may be strange, but it is in full agreement with experiments, and hence nature is already both continous and discrete. However, this was not the meaning of FQXi contest, and all this was already well known. The problem is at quantum gravity and here nature may ultimately be discrete. What was not well known was the algebraic-geometry duality and its application for standard model.

Connes generalized all this by describing a geometry in terms of a spectral triple and this works in ALL cases including all type II and III cases of a von Neuman algebra. By now we have a full mathematical machinery in place to see how discretness is intimately unified with continous and how to translate any problem from a domain to the other. Here I disagree with FQXi on the contest topic. It was like asking: is nature ultimately a CFT or an AdS theory? String theory dualities are well known and such a question is obviously silly. On the other hand Connes duality is not well known.

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Cristinel Stoica replied on Apr. 7, 2011 @ 05:09 GMT
Dear Florin,

Great article, congratulations. Clearly this post is well-documented, and you made a solid and rewarding investment in studying non-commutative geometry, which is a very difficult topic. After doing this documentation and having the inherent revelations given by understanding the connections, no wonder you are enchanted. But I don't share your optimism that with Connes's work physics almost reached its end, and the rest of us are left only with "the hope to further contribute here". Don't get me wrong: I think that Connes's work is great, at least as mathematics, although we are not yet in position to fully appreciate its implications. I also think that probably is a better alternative to unification than the other approaches, and it definitely deserves to be pursued by a comparable number of researchers.

In my opinion, the FQXi contest did not actually intend to ask only whether nature is digital or analog. The range of FQXi's questions is much wider than this. There are many other points which were followed by this contest, and you pointed out right that quantum gravity was in fact the main concern. Of course, I agree that this emphasis on the distinction discrete/continuous is not the most relevant aspect of the foundational research, but definitely it is not settled down, simply because we don't have a final theory and unlimited possibilities to perform experiments.

I think that your claim that Connes's theory settled down the question if nature is digital or analog is a bit exaggerated. A product between a continuous manifold and a discrete set is still a continuous manifold. Chirality is not the only or the most important discrete feature, and it is already present in Dirac's spinors. The Connes duality between algebra and geometry is not the same as the duality discrete/continuous. There are discrete and continuous algebras, as well as geometries. Neither algebra nor geometry can be considered more discrete or continuous than the other, for the same reason why none of them is more Yin or more Yang than the other :).

I agree that there are discrete and continuous features which are unified by non-commutative geometry. Some of them are, at least so far, purely mathematical, while the "unifications" of discrete and continuous from physics are already known from other formalisms, such as that of the Hilbert space, which is contained in the Connes's theory.

Anyway, your post is great, and I think you could produce a good entry to the contest. Even if the work was done by Connes, you are able to present fresh perspectives of it.

Best regards,

Cristi

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Florin Moldoveanu replied on Apr. 8, 2011 @ 05:33 GMT
Dear Cristi,

Thank you for your kind words. First I want to comment a bit on the link between non-commutative geometry and string theory. String theory is much more developed than non-commutative geometry, and it is very likely the two may be the same theory in different formalisms. String theory sufferes from the multiple vacua problem. The same for non-commutative geometry: one may pick any spectral triple one likes and then investigate the consequences. You state: " A product between a continuous manifold and a discrete set is still a continuous manifold.". This is very similar with heterotic string theory where one end of the string lives in one space, and the other end lives in a different space. The point is not the product between a 2-point set and a continous manifold, but the fact that the properties of the 2 points are very diferent.

About the contest, I disagreed already with entering the contest (because I did not do it). Yes, I could have written an entry along the lines of this blog post, but even so, it is not good enough to publish on the archive. I am not yet in a position to make original contributions in this area. I still have a long way to go. What I presented here is only a very impresionistic 10,000 feet view of the material. I wanted to raise awareness of this area because I have yet to meet (in person) another theoretical physicist who is interested by it.

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Florin Moldoveanu wrote on Apr. 7, 2011 @ 04:58 GMT
Dear Lev,

I do not like to play Simon Cowell, but he did have a good point on American Idol. FQXi is a great place where status quo can be challanged freely, but there is a difference between challanging the establishment and getting recognition only by challanging existing results. This is unfair and disrespectful to those who got the results in the first place. They invested blood sweat and tears to achive that and they won the recognition of their peers who worked the same areas and who conceeded that indeed they deserve the recognition.

With regards to ETS, let me start by stating that I know a great deal about computer science and I am intimately familiar with notions of structs, class, object oriented programing and all the known programming languages. To the degree that you publicly presented your theory, ETS displays a naive realism (I don't mean this in a bad way) which is completely at odds with quantum mechanics. ETS is at best a hidden variable theory and we now know for 40 years that nature ruled this out. Granted, there are scientists like t'Hooft who work hard of creating a similar model of reality, but in my oppinion I consider those approaches missguided. (There is another approach which is only supperficially similar and this is done by Adler. However there the core idea is a Wick rotation and the equivalence of field theory with statistical mechanics, which is a very fruitful avenue of research.)

Another idea/topic. Politically corectness was abused in the past here at FQXi to give a patform for nonsensical junk. Case in point: http://www.fqxi.lorg/community/forum/topic/858 But if FQXi will sometimes permit this, it is their business. I however, will speak my mind.

And yes, since you brought it up, I do belive FQXi made a mistake with your entry in the last contest. My reason is that ETS is at odds with quantum mechanics; otherwise it was a well written and provocative essay. I believe FQXi was much more careful with the top prizes which would have significanlty affected their reputation. In my opinion, there were 2 other entries deserving to win a prize.

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Lev Goldfarb replied on Apr. 7, 2011 @ 17:21 GMT
My dear Florin,

You don't even realize how superficial your declarations are. ;-)

But since you made them, let's deal with them. And forgive me for being frank.



1. "ETS displays a naive realism" -- absolute nonsense based on the *complete* misunderstanding of what both naive realism and ETS are.

2. ETS "is completely at odds with quantum mechanics" -- nonsense based on the *complete* misunderstanding of what ETS is. In fact, I did explain in my essay how the known "mysteries" of quantum mechanics might be no more.

3. "ETS is at best a hidden variable theory" -- an absolutely meaningless statement, since ETS has nothing to do with a "hidden variable theory" as it is understood now.

----------------------------

Our main goal in developing ETS was to propose a new, structural, in contrast to the numeric, language, motivated by the considerations of information processing understood very broadly.

Now, as far physics is concerned, I realized that many of the so-called dualities (e.g. particle-wave) may "disappear" when we switch to this new, structural, language, and I consider this to be a critical positive consideration. In general, my philosophy of science is that we should strive for that formalism which engenders least number of fundamental "dualities", mainly because they are engendered by our inability to see the nature in the most appropriate form.

Also, the structured event view of "reality" is most consistent with what we know from elementary particle physics.

