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Does Quantum Mechanics entail that the world is non-local? 1 - Introduction Quantum mechanics, according to the interpretation of the Copenhagen’s school, is a very special theory among the corpus of physics theories. Quantum mechanics, based on quantification of all quantities, is an indeterminist and non-realist theory and appears to be non-local. The quantification of quantum mechanics has been accepted by all physicians, as Einstein, because this theory is only relative to microscopic world which is constituted by particles and their interactions. The indeterminism and the probabilistic interpretation of wave function, introduced in first by de Broglie, has been rejected by some physician as Einstein; even Schrodinger doesn’t agree with the indeterminist and probabilistic interpretation of his equation. Bohm has tried to solve this difficulty introducing the determination of position and two new concepts: the quantum potential and the pilot wave. Bell, studying mathematical consequences of Einstein’s paper and Bohr’s reply, has established a theorem which authorizes to conclude at non-locality of quantum mechanics. Using the up to date technology developed on optical system measurement and generation of entangled particles, Aspect has realized crucial experimentations from 1980 until 1986 demonstrating that it is possible to have system in which there is non-local interaction. The main problem of non-local interaction is the contradiction with the limitation of the light speed according to special relativity. Even there is no agreed understanding of non-local experimental results, we will try, in this essay, to establish that the non-local aspect of quantum mechanics observed in some experiments entails that world is non-local. 2 – The thesis and the argument Most studies on locality concept use references based on entangled couple of particles as photons. But non-locality is not only linked to entanglement. More generally, with a single particle experiment, we can observe a non-local behavior, as for example in a Mach Zehnder interferometer using single photon. According to the complementary principle, we know that every particle can have a double aspect: wave or particle. Wave aspect can be described by Schrodinger’s equation. The choice made by an object, in an experiment, between the two aspects, is only determined by the experimental system. As long as we do not try to make measurement on one particle on its inside path, particle will be described with a wave packet. Since about twenty years, a lot of experiments have been realized using not only photons but also other particles and recently atoms and molecules as fullerene C60. Therefore, every type of particle, photon, neutron or molecules, used in a non-local experimental device, lead to a non-local behavior provided there is no inside procedure12 using an external measurement system. Then the particles get a non-local behavior. In this essay we argue that all particles entangled or not, and not observed by an external measurement system in such way the wave function couldn’t show us the particle aspect, have a non-local behavior. Then the universe, which can’t be under measurement operation by an external measurement system, is globally non-local. 1 Entanglement of particles requires that particles have strong interaction in a sufficient manner and time to be not separable, so to be mathematically described with a unique wave function. Then it becomes impossible to describe only one particle without the other one, the only way is to describe the complete system of both particles, even particles that are separated by a very long range, beyond the authorized value of light speed communication in case of interactions with both particles in a very short interval of time. Entangled particles have been observed, up to now, only via spin or polarization, but some experimental researches are being done to find out other way to entanglement. More often, for one single particle, we can observe non-local behavior, for example in a MachZehnder interferometer, except if we try to directly determine “where the particle is” with an external measurement process. In that case the wave function collapse and particle is observed as a small volume of matter, a classical particle described by classical mechanics. Bohm has tried to explain the non-local behavior of a particle as a direct consequence from what he called “the quantum potential”3. For Bohm, this quantum potential is an overall property of the universe. For him quantum potential is the “one wave function” of the complete universe. Then if a particle “knows” the global description of the interferometer before go to in, it is because quantum potential contents all information about it. That’s for Bohm the explanation of non-locality. More, he explains that if one tries to realize interferences with a beam of single particle, one by one, he will still observe it because the particle will be accompanied by a special stationary wave, “the pilot wave”, discovered by de Broglie4, able to guide each particle to the right position