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FQXi BLOGS

April 23, 2018

I’ve been pondering realism for the past few months. In particular I’ve been thinking about Bell’s theorem, and FQXi member Joy Christian’s claimed disproof of it. I recently posted a paper on this (http://arxiv.org/abs/1107.1007) and I’d like to discuss the topic here.

You can watch Joy Christian describing his research at FQXi’s 2009 conference in the Azores below:

(After reading my post, you should also read Joy Christian's response: here.)

Some background: John Bell coined the word “beable” to capture the essence of any realistic theory of nature. It is made of two parts: “Be” as in Hamlet’s tortured question, “To Be or Not To Be?”, and “able”, an ending shared with “Observ-able”. Beables were supposed to be the building blocks of the observable. If beables exist, however, then they are at odds with quantum mechanics because quantum mechanics on predicts only probabilistic outcomes and also it claims to be complete. (There is a fundamental theorem by Gleason which states that the only prescription of obtaining predictions in quantum mechanics is what quantum mechanics is using. What this means is that quantum mechanics is unique and cannot be improved upon any further.)

For the strong believer in realism there was only a way out: quantum mechanics is incomplete. This is the conclusion reached by Einstein, Podolski, and Rosen in now their famous EPR paper. If quantum mechanics is incomplete, then there must be some hidden variable, some “beable”, theory which captures the essence of nature. These beables cannot be directly measured in any experiments carried out by us, as clumsy macroscopical beasts in the flimsy world of atomic domain. The experimenter must be a hopeless “bull in a china shop,” trampling delicate beables when making any measurement.

For a long time after the EPR paper, neither the realists, nor the supporters and practitioners of quantum mechanics could convince the other that their viewpoint was right. Then Bohm found a hidden variable theory, which claimed to recover all predictions of quantum mechanics, and yet it was a realistic theory. That may sound too good to be true, but the price Bohm paid for this was introducing instantaneous action at a distance. Later on, more serious problems were discovered in his model, like its inability to have a realistic description for spin. (For me what I find disturbing in the Bohmian model is how the hydrogen atom is described: two opposite electric charges standing still at a fixed distance from each other.)

However, after Bohm introduced his model, John Bell studied it in detail and played with other hidden variables models, attempting to find a conclusive proof in favor of realism. Specifically, John Bell was studying the correlations of two physical systems separated at a large enough distances that relativity forbids communication between them during the measurement. What he found in the end (and not without irony) was a result now called Bell’s theorem, which was a turning point in the demise of all hidden variable theories.

So why is Bell’s theorem special? After all, we see correlations in our daily lives and no quantum mechanics is required. For example, if I have one glove in each pocket, and I extract a left glove from my right pocket, I know with certainty without looking that the right glove is left in my left pocket. But here is the catch: if quantum mechanics is right, there are residual effects of its inherent randomness which would result in additional correlations that cannot be explained by any hidden variable theory. We may be clumsy macroscopic objects, but John Bell found a way to circumvent this limitation. And now the discussion between realists and quantum mechanics can come down from the rarefied air of philosophical discussions into experimental verification. The experiment was performed by Aspect and nature ruled in favor of quantum mechanics. Quantum systems exhibit this funny behavior called entanglement where the best knowledge of the whole system does not contain the best knowledge of the subsystems. Hidden variable theories are dead; case closed and let’s move on. Or so it seemed.

But the story does not end there. Along comes FQXi’s Joy Christian, who recently made a very bold and provocative statement: Bell’s theorem is wrong.

Christian argues that Bell proved his theorem by making a “topological error” and by demanding that beables must commute with each other. To see he argument, take rotations in 3-dimensions, for example. It can qualify for the beable status because rotations are trivial macroscopic classical operations. Yet, if you perform two rotations around different axes on a body, you’ll find that the end result depends on the order you carry out the rotations. (If you don’t believe it, there’s a cute demonstration here using a rotating panda.)

Rotations, then, are non-commutative. Therefore it looks like one of the assumptions in John Bell’s theorem is artificial and not physically justified. So what happens if this assumption of commutativity is dropped? Here is the remarkable thing: Joy Christian managed to prove in several important cases that entanglement is an illusion due to our commutative prejudice, and complete separable descriptions—that is descriptions of the two physically separated subsystems independent of each other—are possible.

It was at this point that I became very interested in his result, and recently I had completed an analysis of it attempting to put the result in the proper context (http://arxiv.org/abs/1107.1007). Let me try to explain Joy Christian’s results and why, in my opinion, the claim that Bell’s theorem is wrong in not fully justified.

The way Joy Christian proceeds is by counting all elements of reality in a given experimental setting, meaning that he counts both factuals and counterfactuals. This is not what usually is understood in the context of Bell’s theorem, which is supposed to explain correlations between actual experimental results, but let’s follow along. The space of all actuals and counterfactuals forms a topological space. For example, in Bohm’s variant of the EPR experiment, the experimenter measures spin on one direction, and the outcome can be plus or minus one. The topology of the actual results is a disconnected set of two points (plus and minus one), while the topology of all actuals and counterfactuals is an ordinary two-dimensional sphere corresponding to measuring spin on all possible directions in space. This “S2” sphere is embedded into an “S3” sphere where the so-called Hopf fibration construction is possible.

(The reason “S3” is used is because “S3” is parallelizable. To see what this means let’s start with a regular 3-dimensional sphere S2 and use the so-called “hairy ball theorem”. Imagine adding hair at any point on this sphere. Then try to comb the hair continuously with no singularities anywhere. This cannot be done: there will always be at least one singularity (in an actual head called a cowlick). S3 is different because this combing can always be performed. The “combed hair” in S3 can represent for example a vector field arising from tracing a particular dynamical evolution of the system. When you can always comb without singularity a manifold, that manifold is called parallelizable.)

So here is Joy Christian’s prescription: start with an experimental setting, count all potential experimental outcomes, and then embed this result in a parallelizable manifold. Call the resulting topological space Omega and this represents elements of reality or beables. The particular parallelizable manifolds Joy Christian used were spheres. There are only 4 spheres which are parallelizable: S0, S1, S3, and S7 corresponding to the four normed division algebras: real numbers, complex numbers, quaternions, and octonions. There are other parallelizable manifolds, but the spheres enjoy an additional property critical for disproving Bell’s theorem: in any normed division algebra, the norm of the product is the product of the norms. This core property is the key of proving entanglement wrong because one can “disentangle” or separate the whole into parts neatly. This method was applied for the original spin one half EPR-Bohm experiment, for GHZ states, and for Hardy-type theorems. So it seems that Bell’s theorem was “disproved” by counterexample.

The original reaction of the physics community was to search for mathematical errors in Joy Christian’s arguments. Joy Christian uses geometric algebra for his results, and many original criticisms were plagued by mistakes in using this unusual mathematical formalism.

So is Joy Christian right or wrong? Both actually. His counterexamples are valid entangle-free realistic models. This is were he is right. But one still cannot exceed Bell’s classical correlations using only local resources. Rotations as beables are not “actionable beables” and any mechanical device realizing them in forms of gears like the ones used in clocks, for example, cannot exceed Bell’s correlations for spatially separated subsystems because relativity forbids rigid bodies. In fact there are two theorems by Clifton (arXiv:quant-ph/9711009v1) demanding commutativity for beables in two very critical cases: relativistic field theories with bounded energies, and for what I would call “non-contextual ontologies”. Joy Christian counterexamples are in fact contextual “environmental” hidden variable theories. What do we mean by that? Broadly speaking hidden variable theories falls into two main classes: contextual and non-contextual, while the non-contextual ones sub-separate into two more subclasses: “algebraic” and “environmental”. It takes too long to explain in detail here, so I will take a shortcut instead.

Let’s take a look at the space Omega. The topology of this space depends critically on which experiments are about to be performed. For the same initial preparation of the system, select different measurements and you may get different separable beables and hidden variables. The ontology of the realistic model is contextual (dependent) on the experimental setting. Contextual realism is almost a contradiction of terms. All interpretations of quantum mechanics aimed at explaining it in usual classical terms suffer from a problem or another: Bohm’s theory demands a faster than the speed of light “quantum potential”, transactional interpretation uses signals from the future, etc. Joy Christian’s local realistic model demands a contextual ontology which is at least just as strange as quantum mechanics itself. Common sense everyday activities have no place for contextual ontology—althoughpoliticians love contextual ontology as they usually claim: “I was not flip-flopping, I was merely cited out of context”, to an average person this is a sign of dishonesty and not a valid explanation. (Who knows, maybe if Nixon had known about quantum mechanics, he would have said: but this is how quantum mechanics and nature works, I am not a crook.)

Joy Christian’s examples cannot be non-contextual hidden variable theories as they are ruled out by the Kochen-Specker theorem. They cannot be algebraic hidden variables theories because all predictions of quantum mechanics are recovered in the particular experimental setting. The only possibility left are environmental contextual hidden variable theories. And indeed, one can find a particular example where this becomes explicit: an EPR-Bohm experiment with spin one particles (the Heywood-Redhead experiment). The beauty of this experiment is two-fold. First, for spin one, we can use the Kochen-Specker theorem and prove that all hidden variable theories in this case are contextual. Second, Howell and collaborators (arXiv:quant-ph/0105132v2) showed the equivalence of this experiment with two spin one-half EPR-Bohm settings where we can apply directly Joy Christian’s analysis. All that is left to do is to marry the two lines of argument and show explicitly that indeed Joy Christian’s model for spin one-half is a contextual environmental hidden variable model.

So now is time to tally up the pluses and minuses of Joy Christian’s claims.

On the plus side:

Joy Christian’s results are important because they show that entangled particles can be disentangled sometimes in a particular mathematical formalism. Entanglement is no longer universal as it depends on the mathematical formalism used. Bell’s theorem alone cannot rule out all contextual hidden variable theories obeying local realism. Joy Christian’s result does chip away some of the importance and glamour from Bell’s theorem, as it cannot be regarded anymore as the silver bullet which killed all hidden variable theories.

On the minus side:

Bell’s limit from Bell’s theorem still stands and local realistic models of quantum mechanics are still not possible for ALL experimental contexts. Bell’s theorem is not “disproved” mathematically because Joy Christian starts with different mathematical assumptions. Bell’s theorem importance is not “disproved” because Bell’s limits continue to stand for all local operations and classical communication processes. Bell’s and Clifton's theorems together now do the job of what people originally attributed to Bell’s theorem alone. Hidden variable theories remain a dead end in physics.

I'm grateful to Joy Christian for posting his response to my thoughts: "Quantum Music from a Classical Sphere".

this post has been edited by the forum administrator

report post as inappropriate

You can watch Joy Christian describing his research at FQXi’s 2009 conference in the Azores below:

(After reading my post, you should also read Joy Christian's response: here.)

Some background: John Bell coined the word “beable” to capture the essence of any realistic theory of nature. It is made of two parts: “Be” as in Hamlet’s tortured question, “To Be or Not To Be?”, and “able”, an ending shared with “Observ-able”. Beables were supposed to be the building blocks of the observable. If beables exist, however, then they are at odds with quantum mechanics because quantum mechanics on predicts only probabilistic outcomes and also it claims to be complete. (There is a fundamental theorem by Gleason which states that the only prescription of obtaining predictions in quantum mechanics is what quantum mechanics is using. What this means is that quantum mechanics is unique and cannot be improved upon any further.)

For the strong believer in realism there was only a way out: quantum mechanics is incomplete. This is the conclusion reached by Einstein, Podolski, and Rosen in now their famous EPR paper. If quantum mechanics is incomplete, then there must be some hidden variable, some “beable”, theory which captures the essence of nature. These beables cannot be directly measured in any experiments carried out by us, as clumsy macroscopical beasts in the flimsy world of atomic domain. The experimenter must be a hopeless “bull in a china shop,” trampling delicate beables when making any measurement.

For a long time after the EPR paper, neither the realists, nor the supporters and practitioners of quantum mechanics could convince the other that their viewpoint was right. Then Bohm found a hidden variable theory, which claimed to recover all predictions of quantum mechanics, and yet it was a realistic theory. That may sound too good to be true, but the price Bohm paid for this was introducing instantaneous action at a distance. Later on, more serious problems were discovered in his model, like its inability to have a realistic description for spin. (For me what I find disturbing in the Bohmian model is how the hydrogen atom is described: two opposite electric charges standing still at a fixed distance from each other.)