However, in light of ETS, it does follow that before we get used to seeing reality via structural representation, we should, at least for a while, put aside the conventional view of reality via equations. Yes it is a very radical idea, but one should not get too "scared" by it. ;-)

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John Merryman replied on Apr. 7, 2011 @ 17:51 GMT
Lev,

What if reality really is dualistic? There are quite a number of examples of dualism and it seems one of the properties is that each side gives a seemingly complete, though reductionistic view, while any attempt to synthesize the two sides creates a lack of such focus and clarity. It's as though we take a picture of a car from either side and it seems whole, but a picture of the interior is neither whole or a synthesis of the two sides.

What if an events based view is only one side of the larger reality? Say there is an underlaying energy manifesting those events and the energy is constantly coalescing into and dissolving away from particular events/particles/mass/structure/structs? So we see and measure this structure, while the energy is too amorphous to delineate, but it is still the energy manifesting the structure and without it, there would be no structure/events.

Whether you accept this point, just for perspective, how would you go about defining that larger reality, without primarily referencing its two aspects? Which is to say that while reality is wholistic, our ability to understand it relies on the relationships between opposing views.

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Lev Goldfarb replied on Apr. 7, 2011 @ 19:54 GMT
John,

"Whether you accept this point, just for perspective, how would you go about defining that larger reality, without primarily referencing its two aspects? Which is to say that while reality is wholistic, our ability to understand it relies on the relationships between opposing views."

This is a fair question. My answer is simple. I can think of the only way to get to a more "wholistic" view of reality: to switch to a more universal "language".

The really big question is whether such process will converge on the final universal language. And, since I'm an optimist, I answer that it will. ;-)

Now, I have high hopes for the structural languages similar to ETS. Why?

Structured events appear to be the universal currency in nature, meaning that we might be getting very close to the true language of the Universe. This, of course, can *relatively* easily be verified experimentally, but from the glimpse that quantum events have offered us so far I hope it might be true. ;-)

If this will turn out to be true, then our formal language will be a "direct copy" of the informational language on the basis of which Nature "runs", so that finally syntax = semantics, bingo!

Keep in mind that numbers and especially equations don't seem to have such authentic status in Nature: they are part of our preliminary language.

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Don Limuti (digitalwavetheory.com) wrote on Apr. 7, 2011 @ 22:19 GMT
Alain Connes: the Standard Model was a "beggar" in search for mathematical "clothes"

The new garment is ugly. Why, because it was made by a very large mathematical committee assembled by Alain. I do not believe that a large number of references to math papers makes for a good theory. I thought he may be on to something with a quantized calculus but I was mistaken.

The mathematical modeling of physics still needs a lot of improvement.

Lev's work is the most interesting to date (IMHO).

Don L.

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Lev Goldfarb replied on Apr. 7, 2011 @ 22:51 GMT
Thanks Don!

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T H Ray wrote on Apr. 7, 2011 @ 22:26 GMT
Lev deserves credit for having a coherent research program, regardless of one's opinion of its viability under current computational capabilities.

I've heard no mention of the main requirement for internal structure, i.e., the role of time evolution. In the ETS formalism as I understand it -- and Lev can correct me -- time shares identity with information. So the way in which 3 dimension information evolves internally in a 4 dimension continuum determines how it appears at the boundary of the 2 dimension manifold. To try and make this simpler to understand, in my essay I included a technical end note ("Mach's principle and the relativistic theory of the non-symmetric field") in which I affirmed that although general relativity frames the universe as finite in time and unbounded in space, there seems to be no physical law or principle that would prohibit the universe being finite in space and unbounded in time.

In this case, the evolving discrete states of time dependent events on the finite manifold (holography) suggests that energy exchanges in the underlying continuous spacetime structure that creates the event space are dissipative. If you look up 't Hooft's lecture, "Classical determinism in quantum mechanics on the Planck scale," I think it's around slide #15 that he shows how information loss may be built into solutions involving quantum nonlocality.

As Lev knows -- we've discussed it -- I don't personally think that there is perfect coincidence (or congruence) between semantics and syntax. It may be nearly so, however, with calculable information loss.

Even though I prefer complex analysis in the Hilbert space, because it's something I understand and am comfortable with, I am not convinced that it can answer every question. I certainly don't think either 't Hooft's or Goldfarb's research is misguided.

Tom

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Florin Moldoveanu replied on Apr. 11, 2011 @ 03:26 GMT
Tom,

Indeed, Lev has a convincing argument and he has a well constructed research program. Unfortunately, so did Hilbert until Godel proved his program a mathematical impossibility. There are mathematical results proving impossible to trisect an angle, and there are mathematical theorems proving impossible to rewrite the language of QM. To the degree that ETS recovers all predictions of QM, it is nothing new. To the degree that it is using bits to make predictions, if the predictions fully agree with nature, it is a mathematical impossibility. If the predictions disagree with nature, it is a pure mathematical exercise with no relevance for physics.

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T H Ray replied on Apr. 11, 2011 @ 12:15 GMT
Florin,

I understand all that. I have argued with Lev in the past along similar lines. However:

The actual substitution of an alternative formalism to mathematical language, as Lev emphasizes, has not been tried. So there's no warrant to believe that predictions made by schema based on pattern recognition algorithms would disagree with nature.

And although it's true, as you say, that uncertainty is built into QM by several theorems and principles, including those of Godel, Bell and Bohr, the possibility that any system of measurement (i.e., of formal calculation) can interpret itself, with itself, seems remote. What interests me personally in Goldfarb's program, though, remains as valid now as it ever was:

I.e., the role of time. If time and information (program bits) share identity, then the dissipation (increasing entropy) of useful communication may account for uncertainty in the measurement process, while preserving negative entropy in the internal structure of the unmeasured object. (This gets to another point I brought up in my essay, that it is not possible, in principle, to differentiate process from reality.)

Therefore, the uncertainty in a local measurement does not obviate some form of classical determinism that allows all measurement to be local while physics as a whole remains nonlocal -- that's what I mean when I say that relativity, which prescribes a finite time unbounded in space, is wholly consistent with a finite space unbounded in time.

In my personal research, my domain is still the Hilbert space, allowing continuation of the time metric over n-dimension manifolds -- where any entropy decrease in d =< 4 is paid for by increased entropy in d > 4. So I would not be surprised if Lev's idea of the time evolution of independent structs corresponds to regions of entropy decrease in d = (3,4). That is, we can measure information flow only in one direction, which measurement determines how information flows in the opposite direction -- (and yes, I know that this is still consistent with quantum mechanics in the Hilbert space formalism) -- yet while time is unity in (non-relativistic) QM, the dissipation of time (i.e., information) implies a kinematic and dynamic theory of structural evolution that we may be able to deduce by the implications of what we _don't_ measure. Classic reversal of the time trajectory can thereby be preserved, coexistent with irreversible evolution in the measurement process.

Tom

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T H Ray replied on Apr. 11, 2011 @ 14:09 GMT
Correcting my poorly constructed sentence:

"And it's true, as you say, that uncertainty is built into QM by several theorems and principles, including those of Godel, Bell and Bohr, which makes the possibility that any system of measurement (i.e., of formal calculation) can interpret itself, with itself, seem remote.

