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Essay Abstract

The digital model of the universe or \It From Bit" is not decidable. A model of the physical universe encoded by algorithmic means will not compute reality. One unknown domain argued to be outside any computerized model based on current quantum eld theory is quantum gravity. A change in axiomatic basis is proposed to address eld nonlocality in quantum gravity.

Author Bio

Doctoral work at Purdue. Worked on orbital navigation and currently work on IT and programming. I think it is likely there is some subtle, and in some ways simple, physical principle that is not understood, or some current principle that is an obstruction. It is likely our inability to work quantum physics and gravity into a coherent whole is likely to be solved through new postulates or physical axioms, or the removal of current ones.

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Hi LC,

Nice to see you here.

I am going to read your essay and to comment it. I will sent my entry in June.

Cheers,

Ch.

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Author Lawrence B Crowell replied on May. 15, 2013 @ 00:32 GMT

Of course this means I have an added information management issue. I almost didn't submit anything this time. However, this idea came to me last month and after some calculations decided to give it another try. This was a bit fun to work through and write up.

Christian Corda replied on May. 15, 2013 @ 09:01 GMT

It looks that my previous post was a lucky rabbit's foot for you. In fact, after such a post your Essay became the leading one.

Cheers,

Ch.

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Philip Gibbs replied on May. 15, 2013 @ 12:49 GMT

Glad to see you decided to join in. The essay covers a lot of great material and I will have to read it a few times.

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" in a nonlocal manner a quantum particle 'knows' how to evolve by sampling all possible paths.......it can still be argued there is either an underlying or a dual perspective on nature which is continuous and not digital."

IOW: an aether

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Author Lawrence B Crowell replied on May. 16, 2013 @ 00:32 GMT

The quantum vacuum is not an aether exactly. It is not an aether in the old fashioned sense with a continuum of degrees of freedom. The vacuum does however admit configuration variables, and these can be continuous.

LC

All physical theories are effective theories, or ultimately models. One should never take any theory as being somehow absolute. Even if we end up with a cosmology theory that is at the limits of our observing capabilities we should never assume we have it all. "It From Bit" is really a way in which we could run quantum cosmology on a quantum computer. However, the algorithm that is run is...

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All physical theories are effective theories, or ultimately models. One should never take any theory as being somehow absolute. Even if we end up with a cosmology theory that is at the limits of our observing capabilities we should never assume we have it all. "It From Bit" is really a way in which we could run quantum cosmology on a quantum computer. However, the algorithm that is run is ultimately a system of physical axioms (postulates) which are incomplete. They can never be complete. So the quantum cosmology run on our quantum computer is mo more "IT" than can my piffle of a lap top crack all public key encryption codes or RSAs. With the universe at large the quantum computer idea means the universe computes itself, which means by default that the universe is itself incomplete.

BTW. the quantum computer will at first be a boon for physics and cosmology, in particular with modeling the SLOCC systems for BPS and SUSY black holes. In the long run though, I look upon the quantum computer with trepidation and dread. If you think the world is getting loopy and strange due to information complexity, just wait until the quantum computer dominates the scene.

In my essay I draw a comparison between Godel's second theorem and David Hume's conclusion about the naturalist or "is ought" fallacy. This was the basis for his argument that causality is not strictly proven by logic. To assume the occurrence of an event, or the existence of some physical state, is logically derived is a fallacy. The second theorem of Godel is related to this. It means that mathematics is in a way a bit of an empirical subject. It the universe then computes itself, it does so in the same way we study a subject like math or physics: The universe in effect discovers itself.

This then suggests that we can’t assume that all of existence is defined by an algorithm which computes itself. The algorithm doing this is similar to a universal Turing machine that is incapable of determining its own halting status as it evaluates all other possible algorithms. This does not mean It From Bit is false, but it is not something which can be proven. The fact it can’t be proven means that what ever algorithm or formal system of computing Bits we have it is incomplete and the “It” will as a result always be found to be larger. To assume otherwise is to commit the naturalist fallacy pointed out by Hume.

Cheers LC

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John Merryman replied on May. 16, 2013 @ 17:53 GMT

Lawrence,

" the universe is itself incomplete."

And hopefully will remain so. When it is finished, it is finished.

Remaining within the dynamic processes, it seems there are some revealing patterns. One of these seems to be that complexity is part of the overall pattern and is not just a linear progression into ever more complexity, but is a process that leads to...

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Lawrence,

" the universe is itself incomplete."

And hopefully will remain so. When it is finished, it is finished.

Remaining within the dynamic processes, it seems there are some revealing patterns. One of these seems to be that complexity is part of the overall pattern and is not just a linear progression into ever more complexity, but is a process that leads to breakdowns. This might be considered the Tower of Babel syndrome. You could say the algorithm informing it, or the energy motivating it, reaches limits and its wave of applicability peaks.

As is happening in physics, or the world economy, it seems the alternative is breakdown and chaos, yet this too is part of the pattern, as the linear pushes into an increasingly disturbed non-linear environment.

Rather than ask what comes next, perhaps we should back up and ask why each step becomes ever more complex. Why each floor of the structure requires more re-enforcement of the lower levels, why cars and buildings and society become ever more complex. Much of it has to do with the fact the environment is fundamentally non-linear and while progress seems like a vector, it is actually a scalar. Each level magnifies and multiplies the issues and the complexities, until they overwhelm the endeavor. Yet we continue to view reality as linear. We even see the universe as beginning at a point of origin and pushing outward, because we see the most basic unit of energy as a point that doesn't expand, but moves along a vector for billions of years. The expansion has been relegated to a statistical probability. Yet these "probabilities" and anomalies multiply until they overwhelm the model.

There really is no way around this. There is no path to Nirvana, no all-encompassing algorithm, just a rising and falling of waves in an eternal sea. To be more "objective," we need to be able to be more objective about our own situation, in order to be able to ride these waves and know when to get off one and onto another. Even to accept our own mortality as part of this process.

It is only when we insist our path is the only one, all others are wrong and it is going to the promised land, that we delude ourselves.

Not trying to get too philosophical on your thread, but just trying to put the effect of complexity into a larger contextual process.

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I an not sure what you mean by "linear." This is not covered at all in my essay, but I think there is an elementary quantum statistics of a 2 + 1 spacetime that underlies a lot of the complex physics of strings and supersymmetry. I am not going into that in detail, for it would be too much. However, I think there is a degeneracy of states or superselection from which heterotic string theory emerges. Since this involves the octonion group E_8 this touches on the matter of nonassociativity.

LC

John Merryman replied on May. 17, 2013 @ 03:43 GMT

Lawrence,

I'm no match for you in terms of the leading edges of complex theory. I'm simply making a general point about the nature of complexity. For example, there are literally billions of microbes in a person's gut. What level of computational complexity would it take to describe every relationship? Necessarily it would be far beyond any computational ability we currently have, yet one could make the general statement that it is a digestive process. So do we have to construct a precise, bottom up model of the entire system in order to effectively understand it? We can't. We would drown in detail and lose sight of what we are trying to do. A map can't show every detail, or it is useless for any particular purpose.

So the point is whether physics is drowning in detail, literally off in other universes, to the point of losing sight of what it is trying to understand. There is no ultimate algorithm which will explain the universe to humanity and when even the field is starting to throw up their collective hands over the fact the most developed concepts, such as string theory, have nothing to offer beyond a big question mark, then it might be time to consider if the path taken is anything more than a sticky trap. I know what I say has little weight, but I think you will find there will be more and more people like me. Eventually string theory is not going to be putting food on anyone's table.

You and I have argued over my ideas enough, not to go there, but you do have the ability to clarify your arguments, as you did to Phil in the above comment, so keep it up and keep breaking down all those beautiful ideas and see what further patterns emerge and what are just empty bubbles. If it requires other universes, that should be a hint some factor has been overlooked.

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The level of complexity or the amount of information we observe is determined by the number of states, say the dimension of a Hilbert space or the size of a coarse grained phase space, call that dim H and entropy is S = ln(dim H). The amount of complexity we observe around us is huge. However, I think that much of the huge complexity around us is due to a redundant set of copies of fundamental states on different configuration variables. This means potentially there is only one electron in the universe, but where the huge number we observe are copies of that one state in different configuration variables. This huge redundancy has a relationship to the occurrence of event horizons and holography. I will have to leave this conjecture at this stage, for it gets a bit subtle.

LC

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John Merryman replied on May. 17, 2013 @ 17:31 GMT

Lawrence,

Let me go back and clarify my distinction of linear vs. non-linear. Obviously linear is sequential, yet this is a very broad category, from simple steps to complex changes. Non-linear is randomness. For example, think molecules of water. Yet there is a great deal of order in this as well. For one thing, it can be measured as a scalar, be it temperature, pressure, weight. There...

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Lawrence,

Let me go back and clarify my distinction of linear vs. non-linear. Obviously linear is sequential, yet this is a very broad category, from simple steps to complex changes. Non-linear is randomness. For example, think molecules of water. Yet there is a great deal of order in this as well. For one thing, it can be measured as a scalar, be it temperature, pressure, weight. There is also the entropic effect, as the various parts bounce into each other and trade energy, speeding the slower and slowing the faster ones, to reach an equilibrium state. There is also Newton's dictum of every action being matched by an equal and opposite reaction. Logically the action, being so defined, is linear, while the reaction of its environment is non-linear, so there is a natural balance between the motion of the particular and the reaction of its environment.

Now these two processes are intimately entwined, like the non-linear gut activity propelling the organism. Evolution is a good example of the situation, as we think in terms of linear progression, such as through generations of organisms. Yet it is much more of a scalar process, as progress needs to be supported by all the activities of the environment, as simple forward action tends to be balanced and negated by the larger quantity of activity. So there has to be the constant feedback and the resulting scalar activity is what actually determines the overall direction. Sort of like a tree has to grow out in all directions for the sequencing of rings to form. Like trying to introduce modern technology into a less complex society that lacks the broad cultural knowledge to use it.

So there is this mutual dichotomy of the actions of the particular and that of the mass of activity. Nodes and networks are a model of this relationship.

You might say the non-linear is the "course-graining" within the particular frame or space.

Now the problem, as I see it, is that there is an overwhelming bias to describe the particular, the node, as fundamental, but the logic doesn't really support this.

Consider how you conflate "state" with one electron. The idea of the entire universe as one "atom" was most forcefully put forward by LeMaitre, in his original argument for what ended up being called Big Bang theory.

Yet "one" is something clearly defined as a unit, ie. is distinct from its environment. On the other hand, a state, particularly a neutral state, is more of a zero. There is no set of boundaries or distinctions. It could well be infinite, as once it is clearly finite, then it becomes, not so much a state, but a set of all that it contains and thus a unit within the larger context.

This goes to the heart of my arguments against Big Bang Theory, in that it argues for the entire universe as a particular unit and attempts to totally erase any concept of a larger context. Now this model is having to admit other universes, yet still cannot condone the idea of any environment to form and contain them. Yet whether we want to admit to a larger context or not, it is essential to creating the unit, by setting boundaries. As it is, our current theories have any number of holes, from the singularity to dark energy, to suggest outside connections.

The electron could as well be a fluctuation of the void. One node popping up in the infinite network of potential.

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Author Lawrence B Crowell replied on May. 18, 2013 @ 01:06 GMT

The big bang has a lot of empirical support for it. I don't particularly want to get into trying to argue the points for inflationary multiverse theory. It is though likely that just as solar systems operate not by some geometric order of planetary orbits, but rather by a more fundamental set of principles, so too are the gauge field constructions in a vacuum nucleation or pocket universe. In medieval to the renaissance cosmology it was thought the solar system was arranged by a set of geometrically ordered "orbs." Kepler worked on something like this. It appears likely that the universe is far grander, and what we observe as the spacetime universe is just one bubble out of a vast number of such on an inflationary spacetime that is often called the multiverse.

Cheers LC

John Merryman replied on May. 18, 2013 @ 02:42 GMT

Lawrence,

I'm not really trying to start the cosmological argument, so much at trying to describe how various dichotomies, order/randomness, linear/non-linear, vector/scalar, node/network, organism/ecosystem, are aspects of an fundamental underlaying process.

It really isn't so much to argue about cosmology, but to make the deeper point that our logical concepts are generally based on one side of this relationship, that of the linear, ordered, singular organism, since it is the basis of our narrative, cause and effect descriptions of reality and the resulting atomized view affects many aspects of our understanding and relationship to nature, from monotheism to the Big Bang.

It's not the math is wrong, since it is distilled pattern, but how we apply it. For example;

" This means potentially there is only one electron in the universe, but where the huge number we observe are copies of that one state in different configuration variables."

"what we observe as the spacetime universe is just one bubble out of a vast number of such on an inflationary spacetime that is often called the multiverse.'

I can see how the math for this might be quite logical, but that in editing the variables, some important details might have been left on the cutting room floor. If the universe is one electron , might it be equally mathematically provable that every electron is a universe? If A=B, then does B=A? I tend to see multiverses as a version of C. S. Escher sketches of waterfalls and stairways going in circles. Quite interesting on paper, but problematic in reality.

So my point is, again, that we are not taking that scalar randomness into account as the background and balance to the logical vector.

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What on earth does any of this incomprehensible abstract senseless physics babble have to do with reality? As I have thoughtfully pointed out in my understandable essay BITTERS, the Universe is unique, once and every seeming piece of the real Universe is unique once. Each real snowflake is unique. Each man-made particle is unique. Whereas scientists seek out repeatable abstract theories of abstract structures and abstract histories and abstract continuations, real unique has none of these abstract qualities.