However, after Bohm introduced his model, John Bell studied it in detail and played with other hidden variables models, attempting to find a conclusive proof in favor of realism. Specifically, John Bell was studying the correlations of two physical systems separated at a large enough distances that relativity forbids communication between them during the measurement. What he found in the end (and not without irony) was a result now called Bell’s theorem, which was a turning point in the demise of all hidden variable theories.

So why is Bell’s theorem special? After all, we see correlations in our daily lives and no quantum mechanics is required. For example, if I have one glove in each pocket, and I extract a left glove from my right pocket, I know with certainty without looking that the right glove is left in my left pocket. But here is the catch: if quantum mechanics is right, there are residual effects of its inherent randomness which would result in additional correlations that cannot be explained by any hidden variable theory. We may be clumsy macroscopic objects, but John Bell found a way to circumvent this limitation. And now the discussion between realists and quantum mechanics can come down from the rarefied air of philosophical discussions into experimental verification. The experiment was performed by Aspect and nature ruled in favor of quantum mechanics. Quantum systems exhibit this funny behavior called entanglement where the best knowledge of the whole system does not contain the best knowledge of the subsystems. Hidden variable theories are dead; case closed and let’s move on. Or so it seemed.

But the story does not end there. Along comes FQXi’s Joy Christian, who recently made a very bold and provocative statement: Bell’s theorem is wrong.

Christian argues that Bell proved his theorem by making a “topological error” and by demanding that beables must commute with each other. To see he argument, take rotations in 3-dimensions, for example. It can qualify for the beable status because rotations are trivial macroscopic classical operations. Yet, if you perform two rotations around different axes on a body, you’ll find that the end result depends on the order you carry out the rotations. (If you don’t believe it, there’s a cute demonstration here using a rotating panda.)

Rotations, then, are non-commutative. Therefore it looks like one of the assumptions in John Bell’s theorem is artificial and not physically justified. So what happens if this assumption of commutativity is dropped? Here is the remarkable thing: Joy Christian managed to prove in several important cases that entanglement is an illusion due to our commutative prejudice, and complete separable descriptions—that is descriptions of the two physically separated subsystems independent of each other—are possible.

It was at this point that I became very interested in his result, and recently I had completed an analysis of it attempting to put the result in the proper context (http://arxiv.org/abs/1107.1007). Let me try to explain Joy Christian’s results and why, in my opinion, the claim that Bell’s theorem is wrong in not fully justified.

Key-Ring Model of Hopf Fibration |

(The reason “S3” is used is because “S3” is parallelizable. To see what this means let’s start with a regular 3-dimensional sphere S2 and use the so-called “hairy ball theorem”. Imagine adding hair at any point on this sphere. Then try to comb the hair continuously with no singularities anywhere. This cannot be done: there will always be at least one singularity (in an actual head called a cowlick). S3 is different because this combing can always be performed. The “combed hair” in S3 can represent for example a vector field arising from tracing a particular dynamical evolution of the system. When you can always comb without singularity a manifold, that manifold is called parallelizable.)

So here is Joy Christian’s prescription: start with an experimental setting, count all potential experimental outcomes, and then embed this result in a parallelizable manifold. Call the resulting topological space Omega and this represents elements of reality or beables. The particular parallelizable manifolds Joy Christian used were spheres. There are only 4 spheres which are parallelizable: S0, S1, S3, and S7 corresponding to the four normed division algebras: real numbers, complex numbers, quaternions, and octonions. There are other parallelizable manifolds, but the spheres enjoy an additional property critical for disproving Bell’s theorem: in any normed division algebra, the norm of the product is the product of the norms. This core property is the key of proving entanglement wrong because one can “disentangle” or separate the whole into parts neatly. This method was applied for the original spin one half EPR-Bohm experiment, for GHZ states, and for Hardy-type theorems. So it seems that Bell’s theorem was “disproved” by counterexample.

The original reaction of the physics community was to search for mathematical errors in Joy Christian’s arguments. Joy Christian uses geometric algebra for his results, and many original criticisms were plagued by mistakes in using this unusual mathematical formalism.

So is Joy Christian right or wrong? Both actually. His counterexamples are valid entangle-free realistic models. This is were he is right. But one still cannot exceed Bell’s classical correlations using only local resources. Rotations as beables are not “actionable beables” and any mechanical device realizing them in forms of gears like the ones used in clocks, for example, cannot exceed Bell’s correlations for spatially separated subsystems because relativity forbids rigid bodies. In fact there are two theorems by Clifton (arXiv:quant-ph/9711009v1) demanding commutativity for beables in two very critical cases: relativistic field theories with bounded energies, and for what I would call “non-contextual ontologies”. Joy Christian counterexamples are in fact contextual “environmental” hidden variable theories. What do we mean by that? Broadly speaking hidden variable theories falls into two main classes: contextual and non-contextual, while the non-contextual ones sub-separate into two more subclasses: “algebraic” and “environmental”. It takes too long to explain in detail here, so I will take a shortcut instead.

Let’s take a look at the space Omega. The topology of this space depends critically on which experiments are about to be performed. For the same initial preparation of the system, select different measurements and you may get different separable beables and hidden variables. The ontology of the realistic model is contextual (dependent) on the experimental setting. Contextual realism is almost a contradiction of terms. All interpretations of quantum mechanics aimed at explaining it in usual classical terms suffer from a problem or another: Bohm’s theory demands a faster than the speed of light “quantum potential”, transactional interpretation uses signals from the future, etc. Joy Christian’s local realistic model demands a contextual ontology which is at least just as strange as quantum mechanics itself. Common sense everyday activities have no place for contextual ontology—althoughpoliticians love contextual ontology as they usually claim: “I was not flip-flopping, I was merely cited out of context”, to an average person this is a sign of dishonesty and not a valid explanation. (Who knows, maybe if Nixon had known about quantum mechanics, he would have said: but this is how quantum mechanics and nature works, I am not a crook.)

Joy Christian’s examples cannot be non-contextual hidden variable theories as they are ruled out by the Kochen-Specker theorem. They cannot be algebraic hidden variables theories because all predictions of quantum mechanics are recovered in the particular experimental setting. The only possibility left are environmental contextual hidden variable theories. And indeed, one can find a particular example where this becomes explicit: an EPR-Bohm experiment with spin one particles (the Heywood-Redhead experiment). The beauty of this experiment is two-fold. First, for spin one, we can use the Kochen-Specker theorem and prove that all hidden variable theories in this case are contextual. Second, Howell and collaborators (arXiv:quant-ph/0105132v2) showed the equivalence of this experiment with two spin one-half EPR-Bohm settings where we can apply directly Joy Christian’s analysis. All that is left to do is to marry the two lines of argument and show explicitly that indeed Joy Christian’s model for spin one-half is a contextual environmental hidden variable model.

So now is time to tally up the pluses and minuses of Joy Christian’s claims.

On the plus side:

Joy Christian’s results are important because they show that entangled particles can be disentangled sometimes in a particular mathematical formalism. Entanglement is no longer universal as it depends on the mathematical formalism used. Bell’s theorem alone cannot rule out all contextual hidden variable theories obeying local realism. Joy Christian’s result does chip away some of the importance and glamour from Bell’s theorem, as it cannot be regarded anymore as the silver bullet which killed all hidden variable theories.

On the minus side:

Bell’s limit from Bell’s theorem still stands and local realistic models of quantum mechanics are still not possible for ALL experimental contexts. Bell’s theorem is not “disproved” mathematically because Joy Christian starts with different mathematical assumptions. Bell’s theorem importance is not “disproved” because Bell’s limits continue to stand for all local operations and classical communication processes. Bell’s and Clifton's theorems together now do the job of what people originally attributed to Bell’s theorem alone. Hidden variable theories remain a dead end in physics.

I'm grateful to Joy Christian for posting his response to my thoughts: "Quantum Music from a Classical Sphere".

this post has been edited by the forum administrator

report post as inappropriate

The issue with the parallelizable spheres and the topology which Joy Christian cites as the error in Bell’s theorem may suffer from a little problem. The Hopf fibration

S^3 -- > S^7 --- > S^4,

defines the Hopf invariant, which tells us how to link 3 dimensional spheres in 7 dimensions. The S^7 satisfies the Hopf fibration at the next level

S^7 -- > S^15 --- > S^8

Where the three spinors which span S^3 exist in 7 combinations according to the Fano plane “rules,” and these are dual to the S^4 elements which include the unit plus three e_i elements, again in 7 possible combintations. This has some deep implications, which includes this matter of commutative beables. We may then say that the quaternion field data on the S^4 is equivalent to the spinor field data on S^3. This is why the Weyl equations do reproduce the same information as the more compact Dirac equation. By way of illustration I propose how this might fit into field theory, which then brings us to the issue here.

A particular basis of S^3 will obey an associator condition, as will the dual quaterions on S^4. The associator means these two rules then operate in a single system with two groups of 4 qubits which form an exceptional algebra of 8 qubits. These are octonion valued with a basis 1, e_i i = 1, …,7. The nontrivial elements define associative triplets which satisfy multiplication rules on the Fano plane. The triplets define an associative 3-form

Ω^(3)(x, y, z) =

The remaining components are then nonassociative elements of S^8. This nonassociativity means that the structure constant for any algebraic structure is not constant so [e_i, e_j] = 2e_ie_j = t_{ijk}e_k. The associator gives

(e_ie_j)e_k - e_i(e_je_k) = t_{ijl}e_le_k - e_i t_{jkl}e_l

and there is a commutator [e_i, t_{ijk}] =! 0. There is then a teleparallel connection or torsion associated with nonassociativity. To define the nonassociative half of S^8 according to an associative algebra define the four-form

Ω^(4)(w, x, y, z,) = 1/2(< w, x(y-bar z)> - < w, (x, z-bar y>),

over the coassociative algebra dual to the associative subspace . The full eight dimensional space has the two dual operators Ω ± iΦ as the twistor description of the spacetime.

The spacetime is Ω^{(4)} = Re C^4, which has the group action U(4). This is decomposed into U(4) = spin(6)x U(1). The 15 dimensional Spin(6) is a conformal group that contains the Spin(5) ~ SO(3,2) de Sitter isometry group. The remaining 5 parameters from the Spin(6) are a diliton factor and four conformal factors. This is a form of the AdS/CFT correspondence.

The data on the S^3 is given by a Hopf invariant ∫Ω^(3) = 4πn, as the link number. This information is dual to the data on S^4, which is not a parallizable space. Hence the data which is presumed to be missing in the Bell theorem could be argued to be inconsequential.

Cheers LC

report post as inappropriate

S^3 -- > S^7 --- > S^4,

defines the Hopf invariant, which tells us how to link 3 dimensional spheres in 7 dimensions. The S^7 satisfies the Hopf fibration at the next level

S^7 -- > S^15 --- > S^8

Where the three spinors which span S^3 exist in 7 combinations according to the Fano plane “rules,” and these are dual to the S^4 elements which include the unit plus three e_i elements, again in 7 possible combintations. This has some deep implications, which includes this matter of commutative beables. We may then say that the quaternion field data on the S^4 is equivalent to the spinor field data on S^3. This is why the Weyl equations do reproduce the same information as the more compact Dirac equation. By way of illustration I propose how this might fit into field theory, which then brings us to the issue here.

A particular basis of S^3 will obey an associator condition, as will the dual quaterions on S^4. The associator means these two rules then operate in a single system with two groups of 4 qubits which form an exceptional algebra of 8 qubits. These are octonion valued with a basis 1, e_i i = 1, …,7. The nontrivial elements define associative triplets which satisfy multiplication rules on the Fano plane. The triplets define an associative 3-form

Ω^(3)(x, y, z) =

The remaining components are then nonassociative elements of S^8. This nonassociativity means that the structure constant for any algebraic structure is not constant so [e_i, e_j] = 2e_ie_j = t_{ijk}e_k. The associator gives

(e_ie_j)e_k - e_i(e_je_k) = t_{ijl}e_le_k - e_i t_{jkl}e_l

and there is a commutator [e_i, t_{ijk}] =! 0. There is then a teleparallel connection or torsion associated with nonassociativity. To define the nonassociative half of S^8 according to an associative algebra define the four-form

Ω^(4)(w, x, y, z,) = 1/2(< w, x(y-bar z)> - < w, (x, z-bar y>),

over the coassociative algebra dual to the associative subspace . The full eight dimensional space has the two dual operators Ω ± iΦ as the twistor description of the spacetime.

The spacetime is Ω^{(4)} = Re C^4, which has the group action U(4). This is decomposed into U(4) = spin(6)x U(1). The 15 dimensional Spin(6) is a conformal group that contains the Spin(5) ~ SO(3,2) de Sitter isometry group. The remaining 5 parameters from the Spin(6) are a diliton factor and four conformal factors. This is a form of the AdS/CFT correspondence.