to produce interference figures. Stationary matter wave discovered by de Broglie has a wave length given by = = ² 1 − ², where m is the mass of particle and its speed measured in an inertial frame. It is constituted by two waves, one delayed and one advanced, this one, quite strange, could be explained in Bohm theory as coming from the global wave function of universe. We see that wave length is proportional with the reverse of mass, then for macroscopic objects, the wave length will be too small, so unmeasurable. Thus macroscopic world can be described using continuous classical mechanics and relativity. We have now to look at the origin of this global wave function. At the origin of universe a Big-Bang was happening. According with the cosmological standard model, the universe at the beginning was very small: physicists estimate his diameter was about 10-51 meter. From time about 10-34 seconds to 10-32 seconds, there was an inflationist period meanwhile the universe was growing by a factor higher than 1060. During the inflation period, all existing particles were generated from the vacuum, in a very small volume, under the effect of a scalar file, the inflaton. Thus all particles of the universe, at this time, had interactions strong enough to build up a global entanglement system and then a global universe wave function. That one has been defined by Bohm as the quantum potential, the global wave function of universe. Then, if all particles of universe can be described by a global wave function, which is a superposition of all individual states of particles, world should be non-local few times after universe’s birth. But an important question is pending: how come this global wave function can still exist after a so long time? 2 As far as we understand quantum mechanics, the non-local characteristic linking some particles can be gotten by two main procedures: entanglement or physical objects interacting with system without any in between external measurement procedure. In the entanglement effect, a source system generates two identical particles at the same time and from the same generation procedure. For example, a Rydberg atom coupled with microwave cavity is one possibility. Such entangled states aren’t separable. Let’s take an example: two particles having only two states ∣ and ∣ − ; a nonentangled state of these two particles will be described by the global wave function: = √ ∣ √ ∣ ∣− −∣ − ∣− = √ ∣ −∣ − ⊗∣ − , And an entangled one by the global wave function: = ∣− −∣ − ∣ . This special state is a result of a so strong interaction between two or more particles leading to the impossibility to describe separately each particle. This configuration is totally different from having two linked particles described in a unique inertial framework. For entangled particles, any measurement action on one component of entangled state determines immediately characteristics measured for the other parts of the system, even components are at supraliminal distance, by the collapse of entangled particles wave function. The nature of entangled state is still unexplained. Until now we get entangled system with photons and some particle with mass5. But hopefully, entanglement is not the only way to get non-local behavior for particles. Some experimental results cannot be explained without non-local argument. That is the case for Mach Zehnder interferometer. Such experimental system uses semitransparent mirror to get two different optical paths for photons. Mirrors are disposed in such way that the two different paths, geometrically of the same length, have optical lengths which differ by a 180° difference of phase (see figure). At the output of last semitransparent mirror, there are two detectors which count the number of photons arriving. For a light beam, as a laser, all photons will be detected by the counter in path with the 0° phase’s difference (TT or TR), and none in the other one (RT or TR). That the result of classical optical laws according with Maxwell theory and coherence length of used light. Now, if we use a very weak beam able to generate photon one by one, we will continue to receive all photons on the same detector. But on the first semitransparent mirror, each photon makes a choice corresponding to only one path. So we should detect the same number of photons in both counters, because there is not anymore interference between different photons using different paths. But anyway, we still detect all particles on the same detector. The only explanation on this result seems to be instantaneous information of the global experimental system got by the photon arriving at the first semitransparent mirror. So it is non-local behavior for photons. Of course this detection on only one counter is conditioned to no one external measurement in any way and to any point on the possible paths followed by photons. If we try to do any measurements on photon during the time 3 transit from input to output, wave function will collapse and we will detect 50% photons, as pure particles behavior, on each counter. Now, getting explanation of this strange particle behavior, we do have a look on Bohm