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Author Lawrence B Crowell replied on May. 18, 2013 @ 01:41 GMT

The physical world and universe is rather contrary to our common sense. For instance you say that every particle is unique, but it is well known by the Pauli exclusion principle that this is not the case. Two electrons are not distinquishable in quantum entanglement. The advancement of our understanding of the physical world is not going to conform closer to our common sense, it will challenge it.

LC

Joe Fisher replied on May. 18, 2013 @ 16:04 GMT

Do try to make a better effort to be accurate. The real physical world and real Universe are unique and have to conform to our common sense assessment. There are no quantum entanglements in reality. You can waste your time as much as you like pretending to know how abstract invisible electrons operate, if each particle is not unique, why is CERN trying so hard to isolate the Higgs boson?

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Author Lawrence B Crowell replied on May. 19, 2013 @ 03:10 GMT

The physical world just does not conform to that way of thinking. The trend since the time of Galileo has generally been in this direction. I think it is apparent that you are not have an extensive education in physics. As our knowledge of the universe has increased it has become increasingly removed from our everyday expectations of things and what might be called common sense.

LC

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Joe Fisher replied on May. 19, 2013 @ 15:14 GMT

Do you seriously believe that you and your fellow physicist’s obsessive compulsive abstraction addictions could in any way be superior to my common-sense grasp of reality? Unique is not optional. Each real snowflake is unique once; therefore everything real is unique, once. Each unique thing is neither superior to, inferior to, nor equivalent to any other unique thing. It is impossible for the unique to increase, decrease or remain equivalent to any other unique. Abstract knowledge of an abstract Universe may have increased for a certain selective essentially religious group of white male physicists, fortunately, because reality is unique, it is an easy task to expose them for the pretentious fabulists they are.

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Author Lawrence B Crowell replied on May. 19, 2013 @ 21:05 GMT

Things become distinguishable with the breaking of symmmetry. This results in a scale dependency and/or a broken degeneracy which permits that. The world around us has lots of distinguishing features because it is in a low energy or low temperature state. In the case of snowflakes or water in the frozen state there has been a phase change which breaks a symmetry for the equiprobability for an H_2O molecule in each volume of space.

It is rather clear that you are not that familiar with the nature of physics, or with what Feynman wrote in "Character of Physical Law." The problem is this discussion has reached an impass. I will simply say that your assessment of things is simply wrong. I doubt that anything I write here will convince you of that.

LC

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Hi Lawrence,

this is a very intriguing essay that touches on a lot of things that I have dimly glimpsed in my own thinking. In particular, the issue of how undecidability relates to physics is something that is intermittently on my mind. There's been a recurring trend to look for undecidability as somehow related to the measurement problem, or other quantum mechanical weirdness, starting...

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Hi Lawrence,

this is a very intriguing essay that touches on a lot of things that I have dimly glimpsed in my own thinking. In particular, the issue of how undecidability relates to physics is something that is intermittently on my mind. There's been a recurring trend to look for undecidability as somehow related to the measurement problem, or other quantum mechanical weirdness, starting with maybe Zwick in 1978, and continued by people such as Mittelstaedt or Thomas Breuer (who uses diagonal arguments to establish the impossibility of perfect self-measurement in theories assumed to be universally valid, that is, apply to observer as well as observed). A relatively recent development is the idea that the randomness of quantum measurement outcomes is related to the undecidability of the outcome from axioms encoded in the state preparation, as developed by Paterek et al. There's also interesting work by Karl Svozil, Christian Calude, and others, in investigating quantum randomness and uncertainty from the point of view of Chaitin's algorithmic information theory.

All of which is just to say that a lot of people have seen some common ground here, while apparently nobody has been able to find a rigorous formulation. Your take on the issue is a new one to me: as far as I understood, you seem to be saying that independent axioms may be repealed in order to allow greater mathematical freedom, citing the case of abandoning the parallel postulate in order to lead in a profitable way to new formulations of geometry. But of course, in any theory, all axioms are logically independent of one another, no? Otherwise, if any axiom can be derived from the other axioms, you can just strike it out, and you'll be left with the same theory. This was what drove the attempts to derive the parallel postulate from the other axioms: it was seen as a blemish on the theory, and it was hoped that the theory would hold up unchanged without it. The construction of geometries inequivalent to Euclid's by Lobachevsky and others ultimately was what killed this hope. (And besides, isn't Euclidean geometry decidable anyway?)

So the parallel postulate ultimately isn't derivable from the theory in the same sense that, say, the existence of the square root of -1 isn't derivable from the field axioms: the incompleteness here is in a sense trivial, and different from the Gödelian case in the sense that one probably wouldn't want to insist that the field axioms are complete in the sense that they derive every true position they can express. So it seems to me that there's a difference between the independence of the parallel postulate and the independence of, say, the continumm hypothesis from Zermelo-Fraenkel.

Also, even though there are undecidable propositions about any sufficiently complex system (any system capable of universal computation), this does not imply any 'uncertainty' about the fundamental laws (though I'm not sure if you're arguing for that): take, for instance, a universal cellular automaton such as the Game of Life. It's 'fundamental laws' are simple enough, and can be completely specified without any problem; nevertheless, there exist undecidable propositions, such as whether or not a specific configuration will ever turn up. But of course, GoL can be simulated on a computer; so the mere existence of undecidability does not imply anything about the uncomputability of physical evolution. So this does not put the hypothesis of the universe being, in some sense, a 'giant computer' to rest: in fact, I would rather consider it evidence in its favour, since as I said, every universal system gives rise to undecidable propositions.

But I'm not quite sure if I'm not arguing past your points; I need to re-read your essay in some calmer moment, I think.

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Author Lawrence B Crowell replied on May. 18, 2013 @ 13:57 GMT

This essay I kept on the level of modal logic so the presentation could be kept on a somewhat informal level. I think on a deeper level this connects with the Langlands program. The proof of the Tanyama-Shimura conjecture is a two dimensional form of a more general theorem, or set of theorems, of elliptic curve cohomology. In four or eight dimensions there are similar results for conformal systems, such as in four dimensions with the Cardy theorem. When extended to eight dimensions this climbs up the Cayley numbers into the exceptional group E8 and potentially octonions. This may connect to some axiomatic basis for a putative proof of the Riemann zeta function conjecture. I think the zeros of the zeta function and prime distribution may be mapped into the set of eigenstates for quantum gravity.

I have been reading the paper by Mathur, where he introduces early on the nature of wave functions on spatial splittings of the Schwarzschild spacetime. Wave functions of different wavelengths near the horizon, here the horizon considered classically, will scatter into the exterior and inferior of the BH in different ways. Those wave functions though are defined by the action of field operators on a Fock space or vacuum occupation space. If the horizon is “quantum uncertain” I think there is then an underlying associative property for these field amplitudes.

I have read a couple of papers by Mittelstaedt. Most of his work was done in the 1970-80 time period. I have not followed anything he may have done later.

I have not yet scored any essays on FQXi. I have only read a handful at this time. I see that you have an essay here as well. I will try to get to it in the next few days. I generally score essays after I have some idea of what a number of them look like. I usually keep a copy of the essay page where I put in a tentative score on the file before I actually score them on the FQXi page.

Cheers LC

Philip Gibbs replied on May. 18, 2013 @ 15:46 GMT

The undecidable reminds me of Wangs Tiles and how Egan used them in Diaspora. It may be possible to build such tiles out of amino acids and just mix them together to see what happens.

Your idea is different and based on taking out associativity as an axiom, is that right? It's an interesting way of looking at.

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Author Lawrence B Crowell replied on May. 18, 2013 @ 23:56 GMT

That is one way to think of it. Another is if you think of the physics as having two representations. One representation involves quaternions where associativity holds. The other involves the octonions.

A cloth item or garment will when hung over a chair or a hanger or thrown on a surface assume a shape that minimizes the stress per area on it. This is a function of the topology of the garment and the geometry which involves these stresses per unit area. The elementary case is that of a skirt, where the boundary at the top is equal to the boundary at the bottom. These two boundaries define a simple cobordism. A more complicated case is that of a pair of pants. Here the boundary at the top is one circle and the boundary at the bottom consists of two circles. Think of the top circle on both the pants and the skirt as a group G which has some decomposition into SL(2R)^n. The skirt provides a simple deformation retract of G to the bottom. The pair of pants has two circles we think of as a group G' that each decompose into SL(2,R)^{n2/}.

The skirt represents the elementary view, say the 8-bit SLOCC. The pants are more complicated where this decomposes into two copies of a 4-bit SLOCC. These two copies have a duality relationship, such as with Yangians. The pants are then the perspective we have of physics, or fields that are quaternion valued. They are associative = "nice," or nice according to how we normally think of physics, and there are conformal dualities. The skirt represents the world more fundamentally. In moving between the two perspectives we turn on and off the axiom of associativity.

Cheers LC

Dear Lawrence,

Very nice and rich essay! I must confess that am still trying to connect all the dots, but for what I understand so far, especially after the clarrifications in your comments, I very much agree with you.

I may return with some questions.

Best regards,

Cristi Stoica

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Author Lawrence B Crowell replied on May. 18, 2013 @ 13:53 GMT

Thanks for the positive response. I have been intending to write more fully on your essay, since I have now read it a couple of times. I will try to do that later today or tomorrow.

LC

Hi Lawrence,

I have found your essay interesting and difficult so it took me a lot of time to study and maybe you will find my comment not clear? But I have to try.

I would like to refer to your statements: ‘The quantum computer perspective of the world describes the universe as some master quantum Turing machine that deterministically computes information states. This is really a...

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Hi Lawrence,

I have found your essay interesting and difficult so it took me a lot of time to study and maybe you will find my comment not clear? But I have to try.

I would like to refer to your statements: ‘The quantum computer perspective of the world describes the universe as some master quantum Turing machine that deterministically computes information states. This is really a modern version of the clockwork world. Conversely the path integral perspective tells a somewhat different story, for the evolution of a physical system or quantum states is due to the extremization of the action. In this setting the evolution is less due to the deterministic automata processes of a Turing machine than they are due to a continuous extremization…. The issue of determinism in a "clockwork" or computer fashion is equivalent to an ordering of states, as well as a statement about logical necessity, or modal logic…’

The theories that combine digital physics with loop quantum gravity are well known and formulated e.g. by Paola Zizzi (Computational LQG). There is no room here for citations. Additionally according to Lee Smolin (LQG) self-organized critical systems are statistical systems that naturally evolve without fine tuning to critical states in which correlation functions are scale invariant. My own view seems to support the view of Smolin in the meaning that the universe is a dissipative coupled system that exhibits self-organized criticality. The structured criticality is a property of complex systems where small events may trigger larger events. This is a kind of chaos where the general behavior of the system can be modeled on one scale while smaller- and larger-scale behaviors remain unpredictable. The simple example of that phenomenon is a pile of sand.

Why I have touched that issue? This has a lot to do with determinism, computability, TM and emergence. My conclusion is: when QM and GR are computable and deterministic (however non scale-invariant), the universe evolution (naturally evolving SOC system) is non-computable and non-deterministic. It does not mean that computability and determinism are related.

I would argue for a "top-down" physics with the emergence of higher level properties. I think that there is not only a prospect for playing a role but at the moment it plays a role in the emergence of biology and even consciousness.

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Hi Jacek,

I have been curious about the role of LQG. I will confess that I am primarily oriented towards the string theory perspective. I do think LQG has some relevancy to physics, but it is uncertain what that is. LQG comes from the ADM approach to general relativity, which give constraint equations NH = 0 and N^iH_i = 0 with no explicit time dependency. The lack of time dependency...

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Hi Jacek,

I have been curious about the role of LQG. I will confess that I am primarily oriented towards the string theory perspective. I do think LQG has some relevancy to physics, but it is uncertain what that is. LQG comes from the ADM approach to general relativity, which give constraint equations NH = 0 and N^iH_i = 0 with no explicit time dependency. The lack of time dependency means that energy is not defined. This is a manifestation of Gauss' law, where on a general manifold there is no boundary from which to integrate over to define mass-energy as the source of the field. So the Wheeler DeWitt equation, and spinor variations on that theme in LQG, are in effect constraint systems. The problem is that we do not know what this contrains exactly.

I have thought that LQG is some sort of "target" of a renormalization group flow in string/M-theory. However, string theory has at its IR limit a graviton in a weak coupling regime on a background. This theory is renormalizable as a perturbative field theory, even if we know it is a weak coupling approximation to quantum gravity. LQG is not renormalizable. So we are sort of left with an open question. Is LQG a strong coupling S-duality to the string weak coupling theory? There are some problems with an idea of this sort. In particular LQG is not easily embedded into a larger unification scheme with gauge fields or supersymmetry.

However, LQG is based upon basic general relativity in a way that is hard to ignore. I suspect it is not completely wrong, as is often thought in the string theory community. However, where it fits into things is unknown.

LQG is related to Regge calculus, which is run on a computer. It is one of the tools numerical general relativists use. However, this approach to general relativity is also a manifestation of the action principle. Underlying it all is an extremal principle. Extremization is a continuous process and from a set theory perspective it is a manifestation of a nondenumerable set of numbers, or the reals. This is one motivation to suggest that the universe is not entirely a computer, even if it has some computer or algorithmic-like structures to it.