The data on the S^3 is given by a Hopf invariant ∫Ω^(3) = 4πn, as the link number. This information is dual to the data on S^4, which is not a parallizable space. Hence the data which is presumed to be missing in the Bell theorem could be argued to be inconsequential.

Cheers LC

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Hi Lawrence,

Nice to see your post here. I am a bit confused about your last paragraph: "The data on the S^3 is given by a Hopf invariant ∫Ω^(3) = 4πn, as the link number. This information is dual to the data on S^4, which is not a parallizable space. Hence the data which is presumed to be missing in the Bell theorem could be argued to be inconsequential."

Is your point that duality between a parallelizable manifold and a non-parallelizable one causes trouble? If yes, I have an argument why this is not important, if no, I did not get your point and please clarify it.

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Nice to see your post here. I am a bit confused about your last paragraph: "The data on the S^3 is given by a Hopf invariant ∫Ω^(3) = 4πn, as the link number. This information is dual to the data on S^4, which is not a parallizable space. Hence the data which is presumed to be missing in the Bell theorem could be argued to be inconsequential."

Is your point that duality between a parallelizable manifold and a non-parallelizable one causes trouble? If yes, I have an argument why this is not important, if no, I did not get your point and please clarify it.

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Florin,

My point is that this is clearly not a problem. The octonions define states in two sectors of the form |1abc> and |abcd>, where here the states abcd and so forth sit in four of 8 slots | , , , , , , , >, with the others “blank.” The first entry is the unit and the other seven are the octonions e_i, i = 1, …, 7. Each slot corresponds to an SL(2,C) decomposed from the E_{8(8)}. The stochastic local operations & classical communication group decomposed to SL(2,C)^8 contains nilpotent orbits equivalent to the real valued SL(2,R)^8. The Argand plane C ~ Riemann sphere by stereographic projection, and this “offending” point which causes this disruption is not a part of the orbit set. Therefore the nilpotent orbits on the S^3 are equivalent to those on the S^4. This is a bit informal, but I think this is from a mathematical perspective why this is not a problem.

Cheers LC

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My point is that this is clearly not a problem. The octonions define states in two sectors of the form |1abc> and |abcd>, where here the states abcd and so forth sit in four of 8 slots | , , , , , , , >, with the others “blank.” The first entry is the unit and the other seven are the octonions e_i, i = 1, …, 7. Each slot corresponds to an SL(2,C) decomposed from the E_{8(8)}. The stochastic local operations & classical communication group decomposed to SL(2,C)^8 contains nilpotent orbits equivalent to the real valued SL(2,R)^8. The Argand plane C ~ Riemann sphere by stereographic projection, and this “offending” point which causes this disruption is not a part of the orbit set. Therefore the nilpotent orbits on the S^3 are equivalent to those on the S^4. This is a bit informal, but I think this is from a mathematical perspective why this is not a problem.

Cheers LC

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happy to see people focus on my theory, don't stop.

Insert physical spheres and also the volumes, more my equations ,you shall see the real proportions if the pure serie of the quantum number is inserted also.

The COMMUTATIVITY AND THE ASSOCIATIVITY of course like a torch of foundamentals.

Interesting discussion that said dear Florin and Joy, interesting work and extrapolations. Congratulations.

Steve

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Insert physical spheres and also the volumes, more my equations ,you shall see the real proportions if the pure serie of the quantum number is inserted also.

The COMMUTATIVITY AND THE ASSOCIATIVITY of course like a torch of foundamentals.

Interesting discussion that said dear Florin and Joy, interesting work and extrapolations. Congratulations.

Steve

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Dear Spherical Steve,

Your theory? Joy is working with 7-dimensional spheres that geometrically represent the NON-commutative and NON-associative properties of Octonions as well as the 'expected' properties of commutativity and associativity.

I would further make a case that a rotating sphere (a 7-sphere, a 3-sphere - I do not care which) is unstable due to the Hairy Ball Theorem, and would most likely prefer to 'morph' into a torus of appropriate dimensionality.

Have Fun!

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Your theory? Joy is working with 7-dimensional spheres that geometrically represent the NON-commutative and NON-associative properties of Octonions as well as the 'expected' properties of commutativity and associativity.

I would further make a case that a rotating sphere (a 7-sphere, a 3-sphere - I do not care which) is unstable due to the Hairy Ball Theorem, and would most likely prefer to 'morph' into a torus of appropriate dimensionality.

Have Fun!

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he man, Fuck you ok , I fuck the system and IT IS MY THEORY

BUSINESS MAN

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BUSINESS MAN

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Florin,

Just a tiny detail, not affecting the overall exposition, but I have to tell you, because you may, unwillingly, initiate a misconception about what "parallelizable" means.

S^{3} is indeed parallelizable, but not just because it can be combed. "Uncombable" implies "non parallelizable", but the reverse is not true, hence it is not true that "When you can always comb without singularity a manifold, that manifold is called parallelizable". Take as an example the Moebius strip: one can comb its hair, but one can't find n global vector fields which form a basis to the tangent space at any point. So, to be parallelizable, a manifold has to wear simultaneously n hair-styles which are linear independent at any point.

Cristi

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Just a tiny detail, not affecting the overall exposition, but I have to tell you, because you may, unwillingly, initiate a misconception about what "parallelizable" means.

S

Cristi

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Good catch Cristi,

Thank you for pointing this out. (I was a little sloppy in the blog post).

How do you like the two posts so far? I am trying to make things as clear as possible. I am compiling a massive rebuttal to Joy, (and I am not yet sure on how I will post all of it).

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Thank you for pointing this out. (I was a little sloppy in the blog post).

How do you like the two posts so far? I am trying to make things as clear as possible. I am compiling a massive rebuttal to Joy, (and I am not yet sure on how I will post all of it).

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I'm a little confused. On the one hand, I appreciate Joy Christian's result, and on the other hand I think his conclusions are a bit strained.

One does not dispove a theorem, and I wish the result had not been presented that way. Joy's result might possibly subsume Bell's theorem (though my opinion is reserved for now), but could never replace it. Mathematics doesn't work that way -- no theorem is ever ejected from the canon. "Theorem" MEANS "a mathematically true statement."

I want to respond to Joy's closing statements:

" ... I take measurement results to be the points of a parallelized 7-sphere, whereas Bell incorrectly assumed that they are points of the real line."

This I utterly fail to understand. All measurement results are points of the real line, no matter the domain. That's why arithmetic (and geometric algebba)

are so powerful in describing natural phenomena; a natural counting order is consistent with "real" experience.

"More importantly, my framework is entirely consistent with the EPR criteria of locality, reality, and completeness, and it also fully respects Bell’s own criterion of factorizability. Therefore, in my opinion---although Bell’s theorem may well retain some of its relevance for the information and communication engineering as Florin has argued---it has no relevance for the future 'theory of everything.'"

Actually, by definition, no single theorem has relevance to a theory of everything. This claim is tantamount to saying that the Christian result subsumes all known physics. I don't think he means to go that far.

"Indeed, in the light of my results I believe that the successful 'theory of everything' will be a *locally causal* theory in which contextuality will play a role no different from the role it plays in general relativity. In other words, in my opinion all attempts to build a non-local theory of quantum gravity will fail miserably, just as anticipated by Einstein."

I guess there's no reason that quantum mechanics -- which is incoherent without nonlocality -- can't be subsumed by a local theory of quantum gravity. However, it brings into question what one means by "local" when extending causality to 8 dimensions. I don't see the enchantment of S^7. As my ICCS 2006 paper details (see esp.discussion pp 8 - 9 and figs 1 & 2), S^3 is sufficient to allow continuation over S^n manifolds while preserving commutativity (and Poincare recurrence) on S^3. So S^3 (the space of general relativity) is the "special" topology; I don't see that the loss of closed algebraic properties in the "hyper" numbers -- quaternions and octonions -- contributes to our physical understanding of generalized measurement. I don't think we need them.

Tom

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One does not dispove a theorem, and I wish the result had not been presented that way. Joy's result might possibly subsume Bell's theorem (though my opinion is reserved for now), but could never replace it. Mathematics doesn't work that way -- no theorem is ever ejected from the canon. "Theorem" MEANS "a mathematically true statement."

I want to respond to Joy's closing statements:

" ... I take measurement results to be the points of a parallelized 7-sphere, whereas Bell incorrectly assumed that they are points of the real line."

This I utterly fail to understand. All measurement results are points of the real line, no matter the domain. That's why arithmetic (and geometric algebba)

are so powerful in describing natural phenomena; a natural counting order is consistent with "real" experience.

"More importantly, my framework is entirely consistent with the EPR criteria of locality, reality, and completeness, and it also fully respects Bell’s own criterion of factorizability. Therefore, in my opinion---although Bell’s theorem may well retain some of its relevance for the information and communication engineering as Florin has argued---it has no relevance for the future 'theory of everything.'"

Actually, by definition, no single theorem has relevance to a theory of everything. This claim is tantamount to saying that the Christian result subsumes all known physics. I don't think he means to go that far.

"Indeed, in the light of my results I believe that the successful 'theory of everything' will be a *locally causal* theory in which contextuality will play a role no different from the role it plays in general relativity. In other words, in my opinion all attempts to build a non-local theory of quantum gravity will fail miserably, just as anticipated by Einstein."

I guess there's no reason that quantum mechanics -- which is incoherent without nonlocality -- can't be subsumed by a local theory of quantum gravity. However, it brings into question what one means by "local" when extending causality to 8 dimensions. I don't see the enchantment of S^7. As my ICCS 2006 paper details (see esp.discussion pp 8 - 9 and figs 1 & 2), S^3 is sufficient to allow continuation over S^n manifolds while preserving commutativity (and Poincare recurrence) on S^3. So S^3 (the space of general relativity) is the "special" topology; I don't see that the loss of closed algebraic properties in the "hyper" numbers -- quaternions and octonions -- contributes to our physical understanding of generalized measurement. I don't think we need them.

Tom

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Tom,

You state: "One does not dispove a theorem, and I wish the result had not been presented that way. Joy's result might possibly subsume Bell's theorem (though my opinion is reserved for now), but could never replace it. Mathematics doesn't work that way -- no theorem is ever ejected from the canon. "Theorem" MEANS "a mathematically true statement.""

Indeed, Joy did not disprove Bell's theorem as this theorem remains mathematically correct. What he actually trying to "disprove" is Bell's theorem importance only. People usually take Bell's theorem as evidence and say: hidden variable theories are nonsense. Joy constructs a hidden variable theory and says: look here, I have a local realistic theory free of philosophical blemishes which recovers all QM results. Bell's theorem was "fool's gold" for detractors of hidden variable. Therefore I "disprove" it with a counterexample.

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You state: "One does not dispove a theorem, and I wish the result had not been presented that way. Joy's result might possibly subsume Bell's theorem (though my opinion is reserved for now), but could never replace it. Mathematics doesn't work that way -- no theorem is ever ejected from the canon. "Theorem" MEANS "a mathematically true statement.""

Indeed, Joy did not disprove Bell's theorem as this theorem remains mathematically correct. What he actually trying to "disprove" is Bell's theorem importance only. People usually take Bell's theorem as evidence and say: hidden variable theories are nonsense. Joy constructs a hidden variable theory and says: look here, I have a local realistic theory free of philosophical blemishes which recovers all QM results. Bell's theorem was "fool's gold" for detractors of hidden variable. Therefore I "disprove" it with a counterexample.

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Since commenting on Joy's reply, I thought I should comment here. Florin makes some very good points. I want to agree with Florin that Joy's result does not mar the importance or significance of experiments on non-locality and entanglement. I disagree with Joy's claim that his idea is a disproof of Bell's theorem, per se.

Instead; he provides an alternate description which renders some of the paradoxes resolved and some of our contradictory dual descriptions unnecessary. At the same time; it is a far cry from a complete theory - robust enough to replace the current view. As TH Ray says, he does not have an alternate structure to 'subsume all of known Physics.'

But I think he is on to something important. My guess is that it has to do with extended vs compact dimensions, which relates to our concept of locality. A 4-sphere has maximal hypervolume. When we add spatial dimensions beyond 5, they must therefore be compact! I agree with Joy's comment that octonions are simply the most general case (numbers and algebras), and feel that if we treat them as fundamental some of the paradoxes are seen as alternate projections of one framework.

So I believe his approach could work, and explains much, but takes nothing away from the validity of other work or the utility of other constructions.