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Xiang He wrote on Apr. 8, 2011 @ 05:50 GMT
Dear Florin,

Thanks again for your post (enclosed at the bottom for easy reference). I am starting a new thread here as I find it a bit difficult to go through the hidden replies.

I welcome your stating a clear position and trying to defend it with evidences. I shall do the same (although it will be more challenging for me as I am not trained as a scientist or mathematician). ...

view entire post


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Florin Moldoveanu replied on Apr. 8, 2011 @ 06:19 GMT
Dear Xiang,

It is late, but I will try to very quicky answer your post. I conceed on the first point: indeed, our observations may be imprecise, and the rotation speed may be below our current ability to detect it.

On Godel, you cannot argue with his math because it is correct. But consider the consequences: lots of time travelers from the future. You may say: we are not interesting so that is why we don't see them. Here I disagree: in a Godel universe there are plenty time travelers: photons, electrons, protons from the future. There may not be intelligent time travelers, but our universe would be filed with light and particles from both past and future (similar with today's photons and particles from the past). So what? How can we tell if a photon is from past or future? You cannot for photons, but we can for particles. Patricles obey the CPT symmetry. The particles from the future would appear to us as anti-particles. And the current imballance between particles and antiparticles would not exist anymore. A rotating Godel universe would have only radiation and equal amounts of particle and antiparticles. This is not how our universe is. There is no rotation. Any rotation, however small over sufficiently large distances would be fast enough to cause a time travel loop.

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Xiang He replied on Apr. 8, 2011 @ 17:45 GMT
Dear Florin,

You said, categorically, that “the universe does not rotate as a whole”. You provided two pieces of evidence to support your position, the first one of which as you have agreed to is not solid. As for the second one, you seemed to have missed my point: I am not arguing whether Godel’s math was correct or wrong – I am in no position to do that – I do argue, however, that the rotating universe he was describing is different from the one I am presenting, with the critical difference being the rotating systems within the rotating universe. If you wish, you could easily come back and refute me after you check with Godel’s model, but I suspect that his calculations did not take into consideration all the centrifugal and centripetal forces associated with different levels of local rotating systems within the overall rotating universe and their dynamic interactions with the centrifugal and centripetal forces associated with the overall rotation of the universe as a whole.

Do disagree with me if you are not convinced, but at least you should understand the point I was making. That way, you would not have used the “ugly” consequences associated with Godel’s model as arguments against my rotating model.

Once we venture into the discussion on fundamental concepts, you will see that I am indeed not interested in “time travellers” – not that they would not be interesting, but that time does not exist, let alone time travellers – unless, of course, when you are asked to describe the phenomenon of a basket ball, you would insist that there are at least three things that exist: the basket ball, the roundness, and the brownness.

Now, let me be a gentler man than I actually am and say this: even if Godel’s math was correct, so what? Would a correct math constitute a valid piece of physical evidence in reality? I don’t think so. For example, there are ten apples on the table, imagine that I eat 15 of them, there should be only minus 5 left on the table. The math is perfect, its physical meaning nonsense.

By now, do you still consider yourself to be in possession of any solid evidence either in support of a non-rotating universe or against the rotating universe I have described? Or are you also in fact holding on to the notion of a non-rotating universe for conceptual reasons (or even worse, for no reasons whatsoever), just like the majority of people?

And you have yet to address the astronomical observations I have provided as evidence for a rotating universe.

Best,

xiang

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Florin Moldoveanu replied on Apr. 9, 2011 @ 05:49 GMT
Dear Xiang,

You say: " I do argue, however, that the rotating universe he was describing is different from the one I am presenting, with the critical difference being the rotating systems within the rotating universe."

I don't get this, please explain. Here is how I view it: "...rotating systems within the rotating universe" means that the universe does rotate, right? Then the internal dynamics is irrelevant. To create time travel you need to rotate faster than the speed of light, and for any angular velocity, at sufficient distance from the axis of rotation, the local speed would be faster than the speed of light regardless of other motions inside the universe. So you are back to particles from the future which would look to us like antiparticles.

About the astronomical observations, I am not an astronomer and I cannot comment intelligently about the current evidence.

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Florin Moldoveanu wrote on Apr. 8, 2011 @ 06:06 GMT
Lev,

Please, by all means do be frank, I don't mind at all. I do think I understand ETS very well, but let's go with the assumption that I am completely clueless. Here is a simple litmus test: what concrete problem of physics does ETS solve? Not what it may solve, not potentiality. What does it do so far?

Second question. About naive realism (which by the way it is a well defined philosophical term and it is not a derogatory term). Would the ETS description change upon measurement? From what I understand, it does not. Hence naive realism. If it does, does it contain all the information about the physical system? Can you make predictions from it? If yes, there is a unique mathematical object with those properties: the wavefunction.

Any description of nature can fall only in one or two categories: quantum mechanics or classical (naive) realism. There are no other possibilities. And quantum mechanics is very rigid: its mathematical structure is unique. There is much more flexibility in naive realism.

By the way, 't Hooft,s theory pays a very dear price for modeling quantum mechanics: in his theory information is not conserved. Therefore I consider his theory unphysical and misguided. When information is not conserved, one may pull rabits out of any hats with no difficulty.

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Georgina Parry replied on Apr. 8, 2011 @ 08:21 GMT
Florin ,

did you mean one or two, or one of two? QM or classical realism, or QM and/ or classical realism?

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T H Ray replied on Apr. 8, 2011 @ 12:52 GMT
Florin,

In his day, the lines of magnetic force that Faraday discovered were by themselves little more than a scientific curiosity. After Maxwell supplied the mathematical model for electromagnetism, the field properties were easier to generalize and adapt to the great variety of applications that continue today.

Suppose, however, that there were no Maxwell. Suppose that instead of having a theory of interacting fields described by PDEs, another theory developed around the evolution of the lines of force that appear on the 2 dimensional surface of a 3 dimension field (analagous to the magnetic patterns of iron filings on glass). I expect that at first we would describe the changing field lines in terms of rigid geometric transformations, then, failing to capture the infinite variety of complicated rotations and translations, we might develop a more general topological model by which we could recognize repeating relations between topologies (homeomorphisms) corresponding to specific changes in the internal structure.

The pattern recognition algorithms resulting from this approach would necessarily rely on experimental techniques rather than mathematical programming. To my understanding, what Lev advocates in principle is a formalism in which naturally evolving internal information corresponds to an evolving external structure. The discrete information, such as that encoded in an arithmetic sequence, is nonlocal information unavailable to local experience. (I spoke of this in my current essay.) The advantage of such programming over classical computation is that the nonlinearity of forms evolving at different rates allows nonlocal correspondence at coinciding points of linear time in a network configuration space.

Though I differ with Lev over whether semantics and syntax perfectly coincide, or even can coincide, I do not question the basic idea that the choice of language (formalism) determines the output. Chaitin showed that there is randomness even in arithmetic, such that the choice of programming language produces different and unpredicable values from the same algorithm. With this result, and the shared identity between time and information, there is no physical principle that obviates a pattern recognition algorithm based on network connections of independently evolving patterns.