Cheers LC

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Jacek Safuta replied on May. 20, 2013 @ 20:18 GMT

Hi Lawrence,

I do not believe that LQG /CLQG is a serious candidate for quantum gravity and it is not my favorite. In LQG the space is granular (a network of finite loops) and this is contradictory to my view of continuous spacetime. However I like its evolutionary aspect in the sense of SOC and the scale-invariance that is crucial to fill the gap between GR and QM. I have mentioned LQG / CLQG only for reference to your determinism in a "clockwork" and evolution. After all the evolution notion is used very often by physicists but usually in the common meaning as a process of a change e.g. stellar evolution. But this has nothing to do with self-organized criticality. I would like to apply Darwinism beyond its original sphere of organic evolution on Earth using SOC.

I like the extremal principle in a sense of non-equilibrium thermodynamics to look for the likely steady states. This is also a kind of evolution of a far-from-equilibrium system to a steady state.

String theories do not generate predictions so they are non-falsifiable.

And finally I am sorry but the language of modal logic is not my ‘mother tongue’… just like English. Maybe I should start to learn...

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Author Lawrence B Crowell replied on May. 21, 2013 @ 00:30 GMT

I think spacetime is continuous or granular depending upon which sort of measurement you make. The Planck scale is just the minimal length scale which can contain a qubit of information. Space or spacetime on a smaller scale can not contain a qubit with any certainty. An experiment that involves the transmission of information over a vast time distance has no uncertainty with respect to the...

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I think spacetime is continuous or granular depending upon which sort of measurement you make. The Planck scale is just the minimal length scale which can contain a qubit of information. Space or spacetime on a smaller scale can not contain a qubit with any certainty. An experiment that involves the transmission of information over a vast time distance has no uncertainty with respect to the existence of it information or qubit content due to quantum gravity. As a result spacetime appears perfectly smooth. An experiment on the other hand which attempts to localize a very small region of space, say at high energy, will then register a different perspective on spacetime. In that setting it may appear highly choatic and granular.

The predictions of string theory involve cosmology and black holes. In a stringy universe there are some observable consequences, in particular with respect to multiple vacuum nucleations or bubbles that we call a "universe." Signatures of this may be imprinted in the fine grain detail in the CMB anisotropy. The graviton has quantum numbers equivalent to an entangled pair of QCD gluons, or a bi-gluon system, that is neutral with respect to color charge. This means that plasmas of gluons can be formally equivalent to a black hole. In a funny way it is a black hole. So holographic physics should in principle be testable in heavy ion collisions. These are admittedly rather indirect or oblique sorts of tests, and even if confirmations of string predictions are found the whole string-M/theory enterprise is likely to remain on rather unsteady ground.

The real problem is that we appear to be reaching a sort of ceiling of technological possibilities. One of these is of course directly testing Planck scale physics. Other limits seem to be with high density energy sources such as fusion, that seems as remote as ever, the future of manned spacetravel appears in trouble, and there are slow downs with Moore's law with computers. We also need to consider the pile up of huge problems like global warming. We may be approaching the end of the foundations of physics because of our limitations.

Cheers LC

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Jacek Safuta replied on May. 21, 2013 @ 16:14 GMT

Dear Lawrence,

I agree we are hitting the technological limits within contemporary experimental physics. However there is a hope - a new idea falsifiable with a simple experiment. I have proposed one that could be even an exercise for students. But to carry out the experiment we need someone who is ready to risk his authority like J.A.Wheeler.

Best regards

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Author Lawrence B Crowell replied on May. 22, 2013 @ 02:38 GMT

I am slowly making my way through the essays. I have not yet gotten to yours. Are you proposing this experiment in your essay? I will try to get to yours in the next few days. I can only read one of these papers in a day, so it is a bit slow going.

Cheers LC

Jacek Safuta replied on May. 23, 2013 @ 08:58 GMT

Dear Lawrence,

In my essay I have only mentioned the spin experiment but in references you can easily find a link.

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Author Lawrence B Crowell replied on May. 23, 2013 @ 15:21 GMT

I just pulled up your essay and gave it a quick reading. It is not terribly long. It appears that you are asking whether certain properties are physical or geometrical. At this time I don't have an assessment of your work. I will need to read a bit more.

Cheers LC

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Dear Lawrence,

I have followed your past postings(your personal theories) and they were interesting. But this time you have gone a bit philosophical, so I want to understand what you are saying. Lets say what you are saying is true, so in what sense that affects physics in any meaningful practical way. I mean are you saying no ultimate laws can be formulated, or the constants of nature will never be found, or no ontology exists or can be known, or particles inherently have no trajectories, EXACTLY what?

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Author Lawrence B Crowell replied on May. 20, 2013 @ 02:42 GMT

The metaphysics, or analytical mathematircal philosophy, baseically is that any scheme for causality is going to be incomplete. It will not be able to encode all possible physical states. As a result it means there exists a deeper foundation to the universe. In the second half of this paper I argue this involves the associative property of the vacuum with respect to quantized event horizons.

Cheers LC

Thanks for the reply.

"baseically is that any scheme for causality is going to be incomplete. It will not be able to encode all possible physical states"

In which physics problem this problem appears. Is it in scattering s-matrix or in describing proton wavefunction. I mean EXACTLY which physical problem you are having trouble solving because of this issue. Sorry for repeating my question, I hope I am more clearer this time.

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The situation pertains when there is an uncertainty fluctuation of event horizons. This is a possible window into quantum gravity. The physical states in the S-matrix channel are entangled states, with entanglements across the horizon. If the event horizon is classical then everything is nicely associative. A fluctuation in the horizon results in this uncertainty in associating states interior and exterior to the black hole/

The graviton has quantum numbers equivalent to an entangled pair of QCD gluons, or a bi-gluon system, that is neutral with respect to color charge. In that sense this form of S-matrix does connect in formalism with the old S-matrix theory or the so called "bootstrap." In fact string theory is really that unitary bootstrap theory in another guise.

I hope this answers your question.

Cheers LC

Hello Lawrence Crowell,

First off, I’d like to say I like your style, and the way that you seem to put issues in their proper perspective! It brings a calming sense of reason to an area of question that retains so much hype that it no doubt triggers numerous thoughts every time one hears Q.M. and locality are mentioned. Secondly, I don’t think determinism should dictate the development of a new theory. It, as your historical view has made clearer to me, is an idea used to adapt old world views into current problems.

About the idea that the computer, either a real one or the universe as one idea, being faulty because it doesn't model the entire set of events, could it be that this is not against saying that there is a separateness between real entities in space which unaccounted for doesn't describe all events in the universe? Or, does a clock here have to do with one spatially separated over there? Not being mathematically trained enough to see clearly the math in or around the black holes, I will leave this comment with one question only. As an aside, I’m glad to hear someone say “bottom-up” once in a while.

Best,

W. Amos Carine

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Author Lawrence B Crowell replied on May. 28, 2013 @ 01:47 GMT

The relationship between events in the universe and causality was noted by David Hume to not have a strict logical relationship. As I indicate in a footnote Godel's second theorem according to modal operations is a form of Hume's argument about causality =/= logic.

I sort of have to make this a bit brief due to other things I have to attend to now. I will say that the issue of clocks with a spatial separation and synchronization is a subject of considerable interest. This involves Cauchy data on spatial surfaces and how to integrate the Einstein field equations.

Cheers LC

William Amos Carine replied on May. 28, 2013 @ 17:13 GMT

Thank you Lawrence C. for giving me something else to look into!

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I agree with you that the universe computes itself and thus discovers itself. I've presented an argument that supports this view. According to this argument Plancks constant h is nothing else than the physical expression of something which is commonly known as "natural digit".

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Author Lawrence B Crowell replied on May. 31, 2013 @ 13:38 GMT

The self computation of the universe probably leads to this Turing-Godel limit with Lambda calculus. There is clearly a computational aspect to the universe, which is a causal structure.

I will take a look at your essay soon. The Planck constant is in naturalized units just "one," and does probably reflect a unit of of natural numbers that sum up to give the total action. I notice yours seems to be in the latest introduction of new essays.

Cheers LC

Lawrence,

When reading; "A model of the physical universe encoded by algorithmic means will not compute reality" I suspected I may enjoy reading your essay. I was right.

You present a very level and balanced view, and more readable by the target audience than previous years. I do suggest something rather radical regarding that above sentence myself!

I also found other resonances with mine; "It is entirely possible this could be used to argue for a 'top-down' physics with the emergence of higher level properties." which I identify in terms of higher 'sample spaces' and subsets and test against the EPR paradox.

I also agree your analysis; "GR is a geometric theory of spacetime, which means that quantum gravity is quantization of spacetime itself. It is not entirely clear what this means. A number of questions have to be answered, and currently there are obstacles in our current theories which do not permit us to address these issues well."

But are the apparent 'obstacles' it not only 'assumptions'? so testing other assumptions may be fruitful (without the feared ether), i.e. that quantized atomic scattering to c maintains the SR postulates locally, (the LT then emerges naturally as a know optical effect).?? (You may recall from my last years effort how modal logic applies to that case).

I hope you can read mine and look forward to your and comments. I'm sure you'll stay in a more elevated position this year.

best of luck.

Peter

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Author Lawrence B Crowell replied on Jun. 4, 2013 @ 22:52 GMT

Hi Peter,

I am true to my usual trend falling behind in reading papers on this list. I just did a scan of your paper. You do reference Godel’s paper on prepositional logic. The main point of my work is that any Lambda-calculus or Turing machine approach to the structure of a causal system is bound to be incomplete. I do get a sense in reading the first couple of pages of your essay that you are leading into something similar.

I probably will not get to reading papers much until this weekend. I’ll post my observations when I do. As I said I am falling behind, and I notice another lot of papers showed up on the list today.

Cheers LC

Hi Lawrence,

I've just had a complete read and I really enjoyed your essay. The quantum nature of information does seem to point towards us concluding that neither it nor bit are more fundamental. I reached a similar conclusion in my essay. I particularly like the idea that this may have applications in consciousness.

Regards

Antony

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Author Lawrence B Crowell replied on Jun. 6, 2013 @ 00:45 GMT

The icosian or 120-cell has two quaternions with length (1/2)(1 +/- sqrt{5}) where the plus one has length 1.618..., which is the golden mean. In fact these quaternions define something called the golden field in a Galois ring. This is related to the Fibonacci sequence.

Cheers LC

Antony Ryan replied on Jun. 25, 2013 @ 02:10 GMT

Lawrence,

Thanks for your comments over on my page. From your example above, I find it absolutely fascinating how nature seems to tie things in together. It reminds me of Marcus du Sautoy's show "The Code".

All the best for the contest,

Cheers,

Antony

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Author Lawrence B Crowell replied on Jun. 25, 2013 @ 15:58 GMT

This is a sort of code. The J^3(O) Freudenthal matrix of 3 octonions or E8s embeds the Leech lattice which is a Steiner system S(5, 8, 24) for error correction.

LC

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Antony Ryan replied on Jun. 30, 2013 @ 11:41 GMT

This reminds me of something I did with E8, Leech and Coxeter numbers to determine kissing number at 5-dimensions.

Interesting area of study!

Antony

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Author Lawrence B Crowell replied on Jun. 30, 2013 @ 15:04 GMT

This mathematics is involved with kissing numbers. The big sourcebook on this is Conway and SLoane, "Sphere Packing, Lattices and Codes." These spheres in the 4-dim case are connected to Planck units of volume. The packing system is the 24-cell or equivalently the F4 group.

These systems are error correction codes. In the case of sporadic groups the quantum error correction is meromorphic which preserves quantum information. In the simple case there is no pole this recovers unitarity. In the study of this it is important to keep the connection to Jacobi theta functions. This also connects up with the Ramanujan Mock theta function and the partition function for the integers. This partition function is related to the density of states of a bosonic string as well as the thermal partition function of a black hole.

There are deep relationships involved with this. My essay here is an attempt to lay down some physical arguments for this.

Cheers LC

Antony Ryan replied on Jul. 2, 2013 @ 09:25 GMT

Hi Lawrence,

I think your essay achieves these goals very well. Also it is nice how across history people have always remained interested in this area of study.

Cheers,

Antony

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Hi Lawrence,

a very interesting essay, I enjoyed to read it. It seems (again) that our approaches are related (see my essay). I also claimed about that the information contained in spacetime is undecidable (by the word problem in group theory).

More later after rereading your essay

Torsten

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Author Lawrence B Crowell replied on Jun. 5, 2013 @ 15:33 GMT

Hi Torsten,

I remember reading an article back in the 1990s about how the classification of exotic R^4s was not enumerable, which had connections to Godel’s theorem.

The exotic R4 structure has its origin in the Casson handles as pointed out by Freeman. A thickened disk D^2 --- > D^2xR^2 can produce various structures, which by the self duality of four dimensions leads to these...

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Hi Torsten,

I remember reading an article back in the 1990s about how the classification of exotic R^4s was not enumerable, which had connections to Godel’s theorem.

The exotic R4 structure has its origin in the Casson handles as pointed out by Freeman. A thickened disk D^2 --- > D^2xR^2 can produce various structures, which by the self duality of four dimensions leads to these strange conclusions. In scanning your paper I see you invoke Casson handles. The number of such structures by h-cobordism turns out to be infinite, which as I say above, I remember this to be nonenumerable. This result was proven by one of the big mavens in this area, Atiyah, Freeman, Taubes, … ?

The one element of this is that the e8 Cartan matrix as the eigenvalued system for an E8 manifold, an exotic R4. It has been a while since I have studied these matters, but as I remember this tells us how to tie 3-manifolds in 7 dimensions in the Hopf fibration S^3 --- > S^7 --- > S^4. The dual to this structure are 4-manifolds. The 7 manifold this knotting is performed is in the heterotic S^7 --- > S^{15} ---- > S^8, and the e8 Cartan matrix gives the eigenvalues for the 7-space.