Regards,

Jonathan

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Instead; he provides an alternate description which renders some of the paradoxes resolved and some of our contradictory dual descriptions unnecessary. At the same time; it is a far cry from a complete theory - robust enough to replace the current view. As TH Ray says, he does not have an alternate structure to 'subsume all of known Physics.'

But I think he is on to something important. My guess is that it has to do with extended vs compact dimensions, which relates to our concept of locality. A 4-sphere has maximal hypervolume. When we add spatial dimensions beyond 5, they must therefore be compact! I agree with Joy's comment that octonions are simply the most general case (numbers and algebras), and feel that if we treat them as fundamental some of the paradoxes are seen as alternate projections of one framework.

So I believe his approach could work, and explains much, but takes nothing away from the validity of other work or the utility of other constructions.

Regards,

Jonathan

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Jonathan,

I've been enjoying your comments.

You say that Joy "provides an alternate description which renders some of the paradoxes resolved and some of our contradictory dual descriptions unnecessary." I would be interested in any elaboration on this remark.

You also say, "At the same time; it is a far cry from a complete theory - robust enough to replace the current view. As TH Ray says, he does not have an alternate structure to 'subsume all of known Physics.'"

I am quite serious when I ask whether you might be willing to specify exactly [or even approximately] what you mean by "all known physics". I am assuming that you are not referring to mathematical theories for which no physics is currently known, such as strings, or SUSY, the Multi-verse, or even the Higgs at this moment in time. In other words what, in your mind, must an alternate theory cover in order to "subsume all known physics"?

Tom, since you were quoted, feel free to answer. In fact I would be interested in anyone's considered response to this question. It is an important question.

Edwin Eugene Klingman

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I've been enjoying your comments.

You say that Joy "provides an alternate description which renders some of the paradoxes resolved and some of our contradictory dual descriptions unnecessary." I would be interested in any elaboration on this remark.

You also say, "At the same time; it is a far cry from a complete theory - robust enough to replace the current view. As TH Ray says, he does not have an alternate structure to 'subsume all of known Physics.'"

I am quite serious when I ask whether you might be willing to specify exactly [or even approximately] what you mean by "all known physics". I am assuming that you are not referring to mathematical theories for which no physics is currently known, such as strings, or SUSY, the Multi-verse, or even the Higgs at this moment in time. In other words what, in your mind, must an alternate theory cover in order to "subsume all known physics"?

Tom, since you were quoted, feel free to answer. In fact I would be interested in anyone's considered response to this question. It is an important question.

Edwin Eugene Klingman

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Thanks E.E.,

Simply put; octonions have some properties that are curious or paradoxical - when compared with familiar commutative and associative algebras and spaces. What these properties do is force an orderly procedural resolution of all terms. There's also the maximal volume thing, and because the last 3 dimensions in octonions are necessarily compact, this messes with our sense of proximal and distal actions.

Thus it would appear that Joy's formulation provides a consistent framework (via the parallelizable spheres and their fibrations) which explains QM action at a distance as a change in the local geometry (so is in some sense locally-realistic).

I have some ideas (well, actually quite a few) about part II, but defining what will 'subsume all of known Physics' will have to wait until I have more time.

Jonathan

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Simply put; octonions have some properties that are curious or paradoxical - when compared with familiar commutative and associative algebras and spaces. What these properties do is force an orderly procedural resolution of all terms. There's also the maximal volume thing, and because the last 3 dimensions in octonions are necessarily compact, this messes with our sense of proximal and distal actions.

Thus it would appear that Joy's formulation provides a consistent framework (via the parallelizable spheres and their fibrations) which explains QM action at a distance as a change in the local geometry (so is in some sense locally-realistic).

I have some ideas (well, actually quite a few) about part II, but defining what will 'subsume all of known Physics' will have to wait until I have more time.

Jonathan

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"Known physics" implies what has been shown by correlation of mathematical theory to experimental result. This comprises the phenomenological body of knowledge from classical physics and quantum physics. Theoretical results would not have to be explained, since it could be assumed that an overarching theory would either replace or subsume those results.

Tom

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Tom

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Dear Peter Van Gaalen,

You placed a post in here a day or so ago to which I responded. Unfortunately, several posts were deleted in an effort by the administrator to keep these blogs on topic.

As I recall, your models equate 'fundamental units' with 'fundamental dimensions'. Is your model now up to 16 dimensions? That could simply be two bundled octonions - exactly double the space with which Joy is working.

It almost seems like all of our 'dimensions' need to be 'modulo 8' because of the periodicity of the normed divisor algebras. Thus, to get 4-D of Spacetime, we need 12, 20, 28, 36,... total dimensions, where we must include all dimensional effects from topology, supersymmetry, and scales.

Have Fun!

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You placed a post in here a day or so ago to which I responded. Unfortunately, several posts were deleted in an effort by the administrator to keep these blogs on topic.

As I recall, your models equate 'fundamental units' with 'fundamental dimensions'. Is your model now up to 16 dimensions? That could simply be two bundled octonions - exactly double the space with which Joy is working.

It almost seems like all of our 'dimensions' need to be 'modulo 8' because of the periodicity of the normed divisor algebras. Thus, to get 4-D of Spacetime, we need 12, 20, 28, 36,... total dimensions, where we must include all dimensional effects from topology, supersymmetry, and scales.

Have Fun!

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The F_4 is the Hurwitz 1152 quaternion representation of the 24-cell, which is a 4 dimensional version of the octahedron. The 24-cell or polyoctohedron is self-dual, and is the minimal Platonic solid in 4-dim. The e_8 decomposes into so(16)\oplus 128, where the Coxeter-Dynkin polytope for so(16) is the 120-cell, which is dual to the 600-cell. These are four dimensional analogues of icosahedron and the dodecahedron. This has a 5-fold structure to it. This is also related to the fact that some of the quaternions or roots have magnitude (1 + sqrt{5})/2, or the golden mean.

The G_2 I can write about tomorrow in some detail. This is the minimal exceptional group, and it does have some bearing on projective 5-dim and parabolic groups. It is getting a bit late to write a whole lot more.

Cheers LC

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The G_2 I can write about tomorrow in some detail. This is the minimal exceptional group, and it does have some bearing on projective 5-dim and parabolic groups. It is getting a bit late to write a whole lot more.

Cheers LC

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Dear Lawrence,

G2 keeps popping up in my models. It is the smallest-ranked group with this '7' factor. Is '7' important as another small prime number, or as the 7 imaginary components of an octonion, or as the 7 surface dimensions of an S^7? I also like G2's relation to SU(3), and think that this leads to an S-duality between an SU(3) of color (the strong coupling of the S-duality) and a possible G2 of generations (the weak coupling of the S-duality).

I agree with everything you said about F4. You and I have been discussing these constructs for a couple of years now. I like the 4-D 24-cell because of its apparent similarities with the rank-4 SU(5) Georgi-Glashow GUT. SU(5) has always been one of my favorite GUT models, but we all know it is an incomplete representation of any true TOE. The relavance of the Golden Ratio is in Scale Invariance, so any TOE needs this '5' factor from F4.

I definitely see the relations between E8 and SO(16)~SU(11)~icosahedral group and between E8xE8*~SO(32), but what about E8->H4xH4*? Isn't H4 also related to the 120-cell and its dual 600-cell? And a rank-4 H4 is a reasonable representation for a 4-D quaternion. Thus saying that E8->H4xH4* is equivalent to saying that the octonion decomposes into a pair of quaternions (which were already related via Cayley-Dickson construction).

A couple of years ago, we were talking about a potential TOE consiting of a rank-14 E8xH4xG2 where E8 represents octonion algebra, H4 represents quaternion algebra, and G2 represents complex algebra. Of course, we know that a proper lattice representation of bosons, fermions, and SUSY requires us to also introduce the dual lattices. Now we have a potential TOE with rank-28 and 28-D. The E8 and G2 are each self-dual, but the H4 isn't, and it may be useful to think of H4 in terms of F4 at this point.

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G2 keeps popping up in my models. It is the smallest-ranked group with this '7' factor. Is '7' important as another small prime number, or as the 7 imaginary components of an octonion, or as the 7 surface dimensions of an S^7? I also like G2's relation to SU(3), and think that this leads to an S-duality between an SU(3) of color (the strong coupling of the S-duality) and a possible G2 of generations (the weak coupling of the S-duality).

I agree with everything you said about F4. You and I have been discussing these constructs for a couple of years now. I like the 4-D 24-cell because of its apparent similarities with the rank-4 SU(5) Georgi-Glashow GUT. SU(5) has always been one of my favorite GUT models, but we all know it is an incomplete representation of any true TOE. The relavance of the Golden Ratio is in Scale Invariance, so any TOE needs this '5' factor from F4.

I definitely see the relations between E8 and SO(16)~SU(11)~icosahedral group and between E8xE8*~SO(32), but what about E8->H4xH4*? Isn't H4 also related to the 120-cell and its dual 600-cell? And a rank-4 H4 is a reasonable representation for a 4-D quaternion. Thus saying that E8->H4xH4* is equivalent to saying that the octonion decomposes into a pair of quaternions (which were already related via Cayley-Dickson construction).

A couple of years ago, we were talking about a potential TOE consiting of a rank-14 E8xH4xG2 where E8 represents octonion algebra, H4 represents quaternion algebra, and G2 represents complex algebra. Of course, we know that a proper lattice representation of bosons, fermions, and SUSY requires us to also introduce the dual lattices. Now we have a potential TOE with rank-28 and 28-D. The E8 and G2 are each self-dual, but the H4 isn't, and it may be useful to think of H4 in terms of F4 at this point.

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Dear Ray,

Yes my model has 16 dimensions. Time and the three spatial dimensions, are elements of classical 4 dimensional spacetime, described by the hyperbolic quaternion. Time as the scalar part and the spatial quantities as the imaginairy vector part. This suggest that there is also a scalar quantity with sign opposite of time, and also a vector quantity with opposite sign of the spatial quantities. 4-dimensional spacetime is doubled in dimensions. there are more dimensions possible, but there is a kind of periodicity. There are more scalar quantities with the same sign as time, and more vector quantities with the same imaginary sign as the spatial vector quantities but they are superfluous in the description of extended-spacetime. In extended-spacetime 8 dimensions are sufficient. Al those dimensions differ from each other by a certain power of 'ic' (speed of light with imaginairy sign i, j or k, because velocity is a vector quantity)

The other relevant constant is G. So those 8 dimension are doubled by the product of 'iLG' (gravitational constant G with imaginary sign 'iL', 'jL' or 'kL' because G also is a vector quantity, according to dimensional analysis) Again there is periodicity, so 16 is the maximum ammount of dimensions to describe the extended energymomentum-spacetime continuum. The description of this extended energymomentum-spacetime is done by using two octonions of opposite signature. Dependend on the different combination of the 16 quantities to compose a quaternion, you can use hyperbolic quaternions, split octonions, regular octonions etc.

Quantum mechanics is al about those 16 quantities. The planck constant is dimensional the product of two of those quantities (time and energy or length and momentum) divided by phase. So the description by Joy Christian of Bell's Theorem using the 7 imaginary parts seems logical.

Other quantites like electric charge or magnetic flux have nothing to do with it. They are excluded from the description.

Friendly regards,

Peter

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Yes my model has 16 dimensions. Time and the three spatial dimensions, are elements of classical 4 dimensional spacetime, described by the hyperbolic quaternion. Time as the scalar part and the spatial quantities as the imaginairy vector part. This suggest that there is also a scalar quantity with sign opposite of time, and also a vector quantity with opposite sign of the spatial quantities. 4-dimensional spacetime is doubled in dimensions. there are more dimensions possible, but there is a kind of periodicity. There are more scalar quantities with the same sign as time, and more vector quantities with the same imaginary sign as the spatial vector quantities but they are superfluous in the description of extended-spacetime. In extended-spacetime 8 dimensions are sufficient. Al those dimensions differ from each other by a certain power of 'ic' (speed of light with imaginairy sign i, j or k, because velocity is a vector quantity)

The other relevant constant is G. So those 8 dimension are doubled by the product of 'iLG' (gravitational constant G with imaginary sign 'iL', 'jL' or 'kL' because G also is a vector quantity, according to dimensional analysis) Again there is periodicity, so 16 is the maximum ammount of dimensions to describe the extended energymomentum-spacetime continuum. The description of this extended energymomentum-spacetime is done by using two octonions of opposite signature. Dependend on the different combination of the 16 quantities to compose a quaternion, you can use hyperbolic quaternions, split octonions, regular octonions etc.