Tom

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Lev Goldfarb replied on Apr. 8, 2011 @ 15:12 GMT
Florin,

"I do think I understand ETS very well"

Please don't talk yourself into this: you will see shortly why. By the way, I understand quantum mechanics *much* better than you understnd ETS, but I will never allow myself to say that "I understand QM very well". (What did Feynman say about QM? "I think I can safely say that nobody understands Quantum Mechanics" Of course, you are probably an exception ;-) )

1. "what concrete problem of physics does ETS solve? Not what it may solve, not potentiality. What does it do so far?"

a) The ETS was not developed to solve the "typical" problems of physics

b) However, it suggests a completely different approach to "physics". If we record our observations in the form of structs, we can classify future observations as belonging to one of several classes.

Yes, my dear Florin, classes, classes, and classes. This is how all biological species perceive reality and hence there must be some deep reasons why we are endowed with such information processing mechanism, with such view of reality.

2. "Second question. About naive realism (which by the way it is a well defined philosophical term and it is not a derogatory term). Would the ETS description change upon measurement? From what I understand, it does not. Hence naive realism. If it does, does it contain all the information about the physical system? Can you make predictions from it? If yes, there is a unique mathematical object with those properties: the wavefunction."

a) Of course, my dear, I know that "naive realism" ... is a well defined philosophical term".

b) Of course, "the ETS description change upon measurement". I.e. the observed process will be classified as belonging to some old or new class.

c) The resulting ETS representation "contain all the information about the physical system" only if the God has been doing the observation.

d) I wouldn't be so sure at all about your "unique mathematical object with those properties: the wavefunction."

3. "Any description of nature can fall only in one or two categories: quantum mechanics or classical (naive) realism. There are no other possibilities. And quantum mechanics is very rigid: its mathematical structure is unique. There is much more flexibility in naive realism."

This is a very immature statement. ;-)

So I will not comment it at all.

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Cristinel Stoica wrote on Apr. 8, 2011 @ 09:24 GMT
Let's take the presently existent theories dealing with foundational physics. Some of them are undeveloped, like many ideas presented at this contest, while others are well developed, logically, mathematically, and even have predictions corroborated by experiments. But none of them is complete (at least so far), in the sense of being developed and tested to make sure that it explains accurately...

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John Merryman replied on Apr. 8, 2011 @ 10:52 GMT
Cristi,

I admit to pushing a few of my own ideas, but I'd like to raise another conflict bubbling through these debates, between the math devotees and the math skeptics. Being one of the latter, it seem to me there is a certain lack of conservatism among those who feel that if the math says there are multiverses, or multiworlds, there must be. Rather than considering the possibility some junk has been incorporated into the equations and these mathematical unicorns are junk out.

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Cristinel Stoica replied on Apr. 8, 2011 @ 12:03 GMT
Dear John and other "math skeptics",

Let me start by assuring you that I respect ("respect", not just "tolerate") your right to see the world how you wish, without judging you for this. I don't know for sure what you mean by "math skeptic". I can try to guess, but I would not like to argue against a viewpoint I may attribute to you by mistake. So, maybe I can understand what you and others...

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Cristinel Stoica replied on Apr. 8, 2011 @ 12:07 GMT
#1. Do you think that knowing mathematics is in general a handicap for someone who tries to understand the physical world? If yes, why?

#2. Do you think that you may understand better physics, and you may be able to develop better your vision about the physical world, by learning the appropriate mathematics?

#3. Do you think that a theory can be improved by consistently developing consequences from its principles? (you need to have what to falsify after all)

#4. Which one is true: (a) math can say anything by itself, or (b) only in conjunction with a set of premises?

#5. Let's assume that you accept a set of principles, and from them follows, through mathematical proof, a consequence which you reject on the basis that you consider it false or absurd. If you accept that the proof is correct from mathematical point of view, what would you reject: the mathematics, or the principles which led to that absurd consequence?

#6. I agree that often mathematics is abused. Is this the fault of mathematics? Is there any domain that cannot be abused? If you state clearly the axioms, and apply the rules of inference, isn't this the best defense against abuses?

#7. The mathematical theories are based on a few number of axioms, but from them an infinite number of consequences can be derived. Doesn't this economy make it the ideal candidate to describe complex worlds starting from a few number of fundamental principles?

#8. Do you think that, if two principles are mutually inconsistent from mathematical viewpoint, they cannot be simultaneously true*?

#9. Do you think that the world cannot respect laws which can be expressed mathematically, because mathematics is so difficult to learn and understand by us?

#10. Do you admit the possibility that the difference between "math skeptics" and "math devotees" is that the former are just making excuses because math is hard, while the latter are willing to make these efforts, because "they've been there" and they know the prize?

_______________________________________________

* You may argue that "waves" are inconsistent with "particles" mathematically, but still they have physical existence. I would say that this simply means that the definitions or the axioms are inconsistent, so the formalism is not the appropriate one. This has nothing to do with mathematics being wrong.

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John Merryman wrote on Apr. 8, 2011 @ 17:49 GMT
Cristi,

Thank you for the very considerate response.

1)No, but I would also like them to have as much experience in the field as well.

2)Yes. Math is a concept which has many applications in many fields and is fundamental. It would be like asking if architecture or banking is possible, without the appropriate mathematical skills. That said, math is a tool and if it is...

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Cristinel Stoica replied on Apr. 8, 2011 @ 20:18 GMT
Thank you, John, for answering.

It seems to me that we agree at many points. I will try to address only the differences. And, as far as I understand, the problems you raise are not to be blamed on math, but on the human factor.

#1. Probably some physicists could use more understanding of the physical world, as some could use more understanding of math, but I don't think we can make...

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John Merryman replied on Apr. 9, 2011 @ 00:28 GMT
Cristi,

I was probably a little too expressive in using the terms "devotee" vs. "skeptic." I agree it is not the fault of the math, but that as a discipline, it has acquired a reputation for veracity which is occasionally abused.

In fact, as a process, it is so effective that it magnifies errors, rather than concealing them. Much like with navigation, small initial errors multiply the longer they go uncorrected. So, for me, when the theory gets to the point of proposing multiworlds emerging from quantum indeterminacy, especially when you consider the incredible number of realities created, it is the math itself which is flashing a huge error sign. Much as if I set sail for England and ended up in Belize, I would realize I made a mistake. Yet it seems that for some, such errors are not possible, so they insist they are in England, evidence to the contrary be damned.

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Cristinel Stoica replied on Apr. 9, 2011 @ 06:03 GMT
Dear John,

I think that you captured some essential feature of maths when saying "as a process, it is so effective that it magnifies errors, rather than concealing them".

Indeed, one of its "superpowers" is that it magnifies errors. You start with a small mistake, an innocent assumption, and eventually the conclusion becomes a monstrosity. Physicists use this feature to test their hypotheses: when the conclusions become absurd, it follows that the hypothesis is wrong.

A mathematics which "adjusts itself" to conceal the errors is in fact a patching like that you refuted earlier. But, as we both said repeatedly, one should use the wrong conclusion to go back and input different hypotheses, to learn from the errors revealed by this magnifying glass.