The interesting thing about the E8 is that the 8-dimensional space is equivalent to the group in a lattice construction; the root-weight space is ~ the space itself. The E8 manifolds of Freeman are I think embedded in the set of possible 8-spaces. This suggests a duality between the smooth manifold in 4-dim and a discrete or noncommutative manifold in a quantum sense.

Physically this seems evident from data obtained so far. Measurements of the dispersion of light from extremely distant sources invalidate a discrete structure to spacetime. This tells us that a measurement of spacetime structure by measurement of photons that traverse a large distance give no signature of grainy structure. Yet a lattice perspective of spacetime with the Grosset polytope and the 120-polytope of quaternions in 4-dim would suggest a noncommutative geometry. However, if the lattice is equivalent to the space, then this smooth structure is dual to a grainy picture of spacetime. This structure should emerge in an extremely high energy experiment that probes small regions, rather than testing across vast distances.

Cheers LC

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Dear Lawrence,

Your essay is very stimulating and certainly enrich the 'it from bit' discussion. It contains several deep relationships between quite sophisticated branches of maths and foundational questions in physics.

First I like that you put the information paradigm in a historical perspective as was the 'clockwise universe'. Then I learned about modal logic from you. I wonder if it cannot be related to the current Abramski's work relating logic and contextuality as in http://xxx.lanl.gov/abs/1203.1352

An important statement of yours is 'this nonlocality is an undecidable proposition of the above modal theory of causality'. For me, it means that the modal approach is not the right one for approaching the subject, as is the von Neumann interpretation of quantum mechanics. My view (to my understanding, Bohr would agree) is that the quantum universe is unknowable, this is even worse that undecidable, because we can only know what is compatible with the questions we ask (through observables), i.e. quantum reality is contextual.

I agree with you that non-associativity, in addition to non-commutativity, may be very relevant for discussing these issues, as is the 'octonionic' Fano plane or further generalizations, see http://arxiv.org/abs/0712.1647.

With my colleagues we just found that the number of automorphisms of the G2(2) geometry (it is related to the octonions as explained in John Baez http://xxx.lanl.gov/abs/math/0105155) is the number of three-qubit pentagrams as well. Thus several of your ideas fit mines.

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Author Lawrence B Crowell replied on Jun. 14, 2013 @ 13:30 GMT

You state that the quantum universe is unknowable. I would say there is some limit to how much we can know about it. This limit is due to the cut-off in measurable physics at the Planck or string scale. As one considers scales beneath the string length and then beyond the Planck scale spacetime folds up onto itself in such ways that quantum fluctuations result in closed timelike curves and...

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You state that the quantum universe is unknowable. I would say there is some limit to how much we can know about it. This limit is due to the cut-off in measurable physics at the Planck or string scale. As one considers scales beneath the string length and then beyond the Planck scale spacetime folds up onto itself in such ways that quantum fluctuations result in closed timelike curves and things that are "paradoxical." This is probably a domain that is fundamentally unobservable.

A rather simple argument can illustrate how this cut-off on the extremely small scale manifests itself on a larger and I think potentially a cosmological scale. The amplitude computed in a path integral is a summation over 3-metrics g

Z = ∫D[g]e^{iS(g)},

where a standard method is to Wick rotate the phase e^{iS(g)} --- > e^{S(g)}. This is a way to get attenuation of high frequency modes, and it is a “bit of a cheat,” though at the end one must recover the i = sqrt{-1} and “undo the damage” for the most part. This phase then becomes e^{-GM^2}, which illustrates how the action and entropy are interchangeable. The integral measure is the size of the phase space of the system ~ exp(S). The amplitude is then on the order

Z ~ e^{S}e^{-S} = 1.

This holds universally no matter how large the black hole is. A black hole is a sort of theoretical laboratory for the universe at large, where the universe has a cosmological horizon at r = sqrt{3/Λ}. The implication is there is a limit to what we can possibly observe about the foundations of the universe, which probably touch on the amount of quantum information available with respect to quantum gravity/cosmology.

We have of course two different quantities. The volume of the phase space is equal to the exponential of the entanglement entropy of the system, while the e^{-S} is exponential of the thermal entropy. The amount of information is S_{th} – S_{ent}, so this amplitude is not going to be exactly one. There is some “kernel” to the black hole which corresponds to an elementary unit of information. This means that quantum information is ultimately conserved, and that the number of degrees of freedom for a black hole in spacetime is a constant, regardless of the size of the black hole. It also means that the universe as a whole (here thinking of a toy universe with just a black hole) has a finite limit to its domain of observability.

The application of modal logic is a sort of “boilerplate” to examine causality and locality. Further, my considerations are quantum field theory instead of quantum mechanics. QFT involves operators which act on a Fock space to describe quantum states or QM. So this is an underlying physics. Your work seems to illustrate the “traces” of this sort of underlying QFT in matters of CHSH nonlocality.

The paper by Dzhunushaliev looks interesting. Your work with G2(2), which I am presuming is a split form of G2, focuses on the automorphism of the E8 or octonions. The F4 is a stabilizer of E8 (constant under G2 action). The automorphism on E8 defines an invariant interval on C^4 as a twistor space. This in higher forms, say on the magic square can construct generalizations on H^2 and then O, within the CxO, HxO and OxO hierarchy of the magic square. Generalizing the H^2 twistor space to octonions gives O^2, and scattering amplitudes are functions on copies of OP^1, subject to SL(2,O) = Spin(9,1) transformations. Embedding O^2 in O^3, gives OP^1 as a line in OP^2 and SL(2,O)=Spin(9,1) becomes the subgroup of SL(3,O) = E6(-26), consisting of transformations (collineations) that fix a point in OP^2.

The J^3(O) or O^3 has connections to SO(2,1) and I think this rather erudite stuff connects to anyons on a 2-space plus time constructions. All of this I think is some sort of superselection rule on this sort of theory. The question might then be whether your idea about [0, 1, ∞] as the dessin d’enfant is some sort of category theory on the superselection rules according to curves on Ricci flat spaces, such as (K_3)^2 for E_6 twistor theory.

Cheers LC

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Dear Lawrence

Your conclusion is too abstract, so what decided for it?

http://fqxi.org/community/forum/topic/1802

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Author Lawrence B Crowell replied on Jun. 17, 2013 @ 15:17 GMT

As a rule when somebody tells me that something is too abstract or is overly difficult I tend to translate that into, "This is to difficult for me, therefore it must be false." That is not exactly the most appropriate form of reasoning.

Cheers LC

Michel,

I reread your paper again this last Sunday. The desin d'enfant leads at the end to Mermin's pentagons. These are of course an aspect of the Kochen-Specker theorem. This is of course the main theorem on contextuality in QM. In my paper I discuss the quantum homotopies of associators at various dimensions, which are pentagonal systems. I copy this post on my essay blog page, so you...

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Michel Planat replied on Jun. 19, 2013 @ 10:15 GMT

Dear Lawrence,

Thank you for these scholarly remarks.

About the 18-9 proof and the 24-cell, there is the interesting work of Waegell and Aravind http://xxx.lanl.gov/abs/1103.6058. I like to see the 9 bases and 18 rays as the vertices and edges of the Mermin square, as explained in equation (6) of http://xxx.lanl.gov/abs/1204.4275. Now there is the dessin d'enfant of Fig. 3 of my essay that adds the algebraic curve/Riemmann surface view to this building block of two-qubit contextuality.

As you emphasize well, the next step is about the building blocks of three-qubit contextuality, they are related to G2 and E8. I already met the Weyl group of E8 for three qubits and see it as just one step of a higher order hierachy leadind to the Leech lattice, as in http://xxx.lanl.gov/abs/1002.4287.

For sure you would also have something to say about this.

All the best,

Michel

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Author Lawrence B Crowell replied on Jun. 19, 2013 @ 15:35 GMT

Michel,

I don’t have as much time this morning to expand on this, so I will just make this rather brief for now. I will try to expand on this later today or tomorrow.

The three-qubit entanglement corresponds to a BPS black hole. The four qubit entanglement is the case of an extremal black hole. I think there is an underlying relationship between functions of the form (ψ|ψ) = F(ψψψ), an elliptic curve with the cubic form corresponding to the 3-qubit, and the “bounding” Jacobian curve that defines a quartic for G(ψψψψ). This I think is some sort of cohomology.

The G2 I think defines a frame bundle on the E8 which defines the F4 condition for 18 rays in the spacetime version of Kochen-Specker.

As I said I should have more time later to discuss this in greater depth.

Cheers LC

Torsten,

I finally got a little bit of time to write more on what I had mused about a couple of weeks ago. This all seems to center in a way around a type of cobordism with respect to these replacements of handles or Casson handles. The replacement of a circle with a knot suggests a type of theory that involves Hopf links. The trefoil for instance is by the Jones polynomial such that a...

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Torsten Asselmeyer-Maluga replied on Jun. 27, 2013 @ 20:11 GMT

Lawrence,

thanks for the reply. Yes, I know TQFT like the Chern-Simons theory with Wilson lines leading to the knot polynomial.

The Seiberg-Witten invariant for this exotic 4-manifold is the Alexcander polynomial, i.e. a knot polynomial but with a complicated TQFT. The Alexander polynomial is rather a classical then a quantum invariant.

I will think about your ideas more carefully.

Torsten

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Author Lawrence B Crowell replied on Jun. 28, 2013 @ 00:58 GMT

Torsten,

I have more of this sketched out. I wanted to write further today, but I got busy reviewing a paper. As for a classical invariant, check out Agung Budiyono's paper. It is the sort of idea of quantum mechanics that sends most quantum physicists screaming in horror. This is a stochastic approach to QM which along with the Bohm QM is weak, but these ideas I think can have their place.

Cheers LC

Torsten Asselmeyer-Maluga replied on Jun. 29, 2013 @ 22:07 GMT

Dear Lawrence,

I will be absent for the next three weeks with sporadic email check.

You can also write me to my email accout:

torsten.asselmeyer-maluga@dlr.de

I will answer you as soon as possible when I'm back.

All th best for you

Torsten

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Send to all of you

THE ADDITIONAL ARTICLES AND A SMALL TEST FOR MUTUAL BENEFIT

To change the atmosphere "abstract" of the competition and to demonstrate for the real preeminent possibility of the Absolute theory as well as to clarify the issues I mentioned in the essay and to avoid duplicate questions after receiving the opinion of you , I will add a reply to you :

1 . THE...

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Lawrence,

"There is a prospect this may play a role in the emergence of biology and even conciousness."

Would you advocate for consciousness being triggered by the Big Bang and present in space time as some neuroscientists posit? They claim a non-locality quantum-entanglement factor.

Jim

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Author Lawrence B Crowell replied on Jun. 28, 2013 @ 03:47 GMT

My mention of consciousness at the end, in connection with top-down physical or causal theories, was a bit conjectural. In a way I put that in there because I know a lot of people want to hear about consciousness and physics. Call it a bit of self-promotion.

To be honest I don't know what role consciousness has with physcs or the universe. A lot of people think it is a quantum process. I don't know about that honestly. I think it could be argued that consciousness is the ultimate classical or macroscopic non-quantum system. Consciousness at least generates an epiphenonenon of wave function collapse.

Cheers LC

James Lee Hoover replied on Jun. 28, 2013 @ 17:28 GMT

Thanks for your honest answer. It seems to be an important point, considering whether consciousness emerged after our universe matured.

Jim

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Dear

Thank you for presenting your nice essay. I saw the abstract and will post my comments soon.

So you can produce material from your thinking. . . .

I am requesting you to go through my essay also. And I take this opportunity to say, to come to reality and base your arguments on experimental results.

I failed mainly because I worked against the main stream. The...

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Anonymous replied on Jun. 28, 2013 @ 03:55 GMT

Dear S.Gupta,

I will take a look at your paper soon. I have fallen behind in reading these papers because I have had to review or referee a paper for a journal. Thanks for the interest in my paper.

Cheers LC

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Dear Lawrence,

I have down loaded your essay and soon post my comments on it. Meanwhile, please, go through my essay and post your comments.

Regards and good luck in the contest.

Sreenath BN.

http://fqxi.org/community/forum/topic/1827

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Dear Lawrence,

Congratulations on a well written essay dense with impressive references to many relevant issues raised by the fqxi contest question. The technical aspects of your discussion went over my head (and probably for many others here), particularly in the section about logic and in the applicability of the Incompleteness Theorem to the issues at hand.

That said I could confidently say that I agree with several of your points: 1- The need for a 'philosophy' to approach questions of Reality in physics. 2- The undecidability of It/Bit 3- That a density matrix allows the expression of quantum states as qubits (which was my conclusion). In my Theory (see below) GR is reduced to a density gradient. 4- That "in theoretical physics there may exist assumptions that act as excess baggage that prevent workers from addressing fundamental problems" which was a major argument in my paper, although your saying it sounded much less presumptuous than when I did. Not only in this contest, but in my last year's "Fix Physics!" essay - since most of my ideas are qualitative. 5- The relevance of causality sets which in my Beautiful Universe Theory also found here are simply the Hamiltonians of qubit-like (spherical degree of freedom at every point) transfer of angular momentum locally, causally and linearly in a Universal lattice.

On a personal note I visited Purdue around 1965 to visit my brother-in-law who did his PhD in physics there. One is wont to believe in a Flat Universe in that locale!

With best wishes for your success

Vladimir

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Author Lawrence B Crowell replied on Jul. 1, 2013 @ 16:36 GMT

Hi Vladimir,

Indiana is not just a case of a flat universe, but a flat Earth. It is in many ways socially backwards, and there were Ku Klux Klan rallies in the 1980s when I was there. That is rather embarrassing.