Quantum mechanics is al about those 16 quantities. The planck constant is dimensional the product of two of those quantities (time and energy or length and momentum) divided by phase. So the description by Joy Christian of Bell's Theorem using the 7 imaginary parts seems logical.

Other quantites like electric charge or magnetic flux have nothing to do with it. They are excluded from the description.

Friendly regards,

Peter

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Dear Joy, Florin, and Lawrence,

I made some comments earlier with minor errors and never received a proper response, so I am correcting those errors and reposting those ideas. Joy said that the devil is in the details, and yet some of those details bother me.

Joy is working with a parallelizable and potentially-stable 7-sphere, but he also has these weird statistics that continuously range from negative one (an anti-symmetric fermion wave-function) to positive one (a symmetric boson wave-function). This looks like the real projection of Anyonic statistics with phases of exp(i*theta), where theta ranges from zero to 2*pi. Anyons are quantum particles on 2-dimensional surfaces that don’t behave exactly like fermions or bosons (and may thus be a good place to start in an effort to unify quantum statistics into a TOE). Some examples of possibly important 2-D surfaces are the M2 Blackbrane and the effectively 2-D Graphene lattice of Holographic Theory.

Now suppose that the potentially-stable 7-sphere were to spontaneously decay into an M2 Blackbrane, its dual NS5-brane, and an eighth dimension of time. The M2-brane could explain the occurrence of Anyonic statistics, while the NS5-brane explains why the five-fold Pentagon color graph (see Florin’s Color Me Surprised post with the Kochen-Specker Theorem) is a minimal model for quantum behavior.

The devil may be in the details, but these details seem consistent with M-Theory…

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I made some comments earlier with minor errors and never received a proper response, so I am correcting those errors and reposting those ideas. Joy said that the devil is in the details, and yet some of those details bother me.

Joy is working with a parallelizable and potentially-stable 7-sphere, but he also has these weird statistics that continuously range from negative one (an anti-symmetric fermion wave-function) to positive one (a symmetric boson wave-function). This looks like the real projection of Anyonic statistics with phases of exp(i*theta), where theta ranges from zero to 2*pi. Anyons are quantum particles on 2-dimensional surfaces that don’t behave exactly like fermions or bosons (and may thus be a good place to start in an effort to unify quantum statistics into a TOE). Some examples of possibly important 2-D surfaces are the M2 Blackbrane and the effectively 2-D Graphene lattice of Holographic Theory.

Now suppose that the potentially-stable 7-sphere were to spontaneously decay into an M2 Blackbrane, its dual NS5-brane, and an eighth dimension of time. The M2-brane could explain the occurrence of Anyonic statistics, while the NS5-brane explains why the five-fold Pentagon color graph (see Florin’s Color Me Surprised post with the Kochen-Specker Theorem) is a minimal model for quantum behavior.

The devil may be in the details, but these details seem consistent with M-Theory…

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I have been a bit tied up this week. I made mention a few days ago, as written above on this page, on how the topological singular points involved with this are moved off “to infinity.” The Hopf fibration is a construction of the heavenly sphere, and these points are the point off at “infinity.”

The F_4 group is the automorphism group of the J^3(O) (O = octonion) or Freudenthal system. Perez back in the early 90s demonstrated how the Kochen-Specker theorem can be proven as a result on F_4. The J^3(O) might be thought of as a O^3, and the F_4 on O is the stabilizer of G_2. G_2 in turn fixes an S^7 (the 2x7 elements of G_2) in S^8 according to the Hopf fibration. So these matters of topological obstructions seem to be removed because this system is projective, the multiplication system is on the Cayley projective plane, and so do not contriubute to this problem in the way the JC seems to think.

All of this work of JC does provide some avenues for thinking about these matters, but I don’t think this means there are ultimately classical substructure to QM.

LC

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The F_4 group is the automorphism group of the J^3(O) (O = octonion) or Freudenthal system. Perez back in the early 90s demonstrated how the Kochen-Specker theorem can be proven as a result on F_4. The J^3(O) might be thought of as a O^3, and the F_4 on O is the stabilizer of G_2. G_2 in turn fixes an S^7 (the 2x7 elements of G_2) in S^8 according to the Hopf fibration. So these matters of topological obstructions seem to be removed because this system is projective, the multiplication system is on the Cayley projective plane, and so do not contriubute to this problem in the way the JC seems to think.

All of this work of JC does provide some avenues for thinking about these matters, but I don’t think this means there are ultimately classical substructure to QM.

LC

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Dear Lawrence,

I like your observations. I certainly expect G2 to be relevant - as you said "G_2 in turn fixes an S^7". G2 could also be the 2-D membrane on which the Anyons live. You said "but I don’t think this means there are ultimately classical substructure to QM", and I agree - if Joy's "continuously" variable statistics are due to 2-D quantum Anyons rather than the 3-D classical indistinguishable particles of Maxwell-Boltzmann statistics.

I also agree with the potential importance of F4 (and/or D4). Yes - F4 has the 5-fold symmetry of the Pentachoron within it that could explain the five-fold pentagonal structure of this solution to the Kochen-Specker Theorem that Florin presented earlier.

But now we have two extra dimensions. I think that the eighth dimension is time, and its negative metric-squared inflates the 7-sphere such that the Black Hole "singularity" cannot crush the 7-sphere. But if the expected M-Theory decomposition for a 7-brane is an M2-brane and an NS5-brane, then we need to explain how a 5-dimensional NS5-brane decomposes into a 4-dimensional F4 (or D4).

Perhaps an octonion-like S^7 decomposes into a G2 (because it has the correct symmetries) and an S^5. A rotating S^5 is unstable due to the Hairy Ball theorem and further decomposes into tori of parallelizable quaternion-like S^3's. And these S^3's may be the origin of the Pentachoron and the F4 (or D4) symmetries of the Kochen-Specker Theorem. Now what is the usefulness of these extra tori? Are they the actual Blackbrane?

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I like your observations. I certainly expect G2 to be relevant - as you said "G_2 in turn fixes an S^7". G2 could also be the 2-D membrane on which the Anyons live. You said "but I don’t think this means there are ultimately classical substructure to QM", and I agree - if Joy's "continuously" variable statistics are due to 2-D quantum Anyons rather than the 3-D classical indistinguishable particles of Maxwell-Boltzmann statistics.

I also agree with the potential importance of F4 (and/or D4). Yes - F4 has the 5-fold symmetry of the Pentachoron within it that could explain the five-fold pentagonal structure of this solution to the Kochen-Specker Theorem that Florin presented earlier.

But now we have two extra dimensions. I think that the eighth dimension is time, and its negative metric-squared inflates the 7-sphere such that the Black Hole "singularity" cannot crush the 7-sphere. But if the expected M-Theory decomposition for a 7-brane is an M2-brane and an NS5-brane, then we need to explain how a 5-dimensional NS5-brane decomposes into a 4-dimensional F4 (or D4).

Perhaps an octonion-like S^7 decomposes into a G2 (because it has the correct symmetries) and an S^5. A rotating S^5 is unstable due to the Hairy Ball theorem and further decomposes into tori of parallelizable quaternion-like S^3's. And these S^3's may be the origin of the Pentachoron and the F4 (or D4) symmetries of the Kochen-Specker Theorem. Now what is the usefulness of these extra tori? Are they the actual Blackbrane?

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Still an american pub , that's all a simple pub for some friends who are falses simply. The patriotism is beautiful, here we are on a platform of sciences.

And now the hairy ball theorem, a pure joke yes, you make rational sciences or spielberg has contacted you, say me because there I suspect a smallll problem.

BE RATIONAL PLEASE AND FORGET A LITTLE THE PATRIOTIC BUSINESS PLEASE

Steve

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And now the hairy ball theorem, a pure joke yes, you make rational sciences or spielberg has contacted you, say me because there I suspect a smallll problem.

BE RATIONAL PLEASE AND FORGET A LITTLE THE PATRIOTIC BUSINESS PLEASE

Steve

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Florin,

Having read your article and Joy's response, I look forward to your next response.

You suggest that Bell's theorem "retains its full importance as the key result which suggested experimental tests for settling the hidden variable theory questions."

Is it correct to say that "violation of Bell's inequality is *the* basis for the rejection of local realism in physics"?

Edwin Eugene Klingman

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Having read your article and Joy's response, I look forward to your next response.

You suggest that Bell's theorem "retains its full importance as the key result which suggested experimental tests for settling the hidden variable theory questions."

Is it correct to say that "violation of Bell's inequality is *the* basis for the rejection of local realism in physics"?

Edwin Eugene Klingman

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Edwin,

You asked: "Is it correct to say that "violation of Bell's inequality is *the* basis for the rejection of local realism in physics"?"

In my opinion, yes, but I am in minority here (among the philosophers). Shimony voices the philosopher's majority opinion and he puts Bell's importance in proving impossible some additional contextual hidden variable theories. For the noncontextual ones, there are many other theorems doing the trick.

My opinion (and the majority of physicists not working in foundations) is that Bell's is important because it is a robust result which can be put to the experimental test. The other fancier theorems while nice, they are "brittle" under the usual fluctuations inherent in experiments and hence unusable to draw a definite conclusion for or against realism. And who cares about contextual hidden variable theories anyway? There is no experimental evidence for them whatsoever. Bell's theorem is soly responsible for disproving non-contextual genuine alternatives to QM.

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You asked: "Is it correct to say that "violation of Bell's inequality is *the* basis for the rejection of local realism in physics"?"

In my opinion, yes, but I am in minority here (among the philosophers). Shimony voices the philosopher's majority opinion and he puts Bell's importance in proving impossible some additional contextual hidden variable theories. For the noncontextual ones, there are many other theorems doing the trick.

My opinion (and the majority of physicists not working in foundations) is that Bell's is important because it is a robust result which can be put to the experimental test. The other fancier theorems while nice, they are "brittle" under the usual fluctuations inherent in experiments and hence unusable to draw a definite conclusion for or against realism. And who cares about contextual hidden variable theories anyway? There is no experimental evidence for them whatsoever. Bell's theorem is soly responsible for disproving non-contextual genuine alternatives to QM.

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Dear Steve,

I think that these two blogs - the one by Joy and the one by Florin - are being monitored more closely than the average FQXi blog because you have significant interest from Joy, Florin AND Brendan. Your comments were not the only ones deleted.

I suspect that if we stay on topic (no more comments about President Obama, Mickey Mouse, Perimeter, Star Wars characters, and no...

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I think that these two blogs - the one by Joy and the one by Florin - are being monitored more closely than the average FQXi blog because you have significant interest from Joy, Florin AND Brendan. Your comments were not the only ones deleted.

I suspect that if we stay on topic (no more comments about President Obama, Mickey Mouse, Perimeter, Star Wars characters, and no...

view entire post

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You are a comic, you aren't neither mathematicians(and there also i eat that at my breakfast)in fact you try to make a kind of pseudo complexity. I am not intersted in works of joy or florin or others. I say just that you try with a kind of packaging. And you try also with what , the americans, I love your country like all countries , then your pseudo strategies of kindness.I know.Well tried,You are a team of business men ,that's all, patriotic and not skilling, then you focus on business, we understand you.It's not insults, it's just a simple reality. Joy I agree seems a rationalist, but of course i know he has a responsability of credibility and also a team of business men around.Them they don't interest me , him yes like others rational scientists.In fact you imply just confusions for the public, but not for the real rational part of the sciences community.

You are just a team after all, just a team.But now you are obliged to continue, it's interesting. And you think that the rztionalsist have not seen your play, let me laugh. If your maths to you and friends are real maths, me I am the king of my country(you prefer there).You want real maths I invite you to listen a little Eckard and others rational mathematicians.or Buy a real good GENERAL book, after you shall understand better the distributions of numbers.If you think that I am going to say thanks, yes of course Ray,of course.Joy and my theory has no correlation, my entangled spheres rotate and are proportional in 3D, they are reals, it's not a subjective sphere me, and some superimposings, me i search the real number of this entanglement. and you try all to copy my discovery for this monney and this vanity and this lack of skillings.Let me laugh, You are republicans Ray no?And of course the business of future famillies must be protected, I am not in this logic ray, because i am an universalist.

Steve

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You are just a team after all, just a team.But now you are obliged to continue, it's interesting. And you think that the rztionalsist have not seen your play, let me laugh. If your maths to you and friends are real maths, me I am the king of my country(you prefer there).You want real maths I invite you to listen a little Eckard and others rational mathematicians.or Buy a real good GENERAL book, after you shall understand better the distributions of numbers.If you think that I am going to say thanks, yes of course Ray,of course.Joy and my theory has no correlation, my entangled spheres rotate and are proportional in 3D, they are reals, it's not a subjective sphere me, and some superimposings, me i search the real number of this entanglement. and you try all to copy my discovery for this monney and this vanity and this lack of skillings.Let me laugh, You are republicans Ray no?And of course the business of future famillies must be protected, I am not in this logic ray, because i am an universalist.

