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World Journal of Condensed Matter Physics

Reciprocity Relation between the Mass Constituents of the Universe and Hardy’s Quantum Entanglement Probability

H. H. Otto

Published Jan 1, 2018• 9 citations
Publisher

Abstract

In this short contribution, a reciprocity relation between mass constituents of the universe was explained governed by Hardy’s maximum entanglement probability of φ5 = 0.09017. While well explainable through a set-theoretical argumentation, the relation may also be a consequence of a coupling factor attributed to the normed dimensions of the universe. Also, very simple expressions for the mass amounts were obtained, when replacing the Golden Mean φ by the Archimedes’ constant π. A brief statement was devoted to the similarity between the E-Infinity Theory of El Naschie and the Information Relativity Theory of Suleiman. In addition, superconductivity was also linked with Hardy’s entanglement probability.

DOI
10.4236/wjcmp.2018.82003

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In this short contribution, a reciprocity relation between mass constituents of the universe was explained governed by Hardy’s maximum entanglement probability of φ5 = 0.09017. While well explainable through a set-theoretical argumentation, the relation may also be a consequence of a coupling factor attributed to the normed dimensions of the universe. Also, very simple expressions for the mass amounts were obtained, when replacing the Golden Mean φ by the Archimedes’ constant π. A brief statement was devoted to the similarity between the E-Infinity Theory of El Naschie and the Information Relativity Theory of Suleiman. In addition, superconductivity was also linked with Hardy’s entanglement probability.
Building upon the pioneering work of J. Bell [1] and an incredible result due to L. Hardy [2] it was shown that the probability of quantum entanglement of two particles is a maximum of 9.0169945 percent [2]. This happens to be exactly the golden mean to the power of five (?5) [3-7]. Although it has gone largely unnoticed for a long time, this result was essentially established independently in a much wider context by the present author almost two decades ago [3-6]. The present work gives two fundamentally different derivations of Hardy’s beautiful result leading to precisely the same general conclusion, namely that by virtue of the zero measure of the underlying Cantorian-fractal spacetime geometry the notion of spatial separability in quantum physics is devoid of any meaning [7]. The first derivation is purely logical and uses a probability theory which combines the discrete with the continuum. The second derivation is purely geometrical and topological using the fundamental equations of a theory developed by the author and his collaborators frequently referred to as E-infinity or Cantorian spacetime theory [3-7].
The present work brings together three different fields which depend crucially upon nano hardware under the umbrella of E-infinity theoretical framework. We start by following E-infinity topological methodology by dividing Hardy’s entanglement into two parts, a global ‘counterfactual’ part given by Φ3 where Φ = 2/(1+ √5) and a ‘local’ part Φn where n is the number of quantum particles. For Hardy’s celebrated gedankenexperiment with two quantum particles, which was moreover experimentally confirmed with high accuracy, the quantum probability is found for n = 2 to be P(2) (Hardy) = Φ3+2= Φ5 exactly as calculated by Hardy using orthodox quantum mechanics. Applying the same topological E-infinity entanglement theory to three quantum particles give a maximal Φ6 as well as a three partite much smaller value equal Φ3(1− Φ3)/ = 0.018033989. We conclude by outlining the relevant and extremely timely ideas and remarks on the possible connection, via a state of the art nanotechnology, to the Casimir effect as a conjectured origin of dark energy.
Entanglement is a fundamental feature of quantum mechanics and plays an important role in characterizing many-body systems and quantum phase transitions. A quantitative measure of quantum correlations between subsystems is entanglement entropy. In this thesis, we study the entanglement entropy of an interacting quantum field theory, the O(N) model. In local quantum field theories, the leading-order contribution in the scaling of entanglement entropy obeys an area law. This dominant term is governed by short-distance physics near the entangling surface and depends on the ultraviolet regularization, making it non-universal. Beyond this lead- ing scaling behavior, entanglement entropy can contain subleading universal contributions, which encode intrinsic information about the underlying quantum field theory. In this thesis, we calculate one such universal term: the correlation length coefficient r, which appears as a correction to the entanglement entropy evaluated slightly away from the quantum critical point. The analysis is carried out in D = 2 + 1 spacetime dimensions for an infinite cylindrical geometry. We study the model in the vicinity of criticality using the large-N expansion, which enables controlled analytical calculations. Our main result is that the coefficient r scales linearly with the number of field components N . This behavior is consistent with the interpretation of r as a universal quantity associated with the degrees of freedom of the theory. The calculation is based on the replica method and renormalization group arguments, which are presented in detail. Finally, we discuss the physical meaning of the result and possible methods for verifying it, and we review related results for the O(N) model in different geometries.