The elimination of excess baggage is important. In my elementary demonstration with modal logic it means that certain physical axioms or postulates can be "turned off" in certain domains. It is similar to Godel's theorem, where certain propositions about a mathematical system are not provable and they can be toggled on or off to create different systems. Euclid's fifth axiom is of that nature and its on and off state define euclidean flat geometry and Riemannian geometry respectively. Your FQXi essay reads a bit like a narrative on this sort of thing.

Cheers LC

As a public non-specialist ... This article was on topic, well written, and an interesting read. Its technical and narrative aspects were well interwoven and a strong assist to non-specialists, such as myself. The struggles I underwent in writing my own essay are resolved in this essay. Thank you Lawrence.

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Author Lawrence B Crowell replied on Jul. 1, 2013 @ 17:35 GMT

Darrell,

Your essay does read as some narrative on a similar idea. You take the perspective of an alien. It will be extremely interesting if we should ever get radio contact from ETI to see how different they perceive the universe. The question is whether their mathematics and physics are in some ways mapped into ours, or if there is some isomorphism betewen their math and physics and ours.

Cheers LC

Hi Lawrence,

I agree that ""It From Bit" is not decidable", or rather, that it is a question which belongs to what to me is an outdated paradigm.

I have yet to read an essay which treats the question where all information comes from, how information becomes information. What I mean is this: If there would be only a single charged particle among uncharged particles in the universe,...

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Hi Lawrence,

I agree that ""It From Bit" is not decidable", or rather, that it is a question which belongs to what to me is an outdated paradigm.

I have yet to read an essay which treats the question where all information comes from, how information becomes information. What I mean is this: If there would be only a single charged particle among uncharged particles in the universe, then it wouldn't be able to express its charge in interactions. As it in that case it cannot be charged itself, charge, or any property, for that matter, must be something which is shared by particles, something which only exists, is expressed and preserved within their interactions. If particles, particle properties (its) are both cause and effect of their interactions, of the exchange of bits, if particles only exist to each other if, to the extent and for as long as they interact, exchange information, then you cannot have one without the other nor can one be more fundamental than the other.

If the information as embodied in particle properties and the associated rules of behavior a.k.a. laws of physics must be the product of a trial-and-error evolution, then information only can survive, become actual information when tested in practice, in interactions between its carriers, between actual, physical, material particles, whatever we may mean with 'material'.

What strikes me in all the essays I've read (also of previous contests) is that everybody, without exception, thinks about the universe as an object which has particular properties as a whole and evolves in time, as something we may imagine to look at from the outside and can make statements about, as if it is a mechanism which, once winded up at the bang, after the bang only can unwind in a preordained fashion, as if there is a collection of platonic truths which exist outside the universe, as if there is an absolute, objectively observable reality at the origin of our observations we cannot perceive due to imperfect instruments and to the uncertainty principle.

My point is that if a particle cannot exist, have properties if there's nothing outside of it to interact with, then the same must hold for the universe. The fallacy of Big Bang Cosmology (BBC) is that we can only speak about the properties and state of the universe if there's something outside of it, something it can interact with, and, like the charged particle its charge, something it owes its properties to: if it has been created by some outside intervention. For this reason BBC is an even worse 'theory' than creationism which at least honestly states that, yes, there is Someone outside of it Who created the universe. If a universe which creates itself out of nothing, without any outside intervention has to obey the conservation law which says that what comes out of nothing must add to nothing, then everything inside of it, including space and time somehow must cancel, add to nil, meaning that it has no physical reality as a whole, as 'seen' from the outside, but only exists as seen from within. If in that case it doesn't make sense to speak about the properties it has or the state it is in as a whole, then it also makes no sense to make such statements from within. In other words, we need a completely different approach, an entirely different paradigm if we ever are to comprehend the universe rationally, as opposed to causally, something I'm trying to do in blog, a study which, I'm afraid, is a bit of a mess.

As I argued in a previous essay, this means that we can no longer conceive of the speed of light as the (finite) velocity light moves at, but that c just refers to a property of spacetime, which is something else entirely. (Though you agreed with my statement that we ought to "replace causality with reason ...to understand our world", I hope that you realize, accept that if causality goes out the window, then so does the interpretation of c as the (finite) velocity of light.) In regarding the universe as an object we can imagine to look at from without, a Big Bang Universe (BBU) lives in a time realm not of its own making: as it is the same cosmic time everywhere, here it takes a photon time to travel so here c does refer to the velocity light moves at. In contrast, a Self-Creating Universe (SCU) does not live in a time realm not of its own making: as it contains and produces all time within, here clocks are observed to run slower as they are more distant even if they are at rest relative to the observer. As in a SCU it is not the same time everywhere, here a space distance is a time distance so in this universe a photon bridges any spacetime distance in no time at all, in contrast to a BBU where the photon covers a space distance in (a finite) time. The difference is as subtle as it is crucial to comprehend our universe. Evidently, in a universe where the communication between particles over any spacetime distance is instantaneous, things like the double-slit experiment, the EPR paradox become obvious. The problem is that nobody seems to be able to escape the essentially religious narrative of BBC and start to try to understand the universe from within. Frankly, I'm appalled that everybody takes the word of the heroes of physics as a God's word instead of trying to see whether a different interpretation of observations might solve some of the most glaring contradictions of physics.

Regards, Anton

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Lawrence B. Crowell replied on Jul. 2, 2013 @ 16:32 GMT

Anton,

I am sorry I can’t respond in the length you write. The day is getting a bit on already and I need to attend to other things. There are a couple of points I can make.

If the universe had one charged particle something funny would happen. If we consider the spatial surface of the universe, say on the Hubble frame, as a 3-sphere the lines of electric force from this particle would wind around this sphere endlessly. Indeed these lines of force would densely fill the space. They would also interact with themselves or in effect the charged particle. The charged particle would be “driven” into a divergent condition to rapidly increasing energy. The system would in effect “explode.” It is comparable to an undamped oscillator that is driven by a resonant frequency.

The recent developments with inflationary cosmology now involve bubble nucleations or O-regions that result from a vacuum transition to a small value. This is an aspect of the multiverse. There is some prospect that our O-region, bubble or sometimes called pocket universe interacted with another one in its early phase. This may have left an imprint on the CMB. The de Sitter spacetime where this inflationary expansion occurs may in turn be a vacuum-field configuration on a D-brane, where in this higher dimensional space of 10 or 11 dimensions there is a foliation of such branes. This then leaves the bulk 10/11 dimensional spacetme, which might in turn exist in a 26 dimensional spacetime and so forth. This sort of gets into the proverbial idea, “its turtles all the way down.”

Cheers LC

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Dear Darrell

how can you assess the "undecidability" of any theory, if we cannot doit for just arithmetics?

Cheers

Mauro

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Member Giacomo Mauro D'Ariano replied on Jul. 2, 2013 @ 08:59 GMT

Sorry, my post was supposed to be addressed to Lawrence.

Apologies

Mauro

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Author Lawrence B Crowell replied on Jul. 2, 2013 @ 14:19 GMT

Undecidability is a universal property, such as it is known that not all propositions in Peano arithmetic are decidable. The Church-Turing thesis states that any computable function is run on a Turing machine that halts. Of course it is known that a universal Turing machine is not capable of determining whether all TMs are halting. Hence the λ calculus is incapable of verifying Hilbert's Entscheidungsproblem.

My paper works with certain correspondences between modal logic, Lob's theorem and the Godel theorem. I did not break this out in great detail to avoid turning the paper into a complicated discussion of symbolic logic. To address your question again; I think what you are asking is how can we determine what is undecidable. This is an area of research for people who delve into this subject. There are mathematics on proof theory and hierarchies of undecidability. I will confess that I am not an expert in this area of work, for this deviates seriously from physics.

My argument is then more physical than formal, where I consider a certain algebraic postulate about observables, that being associativity. The physical argument involves observables or quantum amplitudes in a region that contains a black hole.

Cheers LC

Dear Crowell,

Now let us call the most natural automaton simply "heredity" (or indeed any cycle, Carnot or whatever). Then the idea of entropy or 2nd law of thermodynamics is that each stage of evolution within an automaton path does in fact depreciate possibility of return to the initial state; so there must be a halt or "fatalism"

My question is: doesn't your undecidableness amount to what we already know as uncertainty? Such that above a cut-off (Heisenberg Cut?) there is higher probability of return to initial state (what we know as determinism) but below the cut (being what we know as the quantum scale) there is no probability of return to initial state i.e. the system is not well-behaved.

Now I put it to you that once you assume that a well-behavedness (or conversely "uncertainty") is simply put an automaton then it qualifies as the ALGORITHM or computer proper. This computer/algorithm is what I call simply THE OBSERVER (perhaps Wheeler's anticipation).

It is a response to your position that: “...a quantum field is propagating on spacetime,but where spacetime is the quantum field. This heuristically appears self-referential, and the physical ansatz is this nonlocality is an undecidable proposition of the above modal theory of causality.”

By quantum theory, this state is rather at once a Godel "incompleteness" (the uncertainty) and yet a Peano (or Planck) "constant" (i.e. the conservation law).

My "observer" is in other words then the SUPERPOSITION proper.See What a Wavefunction is

So Wheeler's proposition does work! Pls see my essay and prove me wrong on this particular approach.

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Author Lawrence B Crowell replied on Jul. 6, 2013 @ 05:10 GMT

I hesitate to call the Heisenberg uncertainty principle some derivative of Godel’s theorem. However, my ansatz that this incompleteness rests with the associativity of fields is really just another form of the quantum uncertainty. There are limited ways of knowing what propositions about a mathematical system are undecidable, so my assumption here is not a form derivation of any sort. So my idea here is more of a physical assumption than a formal proof or derivation.

The role of an observer is in some ways similar to a self-reference in mathematics. Godel’s trick is to let a mathematical system contain predicates that act on their own Godel numbers as the subject. An observer is ultimately made of quantum particles and the act of a measurement has the appearance of being a sort of physical form of self-reference. Of course my paper is not about the measurement problem or the role of observers, but ultimately the universe is as it is so that observers can exist. This is a sort of strong form of the anthropic principle.

As for fatalism, it is of course the case that the universe will end up as a pure de Sitter vacuum in a sort of heat death. This will be reached in around 10^{110} years. It will probably quantum decay from there over a far longer period of time into a Minkowki vacuum. That might sound like fatalism, just as saying that we are all going to die sounds fatalist. However, in the mean time a lot of different things can happen. In the sense of Plato’s final cause the outcome might be in a sense fated, but what happens before then is not.

Cheers LC

Lawrence,

There are two kinds of scientists, the kind which can perfectly build further on the theories one learned at school, and the kind which tries to find alternative interpretation of observations. However invaluable an education is, its disadvantage is that, since you've learned many theories describing phenomena, it is very hard to dream up a different approach which perhaps might solve some of the many fundamental contradictions and enigmas of present physics. Though it is very understandable that man came up with the big bang idea, I'm afraid that it actually is even a worse 'theory' than creationism which at least honestly, boldly states that the universe has been created by some outside intervention. As far as I am aware of, the universe either has been created by some outside interference (which is the position of both creationism and big bang cosmology), a possibility I reject or it creates itself. If so, then fundamental particles must be as much the cause, the source of forces as their effect, the product of their interactions, meaning that a force cannot be either attractive or repulsive, always, which is the mistaken belief string theory is based upon. String theory, like big bang cosmology don't solve anything but are part of the problem.

Cheers AB

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Dear Lawrence

Your quote from comment to Platan essay:

"What do you think of algebraic curves over [0, 1, ∞] and the Langlands program?"

By coincidence i used long time ago similar trick with pseudoscalar mesons.See my essay. I signify as 1 mass of proton and then observed what position would take place other pseudoscalar mesons.That i got phenomenon 18 degrees.

Do you see some explanation?

Yuri

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Author Lawrence B Crowell replied on Jul. 12, 2013 @ 20:37 GMT

The number 18 is important in Jewish mysticism. I am not sure that has any bearing on what you are saying though.

Is your number something similar to a Cabibbo angle or Weinberg angle?

I'll take a look at your paper later today.

Cheers LC

Yuri Danoyan replied on Jul. 12, 2013 @ 23:18 GMT

It is not common with a Cabibbo angle or Weinberg angle

Just put the values of mass on y=tanx plot, then exploring angles.

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Dear Laurence,

(I copy the reply to your post on my page)

Your post is very stimulating. I need time to look at this possibility of relating black-hole physics and entanglement, and non-associativity. On the other hand, I don't consider that entanglement is a primary category in non-local/contextual questions. It may be that conformal arguments adapted to Grothendieck's approach may approach the subject you are talking about. I should say that I am not familiar enough with black-hole physics to have a motivated opinion I intend to read and understand this Maldacena-Susskind paper before discussing more with you on this topic. Meanwhile, may be you can have a look at recent papers by Frédéric Holweck and co-authors (we are now working together) about entanglement and algebraic geometry.

Thanks and best wishes,

Michel

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Lawrence B. Crowell replied on Jul. 16, 2013 @ 04:12 GMT

The program of finding physics with [0, 1, ∞] can be found with the SL(2,C) group and the linear fractional transformation (LFT)

f(z) = (az + b)/(cz + d),

which has a correspondence with matrices of SL(2,C). The Mobius transformation or LFT is an automorphism group on the Argand plane, and this is equivalent to PSL(2,C). This projective linear group is then the automorphism group of C. If we let the constants a, b, c, d be points in C then the LFT

f(z) = [(z - z_1)/(z - z_2)][z_3 - z_2)/(z_3 - z_1)]

is for the identity f(z) = z a case where z_1 = 0, z_3 = 1, and z_2 = ∞. A matrix representation may be found by dividing through by z_i and taking the limit z_i --- > ∞.