Best wishes,

Cristi

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Cristinel Stoica wrote on Apr. 9, 2011 @ 06:21 GMT
Dear John,

I am not so sure that the multiverse follows from the mathematics. I would say that, in each case, the multiverse did not follow from other principles, but it was postulated to explain some facts.

I am not supporting nor rejecting this idea, because I don't know how the world actually works. I cannot go outside the universe to see whether or not there are other universes. I cannot say that this idea is absurd or not, because I don't remember to have previous experiences with other universes, so I don't know how a "normal" universe is. So, you see, in the following I will not defend them, as it may appear.

There are theories which make predictions which cannot be verified: multiverse, unaccessible extra dimensions, weird stuff at very small scales, hidden variables. Now, just because we cannot verify them, it doesn't make them false or impossible. The scientific method said that we should keep the theories which pass all the tests. If we can't do the test, it is a problem, because the theory does not offer us the possibility to falsify it. I agree.

On the other hand, how can we be so sure that the physical laws and the human brain are such that the latter will be able to verify everything about the former? This assumption needs serious proof. Can we really verify everything about the world? It would be a huge coincidence if we can. It may even suggest a purpose of this world: a God made both the world and the mind, with the purpose that the mind can verify everything about the world. Maybe, maybe the world can be verified by the mind, but I think we should not take this possibility as absolute truth.

Of course, if one theory offers the tools which may refute it, and it passes the tests, then we should prefer it to a theory which predicts, as you said, "unicorns". My position is that we are not yet forced to accept such theories making preposterous untestable predictions, there are still other possibilities. But any TOE we will eventually accept, will make predictions about unaccessible scales, about the distant past or future, about the center of the stars, predictions which will not be (directly) testable. My hope is that between what we can verify and what we can't there is a continuity, the extrapolation is "smooth", the fundamental principles are already visible at our accessible scales. But I cannot know if this will be the case.

Best wishes,

Cristi

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John Merryman replied on Apr. 9, 2011 @ 10:53 GMT
Cristi,

As you say, the multiverse was postulated to explain some facts. That essentially makes it a patch.

My argument is that Everitt's multiworlds does naturally follow from a misperception about time. The point I keep making is that we are looking at it backwards. We think in terms of moving from one event to the next. This creates a spatial sense of linear movement, as though one were walking down a path.

Other the other hand, if we look at it as only the present and all motion combines to create changing configuration, it the the future possibilities which coalesce into the present and are then replaced.

Now the reality is that all the laws governing the actions of all the physical properties are deterministic, otherwise they wouldn't be laws. Presumably if we know the location and momentum of everything, we could predict where it would all go, much like predicting the motions of the planets. The problem is that there seems to be no logical way to know this, especially such actions as quantum decay and the further we go out the more this randomness multiplies. So how do you explain seemingly deterministic laws navigating an ultimately random process? One way would be to argue that all possible occurrences happen, therefore you have both deterministic laws playing themselves out, against random possibilities. Basically it overlays both realities.

On the other hand, if we view time as the events going future to past, it is the very collapse of probabilities, the actual occurrence of those laws governing how properties interact, which creates the effect of time. So we have both probabilistic input, the future, as well as deterministic events/occurrences, the present. Without needing to overlay them and have multiple outcomes.

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Cristinel Stoica replied on Apr. 9, 2011 @ 11:46 GMT
Dear John,

As I said, I did not argue for or against Multiverse. But I wouldn't consider that, if we postulate something to explain the facts, this makes it a patch. You have to start from some hypotheses, nothing is given a priori (except logic). The point is to have the simplest and the most testable hypotheses.

You have your interpretation of QM, which you presented here, and I have mine (which, btw, is deterministic but considers the wavefunction as fundamental). Mine is compatible with the Multiverse, but it does not require it to be true. Probably any theory or interpretation is compatible with the Multiverse, for the simple reason that the Multiverse hypothesis is not objectively testable. This is why I don't care to argue about Multiverse.

Reading here your interpretation of QM, I cannot say that I got your point. It was a short comment, and you did not have enough room to define the terms and develop it. This makes it open to interpretation, and I can interpret your words in a way that makes me thinking that you may find my interpretation compatible with yours. No Multiverse, no hidden variables, just the wavefunction, which evolves deterministically, and "initial conditions" (the "probabilistic input"), which are "delayed" at various points in spacetime (inclusive in the future). A brief summary is in a 5 minutes video here.

Best regards,

Cristi

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John Merryman replied on Apr. 9, 2011 @ 16:41 GMT
Cristi,

Multiverse and multiworlds are entirely different theories. Multiverses are an extension of Inflationary cosmology that has emerged in the last decade or so, for a couple of reasons. To provide an anthropic principle for why this particular universe has properties compatible with life and thus we are here to observe it. Compared to other universes with other constants. Also because it was never really clarified how the inflationary process would slow down, so it was proposed that some areas slow down, while others continue to inflate. Recently, in fact this months cover story on SciAm, Paul Steinhardt, one of the original developers of Inflation Theory, has started to throw cold water on it all, because it raises more questions than it solves.

Multiworlds, the idea that Schrodinger sought to essentially ridicule with the famous cat analogy, was a theory by Hugh Everett 3rd, first proposed in the 50's and mostly ignored for a couple of decades, that reality really does branch out into multiple worlds, due to quantum indeterminacy and the seeming inability to resolve how it relates to the classical world. Max Tegmark is actually one of the strongest current advocates. Like I said, the math seems to be fairly sound, which is why it hasn't gone away.

My point is that the error is in the elemental premise of time as a linear progression from a deterministic past into a probabilistic future. Everett's solution being that it really does physically branch out into multiple realities.

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Edwin Eugene Klingman wrote on Apr. 11, 2011 @ 02:12 GMT
Christi, it has been a pleasure to read your comments. Thanks for providing so much clarity and enlightenment. You and earlier commenters and the rich collection of comments on this thread represent the best of FQXi in my opinion.

John, as you know, the Galilean transformation is perfectly correct mathematics, in which any two velocities can be added to produce the resultant velocity....

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John Merryman replied on Apr. 11, 2011 @ 03:16 GMT
Edwin,

How much does the C field correspond to this description from Carver Mead that I posted further up the thread? I only ask because I truly am ignorant about much of the issues surrounding QM and am trying to triangulate a clearer understanding:

"It's interesting, isn't it? That has hung people up ever since the time of Clerk Maxwell, and it's the missing piece of intuition that we need to develop in young people. The electron isn't the disturbance of something else. It is its own thing. The electron is the thing that's wiggling, and the wave is the electron. It is its own medium. You don't need something for it to be in, because if you did it would be buffeted about and all messed up. So the only pure way to have a wave is for it to be its own medium. The electron isn't something that has a fixed physical shape. Waves propagate outwards, and they can be large or small. That's what waves do.

So how big is an electron?