theory. The de Broglie–Bohm theory is known as the pilot-wave and quantum potential theory. The pilot wave has been established by de Broglie in his thesis. He also postulates in a realist position that an actual configuration, a material device, exists even when unobserved. De Broglie was thinking that evolution of his wave function over time was given by Schrödinger's equation. But it was confused understanding: pilot wave is different from Schrodinger wave function which represents a function of probability density. In addition, de Broglie pilot wave is a stationary one, constituted by two waves: a delayed one and an advanced one. This advanced wave is a strange one: from where this advanced wave is coming from? Bohm can answer to this question, adding four new assumptions to the quantum mechanics: - The wave function is real and not only a mathematical object - Particles exist and their positions are known any time in a deterministic way - It exists a pilot wave accompanying particles with a frequency function of particle’s speed - He adds also a new concept: the quantum potential =− ħ ∇² ! where ! = | | ; this quantum potential is the manifestation of universe wave function Other rules are those of quantum mechanics as described by Copenhagen’s school. Bohm add also a new equation to guide the particles with the pilot wave: $%& ' # = ħ∇& (# ln %& , ' $' The de Broglie–Bohm theory is explicitly nonlocal: the velocity of any particle depends on the value of the guiding equation, which depends on the configuration of the entire universe “This undivided whole is not static but rather in a constant state of flow and change, a kind of invisible ether from which all things arise and into which all things eventually dissolve. Indeed, even mind and matter are united: "In this flow, mind and matter are not separate substances. Rather they are different aspects of one whole and unbroken movement" (Bohm, in Hayward 1987, 25). In de Broglie-Bohm theory, the wave function travels through both slits, but each particle has a well-defined trajectory that passes through only one slit. The final position of the particle on the detector screen and the slit through which the particle passes is determined by the initial position of the particle. Such initial position is not knowable or controllable by the experimenter, so there is still an appearance of randomness in the pattern of detection. The wave function interferes with itself and guides the particles in such a way that the particles avoid the regions in which the interference is destructive and are attracted to the regions in which the interference is constructive, resulting in the interference pattern on the detector screen. Bohm assumption is that the environment is registering the detection effectively separates the two wave packets in space’s configuration. The wave function, and not the particles, determines the dynamical evolution of the system. In Bohm theory, quantum potential is a wave-like term that provides information to the particle, linking it to the rest of the universe. The quantum potential is responsible for the well-known wave-particle duality and all the other strange phenomena. This quantum potential action has been demonstrated by a very famous experiment, the Aharonov - Bohm effect6. Experimental system is an interferometer using electron’s beam. Between slits there is a solenoid giving a magnetic field in a volume covered by a magnetic shield isolating totally solenoid from the rest of the system. So no magnetic field is detectable in the rest of the interferometer. Nevertheless, when the magnetic field, being off, is 4 turning on, we observe a shift in the interference lines and when we reverse magnetic field direction, we get the opposite shift direction for interference lines. Electrons don’t have any information on an existing magnetic field. But the only fact that, somewhere, an event able to potentially modify the path of electrons exists is sufficient to change the interferences figure. If we do the same experiment, but with an electron’s beam going one by one, we get of course the same result. So it appears that a global world wave function exists and not collapses under our measurements. 3 – Argument’s justification Comparing Copenhagen school positions and Bohm one, we find they get similar results in term of experimental explanation and theoretical forecast. In Bohm theory, the particle’s position is known using a separate equation which completes the Schrodinger one. Bohm used for the wave function a / very classical relation: = -. & ħ , where R is a real number and S a phase function. Using this relation in the Schrodinger equation, we get two equations: a guiding equation for particles and a new Schrodinger equation in which appears a new term representing quantum potential. The main question is then to examine whether Bohm theory is describing correctly all quantum mechanics results. Many philosophers have studied this problem, as Bricmont7, and have concluded that Bohm theory is compliant with mathematical corpus of quantum mechanics as described by Copenhagen’s school provided we agree Bohm theory