From this comparatively simple example we may move up to SL(2,H) and SL(2,O). In the case of SL(2,O) ~ SO(9,1), there is an embedding of SO(9) ~ B_4. This in turn is defined with the short exact sequence

F_4: 1 --- > B_4 ---> F_{52/36} ---> OP^2 --- > 1

where the strange symbol in the middle means that the 52 dimensions of F_4 - the 36 dimensions of B_4 ~ SO(9) defines the OP^2 projective Fano plane or OP^2 ~ F_4/B_4.

The B_4 group is the SUSY group that Susskind employs with the holographic principle.

The group F_4 is a centralizer in the E_8, which means it commutes with the automorphism of E_8, which is G_2. We then have a somewhat Rococo form of the same construction. A projective form of SL(2,O), PSL(2,O), defines matrices ~ aut(O) ~ G_2 which map three points to [0, 1, ∞] with the action of the 7 elements in the Moufang plane. I think I can find this matrix in the near future.

Unfortunately I am moving shortly, so that is complicating plans to do much analysis. If I do this in the immediate future it will have to be in the next week.

Cheers LC

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Dear Lawrence, apologies if this does not apply to you. I have read and

rated your essay and about 50 others. If you have not read, or did not

rate "link:fqxi.org/community/forum/topic/1756] my essay The

Cloud of Unknowing please consider doing so. With best wishes.

Vladimir

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Sorry - here is the link: my essay The Cloud of Unknowing

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Author Lawrence B Crowell replied on Jul. 16, 2013 @ 04:30 GMT

I read your essay sometime bzck. I have a list of these papers and which I have scored. I would probably have to reread or at least refresh myself about your paper. As I recall it is a bit of a metatheory.

Cheers LC

Lawrence

Could you please explain where is your theory connected with Golden ratio?

See part Symmetries... PSL(2,Z)etc

http://en.wikipedia.org/wiki/Golden_ratio

Yuri

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Author Lawrence B Crowell replied on Jul. 17, 2013 @ 15:41 GMT

Yuri,

The polytope for the E8 grop, the Grosette polytope with 240 roots can be decomposed into the icosian of 120. The icosian or 120-cell has two quaternions with length (1/2)(1 +/- sqrt{5}) where the plus one has length 1.618..., which is the golden mean. In fact these quaternions define something called the golden field in a Galois ring. This is related to the Fibonacci sequence.

Cheers LC

Lawrence,

I loved your explanation of modal logic in causality. Very succinct! You brought back pleasant memories of doing symbolic logic in university.

The notion that "causality is necessary incomplete" can also be appreciated from a quantum information point of view using a complex valued system. When an EPR state is prepared, all entropies are conditional on the observer, who is a subsystem in an "EPR-triplet". However, in making a measurement, the observer throws away her entanglement information so that the subsystem of the EPR pair is no longer conditional. (See my essay "A Complex Conjugate Bit and It".)

A quantum correlated system thus becomes a classically correlated system. Using Venn diagrams, it becomes apparent that this process can be interpreted as a change in associativity.

Best wishes,

Richard

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Author Lawrence B Crowell replied on Jul. 17, 2013 @ 17:18 GMT

Richard,

Thanks for the kinds words. I agree that quantum measurements and even quantum teleportation involve the destruction of entanglement. Maybe better put the entanglement is transferred to a reservoir of states in an unpredictable manner. The entropy of the system is then indeed conditional, and a measurement loses this.

I propose that the incompleteness has to do with associativity in QFT. My argument then involves the situation of fields near an event horizon. There is a profound difference between the classical case and the quantum case. I am not clear how this plays with standard quantum measurements. Zeh, as I recall, talks of a quantum horizon. Maybe there is some parallel situation there which makes associators play a role.

I will try to read your essay soon. I am rather slowly getting around to as many as I can.

Cheers LC

Dear Lawrence

Could you please find out explanation of symmetric angles picture between mass of proton and pseudoscalar mesons? This is simple parametrization proceeding.

My essay

http://fqxi.org/community/forum/topic/1818

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Author Lawrence B Crowell replied on Jul. 20, 2013 @ 04:15 GMT

It could be due to some aspect of the eigenvalues for gluons in a supergroup. The icosian has quaternions (roots) that have magnitude given by φ. The icosian is in a sense half of the roots space of the E8 group. The masses of hadrons is determined by the quark masses, which is induced by the Higgs field, and by the confinement properties of the QCD gauge field, called gluons. The differences in these fields in the Y-B plane is given by certain roots, and those roots in some cases have the magnitude of the φ = (1 + sqrt{5})/2

That is about the best I can conjecture at this point. There might in some way be some semblance of reason for this.

LC

Hi Lawrence,

I read your essay some time ago but only now got around to rating it -- was delayed in moving from ITB/Bandung to Thailand. In any case I very much liked the use of associators/non-associativity in your essay. Two FSU colleagues of mine (Merab Gogberashvili and Vladimir Dzhunshaliev) have worked on trying to include non-associativity into QFT. Merab in particular had some mantra about the connection of different algebras to physical quantities to the effect--> real numbers are connected with mass; complex numbers with charges; non-commutative numbers with spin; non-associative numbers with the quantum wave-function (actually I do not recall exactly what the last connection was but it was something to do with the quantum nature of matter). In any case you might find Merab's work of interest. Sorry it took so long to finally read your essay.

Also I noticed your address (or one of them) is in Hungary. In this regard you might be interested in a conference Elias is arranging in Prague, Sept. 1 --5. It is a fairly large and broad conference but some of the workshops would seem related to your line of work. In any case the conference site is http://www.icmsquare.net/

I hope this is not considered "advertising". Anyway if this post is not accepted we'll know :-).

Best,

Doug

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Author Lawrence B Crowell replied on Jul. 20, 2013 @ 13:13 GMT

Doug,

I have read several papers by Vladimir Dzhunshaliev on octonion field theory, and Merab Gogberashvili is a familiar name as well. Trying to understand how nonassociative mathematics of operators fits into physics is really the hard part. I think that quantum mechanics is purely complex, or C. Of course classical mechanics is R. Gauge theory can be written according to quaternions...

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Doug,

I have read several papers by Vladimir Dzhunshaliev on octonion field theory, and Merab Gogberashvili is a familiar name as well. Trying to understand how nonassociative mathematics of operators fits into physics is really the hard part. I think that quantum mechanics is purely complex, or C. Of course classical mechanics is R. Gauge theory can be written according to quaternions H. A lot of gauge theory is done though in standard vector form without quaternions. It is interesting though that Maxwell formulated electromagnetism, the first gauge field theory, in quaternions. Field operators in a second quantization act on a Fock space basis to give quantum amplitudes. So we have a relationship that might be heuristically written as π:H --- > C. The question is then whether there is some sort of higher level structure π:O --- > H.

Spacetime I think offers a clue. A black hole horizon has some quantum uncertainty on a scale near the string or Planck length. There will then be an associative uncertainty with three quantum fields, where one of those fields is identified near the horizon. The standard approach to QFT is to assign a harmonic oscillator at every point in space, impose equal time commutators on that spatial surface with the Wightman criterion for commutation, and work from there. Yet that spatial surface on a small scale will have some noncommutative structure and this will lead to a host of uncertainties in assigning QFT operators. If there are event horizons this should lead to an associative uncertainty.

The above “maps” between C, H and O, where a similar map π:C --- > R would be the relationship between quantum mechanics and classical mechanics, are really just forms of the Hopf fibration. The relationship between quantum and classical mechanics is of course a difficult subject in its own right. With each of these “ladders” on the Hopf fibration there is some increased uncertainty. Quantum mechanics saved physics from the UV divergence that classical mechanics predicted with the hydrogen atom. Similarly this may protect physics from divergences with black holes, such as the singularity and maybe with the current big problem of firewalls.

Thanks for the good word. I had a computer crash (virus attack etc) that erased my voting code. I also had it written down on a paper that also went missing. I have not been able to vote on papers for about a week. The FQXi people have so far not serviced my request that it be retransmitted. I have also been a bit slow in reading papers this contest cycle. I see that you have a paper in the list. I seem to remember that last year your paper was riding fairly high, where mine in contrast tanked.

Cheers LC

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Dear Lawrence,

The title of your essay intrigued me because I think that Wheeler wanted us to recognise the same thing.

I read your essay with much interest (I didn't need to understand the math, because the text was clear) and the conclusion that biology and EVEN consciousness will have to play a role is one that I took as essential inmy own contribution.

After reading the essay it is always informative to read your reactions on the posts, which are very informative. Especially one reaction ( of may 20 02.42 GMT was in full correspondence with my own perception :

"Any scheme for causality is going to be incomplete, it will not be able to encode ALL physical states. As a result it means that there exists a DEEPER FOUNDATION to the Universe" This incompleteness I am trying to describe in the infinite number of tones of grey between the digital entities zero and one.

I really hope that can spare some time to read/comment and rate my essay : "THE QUEST FOR THE PRIMAL SEQUENCE" , I am sure you will find some thoughts we share together for a future approach of reality.

respectfully

Wilhelmus

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Wilhalmus,

I suffered recently a big computer virus crash. This machine had my voting code on it. I have not been able to get the code back in spite of my petition to FQXi.

I think that consciousness has some epiphenomenology with generating the appearance of measurement outcomes. In the MWI context the mind may be what generates the appearance of being on one of the split off worlds. In the Bohr Copenhagen interpretation I think consciousness may play a similar role in the so called collapse. In your idea of created reality (creatality) it might be that this is in some ways a mentally generated illusion.

I will score essays again once I get my voting code back.

Cheers LC

Outstanding Paper. Very Logically based. Extremely competent writing.

Similar conclusion as Torsten Asselmeyer-Maluga (incomputable).

I loved the modal logic foundation of this paper, and the expression of Godel’s second theorem in Modal logic, which I had not seen before.

Your proposal to remove associativity as a physical axiom is a profoundly interesting idea. I see how this introduces a different interpretation for quantum nonlocality (similar in some sense to the paper by Ken Wharton?)

But where you come out clearly ahead in here (my favorite quote from the paper):

“This argument employs sufficient and necessary conditions in a tensed fashion, forwards and backwards in time, to give a causal chain.”

Brilliant.

Your figure (on page ? 3) however, seems to assume an irreversible monotonicity in the order of t1, t2 and t3. Is this what you intended to compare to causal set theory? Was this diagram intended to imply a forwards and backwards in time causal chain?

Nice description of the history of S-Matrix, and a very thought-provoking conclusion regarding black holes.

There is also a wealth of tid-bits of mathematical hints in the paper: very insightful. A very worthy read.

Your conclusion that this (causality and undecideability) is a prospect that may play a role in the emergence of biology and even consciousness is very brave. I hope the orthodoxy does not try to dismiss you for this ;-)

I look forward to seeing more of your work in this area.

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Author Lawrence B Crowell replied on Jul. 23, 2013 @ 04:13 GMT

Paul,

Thanks for the very good word on my paper. I see tht you squeeked in a paper right at the deadline. I have entered several essays and I have generally found that submitting a paper around the middle of the time period for entries is about the best. I will read your paper soon. I had a couple of weeks ago a major virus attack on the machine which held my password. I can't vote for essays until FQXi honors my request to have it retransmitted to me.

My essay was inspird in large part by reading David Foster Wallace. He was a philosopher who managed to actually say something. He was also a good writer with his novels "The Broom of the System" and "Infinite Jest." I was reading his essay on the refutation of Taylor's argument for fatalism, and that sort of inspired my FQXi essay. I was originally planning to sit out this essay cycle. I also use the past tense with Wallace for he committed suicide in 2008 since he suffered major depression. I got a deeper appreciation for this problem because my brother suffered from this as well, and the past tense indicates his death by suicide a little over a year ago. He was a molecular biologist of some standing in that community.

I have been in some exchanges with Asselmeyer-Maluga on these issues. There is a theorem that the number of exotic R^4s is uncountable via the Cantor diagonalization and Godel-Turing undecidability. I worked up some calculations on Hopf links and knots with respect to the exotic smoothness of R^4 spaces. He has been on vacation of late, but should have returned this week or so. Generally I tend to leave people at peace during vacations.

As for your question about the mother-daughter relationship between events, which is in Foster's paper, the modal logic employed has no particular sense of reversibility or irreversibility. One could imagine some register or physical memory which permits one to reverse the direction of this diagram.

Cheers LC

Paul Borrill replied on Aug. 1, 2013 @ 05:41 GMT

Lawrence - Thank you for your reply and pointers to David Foster Wallace and Asselmeyer-Maluga on these issues.

I would be honored by your review of my paper. Please make sure your download the latest version (V1.1a) from the comments section.

Thank you.

Kind regards, Paul

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Author Lawrence B Crowell replied on Aug. 1, 2013 @ 15:33 GMT

Paul,

I am rather intrigued by your paper. I will confess that I think this perspective on time may apply to quantum gravity. I will have to read your paper again to firm up my understanding. The two competing ideas are string theory and loop quantum gravity. In LQG gravitation is background independent. However, this is based ultimately on a classical formalism of general relativity where time does not exist. String theory on the other hand has time, but it is not background independent. It also works best in a holographic perspective where one dimension is reduced near an event horizon. The string/M-theory approach is also best looked at in a dual gauge approach with Yangians, which has some overlap with braid constructions in LQG. So there may be some duality here that has some bearing on your idea about time and entanglement.