The theory of relational accommodation postulates that our universe is a specific set of coherently accommodating relations between logical probabilities. This set of accommodating probabilities exists in a bigger framework: the ground state of everything. In this ground state all logical probabilities and their relations exist simultaneously in superposition. This ground state cannot be absolutely nothing, because without even potential, nothing could logically exist. The ground state cannot be some specific probabilities because then it would logically be something. So from a strictly logical perspective the only way something can be nothing is when it is all logical probabilities at once. Because it is not differentiated it is nothing specific and therefore akin to nothing. It is pure potential. Without dimensions. The probabilities in the ground state must be logical. If they are not logical then endless unpredictable realities would arise and no stable reality can form. In this ground state of pure potential there are relations between probabilities. If a relation changes then they all change to accommodate for the change. If a set of relations is coherent then all relations in the set can interact in a way that is coherent with the set. For the set a specific reality forms: the coherence with the set. If a set of relations is stable then it exists further. Our universe is such a set of relations. As long as probabilities and relations are coherent with our set of accommodating relations then they are real to us. The rest is filtered out. They could be part of another set of coherent relations but that set doesn’t share coherence with our set, so we can’t see the other set. To go even further: it would then not exist to us. If one accepts this conclusion, one starts to see that everything must be an accommodated set of relations between probabilities that is part of the total set that is our universe. Once this conclusion has been drawn the next step is to see that particles or massive objects are in fact an enormous number of accommodating relations that must be processed to maintain coherence within the set. Therefore it seems logical that mass is a set of accommodating relations between probabilities. This means that to process a certain amount of mass it would take an amount of time to process the relations. This would mean there are more or less dense areas of processing. This different amount of time it takes to process relations, creates differences in dimensions. Therefore dimensions are not fundamental. They emerge when a coherent set of relations needs to process to stay coherent. I found that there is even a formula to describe this. The system accommodation load of a mass (S) in rest is related to the smallest amount of relations that has dimensions. This is the Planck unit consisting of the Planck time and the Planck length. S(m) = m ∙ l_P / t_P / r (or since l_P / t_P = c:) S(m) = m ∙ c / r. It is in fact the proportion of mass and volume (radius) versus the smallest unit of relations. The system accommodation load is expressed in kg/s. The system accommodation load (S) in itself has relevance if one correlates this to the frame of dimensions it causes. I call this frame A_(xyzt). What is frame A? Frame A is the capacity for creating space and time that is left over when the relations of a specific mass have been processed. The maximum amount of relations a Planck unit can process, is also known in existing physics. Its S = c^3 / G. It is the light speed to the third power divided by the gravitational constant. This number represents the maximum accommodating capacity in kg/s of a Planck unit. Therefore frame A_(xyzt) = 1 – S(m) / S_max. To calculate the dimension frame of a mass and therefore relate distance of time to this mass one can use A. Another addition is that if the object has speed more relations have to be accommodated. This can be added by multiplying with the Lorentz factor (gamma v) γ_v = 1 / √ 1 – v^2 / c^2 which leads to formula: S(m) = (m ∙ c / r) ∙ γ_v. If an object is moving through a space with multiple masses with different speeds the formula gets like this. S_total = S_obj1 + S_obj 2 + S_obj x + … (relative r to obj1). With frame A_total = 1 – S_total / S_max. The results of this calculation are remarkably similar to General Relativity. Except for very heavy objects, when a small deviation is seen. It would be an object for research to analyse why this difference exists. Another factor which can be added is temperature. The reason for that is that raising temperature means more speed for particles. This is an extra gamma factor, which I suspect could be γ_T = 1 / √ 1 – v^2_Th / c^2 or γ_T = 1 + Q / mc^2 or S_Q = Q / rc (S = S_m + S_Q). Adding γ_T leads to formula S(m) = (m ∙ c / r) ∙ γ_v ∙ γ_T expressed in S(kg/s) where m : v : T is an exchange ratio.
The amount of nonlocality in quantum theory is limited compared to that allowed in generalized no-signaling theory [S. Popescu and D. Rohrlich, Found. Phys. 24, 379 (1994)]. This feature, for example, gets manifested in the amount of Bell inequality violation as well as in the degree of success probability of Hardy's (Cabello's) nonlocality argument. Physical principles like information causality and macroscopic locality have been proposed for analyzing restricted nonlocality in quantum mechanics, viz. explaining the Cirel'son bound. However, these principles are not very successful in explaining the maximum success probability of Hardy's as well as Cabello's argument in quantum theory. Here we show that a recently proposed physical principle, namely local orthogonality, does better by providing a tighter upper bound on the success probability for Hardy's nonlocality. This bound is relatively closer to the corresponding quantum value compared to the bounds achieved from other principles.