It expands to fit the container it's in. That may be a positive charge that's attracting it--a hydrogen atom--or the walls of a conductor. A piece of wire is a container for electrons. They simply fill out the piece of wire. That's what all waves do. If you try to gather them into a smaller space, the energy level goes up. That's what these Copenhagen guys call the Heisenberg uncertainty principle. But there's nothing uncertain about it. It's just a property of waves. Confine them, and you have more wavelengths in a given space, and that means a higher frequency and higher energy. But a quantum wave also tends to go to the state of lowest energy, so it will expand as long as you let it. You can make an electron that's ten feet across, there's no problem with that. It's its own medium, right? And it gets to be less and less dense as you let it expand. People regularly do experiments with neutrons that are a foot across.

A ten-foot electron! Amazing

It could be a mile. The electrons in my superconducting magnet are that long.

A mile-long electron! That alters our picture of the world--most people's minds think about atoms as tiny solar systems.

Right, that's what I was brought up on-this little grain of something. Now it's true that if you take a proton and you put it together with an electron, you get something that we call a hydrogen atom. But what that is, in fact, is a self-consistent solution of the two waves interacting with each other. They want to be close together because one's positive and the other is negative, and when they get closer that makes the energy lower. But if they get too close they wiggle too much and that makes the energy higher. So there's a place where they are just right, and that's what determines the size of the hydrogen atom. And that optimum is a self-consistent solution of the Schrodinger equation.

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Marcel-Marie LeBel replied on Apr. 12, 2011 @ 02:56 GMT
John,

It is in fashion for physicists to say cool counterintuitive nonsense, but this as never amounted to plain understanding. “A neutron a foot long”? It may sound cool, amazing but is nevertheless nonsense. The neutron wave is contained within a foot, o.k. The neutron moves continuously within that foot but spends more time in some places in the path according to its wave distribution. This means that the existence of that neutron is spread in time within that foot but not equally everywhere because it exists more where it spends more time! The more time it spends in one place the greater the probability of finding it there and that is a working definition of “existence”.



Being sure the neutron is somewhere within that foot (prob=1) is not the same as the neutron occupying the whole foot at the same time(!). The wave function describes the distributed existence in time of that neutron within that foot i.e. where it is most likely to be found.

Physics is not, and never was, about understanding anything. It is about finding what rules connect various facts. “Understanding”, on the other hand, requires that one questions the logical cause for something to happen. But “facts”, with which physics works, simply do away with that requirement; a fact, like any measurement, requires no cause. It is like taking a picture of a passing car; taking the picture or the picture itself has logically nothing to do with how the car works and what causes it to move. The empirical method is practical but it is ill equipped to understand even the simplest of things.

Marcel,

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T H Ray replied on Apr. 12, 2011 @ 12:06 GMT
"So how big is an electron?

It expands to fit the container it's in."

Right. Even if the container is the whole universe. In fact, Wheeler and Feynman once suggested that perhaps the reason all electrons look alike is that there exists only one electron in the world, traveling back and forth in time. No matter how much it may offend one's naive sensibilities of what the "real world" just has to be, the fact is that most of what we objectively know IS counterintuitive.

Tom

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Wilhelmus de Wilde de Wilde wrote on Apr. 11, 2011 @ 16:13 GMT
Very good post Florin, the clothes you propose are they trendy today ?

It is clear to me that, even when I understood this very readable post, the right half of my brain is better devellopped as the left one, (sometimes I feel naked) although as an architect you have also to use maths, in physics it seems that mathematics more and more take over (string theory), when we talk about infinities ,our 4-D causal deterministic Universe meets a lot of paradoxes, but our consciousness has no problems at all to deal with these infinite structures, so is it our consciousness that is looking for mathematical solutions that perhaps cannot apply for the part of physics that we experiment here on our time line ?

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Florin Moldoveanu replied on Apr. 14, 2011 @ 02:04 GMT
"so is it our consciousness that is looking for mathematical solutions that perhaps cannot apply for the part of physics that we experiment here on our time line ?"

Intereting question. Let me reply with a question of my own: was Pythagoras theorem valid before it was discovered by Pythagoras? If nature can be described logically (barring the supernatural), it must have a consistent mathematical description. Our inability to find the ultimate theory may inspire a Broadway show, but has nothing to do with our consciousness.

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Wilhelmus de Wilde de Wilde replied on Apr. 14, 2011 @ 15:12 GMT
Every formula deducted is a reality in mathematical thinking, for example the Fibonacci sequence that you will find back almost everywhere in nature, so both Pythagoras and Fibonacci were valid before they were wrote down, a formula is just ONE way to express our consciousness about nature and the Universe.

You mention that our inability to find an ultimate theory has nothing to do with our consciousness, but in my opinion it is just the reason that our consciousness is able to "understand" the whole shebang, but it will never be possible to write it down with the means that we have available in our 4-D Universe with its own limits.

If you are interested you can read more about my view in my essay, thank you for your time

Wilhelmus.d@orange.fr

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Marcel-Marie LeBel wrote on Apr. 12, 2011 @ 22:07 GMT
Tom,

In order for the universe to evolve by itself it has to operate logically on every part of itself. For this, it has to be made of only one substance and variations of the same nature. The whole universeis made of only one kind of stuff!!

The universe is crazy enough as it is, and it just doesn’t need anyone to make his/her own ignorance (or ignorance of the quoted) translated into pseudo-weird appealing crazy counterintuitive statements. It’s just not constructive ...

my opinion, of course

Marcel,

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Xiang He replied on Apr. 13, 2011 @ 04:07 GMT
Hi Marcel,

I haven't gone through all relevant threads yet (i.e. I am not aware of the full context in which you made your above comments), but let me earnestly add my opinions to yours here that I completely agree with what you said in your first paragraph. Your 'only one kind of stuff" idea was also the conclusion of my favorite Chinese philosopher, Zhang Zai, who lived in the 11th century. In the West, Spinoza can be argued to have figured out this logic as well, although he might not be able to finish the last step due to the time and environment he was living in.

If I have to disagree with you, it's regarding your comment "the universe is crazy enough as it is". I would argue that the universe is not crazy at all, but extremely beautiful and elegant, able to sustain itself eternally. It would be a entirely different matter if you were referring to the human part of the universe though...

Best,

xiang

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Peter Jackson replied on Apr. 13, 2011 @ 08:08 GMT
Marcel, Xiang

What a lovely blast of fresh air! Just to confirm my support, for what it's worth. The first sentence of my essay sums it up in a slightly different way. The illogical weirdness is due to shortcomings in ourselves not nature. Please do read my essay (but carefully) and comment if you can. There are a number of connections in there. http://fqxi.org/community/forum/topic/803

Best wishes

Peter

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Xiang He replied on Apr. 14, 2011 @ 04:31 GMT
Hi Peter, I think your statement "The illogical weirdness is due to shortcomings in ourselves not nature" echoes well with my position that current mainstream scientific thinking suffers from a fundamentally flawed conceptual framework. That is not to say, however, that the flaws -- or the "shortcomings in ourselves" -- cannot be corrected. I will read your essay with great interest.