Steve

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Ray,

The exceptional group G2 is the automorphism on O, or equivalently that F_4 x G_2 defines a centralizer on E8. The fibration G_2 - -> S^7 is completed with SO(8), where the three O’s satisfy the triality condition in SO(8). So the three octonions in the exceptional J^3(O) exhibit a triality condition inherited from SO(8) by the fibration of G_2. BTW, the triality condition of...

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The exceptional group G2 is the automorphism on O, or equivalently that F_4 x G_2 defines a centralizer on E8. The fibration G_2 - -> S^7 is completed with SO(8), where the three O’s satisfy the triality condition in SO(8). So the three octonions in the exceptional J^3(O) exhibit a triality condition inherited from SO(8) by the fibration of G_2. BTW, the triality condition of...

view entire post

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And you recome with the word exeptional what? ...a pure joke, Lisi and you are falses and just try to have founds and investments. A pure global patriotic irony. Just for this papper, and they insist furthermore, pay attention they are going to invent a time machine because their pseudos mathematics say some bizare things. Just a team of business ma, they are 8 perhaps also ahahah

A toe exeptional , yes of course and also we are going to pay the air soon, we know we know.

Lawrence just a pub , that is all, just a pub you make that's all.But well tried, good job apprently, have a good salary, i hope....

You do not make maths and sciences, you just mix and imply some confusions for the public. I can't accept that, I can't accept that even these stupidities are learned or teached at school, it is simly not admissible and acceptable for the global rational sciences community.I am not crazzy but simply rational and just. All that must be said. It's not against the creativity and the imaginative creations, no just against the stupidities and its ironies. The universities have a big responsability.Then the international language must be irrational, ....never .....

Octonions no but frankly and also what a quaternion is logic for the spacetime and reversibility of times and decoherences also no??? Well well well , you confound a little the real meanings of what is a finite group or infinite and also the series about pure determinism. You do not see the real meaning of whai is the relativity of Einstein. I invite some people to really learn what is the relative space time evolution.A constant is a constant even if this constant is different in the past or in the future. The locality , the continuity and the globality appear more easilly. But it's just a suggestion of course.Not need of extradimensions and exotic particles...just a 3D evolution and a time constant like duration...see my spheres when they rotate....PROPORTIONAL AND PURELLY LINKED WITH THE TIME CONSTANT.

Your real problems to all extradimensionalists, it is your domains and your lack of universality and whole point of vue. If you do not understand the aim of this universe and its laws, how can you ponder interesting things.It's purelly not possible.

Steve

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A toe exeptional , yes of course and also we are going to pay the air soon, we know we know.

Lawrence just a pub , that is all, just a pub you make that's all.But well tried, good job apprently, have a good salary, i hope....

You do not make maths and sciences, you just mix and imply some confusions for the public. I can't accept that, I can't accept that even these stupidities are learned or teached at school, it is simly not admissible and acceptable for the global rational sciences community.I am not crazzy but simply rational and just. All that must be said. It's not against the creativity and the imaginative creations, no just against the stupidities and its ironies. The universities have a big responsability.Then the international language must be irrational, ....never .....

Octonions no but frankly and also what a quaternion is logic for the spacetime and reversibility of times and decoherences also no??? Well well well , you confound a little the real meanings of what is a finite group or infinite and also the series about pure determinism. You do not see the real meaning of whai is the relativity of Einstein. I invite some people to really learn what is the relative space time evolution.A constant is a constant even if this constant is different in the past or in the future. The locality , the continuity and the globality appear more easilly. But it's just a suggestion of course.Not need of extradimensions and exotic particles...just a 3D evolution and a time constant like duration...see my spheres when they rotate....PROPORTIONAL AND PURELLY LINKED WITH THE TIME CONSTANT.

Your real problems to all extradimensionalists, it is your domains and your lack of universality and whole point of vue. If you do not understand the aim of this universe and its laws, how can you ponder interesting things.It's purelly not possible.

Steve

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The body/eye enjoins invisible/visible space where vision/space begin -- inside the body/eye. See the black space(INERTIAL) beginning of space/vision in the eye/body? Then FULL GRAVITY is felt at the feet/ground -- the end of space/vision. The top of the body/head is also enjoining invisible space while waking/standing.

When we have EQUALLY (and both) visible and invisible space -- as we do in dreams -- then it is all the same space -- with half inertia and half gravity; as space/vision begins [equivalently] as/where it all ends.

This is why space is semi-detached from touch in dreams. Half gravity and half inertia.

This is why the manifestations of force/energy in dreams are at [a maximum of] one half of that of the force/feeling that is felt at the feet/ground while waking/standing.

Sorry folks, the math games are a joke for the most part, as I have fundamentally unified physics.

DREAMS DEMONSTRATE SPACE MANIFESTING AS INERTIAL/GRAVITATIONAL/ELECTROMAGNETIC ENERGY.

I DEMAND ACTION FQXI.ORG. STOP THE LIES IN PHYSICS.

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When we have EQUALLY (and both) visible and invisible space -- as we do in dreams -- then it is all the same space -- with half inertia and half gravity; as space/vision begins [equivalently] as/where it all ends.

This is why space is semi-detached from touch in dreams. Half gravity and half inertia.

This is why the manifestations of force/energy in dreams are at [a maximum of] one half of that of the force/feeling that is felt at the feet/ground while waking/standing.

Sorry folks, the math games are a joke for the most part, as I have fundamentally unified physics.

DREAMS DEMONSTRATE SPACE MANIFESTING AS INERTIAL/GRAVITATIONAL/ELECTROMAGNETIC ENERGY.

I DEMAND ACTION FQXI.ORG. STOP THE LIES IN PHYSICS.

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The self ultimately represents, forms, and experiences a comprehensive approximation of the totality of experience. This means that being/experience is ultimately integrated and interactive, of course. This requires a fundamental and profound revision of physics/physical analysis.

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The primairy discussion between Florin and Joy is at the basis of our scientific reasoning, as we are (like at every moment in history) at the entry of an important new era, these discussions contribute to the addition of more coulours in the rainbow of physiscs and mathematics, be aware of staying inside your "sphere" and staying centered in the middle, perhaps it is wiser to think that the twodimensinal surface of the sphere is the origin of the holographic experience (pub) we are living in.

keep on thinking free

Wilhelmus

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keep on thinking free

Wilhelmus

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Yes they are going to win the noble prize and after they shall drink a belgian beer in a pub .

Steve

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Steve

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Dear Wilhelmus,

Happy Late Birthday! It is easy to remember yours because mine is the day before.

I agree that 2-D membranes are relevant. The AdS/CFT boundry is often modeled with an effectively 2-D graphene lattice. The odd thing here is that true graphene is flat, i.e. has in infinite radius of curvature, whereas our Universe has a very large but finite radius of curvature. This requires the AdS/CFT boundry to warp slightly, or to contain a few pentagons with the many hexagons. I think that 12 pentagons in a very large number of hexagons is sufficient to curve this graphene boundary into a sphere-like AdS/CFT boundary.

However, spinning 2-spheres are unstable due to the Hairy Ball Theorem. In our recent paper in PSTJ, Jonathan Dickau and I gave an example (Example 5) of rotating 2-spheres decomposing into rotating tori.

It seems that the only types of spheres that are stable against generalizations of the Hairy Ball Theorem are the parallelizable ones: an 'octonion-like' 7-sphere, a 'quaternion-like' 3-sphere, a 'complex-like' 1-sphere, and the (real-like?) 0-sphere. This would apparantly kill the rotating 2-sphere - unless other effects (that would need to be explained in detail) are at action.

Spacetime resembles the (3+1)-D nature of a Quaternion. Now why would Joy's 7-sphere be relevant, or why would a supposedly stable 7-sphere decompose into 3-spheres?

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Happy Late Birthday! It is easy to remember yours because mine is the day before.

I agree that 2-D membranes are relevant. The AdS/CFT boundry is often modeled with an effectively 2-D graphene lattice. The odd thing here is that true graphene is flat, i.e. has in infinite radius of curvature, whereas our Universe has a very large but finite radius of curvature. This requires the AdS/CFT boundry to warp slightly, or to contain a few pentagons with the many hexagons. I think that 12 pentagons in a very large number of hexagons is sufficient to curve this graphene boundary into a sphere-like AdS/CFT boundary.

However, spinning 2-spheres are unstable due to the Hairy Ball Theorem. In our recent paper in PSTJ, Jonathan Dickau and I gave an example (Example 5) of rotating 2-spheres decomposing into rotating tori.

It seems that the only types of spheres that are stable against generalizations of the Hairy Ball Theorem are the parallelizable ones: an 'octonion-like' 7-sphere, a 'quaternion-like' 3-sphere, a 'complex-like' 1-sphere, and the (real-like?) 0-sphere. This would apparantly kill the rotating 2-sphere - unless other effects (that would need to be explained in detail) are at action.

Spacetime resembles the (3+1)-D nature of a Quaternion. Now why would Joy's 7-sphere be relevant, or why would a supposedly stable 7-sphere decompose into 3-spheres?

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any sense, without meaning....a real marketing for frustrated and the team.Just still a marketing. Perhaps Joy,Jonathan, and lisi can help you with lawrence and florin, beautiful team and who also....and what also, you shall share the nobel prize, band of comics loving monney. In fact fortunally you are there also for my theory perhaps No? Perhaps my theory is yours now also no? perhaps my theory had need for your pseudo complexity also No?? A pure wind of nothing.It's simple, as is the simplicity of water.Return at reason dear business, you shall not steal, you shall not kill, ....you know the 5 others no?

Steve

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Steve

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Steve is right about the rampant misdirection and diminishment of physics/truth/reality here at FQXi.org. It is shameful.

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Why ignore this: ULTIMATE TRUTH IN PHYSICS DEPENDS UPON BODILY EXPERIENCE.

The self ultimately represents, forms, and experiences a comprehensive approximation of the totality of experience. This means that being/experience is ultimately integrated and interactive, of course. This requires a fundamental and profound revision of physics/physical analysis.

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The self ultimately represents, forms, and experiences a comprehensive approximation of the totality of experience. This means that being/experience is ultimately integrated and interactive, of course. This requires a fundamental and profound revision of physics/physical analysis.

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I may be stepping deeply into it, to do this, but I already opened my mouth, so I would like to offer this partial draft of a paper I have been working on for quite a while that I think is on topic for employing algebraic, topological and analytical techniques -- toward analytical continuation over topological manifolds. I decided that I might as well reveal it while the subject is hot.

Joy identifies S^7 as the "special" topology. I think, however, that S^3 is the one, and that we need all the rational functions of the closed algebra.

Tom

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Joy identifies S^7 as the "special" topology. I think, however, that S^3 is the one, and that we need all the rational functions of the closed algebra.

Tom

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Hi Tom,

I see that you have been building on years worth of ideas. Some of this paper is familiar, but you have clearly added a lot of new stuff.

Jonathan Dickau and I have been having private discussions about S^7 and S^3. Our conclusion is that both are relevant to the evolution of Reality, but that an imaginary quaternion of S^3 (a real and an imaginary quaternion S^3 have similarities to a real and an imaginary F4 24-cell) is more stable, and more properly represents (3+1)-D Spacetime than does an imaginary octonion of S^7 (a real and an imaginary octonion S^7 have similarities to a real and an imaginary E8 Gosset lattice).

We contend that S^3 is more stable than S^7 because of Geometric and Thermodynamic considerations - 1) Unit Hypersphere Volume is maximized, and thus Free Energy density is minimized, for the 4-sphere, and 2) Unit Hypersphere Surface is maximized, and thus Entropy is also maximized (per Bekenstein-Hawking Event Horizon entropy), for the 6-sphere. Thermodynamics prefers minimzed Enthalpy (which is a calculus of variations balance between minimized Free Energy and maximized Entropy) such that the 7-sphere will decompose into either a 4-, 5- or 6-sphere (depending on whether Free Energy effects outweigh, balance, or underweigh Entropy effects). Spinning 4-, 5- and 6-spheres are all metastable due to hyper-generalizations of the Hairy Ball Theorem, and will thus decompose into the largest stable (stable against Geometric, Thermodynamic and Hairy Ball effects) hypersphere, the parallelizable S^3 3-sphere.