is a non-local one. But Bohm theory is really a non-local theory, non-relativistic, and also a realist and determinist one. In quantum mechanics, any particle is described by a wave function, until any physical characteristics of the particle is measured by the means of an external system. That’s the complementary principle postulated by Bohr and never been pushed in fault by any experiment. So using the superposition principle, and Bohm world representation, we can assume that all particles in the world, provided they are not under measurement procedure of physical characteristics are described by a unique wave function. This global wave function is a non-local one as long as we don’t make measurement by an external system. The fundamental question is now how to prove that “unique wave function for the universe” exists. The answer is on the quantum potential, whose realism Aharonov and Bohm have experimentally proved. But we can object that, since a long time, we have often done some measurements on some parts of the world system to understand physical laws. Then global wave function should have been collapsed since a long time ago. In fact, all experiments trying to measure such physical parameter of a system need two things: a physical system in which we do experiment and an external measurement apparatus. When all these conditions are gathered, the wave function will collapse and provide a result, a numerical value on the measurement apparatus screen. Bigger is the 5 measurement apparatus, faster the wave function will collapse. But we are necessarily inside the universe, inside the system described by the global wave function at the beginning of the universe, and every measurement apparatus also. All objects in the world are parts of the global system described by the universe wave function. Then the global wave function can’t collapse. At the end we must be sure that the process to get this global wave function has existed in the past. Many theories exist to explain the beginning of our universe, some of them agree with inflation model, the other ones do not, but all describe a period of time during which particles have been created with a very strong interaction each other, enough to create a global wave function including all particles. We know that particles which have a strong interaction must be described by a unique wave function sum of different states of those particles. 4 – The context The main opposition to this thesis is Einstein realism position according to the transmission of information at a higher speed than the light speed; for him it is simply impossible and non-locality doesn’t exist. It is indeed difficult to agree that “something” is linking two objects without interaction and with a distance corresponding to a supraliminal interaction. In Einstein EPR paper, Einstein describes an interaction between two particles to create a unique wave function describing both particles (states superposition). Einstein makes assumption, when particle are at a sufficient distance, that is impossible to collapse wave function for both particle if operation of measurement is realize on only one particle. EPR paper and Bohr’s reply was written in 1935. They can’t know results of experiments as those from Aspect or Mach-Zehnder interferometer. They should have been very surprised by the result of experiment called “quantum eraser with late choice”8 or “Entanglement between photons that have never coexisted”9. All these experimental results support the non-local idea but without answering to the question of how it happens. Then our answer to Einstein opposition cannot be complete. We only justified the validity of our assumption concerning the non-locality of the universe, not the nature of the “link”. But there is another argument against our assumption: the global wave function decoherence. This idea was developed by some physicians as Haroche. This theory attempts to explain transition between quantum mechanics and classic one. In microscopic world, particles follow the principle of complementarity. So for macroscopic objects, the corresponding wave function is the sum of all particles individual wave functions. Decoherence theory argues that in this case, under the interaction with external environment, it will appear destructive interferences which is equivalent to describe macroscopic system in terms of classical mechanics. Then a global world wave-function is impossible. Decoherence is an interaction with environment10. More complex is the environment, faster the wave function collapses. 