Thanks.

xiang

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Michael Jeub wrote on Apr. 13, 2011 @ 07:00 GMT
I agree that (A, H, D) works fine on the standard model. There are other operators on hilbert spaces besides the self adjoint one characterized by C* algebra, that could play some role in parameterizing and modeling. In other words, does the (A,M,D) model allow for non-trivial operators that are not self adjoint when clothing the standard model? It seems that fermions need a kind of operator and bosons need another kind in spectral theory where there are both bounded (the fermions)and unbounded(the bosons) operators. This is the toughest stuff I've encountered and only recently have come to appreciate that the linear operator is continuous whereas the continuous one is not necessarily linear. Does anyone have a checklist of operators on hilbert spaces? I've got about eleven kinds so far.....It was much easier to get a handle on grad dot cross div del curl than this stuff that definitely causes a headache. Is there some geometrization principle of operations on the hilbert space, and doesn't M- theory answer this in the affirmative with certain finite discrete characterisitics of operators on a hilbert space, if one allows for the multiple vaccui? Does the axiom of choice prevent us from perfecting this grammar of the kinds of operators in which to cloth the naked frailties of the SM? Can anyone say with confidence whether the standard model should be Reimannian as opposed to pseudo-Reimannian?

One needs a method of accounting for submanifolds and boundaries on the one hand and unbounded maxwell like 2-forms or dualities on the other. String theory takes care of the clothing of the beggar, feeds him, and lets him grow rich. I very much am interested but need to connect more right brain with left movers.

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Edwin Eugene Klingman wrote on Apr. 14, 2011 @ 20:16 GMT
Particle/wave vs Particle-plus-wave and Quantum Incompleteness

--OPEN INVITATION TO ALL--

My Apr. 11, 2011 @ 02:12 GMT comment above has gotten sidetracked, so I have extracted the logic of my comment as follows and invite anyone to expose the fault in my logic:

Bohr's "complementarity principle", the basis of the Copenhagen interpretation, refers to wave/particle duality.

Einstein: "In a complete theory there is an element corresponding to each element of reality."

deBroglie-Bohm-type theories posit a 'particle plus pilot wave', based on TWO elements of reality.

Quantum mechanics offers only ONE element of reality, the 'wave function' which corresponds only to the 'pilot wave'.

The wave-function does NOT correspond to the particle.

Instead a 'superposition' of wave functions uses Fourier mathematics to 'construct' a particle.

John Bell points out that this wave-packet 'disperses', and only the extremely ugly GRW 'stochastic collapse' currently 'solves' this problem [a true 'patch' in John's sense of the word].

Einstein: "Maxwell's equations are laws representing the *structure* of the field."

Maxwell/Einstein's generalization of these laws to include gravito-magnetism enlarges the set of possible field structures.

[Assume that] these field equations can, in a Yang-Mills, Calabi-Yau-compatible sense, incorporate stable particles.

Superposition of linear wavefunctions can never manage to create 'stable' particles.

Therefore, if, as John Bell preferred, reality is best described by a Bohm-like 'particle plus wave' rather than as a Bohr-like 'particle/wave', then the quantum mechanics wave function corresponds only to the 'wave' element of reality and quantum mechanics is incomplete.

Edwin Eugene Klingman

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Author Frank Martin DiMeglio replied on Apr. 14, 2011 @ 20:34 GMT
Edwin, life and experience originate (and vary) in relation to (and as) what is a center of body experience. That is how we are/experience, and that is how we got here.

Quantum mechanical origins are fundamentally understood as shifting and variable manifestations of what is essentially the same. This is how we grow and become other than we are. This, in turn, changes our experience, of course.

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Florin Moldoveanu replied on Apr. 14, 2011 @ 22:29 GMT
Dear Edwin,

Let me poke one hole in your logic. Bohm's model DOES NOT WORK. It looked like it was a good model in the beginning, but his model cannot explain spin properly. It is a very simple way to see this. Bohm's model depends on his "pilot wave", or "quantum potential". This demands the presence of an interaction. However, in a GHZ state (which can be obtained using spin states) one derives an equality which contradicts hidden variables, and moreover, it involves NO INTERACTION. A GHZ state cannot be explained by Bohm's model because there is no quantum potential available there in the first place.

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Edwin Eugene Klingman replied on Apr. 14, 2011 @ 22:48 GMT
Florin,

That is not a hole in the above logic. The above logic deals with 'particle plus wave'. deBroglie, Bohm, Einstein, Bell and others preferred this model. Bohm offered a SPECIFIC INSTANCE of this model, which, as you state [probably] does not work. This is not relevant to the GENERAL case of a theory that consists of a 'particle PLUS pilot wave', since, for example, it does not apply to my model.

Therefore I restate the relevant step as follows:

'Some' theories posit a 'particle plus pilot wave', based on TWO elements of reality.

I have in the past told you that I am not selling Bohm's specific model when I address the 'particle plus pilot wave'. I would hope that this is the last time we have to cover this point. So consider a theory that does not have a 'quantum potential' but that does provide a proper spin. Forget Bohm-based specifics. That is beside the point, and not part of the above logic. And therefore the 'hole' does not exist.

Edwin Eugene Klingman

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Steve Dufourny wrote on Apr. 15, 2011 @ 10:47 GMT
"deBroglie, Bohm, Einstein, Bell and others preferred this model". That does not sound like logic to me, but it sounds more like a "a political position than a physicist's argument."

All is said !!! Indeed Edwin indeed unfortunally.And Copenaghen in the heart of real searchers.....

why particles have the wave properties? The sense of rotation changes and thus mass and light are.....

regards and viva el rationalization of our foundamental determnistic axiomatization of our reals.....

Steve

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Edwin Eugene Klingman wrote on Apr. 15, 2011 @ 20:16 GMT
1. In a complete theory there is an element corresponding to each element of reality.

2. QM has ONE element of reality, the wavefunction.

3. QM addresses 'particle/wave' physics, which has ONE element of reality.

4. 'Particle plus wave' physics has TWO elements of reality.

5. QM cannot address BOTH elements, 'particle plus wave', with the wavefunction.

6. If reality consists of 'particle plus wave', then QM is incomplete.

7. If reality is 'particle plus wave', then QM arguments against it are irrelevant.

Notes:

a. Florin has rejected the logic of step 1, but step 1 is not a statement of logic, it is a definition.

b. Florin claims 'particle plus wave' means Bohm's theory, but my essay describes a theory of particle plus wave and it is *not* Bohm's theory.

c. I am sincerely interested in the above logic, which I believe to be correct. Can anyone argue these points without descending into irrelevant history or polemics. Each statement seems to stand alone. Which statement, if any, is incorrect?

Edwin Eugene Klingman

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Georgina Parry replied on Apr. 15, 2011 @ 20:42 GMT
Dear Edwin,

I don't disagree with any of those statements.I have added a diagram to explain how I see QM and relativity being related to the entirety of reality, on my essay competition thread. It is easy to follow so might be accessible to the mathematically minded who dislike long verbal descriptive ramblings.

It shows how QM relates to one facet of reality and relativity the other. The particle idea belonging with the structure of the relativity model, which is a model of the observed manifestation of reality and the wave function belonging to QM , which is a model of the unobserved reality becoming manifest. It shows how wave function collapse is related to observation. The diagram shows that both models are part of a fuller description of reality and neither is sufficient on its own.