Now lets build a hyperspace model on dual F4 24-cells - I know that Lawrence has been contemplating that problem for a couple of years.

Have Fun!

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I see that you have been building on years worth of ideas. Some of this paper is familiar, but you have clearly added a lot of new stuff.

Jonathan Dickau and I have been having private discussions about S^7 and S^3. Our conclusion is that both are relevant to the evolution of Reality, but that an imaginary quaternion of S^3 (a real and an imaginary quaternion S^3 have similarities to a real and an imaginary F4 24-cell) is more stable, and more properly represents (3+1)-D Spacetime than does an imaginary octonion of S^7 (a real and an imaginary octonion S^7 have similarities to a real and an imaginary E8 Gosset lattice).

We contend that S^3 is more stable than S^7 because of Geometric and Thermodynamic considerations - 1) Unit Hypersphere Volume is maximized, and thus Free Energy density is minimized, for the 4-sphere, and 2) Unit Hypersphere Surface is maximized, and thus Entropy is also maximized (per Bekenstein-Hawking Event Horizon entropy), for the 6-sphere. Thermodynamics prefers minimzed Enthalpy (which is a calculus of variations balance between minimized Free Energy and maximized Entropy) such that the 7-sphere will decompose into either a 4-, 5- or 6-sphere (depending on whether Free Energy effects outweigh, balance, or underweigh Entropy effects). Spinning 4-, 5- and 6-spheres are all metastable due to hyper-generalizations of the Hairy Ball Theorem, and will thus decompose into the largest stable (stable against Geometric, Thermodynamic and Hairy Ball effects) hypersphere, the parallelizable S^3 3-sphere.

Now lets build a hyperspace model on dual F4 24-cells - I know that Lawrence has been contemplating that problem for a couple of years.

Have Fun!

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Dr. Ray Monroe,

Have appreciated reading your posts and hope that you have a good day?

James

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Have appreciated reading your posts and hope that you have a good day?

James

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Dear James,

Yes - I am having a good day, and I hope you are as well. I consider most of the people on this site friends, but friends should be able to 'agree to disagree' without continual insults.

Have Fun!

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Yes - I am having a good day, and I hope you are as well. I consider most of the people on this site friends, but friends should be able to 'agree to disagree' without continual insults.

Have Fun!

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No it's not insulst, it is the pure reality, you copy all and are packagers, and some politness of some virtual friends won't change this reality. You consider bloggers as friends, yes of course. You consider your friends just your team evn if they are falses and evn if their comportments aren't well. You aren't skilling to ponder equations and theories, you, lawrence, lisi, tom, jonathan,and your friends, you aren't simply not able to invent general things and new universal things. We are not in a film where all is possible, no Ray we are in the reality and our foundamentals are our foundamentals.It exists good scientists and bad scientists like it exists good cookers and bad cookers.If you were general, never you shall ponder these stupidities you and your friends.

Frankly it's ironic.And you insist furthermore, impressing.

Steve

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Frankly it's ironic.And you insist furthermore, impressing.

Steve

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Dr. Monroe,

Yes I am having a good day thank you. I am 68 and still around to debate with Tom. :) A subject about "What is physics?" came up in another forum. I have tried to make this matter clear to them but there is unreasonable resistance. :) Anyway, it is good to have you around.

James

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Yes I am having a good day thank you. I am 68 and still around to debate with Tom. :) A subject about "What is physics?" came up in another forum. I have tried to make this matter clear to them but there is unreasonable resistance. :) Anyway, it is good to have you around.

James

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Ray You have misundertood what I said simply, and of course all my posts are deleted still no but frankly it's what that Brendan. I made a comparaison Ray , never I said that about you no but frankly .

Reread my post in french but they have disappeared. Incredible that.Where are my french posts ? still a stategy because you fear of my language.It is what That???? In fact you are a real band of what??? I can ask me several questions with all these comportments.

Steve

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Reread my post in french but they have disappeared. Incredible that.Where are my french posts ? still a stategy because you fear of my language.It is what That???? In fact you are a real band of what??? I can ask me several questions with all these comportments.

Steve

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Dear Steve,

In High School, I took two years of Latin. And in College, I took two years of German. I do not use any language - other than English - often enough to be proficient. I admit that I used Google Translate, and it may have mis-translated a comparison or an ironic comment.

I do not know why the French posts were deleted. I ran those through Google translate, and generally understood (or thought I understood) those posts better than your typical posts in English.

I propose that we try to stay on topic so that Brendan, Florin and Joy may better-tolerate our comments.

Have Fun and Think Free!

Ray

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In High School, I took two years of Latin. And in College, I took two years of German. I do not use any language - other than English - often enough to be proficient. I admit that I used Google Translate, and it may have mis-translated a comparison or an ironic comment.

I do not know why the French posts were deleted. I ran those through Google translate, and generally understood (or thought I understood) those posts better than your typical posts in English.

I propose that we try to stay on topic so that Brendan, Florin and Joy may better-tolerate our comments.

Have Fun and Think Free!

Ray

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Ray , They can delete, they can make what they want, it is my theory , it is only simple as that, Joy and Florin makes just a kind of public comedy of pseudo mathematical complexity where all is mixed without a real rational road. They just continue their strategy or their business plan. But it is comic to see that.So ironic.

Tolerate , ahaha like if their agreements or approvements were important for me,let me laugh Ray, They are just two scientists who tries to be really recognized, I will invite them perhaps ahahah The humility is like a water drop, pure and simple. Tolerate , it is me who perhaps in the future will tolerate the people in my team and my revolutions. It is totally different, me I just begin you know. Be sure my theory will rest.They rotate then they are ..EUREKA.With or without the approvements of pseudos scientits or jaleous and their stupids ideas for business.It is not a free thinking that, it is a lost of monney, and of course it is not possible to accept that.If the world is like that it is just due to this enormous lost of monney in the researchs and funds and experiments. The sciences are there to help humanity, not to imply a lost of monney.Frankly your experiment is not useless and purelly stupid Joy at a momment so sad for this earth. So many labs and no real solutions for our earth. A big lost of monney yes, that's all.A director of an institute here, an assistant for a pseudo research at a ibm lab and this and that....it is so ironic.And all in competition of course , we dream in live. A pure lost of monney.The funds must be distrubuted with the biggest rationality of harmonious evolution. The rest is vain, a pure universal responsability becomes a simple key.If people wants to ponder things, please ponder well and with univetrsality. If the world doesn't turn correctly, it is due to this lost of monney everywhere in several labs, institutes or universities.Their responsability is so important and essential for a harmonious evolution.Why then? Just for this monney dear all.

Steve

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Tolerate , ahaha like if their agreements or approvements were important for me,let me laugh Ray, They are just two scientists who tries to be really recognized, I will invite them perhaps ahahah The humility is like a water drop, pure and simple. Tolerate , it is me who perhaps in the future will tolerate the people in my team and my revolutions. It is totally different, me I just begin you know. Be sure my theory will rest.They rotate then they are ..EUREKA.With or without the approvements of pseudos scientits or jaleous and their stupids ideas for business.It is not a free thinking that, it is a lost of monney, and of course it is not possible to accept that.If the world is like that it is just due to this enormous lost of monney in the researchs and funds and experiments. The sciences are there to help humanity, not to imply a lost of monney.Frankly your experiment is not useless and purelly stupid Joy at a momment so sad for this earth. So many labs and no real solutions for our earth. A big lost of monney yes, that's all.A director of an institute here, an assistant for a pseudo research at a ibm lab and this and that....it is so ironic.And all in competition of course , we dream in live. A pure lost of monney.The funds must be distrubuted with the biggest rationality of harmonious evolution. The rest is vain, a pure universal responsability becomes a simple key.If people wants to ponder things, please ponder well and with univetrsality. If the world doesn't turn correctly, it is due to this lost of monney everywhere in several labs, institutes or universities.Their responsability is so important and essential for a harmonious evolution.Why then? Just for this monney dear all.

Steve

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Tolerate, no but frankly, it is just a play of vanity and with a kind of publicity also. A blog for florin and a blog for Joy, and hop at the same time and hop 1 is deterministic and hop the other is irrational....well if they want make a kind of EPR vs Copenaghen please say them to make it well please. They just write some messages, and they say that they have few time. And after what a new lab also. I see Just a simple strategy , without real relevances and innovations. It is simple and evident. If I will see real equations or reals convergences or reals calculations about our mass, I will agree, but frankly.I don't see real interesting innovations.But I can recognize a simple good detailled work about our QM like it exists so many in arxiv. It is just a small imrpovement of a thing already known for the pure rationalists. But it is cool they show us their works. After all they must write pappers for the business team and the enterprize, always this monney dear scientists, always this monney. Forget your chains dear scientists and work for humanity and for this earth. Ray it is that the real freedom and free thinking....

Steve

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Steve

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WHERE ARE MY POSTS IN FRENCH???? YOU FEAR OR WHAt of my french ???It is incredible that,some people are really bad people there, just for this monney, but perhaps they want my recognizings and my monney also, never!!!!You fear of my french and my sciences. In fact you thoughts never that about me and now yoyu are in a bizare position, I can understand indeed. Never you thought that my theory was so complete. I understand your desire to profit of my future capitals. Never it's my works.

Steve

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Steve

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Hi Steve,

Sorry , but I think that Brendan is right in deleting the french posts, the language on the FQXi site is English, we are from all over the world it would become a tower of Babel when everybody was going to write in his language.

Furthermore we are discussing Fondamental questions in science, like the discussion between Florin and Joy, of course there are sideways we encounter but it keeps on the subject of awareness of our reality, nobody is stealing anything, we are SHARING our views, please share your views with mine.

keep on thinking free

Wilhelmus

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Sorry , but I think that Brendan is right in deleting the french posts, the language on the FQXi site is English, we are from all over the world it would become a tower of Babel when everybody was going to write in his language.

Furthermore we are discussing Fondamental questions in science, like the discussion between Florin and Joy, of course there are sideways we encounter but it keeps on the subject of awareness of our reality, nobody is stealing anything, we are SHARING our views, please share your views with mine.

keep on thinking free

Wilhelmus

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Joy Christian : after counting all the potential possible outcomes of an experimental setting, and then embed these results in a paralellizable manifold, a topological space is created that he called OMEGA.

These paralellazible manifolds Joy Christian uses are SPHERES, my dear STEVE !!!

How do you react on this ?

keep on thinking free

Wilhelmus

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These paralellazible manifolds Joy Christian uses are SPHERES, my dear STEVE !!!

How do you react on this ?

keep on thinking free

Wilhelmus

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Dear Wilhelmus and Steve,

I completely agree that Spheres and lattices based on Kissing-Spheres are relevant, but these parallelizable spheres seem to be the most important:

1) Joy's 7-sphere represents the (7+1)-D math of an octonion. Furthermore, Kissing-7-Spheres leads directly to the 8-D E8 Gosset lattice.

2) Jonathan and I have thermodynamic arguments for why the 7-sphere should decompose into 3-spheres. The 3-sphere represents the (3+1)-D math of a quaternion. Furthermore, Kissing-3-Spheres leads directly to the 4-D F4 24-cell lattice.

and

3) The 1-sphere represents the (1+1)-D math of complex numbers. Furthermore, Kissing-1-Spheres leads directly to the 2-D G2 hexagonal graphene lattice.

It seems that Steve's 3-D spheres lead to tetrahedral, octahedral, and icosahedral symmetries. These are relevant because the tetrahedral point group may be a geometrical analogy to the Georgi-Glashow SU(5) GUT. Also, the icosahedral group introduces that infamous factor of '5' that we require for the Golden Ratio and properties of Scales.

HOWEVER, rotating 3-D 2-spheres are unstable against the Hairy Ball Theorem, AND it is unclear as to how to generate the higher symmetries (such as 7-fold) with 3-D spheres.

I know that Steve considers it illogical to introduce an unobservable Multiverse, but I think that consistent reasoning requires an infinite Big Bang singularity to produce an infinite Multiverse, and our finite observable Universe is but a fragment of fractal dust within that Multiverse. I like to compare it to Dr. Seuss' "Horton Hears a Who" - the difficult part for the human ego is that WE are the tiny Whos.

Have Fun and Keep Thinking Free!

Ray

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I completely agree that Spheres and lattices based on Kissing-Spheres are relevant, but these parallelizable spheres seem to be the most important:

1) Joy's 7-sphere represents the (7+1)-D math of an octonion. Furthermore, Kissing-7-Spheres leads directly to the 8-D E8 Gosset lattice.

