# Beyond and across space: entanglement

Vasil Penchev

*Institute for the Study of Societies and Knowledge at Bulgarian Academy of Sciences*

Extended abstractEinstein, Podolsky, and Rosen (1935) suggested a thought experiment in order to demonstrate that quantum mechanics was ostensibly incomplete. Furthermore, they showed that the mathematical formalism of quantum mechanics had been granted as complete, it would imply some action at a distance beyond and across space, “spooky” in words of Einstein. Since that kind of action contradicted the principle of physics, quantum mechanics should be incomplete in their opinion. Edwin Schrödinger (1935) also pointed out that quantum mechanics implies some special kind of interaction between quantum systems by means of “vershränkten zustände” using his term. John Bell (1964) suggested a real experiment apt to distinguish quantitatively and observably between the classical case without that “spooky action at a distance” and the quantum one involving a special kind of correlation between physical systems, which can exceed the maximally possible limit of correlation in classical physics. The experiments of Aspect, Grangier, and Roger (1981, 1982) as well as all later ones show unambiguously that the forecast quantum correlations are observable phenomena. Thus that “spooky action at a distance” exists and quantum mechanics should be complete. The new phenomenon was called “entanglement” and a separate branch of quantum mechanics, the theory of quantum mechanics, studying that kind of phenomena has appeared and blossomed out since the 90th of the past century. The theory of quantum information showed that the phenomena of entanglement are underlain by the necessary restriction of the concept of space in relation to the coherent states in quantum mechanics. Space is a well-ordered set of points in relation to any observer or reference frame in it while coherent state in quantum mechanics is a whole of those points, which is inseparable and thus unorderable in principle. Both space and coherent state are initial elements of cognition mutually restricting their applicability. However, space refers to our everyday experience while the concept of coherent state or entanglement to scientific cognition in an area inaccessible to our senses. The concept of space should be limited to the relations between physical bodies of commeasurable mass. If a human is granted as an observer in space, the range of masses comparable with that mass (or energy) determines fussily the domain, in which the concept of space is applicable.

The way, in which the concept of space is being diluted gradually to and the beyond the limits of comparability in mass, can be visualized as follows: A de Broglie (1925) wave can be attached to any physical entity according to quantum mechanics. Its period is reciprocal to its mass (or energy). One can interpret this period as the length of the present moment specific to the corresponding physical entity of this mass (energy). If the masses (energies) of the interacting physical entities are commeasurable, they can share approximately a common enough present. If their masses (energies) are incommeasurable, what is the case in quantum mechanics studying the system of a macroscopic device, which measures one or more microscopic quantum systems, and that or those systems, the lengths of their present moments are also incommeasurable: The present of the entity of much bigger mass (energy) can be idealized as a point on the segment representing the length of the present of the entity with much less mass (energy). Furthermore, the present of the measured quantum systems being an approximately common segment will include as the past as the future rather than the present of the device. The past of the device will be represented as all points of the segment, which are before the point of the present of the device, and its future as those after this point.

Consequently, the concept of coherent state in quantum mechanics refers both to the future and past as well as to the present of the investigated system while that of space only to the present, because of which the condition for the present of all discussed entities to be commeasurable is necessary in the latter case. Indeed the future of any entity is unorderable in principle and just this property of it is rigorously represented by the concept of coherent state. However, the past of any entity is always well-ordered as the series of all past moments in time. Therefor the description in quantum mechanics has to provide the invariance both to the unorderable future and to the well-ordered past. In mathematical terms, this means that the so-called well-ordering theorem equivalent to the axiom of choice is necessarily involved. Furthermore, the present always situating and intermediating between the past and the future is just what any choice transforming future into past shares. Space makes possible choice and thus the transformation of future into past. Entanglement transcending space should be defined as temporal interaction involving the future and past of the macroscopic devices displaying quantum correlations. While any classical correlation should refer only to the present of the correlating entities and thus to the space, in which they are and which they share, any quantum correlation transcends the present and space involving the future and past in order to be able to exceed the maximal possible bound of all classical correlations. Furthermore, the entanglement involves the concept of quantum information. It is a generalization of the classical concept of information in relation to the choice among an infinite set of alternatives.

All those studies in quantum mechanics and the theory of quantum information reflect on the philosophy of space and its cognition. Space should discuss as a “transcendental screen” (a necessary condition of visualization or objectification), on which all phenomena are represented by masses comparable with those of observers granted as human beings. Our sensual experience as well as classical physics observes and studies only phenomena within the framework of space and therefore it cannot transcend it. However, quantum theories can do this allowing of interpreting space newly as the domain of interaction of bodies of commeasurable mass or of physical entities of commeasurable energy and thus as that area of choice, which is able to transform future into past.

References:

Aspect, A, Grangier, R., Roger, G. (1981) Experimental tests of realistic local theories via Bell’s theorem.Physical Review Letters, 47(7), 460-463. Aspect, A, Grangier, R., Roger, G. (1982) Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedanken Experiment: A New Violation of Bell’s Inequalities.Physical Review Letters, 49(2), 91-94. Bell, J. (1964) On the Einstein ‒ Podolsky ‒ Rosen paradox.Physics(New York), 1 (3), 195-200. Broglie, L. de (1925) Recherches sur la théorie des quanta Researches on the quantum theory), Thesis (Paris), 1924.Annales de Physique(Paris, 10-ème série) 3, 22-128. Einstein, A., Podolsky, B., Rosen, N. (1935) Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?Physical Review, 47 (10), 777-780. Schrödinger, E. (1935) Die gegenwärtige situation in der Quantenmechanik.Die Naturwissenschaften, 23(48), 807-812; 23(49), 823-828; 23(50), 844-849.