Cheers LC

Dear Lawrence,

In particle scenario as undecidability is the negation of probability, the difference in density of the undecidables with the probability density, is proportional to the nonlocal Lagrangian for the actions at distances with the observer, in that the nature of gravity is unexplainable. Thus a string-matter continuum scenario is considered as an alternative in that gravitation emerges as a tensor product of the eigen-rotational string-matter segment.

With best wishes

Jayakar

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Author Lawrence B Crowell replied on Jul. 23, 2013 @ 15:36 GMT

The undecidablity is a generic result for any causal model. A causal model of any sort can be represented as some modal logical system of necessity and possibility. The exact structure of this model is not given, but only that causality involves necessity and possibility. The next step is to make some possible hypothesis on what is undecidable about explicit causal structures in quantum field theory. This is not a derivation of what is undecidable, which in mathematics is not itself decidable and only found on a case by case basis, but only to offer up possible physical axioms that can be “toggled” to an on or off state.

LC

Dear Lawrence,

I think you hit the nail on the head in your two concluding paragraphs. “The incompleteness of metaphysical models illustrates the general nature of incompleteness that translate to standard physics.” “. . . but the existence of physical states implied by this set means that certain physical states can exist for reasons not computed by the “rule book.” The heuristic invoked here is that this concerns the nonlocality of quantum gravity and the existence of a new structure. The physical axiom that is proposed to be removed is associativity.”

And, “The incompleteness of modal causal models is argued to justify nonassociativity as a means towards nonlocality of the quantum gravity field. This is a “bottom-up" type of argument, where an incompleteness of a higher level physics requires a more fundamental physics “further down.” It is entirely possible this could be used to argue for a “top-down” physics with the emergence of higher level properties. There is a prospect this may play a role in the emergence of biology and even consciousness.”

Yes! I think you’re onto something regarding a “top-down” approach towards physics with an eye on the possible emergence of higher level properties. I believe that you have pointed the way towards discovering the emergence of biology and even consciousness from the foundation of physics.

As a non-specialist (I’m an attorney with a deep interest in the subject) I am encouraged by your conclusions and the direction of your thinking, so although there were sections that were beyond my understanding, I thought it was an outstanding essay. Thank you.

Best,

Ralph

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Author Lawrence B Crowell replied on Jul. 24, 2013 @ 16:18 GMT

Ralph,

Thanks for the positive word. The incompleteness extends potentially to various levels, including the dichotomy between the quantum and classical world. Complex structures like organisms impose constraints on the micro-causal systems that compose it. How this occurs is not well known. It is the possible that in addition there is a top-down element to this. The physics of...

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Hi Lawrence,

I do not think that we have a real understanding of "possibility" in physics. We treat possibility as a metaphysical condition (e.g. in arguments against fatalism), but when we then try to describe what is "possible" we fall back on epistemology - what is possible given these data, etc. "These data" always refer to local observations of circumscribed systems recorded in...

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Hi Lawrence,

I do not think that we have a real understanding of "possibility" in physics. We treat possibility as a metaphysical condition (e.g. in arguments against fatalism), but when we then try to describe what is "possible" we fall back on epistemology - what is possible given these data, etc. "These data" always refer to local observations of circumscribed systems recorded in memories using classical information.

Our notion of "causality" is similarly local and classical, in the sense that our representations of "cause" and "effect" are written in classical memories, regardless of the notation used. We write down, for example, a "prepared" quantum state that involves some degrees of freedom and not others. Where did this circumscription come from? From local observations.

If we took non-locality seriously, every "event" would be a quantum state of the entire universe, none of which (for an instantaneous event) is observable from our (or any) perspective. We seem systematically unable to think of events this way, or to envision the universe evolving as a whole. In particular, we do not seem able to envision our own brains/minds/awareness evolving not because of something previous, but as part of what is happening now. This is, however, the situation we are in. We are not observing the universe from the outside, however convenient this may be as an methodological or mathematical assumption.

Hence I would like to distinguish between "the universe is (quantum) computing its next state" and "the universe is a (quantum) computer." If the universe is a quantum computer, the data structure on which it acts is its own, complete state. But this is not what we intuitively mean by "computing" - we intuitively think of computing as acting on a data structure that is external to the process of computation. A Turing machine, for example, makes intuitive sense as doing computation because the head is distinguished from the tape and is seen as acting upon it. In the case of the universe, we do not have this luxury; it is not a case of some unchanging parts acting on others that are changed.

Cheers,

Chris

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The term possibility is not quantified very well for physics. I read a paper quite some years ago which stated possibility and plausibility were "unknown unknows" in a Bayesian sense. It is a probability that is not computable because there is no Bayesian prior estimate. The first part of my essay is metaphysics meant to motivate the need to "toggle" some physical axiom between the "on and off" condition.

Nonlocality of field theory is related to topological quantum field theory (TQFT) A TQFT is a quantum field theory up to homotopy. Physically this means that geometric data is removed and real degrees of freedom are determined by topology. This clearly means the TQFT within some homotopy (or topology) is a class of fields up to the diffeomorphism of space (or spactime). This means that local data concerning geometry is removed by taking a quotient with the space of solutions. In doing this we still want to have some concept of locality, which is usually associated with geometric information. Locality is contained in how the manifold is partitioned into pieces, where locality is defined by how those pieces are joined together. In spacetime this can include a space plus time perspective, where spacetime is defined by thin sections with a local time increment. These pieces have then cobordism defined by spatial surfaces.

A topological quantum field theory may be considered to be any data to every geometric entity from a zero-dimensional point up to an n-dimensional cobordism. The n-functor

Z:bord^m(n) --- > A_n

Where A_n is an algebra of dimension n and the bord^m(n) holds for 0

Hello Lawrence

Richard Feynman in his Nobel Acceptance Speech (http://www.nobelprize.org/nobel_prizes/physics/laureates/19
65/feynman-lecture.html)

said: “It always seems odd to me that the fundamental laws of physics, when discovered, can appear in so many different forms that are not apparently identical at first, but with a little mathematical fiddling you can show the...

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Hello Lawrence

Richard Feynman in his Nobel Acceptance Speech (http://www.nobelprize.org/nobel_prizes/physics/laureates/19
65/feynman-lecture.html)

said: “It always seems odd to me that the fundamental laws of physics, when discovered, can appear in so many different forms that are not apparently identical at first, but with a little mathematical fiddling you can show the relationship. And example of this is the Schrodinger equation and the Heisenberg formulation of quantum mechanics. I don’t know why that is – it remains a mystery, but it was something I learned from experience. There is always another way to say the same thing that doesn’t look at all like the way you said it before. I don’t know what the reason for this is. I think it is somehow a representation of the simplicity of nature.”

I too believe in the simplicity of nature, and I am glad that Richard Feynman, a Nobel-winning famous physicist, also believe in the same thing I do, but I had come to my belief long before I knew about that particular statement.

The belief that “Nature is simple” is however being expressed differently in my essay “Analogical Engine” linked to http://fqxi.org/community/forum/topic/1865 .

Specifically though, I said “Planck constant is the Mother of All Dualities” and I put it schematically as: wave-particle ~ quantum-classical ~ gene-protein ~ analogy- reasoning ~ linear-nonlinear ~ connected-notconnected ~ computable-notcomputable ~ mind-body ~ Bit-It ~ variation-selection ~ freedom-determinism … and so on.

Taken two at a time, it can be read as “what quantum is to classical” is similar to (~) “what wave is to particle.” You can choose any two from among the multitudes that can be found in our discourses.

I could have put Schrodinger wave ontology-Heisenberg particle ontology duality in the list had it comes to my mind!

Since “Nature is Analogical”, we are free to probe nature in so many different ways. And you have touched some corners of it.

Regards

Than Tin

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Lawrence B. Crowell replied on Jul. 25, 2013 @ 04:45 GMT

Than,

Nature has an analogical quality to it, or what I see as recherché --- as with Bach’s “Musical Offering.” Certainly one example is how isospin symmetry is applied to the nuclear physics of protons and neutrons in the MeV range and the same symmetry appears in the theory of weak interactions. I base my argument for the need to toggle on or off physical axioms by appealing to a formal incompleteness of any causal model. Godel’s theorem is a recursive aspect of mathematics where a predicate acts upon its own Godel number as the object.

It is taking me a bit of time to get to many of the essays here. Other pressing concerns mount as well. I will try to get to your essay in the near future. I got an email that the contest deadline has been extended a week. That may allow for a bit more time to get to more of the essays.

Cheers LC

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Dear Lawrence,

I am almost sure that I rated your essay at an earlier time. For any reason my vote was not recorded or lost when the system was interrupted. So I reproduced the vote with a bonus due to the high level of your replies.

Good luck,

Michel

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Author Lawrence B Crowell replied on Jul. 26, 2013 @ 16:49 GMT

Michel,

Thanks. I have been in the process of moving, so my ability to engage FQXi has dropped seriously. I also lost my voting code for a while after the machine I had it on was virus attacked. I got the code back the other day.

I think there are underlying relationships between F4 as the group for the KS theorem in 4-d and G2 as the automorphism of E8. F4 is a centralizer in E8, which means it is a “constant of the motion” with respect to G2. I have long thought that general relativity and quantum mechanics share some common basis along these lines.

Cheers LC

Dear Lawrence,

One single principle leads the Universe.

Every thing, every object, every phenomenon

is under the influence of this principle.

Nothing can exist if it is not born in the form of opposites.

I simply invite you to discover this in a few words,

but the main part is coming soon.

Thank you, and good luck!

I rated your essay accordingly to my appreciation.

Please visit My essay.

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Author Lawrence B Crowell replied on Jul. 29, 2013 @ 14:08 GMT

Amazigh,

One interesting duality principle is with Yangians. This is a duality with fields in a braid description that has connections to twistors.

I will try to get to your paper in the near future. My time is pretty limited right now. I have not had much time to engage this contest very much.

Cheers LC

Hi Lawrence,

Congratulations on a fine essay! But I wonder whether the arguments you advance are against a straw man... pertinent to an abstract and continuous theory of reality, rather than what may actually be a discrete and non-continuous material cosmos. You wrote:

> Physical systems in some funny sense have a premonition about how to evolve.... There is no information...

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Author Lawrence B Crowell replied on Jul. 29, 2013 @ 13:56 GMT

Hugh,

Your comments are interesting and thought provoking. I don’t think that nature is strictly continuous or discrete. I think there is some sort of dualism between the two descriptions of reality. I don’t think either description is complete.

I agree that Godel’s theorem involves infinite systems. The use of the Cantor diagonalization implies an infinite set. The use of...

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Hugh,

Your comments are interesting and thought provoking. I don’t think that nature is strictly continuous or discrete. I think there is some sort of dualism between the two descriptions of reality. I don’t think either description is complete.

I agree that Godel’s theorem involves infinite systems. The use of the Cantor diagonalization implies an infinite set. The use of modal logic and the appeal to Godel’s theorem is somewhat qualitative I will admit. I think to do a full formal analysis of this would be an exhausting piece of work. However, the use of “possibility,” which at best can be interpreted as probabilities with a weak or no Bayesian priors (an unknown unknown) is potentially itself “infinite,” or so large that from a physicist perspective we can consider it infinite. Any algorithmic description of the universe must appeal to primitive recursive functions. The analyst in this view is performing a sort of “cut off,” where the “possibility” extends only to some range of estimated probabilities. This may not necessarily cover all of reality or all possible cases. David Hume made a bit of a point about this. Causality can’t be reduced to logic. I make a point of a connection between Hume’s observation and Godel.

The argument concerning the extension of quantum fields from a quaternion basis to octonions is also qualitative. There is no procedure for finding undecidable propositions; the existence of such a putative procedure is itself undecidable. Godel did manage to derive his proof in reference to Diophantine equations, which amounts to deriving a “special case.” Again trying to find how the extension from H to O is a matter of Godelian incompleteness would be a huge undertaking. So my approach is to appeal to a physical argument rather than formal mathematics. After all, while I have learned a fair amount of advanced mathematics I am still primarily a physicist .

I will try to look at your essay today or in the next few days. From your description it does appear interesting. My time has been terribly constrained the last couple of months. I have to keep in mind that voting ends in about a week.

Thanks for the over all positive assessment.

Cheers LC

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Dear Lawrence,

I guess if you have a list of more than 300 essays to choose from it is inevitable you miss out on some of the best. Yours was indeed very well written and argued even though my position is opposite to yours but I was able to follow your thinking especially areas where not too much math is involved. Very nice.

One of the unprovable/ undecidable proposition in mathematics and theoretical physics is whether the fundamental unit of geometry is a zero dimensional or extended object. When I say unprovable I mean using mathematical theorems. However from logic and reductio ad absurdum type arguments a sort of philosophical proof can be found. This is what I have attempted to do.

Following additional insights gained from interacting with FQXi community members, I improved my essay and wrote a judgement in the case of Atomistic Enterprises Inc. vs. Plato & Ors delivered on Jul. 28, 2013 @ 11:39 GMT. You may enjoy it.

All the best,

Akinbo

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Author Lawrence B Crowell replied on Jul. 31, 2013 @ 16:34 GMT

Dear Akinbo,

I will try to read your essay this evening. I am in the process of moving right now, which is taxing me in a number of way --- in particular the growing ache in my back.

Cheers LC

Hi Lawrence,

I saw you were very busy, did you already have the chance to read my essay : "THE QUEST FOR THE PRIMAL SEQUENCE" ?

and if so did you already receive a new code for voting ?

thank you

Wilhelmus.