2) Jonathan and I have thermodynamic arguments for why the 7-sphere should decompose into 3-spheres. The 3-sphere represents the (3+1)-D math of a quaternion. Furthermore, Kissing-3-Spheres leads directly to the 4-D F4 24-cell lattice.

and

3) The 1-sphere represents the (1+1)-D math of complex numbers. Furthermore, Kissing-1-Spheres leads directly to the 2-D G2 hexagonal graphene lattice.

It seems that Steve's 3-D spheres lead to tetrahedral, octahedral, and icosahedral symmetries. These are relevant because the tetrahedral point group may be a geometrical analogy to the Georgi-Glashow SU(5) GUT. Also, the icosahedral group introduces that infamous factor of '5' that we require for the Golden Ratio and properties of Scales.

HOWEVER, rotating 3-D 2-spheres are unstable against the Hairy Ball Theorem, AND it is unclear as to how to generate the higher symmetries (such as 7-fold) with 3-D spheres.

I know that Steve considers it illogical to introduce an unobservable Multiverse, but I think that consistent reasoning requires an infinite Big Bang singularity to produce an infinite Multiverse, and our finite observable Universe is but a fragment of fractal dust within that Multiverse. I like to compare it to Dr. Seuss' "Horton Hears a Who" - the difficult part for the human ego is that WE are the tiny Whos.

Have Fun and Keep Thinking Free!

Ray

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Very interesting article in NEW SCIENTIST , from Lee Smolin and others, his phse space needs 8 dimensions, I do not understand why, but I see some paralels with the topological space OMEGA.

keep on thinking free

Wilhelmus

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keep on thinking free

Wilhelmus

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You have the proof in live of my reasoning, simple and evident.They want my recognizing with the Ex of lisi .Never they can kill me now smolin you are a comic also,.FQXi it is that your member, wawww. Lisi,Lawrence, Tom,Florin,Smolin,Joy mainly are in a pure business for my recognizings simply.And now it is their last strategy , they simply fear , but we can pray for them and their consciousness.

Well tried,just a band of business men sponsorized probably by some privatye capitals.

STEALERS intelligent simply.

Steve

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Well tried,just a band of business men sponsorized probably by some privatye capitals.

STEALERS intelligent simply.

Steve

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I like your points of vue dear Wilhelmus,

How I react, I think it's perhaps the only one who understands really my theory, Joy seems a good scientists, I don't know his generality,nor his universality at this momment. I think he wants simply make a kind of work towards my theory, if it is that and if his work is good, why no? after all my theory is there for a pure sharing indeed.But with a deeper analyze,they want my prizes,that's all wilhelmus, have you seen their strategy, frankly it is just for monney.But after all they are just humans who makes errors. The most important now Ray, you want my prizes, never, you can copy after all, all people knows now it is my theory, and come on APS linkedin, the discussions are relevant also. Wilhelmus, they try that's all for my future capitals and the future billions, never. That's I must be strong. These kinds of people have already stolen me and that continues, it's sad.In fact you know ,they thoughts that my language, my sceinces, and my maths were noty reality.Now they understand and they are in a bizare position for their future credibility. But I can understand them and i can understand that they have a business team behind, you know there people who implies the chaos. And what I am going to say thanks also and accept that people profits of my economical situation. Never, that's why I have written on several platforms for a kind of protection, I was obliged.

Ray, if you say that the works of joy are more important, there yiou proof in live that it is just a business. Don't fear of my french I know I write well in all humility,lol but after all you oblige me to be like that, I am nice, but don't play with my kindness and my spirituality nor my universality. Frankly you are very bad fallen dear Team.You can use all strategies what you want , never that will change. I have nothing against you but You lisi, To and Lawrence, and Florin more now Joy , are just a team which supports the works of each other.Any sense. If now you want make a kind of super discussion between Joy and Florin for a kind of pseudo mathematical complexity, you are very bad fallen also, if you want imply confusions for publics, you are very bad fallen also. If you have no others strategies, I CAN SUGGEST THAT YOU LEARN MY EQUATIONS. E=(c²o²s²)m and mcosV=constant.where of course the number must be inserted with the volumes.Like the entanglement of cosmological spheres, you see the center ray,me yes. Don't copy but be rational.It is not a parano, no I am just conscient of this human nature and his taste for monney and power.I dislike these things simply.

Steve

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How I react, I think it's perhaps the only one who understands really my theory, Joy seems a good scientists, I don't know his generality,nor his universality at this momment. I think he wants simply make a kind of work towards my theory, if it is that and if his work is good, why no? after all my theory is there for a pure sharing indeed.But with a deeper analyze,they want my prizes,that's all wilhelmus, have you seen their strategy, frankly it is just for monney.But after all they are just humans who makes errors. The most important now Ray, you want my prizes, never, you can copy after all, all people knows now it is my theory, and come on APS linkedin, the discussions are relevant also. Wilhelmus, they try that's all for my future capitals and the future billions, never. That's I must be strong. These kinds of people have already stolen me and that continues, it's sad.In fact you know ,they thoughts that my language, my sceinces, and my maths were noty reality.Now they understand and they are in a bizare position for their future credibility. But I can understand them and i can understand that they have a business team behind, you know there people who implies the chaos. And what I am going to say thanks also and accept that people profits of my economical situation. Never, that's why I have written on several platforms for a kind of protection, I was obliged.

Ray, if you say that the works of joy are more important, there yiou proof in live that it is just a business. Don't fear of my french I know I write well in all humility,lol but after all you oblige me to be like that, I am nice, but don't play with my kindness and my spirituality nor my universality. Frankly you are very bad fallen dear Team.You can use all strategies what you want , never that will change. I have nothing against you but You lisi, To and Lawrence, and Florin more now Joy , are just a team which supports the works of each other.Any sense. If now you want make a kind of super discussion between Joy and Florin for a kind of pseudo mathematical complexity, you are very bad fallen also, if you want imply confusions for publics, you are very bad fallen also. If you have no others strategies, I CAN SUGGEST THAT YOU LEARN MY EQUATIONS. E=(c²o²s²)m and mcosV=constant.where of course the number must be inserted with the volumes.Like the entanglement of cosmological spheres, you see the center ray,me yes. Don't copy but be rational.It is not a parano, no I am just conscient of this human nature and his taste for monney and power.I dislike these things simply.

Steve

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My dear Ray,

You mention : infinite Big Bang singulairity.

Isn't that a "contradictio in terminis", surely when you apply this in a causal 4D universe, because when you accept a singulairity as "beginning" in fact it is "nothing", an infinite nothing is a very difficult idea for me.

If you place this origin after the lower limit (as I see it) of our universe the Planck length or the INTEGRAL length (10^-48m) then there is no longer a singulairity problem if you accept that after one of these lengths there is no more causality, but a new dimension wher every possibillity is present (read possible, see my essay wher I call that Total Simultaneity), so in fact your infinite singulairity is a way of expressing something that we cannot understand, perhaps it is comparable with Joy Christian's OMEGA.

keep on thinking free

Wilhelmus

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You mention : infinite Big Bang singulairity.

Isn't that a "contradictio in terminis", surely when you apply this in a causal 4D universe, because when you accept a singulairity as "beginning" in fact it is "nothing", an infinite nothing is a very difficult idea for me.

If you place this origin after the lower limit (as I see it) of our universe the Planck length or the INTEGRAL length (10^-48m) then there is no longer a singulairity problem if you accept that after one of these lengths there is no more causality, but a new dimension wher every possibillity is present (read possible, see my essay wher I call that Total Simultaneity), so in fact your infinite singulairity is a way of expressing something that we cannot understand, perhaps it is comparable with Joy Christian's OMEGA.

keep on thinking free

Wilhelmus

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Hi Wilhelmus,

Actually, 'infinite singularity' is unnecessarily repetitive, not contradictory.

I agree that - by incorporating new physics such as quantum gravity or quantum spacetime - we can regularize everything by truncating at a lower distance scale, say of 10^(-48)m. But such a truncation leads directly to lattices comprised of kissing spheres. Without new physics, the Big Bang tends towards an unrealistic single point with infinite density.

Your last paragraph is very similar to some of my ideas. I think that a proper representation of the TOE requires more dimensions and a Multiverse comprised of self-similar scales. One possible configuration of the Multiverse is MWI in which all possibilities are present.

Aren't you Dutch? Steve lives in Belgiam.

Have Fun!

Ray

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Actually, 'infinite singularity' is unnecessarily repetitive, not contradictory.

I agree that - by incorporating new physics such as quantum gravity or quantum spacetime - we can regularize everything by truncating at a lower distance scale, say of 10^(-48)m. But such a truncation leads directly to lattices comprised of kissing spheres. Without new physics, the Big Bang tends towards an unrealistic single point with infinite density.

Your last paragraph is very similar to some of my ideas. I think that a proper representation of the TOE requires more dimensions and a Multiverse comprised of self-similar scales. One possible configuration of the Multiverse is MWI in which all possibilities are present.

Aren't you Dutch? Steve lives in Belgiam.

Have Fun!

Ray

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No, the multiverses are a pure joke still from some universities. It is just a false road where the business dances. The infinity is bad understood, the physicality also. The dimesnsions for a real evolution rests in 3D and a time constant. The Universe is unique. It is all the principle of entropy in its pure distribution which is not raken with the biggest rationality. It is purelly a joke and an irrational road. Sometimes I say me "but what do you do in your country???" What is all this circus??? Ray your country is better than that, instead to centralize and unify, you divide??? just for the competion,I don't understand that, but don't forget that the sciences aren't a game simply. Instead to improve the world like you made before, you destabilize the global economy, just due to these comportments. A time for all Ray,No? It is very serious there you know the actual state of our earth. The USA in fact is a big project, then why ??? IF THE EARTH IS A FUTURE BIG VILLAGE? THEN WHY???

Steve

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Steve

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Hi Steve,

I think you are making political observations of my country. First realize that I am but one of 300,000,000 people who may have various shares of 'fault' in our current situation. Although I am a fiscal conservative, I see both sides of this political argument. On one hand, Congress' deficit spending is destroying our international credit rating, is indebting our younger generations, and pushing us closer to a default (imagine Greece a hundred-fold), but people still have jobs. On the other hand, the financially-responsible position is to cut spending so as to minimize the deficit (the State of Florida is closer to this position than is the Federal Government), but then you are cutting jobs in the middle of an economy that seems vacillating between Recession and Depression, and such an action would definitely trigger a Depression.

It is a lose-lose situation caused by the American real estate and mortgage bust a few years ago, combined with unreasonable spending by a Democrat-majority Congress (since 2006), combined with two long-term wars (both initaited by Bush and continued by Obama - remember how the war with Afghanistan in the early 80's weakened the Soviet Union's economy?). We don't need to point out blaim. We need to work out reasonable compromises.

I am trying to hold up my share of the economy. My company still employs 25 people - that is down from our peak of 28 five years ago, but we are trying...

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I think you are making political observations of my country. First realize that I am but one of 300,000,000 people who may have various shares of 'fault' in our current situation. Although I am a fiscal conservative, I see both sides of this political argument. On one hand, Congress' deficit spending is destroying our international credit rating, is indebting our younger generations, and pushing us closer to a default (imagine Greece a hundred-fold), but people still have jobs. On the other hand, the financially-responsible position is to cut spending so as to minimize the deficit (the State of Florida is closer to this position than is the Federal Government), but then you are cutting jobs in the middle of an economy that seems vacillating between Recession and Depression, and such an action would definitely trigger a Depression.

It is a lose-lose situation caused by the American real estate and mortgage bust a few years ago, combined with unreasonable spending by a Democrat-majority Congress (since 2006), combined with two long-term wars (both initaited by Bush and continued by Obama - remember how the war with Afghanistan in the early 80's weakened the Soviet Union's economy?). We don't need to point out blaim. We need to work out reasonable compromises.

I am trying to hold up my share of the economy. My company still employs 25 people - that is down from our peak of 28 five years ago, but we are trying...

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Florin,

I searched through the messages. I didn't see one of yours about the 'von Neumann theorem'. I went through it message by message twice. I did use 'von Neuman' as my key words to spot. Perhaps I should be using other key words to look for?

James

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I searched through the messages. I didn't see one of yours about the 'von Neumann theorem'. I went through it message by message twice. I did use 'von Neuman' as my key words to spot. Perhaps I should be using other key words to look for?

James

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I'm not exactly sure what you are looking for, but I remember Florin talking about Von Neumann and Bell in the text of this article he wrote last year:

Part 2 of To Be or Not To Be (a Local Realist)

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Part 2 of To Be or Not To Be (a Local Realist)

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