It is a bit untidy as quickly thrown together in response to argument that the ideas are abstract, lack precision and are unhelpful to physics.I have tried making the image smaller to fit the page more easily but the smaller writing is then not clearly visible . (I might try turning it around.)I would be grateful if you would take a look at it (and excuse the hugeness and amateur appearance) I think it is relevant to the discussion you are having with Florin, and would also appreciate any feedback on its structure.

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Edwin Eugene Klingman replied on Apr. 15, 2011 @ 21:15 GMT
Hi Georgina,

I seem to be missing the link to your diagram...

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Edwin Eugene Klingman replied on Apr. 15, 2011 @ 21:17 GMT
Oops, I'll go to your thread.

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Lawrence B Crowell wrote on Apr. 15, 2011 @ 21:38 GMT
Quantum mechanics has only one element that is real, those are eigenvalues. The operator O acts on a state vector |n> and gives O|n> = o_n|n>, where o_n is a real valued number corresponding to something observable. These are also Hermitian and satisfy a number of mathematical properties which insure these eigenvalues are real. A wave function is composed from the vector

|ψ> = sum_n c_n|n>,

according to the position representative as ψ(r) = . The action of that observable is to generate a set of eigenvalues

O|ψ> = sum_n o_nc_n|n>,

So that the expectation of these eigenvalues is given by

= sum_n o_n(c*_nc_n)

for = E|ψ>. This is connected to the duality between particles and waves, where wave-particle duality these days somewhat otiose language BTW. Quantum mechanics does not posit that wave function or the state vectors in Hilbert space are “real,” at least not according to the set of real numbers or in any ontological fashion. The wave function is epistemological, rather than ontological. The wave vector can then select out certain observables that are ontic, but these are not at all direct measurements of a wave.

Cheers LC

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Lawrence B Crowell replied on Apr. 15, 2011 @ 21:48 GMT
I have to resubmit this. I forgot that this does not like carot signs. So my post here got broken up.

BTW, Florin talk about the self-adjointness property in the AHD. What I wrote below is an elementary form of this in QM

Quantum mechanics has only one element that is real, those are eigenvalues. The operator O acts on a state vector |n) and gives O|n) = o_n|n), where o_n is a...

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Edwin Eugene Klingman replied on Apr. 15, 2011 @ 23:03 GMT
Lawrence,

Thanks for responding.

In your first statement, do you mean real as in reality or real as in the real part of a complex number?

You state that "Quantum mechanics tells us that state vectors can't correspond to the ordinary concepts we have of space and realism." But my model produces equivalent state-vectors (see page 6 in my essay) that do correspond to the circulating C-field that is induced by the local particle. And this *does* correspond to just such ordinary concepts, when interpreted appropriately.

You then state: "where wave-particle duality these days somewhat otiose language BTW. Quantum mechanics does not posit that wave function or the state vectors in Hilbert space are "real", at least not according to the set of real numbers or in any ontological fashion. The wave function is epistemological, rather than ontological. The wave vector can then select out certain observables that are ontic, but these are not at all direct measurements of a wave."

If nature is as my model describes it, then instead of the otiose 'particle-wave' there exists a 'particle plus wave' and the standard interpretation of QM is incomplete, and your interpretation (which I do not fault) is also incomplete, and inappropriate to reality. Since QM has no element corresponding to a locally real particle, it is hardly surprising that QM'ers need to have some 'work-around' explanation such as the above.

Just to be sure, which step in my logic are you claiming is incorrect?

Edwin Eugene Klingman

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Lev Goldfarb wrote on Apr. 16, 2011 @ 00:17 GMT
Florin,

Are you paid for writing each new blog entry? ;-)

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Florin Moldoveanu replied on Apr. 16, 2011 @ 05:08 GMT
Ha, ha,

I wish. Even for a penny a pop, I would be rich then.

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Lawrence B. Crowell wrote on Apr. 16, 2011 @ 00:32 GMT
I don't want to discuss your theory in particular. I will say that I read your paper and it clearly does run against a considerable canon of modern physics. The problem with delving into such a discussion is one can't really use a theory to disprove a theory. What disproves a theory is evidence or data for its falsification, which either disproves a theory completely or illustrates how it...

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Edwin Eugene Klingman replied on Apr. 16, 2011 @ 00:58 GMT
Lawrence,

Thanks again for the response.

Since you do not wish to discuss the specific logic, but to write about QM, there is not much left to discuss here. I worked as a quantum physicist for 7 years at NASA, taught QM and other courses at a small college for 5 years, and have dozens of QM, QED and QCD books on my shelf [all of which I have read and/or studied] so your above post is not new to me or particularly helpful. In fact, I had opened a few of these to quote items that contradict, or at least disagree with your above statements about what the state vector 'represents', but without some constraints such as my seven points, it makes no sense for us to throw QM at each other. And as I repeatedly state, and as you have seen in my essay, Bohm has nothing to do with my approach other than the most general concept of 'particle plus pilot wave', and even that is stretching the point.

I would have enjoyed arguing some of these points with you, but only in the context of my approach, which is strongly dependent on my theory.

I very much thank you for your last paragraph above. It is far more open and honest than much of what is claimed for quantum mechanics today, and I agree with what you say there.

Wishing you the best,

Edwin Eugene Klingman

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Lawrence B. Crowell replied on Apr. 16, 2011 @ 02:03 GMT
As I indicated the nature of your theory is sufficiently removed from some canons in physics that I would find it hard to talk about. In fact it is in part related to GEM theory, which is a nest of inconsistencies. As for logic, logic in of itself really says nothing. I suppose the principal difficulty there is that this has the problems the Aristotelean scholasticism. In addition, the premise that the wave function is the ultimate reality of QM. The wave function is not real, either mathematically or physically. It is a mathematical machine which permits us to compute the probable outcome of measurements which correlate with the Born rule. So one might propose a perfectly logical chain of syllogistic reasoning, but if a premise in that chain is wrong the argument is wrong. As I indicated above this seems to be the most problematic element of what it is that you propose.

Cheers LC

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Lev Goldfarb replied on Apr. 16, 2011 @ 02:35 GMT
"we do not fully understand QM, and as we push further into the topic the stranger things get"

Lawrence,

I think you are, conveniently, being *too* generous. ;-)

Regarding QM and physics in general, already in 1934 Schrödinger observed:

"The quantum mechanics of today commits the error of maintaining concepts of the classical mechanics of points--energy, impulse, place, etc.--at the cost of denying to a system in a precisely determined state any definite values for these magnitudes. This shows how inadequate these concepts are. The concepts themselves must be given up, not their sharp definability."

But ignoring him, Einstein, and some others, everyone is only willing to continue the party line, which is much easier to do than to start from the beginning. I guess this is a consequence of being trained and employed as a *professional* physicist. Some, including, Florin, are even trying to put on all of this the impossibility tinge (there is only QM way or the highway, which is a convenient delusion).

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