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Author Lawrence B Crowell replied on Aug. 4, 2013 @ 15:29 GMT

Wilhelmus,

I got my voting code back a week ago. I pulled up your essay this morning and started to read it. I will though have to score it later today. I am about to close down and get back to work.

Cheers LC

Dear All

Let me go one more round with Richard Feynman.

In the Character of Physical Law, he talked about the two-slit experiment like this “I will summarize, then, by saying that electrons arrive in lumps, like particles, but the probability of arrival of these lumps is determined as the intensity of waves would be. It is this sense that the electron behaves sometimes like a particle and sometimes like a wave. It behaves in two different ways at the same time.

Further on, he advises the readers “Do not keep saying to yourself, if you can possibly avoid it. ‘But how can it be like that?’ because you will get ‘down the drain’, into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that.”

Did he says anything about Wheeler’s “It from Bit” other than what he said above?

Than Tin

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Author Lawrence B Crowell replied on Aug. 4, 2013 @ 15:33 GMT

Hi Than,

I guess I am not sure why you posted this. Feynman was right in what he said and was a critic of the hidden variable people who were trying to build up quantum physics from classical like structures. That is not something I am trying to advance.

LC

Hi LC,

We have been in a few contests together. Most the time your entries give me a headache. Of course this is my fault. Your current essay also gives me a headache, But I like it. The conclusion is rational and to my liking. Also your comment to the effect that the informational standpoint may not be correct, but it could be very useful, I find very insightful.

No need to visit my entry. It will just drive you crazy :)

Your score needs a boost!

Don L.

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Author Lawrence B Crowell replied on Aug. 6, 2013 @ 12:48 GMT

Information is sort of a model system. There is nothing logically determined about causality from an information standpoint.

I am traveling now and can only catch some brief wifi time and the like. I hope to be able to give this contest more consideration before it ends after tomorrow.

Cheers LC

I think the title of your essay pretty much sums up your much more rigorous argument. I'm certainly not a logic master but I think I get the gist of your arguments. The maths are a little esoteric and not totally accessible; however, I think your essay is important because is it one of the more original ones (that I have read). I agree with the conclusion and I think that the possibilities that it opens up are well worth looking into.

Please see my essay: All Your Base Are Belong To Math.

- Kyle Miller

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Dear Lawrence,

We are at the end of this essay contest.

In conclusion, at the question to know if Information is more fundamental than Matter, there is a good reason to answer that Matter is made of an amazing mixture of eInfo and eEnergy, at the same time.

Matter is thus eInfo made with eEnergy rather than answer it is made with eEnergy and eInfo ; because eInfo is eEnergy, and the one does not go without the other one.

eEnergy and eInfo are the two basic Principles of the eUniverse. Nothing can exist if it is not eEnergy, and any object is eInfo, and therefore eEnergy.

And consequently our eReality is eInfo made with eEnergy. And the final verdict is : eReality is virtual, and virtuality is our fundamental eReality.

Good luck to the winners,

And see you soon, with good news on this topic, and the Theory of Everything.

Amazigh H.

I rated your essay.

Please visit My essay.

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Late-in-the-Day Thoughts about the Essays I’ve Read

I am sending to you the following thoughts because I found your essay particularly well stated, insightful, and helpful, even though in certain respects we may significantly diverge in our viewpoints. Thank you! Lumping and sorting is a dangerous adventure; let me apologize in advance if I have significantly misread or misrepresented...

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Late-in-the-Day Thoughts about the Essays I’ve Read

I am sending to you the following thoughts because I found your essay particularly well stated, insightful, and helpful, even though in certain respects we may significantly diverge in our viewpoints. Thank you! Lumping and sorting is a dangerous adventure; let me apologize in advance if I have significantly misread or misrepresented your essay in what follows.

Of the nearly two hundred essays submitted to the competition, there seems to be a preponderance of sentiment for the ‘Bit-from-It” standpoint, though many excellent essays argue against this stance or advocate for a wider perspective on the whole issue. Joseph Brenner provided an excellent analysis of the various positions that might be taken with the topic, which he subsumes under the categories of ‘It-from-Bit’, ‘Bit-from-It’, and ‘It-and-Bit’.

Brenner himself supports the ‘Bit-from-It’ position of Julian Barbour as stated in his 2011 essay that gave impetus to the present competition. Others such as James Beichler, Sundance Bilson-Thompson, Agung Budiyono, and Olaf Dreyer have presented well-stated arguments that generally align with a ‘Bit-from-It’ position.

Various renderings of the contrary position, ‘It-from-Bit’, have received well-reasoned support from Stephen Anastasi, Paul Borrill, Luigi Foschini, Akinbo Ojo, and Jochen Szangolies. An allied category that was not included in Brenner’s analysis is ‘It-from-Qubit’, and valuable explorations of this general position were undertaken by Giacomo D’Ariano, Philip Gibbs, Michel Planat and Armin Shirazi.

The category of ‘It-and-Bit’ displays a great diversity of approaches which can be seen in the works of Mikalai Birukou, Kevin Knuth, Willard Mittelman, Georgina Parry, and Cristinel Stoica,.

It seems useful to discriminate among the various approaches to ‘It-and-Bit’ a subcategory that perhaps could be identified as ‘meaning circuits’, in a sense loosely associated with the phrase by J.A. Wheeler. Essays that reveal aspects of ‘meaning circuits’ are those of Howard Barnum, Hugh Matlock, Georgina Parry, Armin Shirazi, and in especially that of Alexei Grinbaum.

Proceeding from a phenomenological stance as developed by Husserl, Grinbaum asserts that the choice to be made of either ‘It from Bit’ or ‘Bit from It’ can be supplemented by considering ‘It from Bit’ and ‘Bit from It’. To do this, he presents an ‘epistemic loop’ by which physics and information are cyclically connected, essentially the same ‘loop’ as that which Wheeler represented with his ‘meaning circuit’. Depending on where one ‘cuts’ the loop, antecedent and precedent conditions are obtained which support an ‘It from Bit’ interpretation, or a ‘Bit from It’ interpretation, or, though not mentioned by Grinbaum, even an ‘It from Qubit’ interpretation. I’ll also point out that depending on where the cut is made, it can be seen as a ‘Cartesian cut’ between res extensa and res cogitans or as a ‘Heisenberg cut’ between the quantum system and the observer. The implications of this perspective are enormous for the present It/Bit debate! To quote Grinbaum: “The key to understanding the opposition between IT and BIT is in choosing a vantage point from which OR looks as good as AND. Then this opposition becomes unnecessary: the loop view simply dissolves it.” Grinbaum then goes on to point out that this epistemologically circular structure “…is not a logical disaster, rather it is a well-documented property of all foundational studies.”

However, Grinbaum maintains that it is mandatory to cut the loop; he claims that it is “…a logical necessity: it is logically impossible to describe the loop as a whole within one theory.” I will argue that in fact it is vital to preserve the loop as a whole and to revise our expectations of what we wish to accomplish by making the cut. In fact, the ongoing It/Bit debate has been sustained for decades by our inability to recognize the consequences that result from making such a cut. As a result, we have been unable to take up the task of studying the properties inherent in the circularity of the loop. Helpful in this regard would be an examination of the role of relations between various elements and aspects of the loop. To a certain extent the importance of the role of relations has already been well stated in the essays of Kevin Knuth, Carlo Rovelli, Cristinel Stoica, and Jochen Szangolies although without application to aspects that clearly arise from ‘circularity’. Gary Miller’s discussion of the role of patterns, drawn from various historical precedents in mathematics, philosophy, and psychology, provides the clearest hints of all competition submissions on how the holistic analysis of this essential circular structure might be able to proceed.

In my paper, I outlined Susan Carey’s assertion that a ‘conceptual leap’ is often required in the construction of a new scientific theory. Perhaps moving from a ‘linearized’ perspective of the structure of a scientific theory to one that is ‘circularized’ is just one further example of this kind of conceptual change.

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Author Lawrence B Crowell replied on Aug. 6, 2013 @ 12:44 GMT

Thanks for the long post here in a summary of things. I am on the road right now and can only catch some brief wifi time. I think "If from Bit" and the converse is similar to issues of causality. there is nothing that id determined about either. They are in a sense model systems imposed by us.

Cheers LC

Hi, Lawrence,

Excellent essay, and were your answers to the comments. In one of them, you suggested that the link discovered by Dyson and Montgomery (which has become popularized as the tongue-in-cheek spectrum of the hypothetical "Riemannium") might indeed prove useful in quantum gravity. This is a tantalizing possibility.

What I am a little queasy about is the possibility of inferences by your readers that may be made from your use of the undecidability of an axiom system for Physics. As you pointed out, Gödel's theorem stops the ability of any given system (which fulfills certain conditions, a clause that you left implicit) to prove its own consistency. However, Gödel's second Incompleteness theorem does not stop this system from having its consistency proven by an extension of that system. Whereas it appears from Bell versus EPR that physics is perforce incomplete, this is not the same incompleteness of Gödel's first theorem. That is, one cannot mix ontological and epistemological uncertainties, even though both exist. (It is a mixture that is tempting, of course: see, for example, the Penrose-Lucas fallacy.)

Epistemologically one cannot prove a given non-trivial description of the universe consistent except by appealing to a higher description, yet paradoxically there is a sort of "existence proof" of the possible existence of such a description, since a model for one exists, namely the universe itself. (This does not mean that this hypothetical description would eliminate the ontological uncertainties.)

Best regards,

David

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Author Lawrence B Crowell replied on Aug. 8, 2013 @ 04:19 GMT

The second theorem tells us that an undecidable theorem is self-referentially true. It may be added to the axiomatic system as an extended system. This new system is consistent or ω-consistent. In a sense that is what I argue, where I argue we should extend the system to one where associativity in general does not hold. We might think of P = not-associativity as the proposition which has a Godel number n(p) = gn(P) such that not[prove(n(p))] is true. Hence P must be true, for if it were false this would be a contradiction.

Of course I do not demonstrate this, but rather argue for the case. There must be some level of undecidability, and a reasonable target I suggest is with associativity. The argument is more based on physical arguments than strict logic. There is no procedure for finding undecidably true propositions in formal systems.

Cheers LC

Hi Lawrence,

I wanted you to know that I read and enjoyed your essay. It took me a little while to work through, mind you, but it was interesting and educational. I especially appreciate the comments about non-associativity and a new form of non-locality. It makes sense that the boundary zone at the event horizon would be highly indeterminate due to spacetime fluctuations and this would make uncertain to define what is inside the BH or just outside it.

There is a definite correspondence as what is within which parentheses in non-associative algebras much like the interiority and exteriority is at the event horizon boundary - one can't just change places.

All the Best,

Jonathan

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Author Lawrence B Crowell replied on Aug. 8, 2013 @ 04:24 GMT

This seems like a fair to decent argument for why there is a role for nonassociatity in physics. A fair amount of octonion work has been done where people just assume nonassociative operators. This seems to connect a physical argument for such with some structure for axiomatic structure; where that structure being a causal (modal) system.

Cheers LC

Jonathan J. Dickau replied on Aug. 8, 2013 @ 23:57 GMT

My congratulations Lawrence!

Your high placement with this essay is well-deserved. I think the expert panel will find a lot to like about it, as did I. Good luck in the finals.

Regards,

Jonathan

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Author Lawrence B Crowell replied on Aug. 9, 2013 @ 13:15 GMT

My essay was basically a two week effort. I happened to be rereading David Wallace’s article that refutes the fatalism of Taylor when this idea leapt out at me. I was not planning on submitting an essay this cycle. So with a week of analysis and another week of writing I put this together.

There is a mathematical theory of unbounded but finite mathematics by Jan Mycielski, that I was recently made aware of. This is maybe useful for this work, for physics usually involves finite systems or involves finite numbers that are measured. I have been pondering whether some Godel numbering scheme that maps quantum numbers to integral solutions of Diophantine equations in this setting might lead to a finite and unbounded version of the Godel theorem. This might provide a more firm understanding of what my essay proposes.

Cheers LC

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Jonathan J. Dickau replied on Aug. 9, 2013 @ 18:18 GMT

Thanks Lawrence,

I appreciate the reference to the work of David Foster Wallace and Jan Mycielski. Gleaning what I could about the Wallace paper it seems your line of reasoning or inspiration runs something like this. You saw in the paper refuting Taylor's work on fatalism a hint that there is a divergence in principle from a purely deterministic view, when using modal logics, and that this has an analogy to non-associative algebras and related structures.

Is that about right?

Regards,

Jonathan

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Author Lawrence B Crowell replied on Aug. 10, 2013 @ 13:06 GMT

Deterministic models of a logical form, such as states defined in some automata model that are mapped into other states in a Turing machine type of logic, are not formally complete. It is not possible to codify such causal models in a complete manner. This was the motivation for this development of mine.

There does appear to be some prospect for pushing this into a more refined form. Godel’s theorem is applicable for infinite sets or formal systems with an infinite number of propositions or predicates. The mathematics of unbounded but finite (finite structures which are not a completion of a formal system) structures might be a way of addressing this in a more complete manner.

LC

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I replied to your comment above.

All the Best,

Jonathan

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Hi LC,

Welcome back within the finalists and congrats for the excellent result. Now let us cross the fingers for the final judgement by the FQXi experts panel.

Cheers,

Ch.

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Author Lawrence B Crowell replied on Aug. 10, 2013 @ 13:08 GMT

This essay did finish a bit better than the one I wrote last year. I guess we have a fairly long wait to see how the final judging occurs. That will be around the end of October.

LC