6 5 – Objections and replies Decoherence theory is indeed the main objection which can be opposed to our thesis. We have explained before how this argument can be used to deduct that wave function must collapse. Decoherence theory is a proved theory provided measurement or interaction is made with an external system. Any internal system will keep the global wave function and could collapse only sub wave function representing part of the global system. So a system will keep its wave aspect until there is an external measurement action, a measurement using an apparatus not included in the measured system. But in our assumption, everything is necessarily inside the system, and then no external measurement devices are possible. There is no reason for the universe wave function to collapse; the global wave function is stable. When we experiment a system on earth, we test a limited part of the global universe, then only a small part of global wave function can collapse. Recently interference figures have been obtained with macroscopic objects as fullerene molecules comprising 60 carbon’s atoms and with 012 312 molecules. So the decoherence effect is not operating from these macroscopic molecules proving that decoherence can happen only in case of external measurement device. Linked to this last objection there is the problem of the reality of the wave function11. Schrodinger thought wave function cannot be real. He imagined the paradox of cat alive and dead at the same time. The wave function implies necessarily this kind of situation. So, if wave function is real, how come can we agree with such unrealistic situation of cat simultaneously dead and alive? In other words, is the wave function real or only a mathematical tool useful to make computation? Even if we assume that wave function should be considered as a mathematical tool, experimental particle behavior is equivalent to a wave packet. If it was not the case, how come could we explain interference figure given by particles as electron or neutron with Young interferometer. Wave behavior for particle can be explained with matter wave discovered by de Broglie and identified as pilot wave in Bohm’s theory. So, even if we claim a mathematical interpretation of wave function, experimental results show real wave behavior of particles. To complete our study, we must examine the leak of delay in the non-local systems. From plasma studies we know that the product of group speed by phase speed is equal to the square of light speed. So, lower is the group speed, faster is the phase speed, which is always greater than the light speed. There is no contradiction with relativity because phase wave does not carry energy. Then, it is possible to understand how a particle can “know” the description of a system. But for a photon this explanation doesn’t work. We can use another property of general relativity: the distance between two points is an invariant: 4²$5² = 4²$'² − $% − $6 − $7² Where 5 is the local time measured by an observer in an inertial frame, and t, x, y, and z the absolute time and coordinates; t mathematically exists but we can’t measure it. For a photon, we get the wellknown relation: 4²$'² = $%² $6² $7². So it means $5 = 0, the local time is ever null. Then for a photon inertial framework time doesn’t exist and for it all instants are present. 6 – Implications A non-local global universe means that every object, or every life form will have an instantaneously and mutual influence. In a certain way, under a global wave function, we are a part from a global 7 “whole”. In this “whole” we include matter, vacuum, energy, and more generally every things which are in the universe. Then any event will have an influence, not a causal effect, on the rest of universe. 7 - Conclusion Quantum mechanics is the alone theory to show us some strange aspects of our universe. Entanglement, non-locality, wave function and its collapse, are some aspects of our realty such as we can know them with our human senses. That a non-local global world could exist shouldn’t surprise us. Three centuries earlier, the sky description seemed very simple, very organized and nevertheless we have been discovering since fifty years a new image of the universe. Non local links between everything in the world, related to a global wave function, should an idea not rejected a priori. Then non local behavior could be understood as an interface with an upper level of reality. 1 Nicolas Brunner, Nicolas Gisin and Valerio Scarani, New J. Phys. 7 (2005) 88 Haack, G. R.; Förster, H.; Büttiker, M. (2010). "Parity detection and entanglement with a Mach-Zehnder interferometer". Physical Review B 82 (15) 3 Christian Knobloch, for the seminar : Ausgewählte Probleme der Quantenmechanik, Faculty of Physics, University of Vienna, WS 2011/2012 4 Louis de Broglie, Recherches sur la théorie des quanta, Paris, 1924 (thèse de physique) 5 A. Aspect, P. Grangier and G. Roger, Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment : A New Violation of Bell’s Inequalities, Phys. Rev. Lett. 49, 91 (1982). 6 Y Aharonov and D. Bohm, Phys. Rev. 115, 484 (1959) 7 Jean Bricmont, philosophie de la mécanique quantique, Vuibert, 2009 8 Delayed choice quantum eraser, Y.-H. Kim, R. Yu, S. P. Kulik, Y. Shih, and M. O. Scully, Phys. Rev. Lett. 84, 001 (2000). 9 E. Megidish, A. Halevy, T. Shacham, T. Dvir, L. Dovrat and H. S. Eisenberg, arxiv: 1209.4194v1 [quant-ph] 19 sep 2012, Entanglement between photons that have never coexisted 10 Brune, Hagley, Dreyer, Mestre, Haroche « Observing the Progressive Decoherence of the “Meter” in a Quantum Measurement » Physical Review Letters, 77, 4887 (1996) 11 Roland Omnès, Les Indispensables de la mécanique quantique, Odile Jacob, 2006 2 8