Coda: On the Meaning of Nonlocality

All things by immortal power, Near or far, Hiddenly, To each other linked are That thou canst not stir a flower Without troubling of a star.

Francis Thompson

Apparently, quantum theory postulates the existence of correlations very similar to the ones implied by the words of the poet. Nonlocal entanglement as well as other long-range quantum correlations seem to have no limits in that they hold independently of the distance between their component "parts." Thus, if one does not for practical purposes simply ignore EPR• type correlations, there are no separable "objects": according to quantum mechanics, an atom on the tip of your finger is literally linked with the faintest stars, right now. But is this really so? Actually, of course, we do not know. In fact, such claims are only extrapolations from our present-day experience, including the corresponding theoretical framework. However, the approach of quan• tum cybernetics presented here has already indicated one possible limita• tion of nonlocal effects in that it takes a finite time for changes to be me• diated along nonlocal distances. Moreover, it is certainly conceivable that in a model beyond today's quantum theory there exists a "noise term" to 136 Coda: On the Meaning of Nonlocality be added to nonlocal correlations. Consequently, with increasing distance between, say, two "parts" of an entangled system, the noise would add up, so that eventually the correlations would break down. Today, the range of nonlocal correlations is proven by experiment up to distances of several kilometers, so one can think of experiments over interplanetary distances, for example, to inquire whether entanglement persists or is faded out due to some "subquantum noise." However, other possible mechanisms are known in present-day theories to produce fairly isolated objects. Both in high-energy - as well as in solid-state - physics, one speaks of so-called "dressed particles" when the "naked particles" of the ordinary theory strongly interact with their en• vironment. Such is the case with collisions of particles at high energies, or with particles strongly bound to the potentials of a solid-state body. Thereby, parts of the environmental effects are added to the newly created object so that it becomes a "dressed particle." In general, it seems that, despite entanglement and EPR correlations, evolution has found ways to break down a holistic symmetry by "self-organizing" objects into organiza• tionally autonomous units. Consequently, one arrives at a characterization of evolution that is somehow opposite to the usual assertion that more and more complex forms of organization arise. However, considering that the word "complex" is derived from the Latin "complector," that is, to put together, we see that a single electron is more "put together" (i.e., more complex) than a dressed particle in a solid-state body: an electron is EPR correlated to the environment of its radiation field with infinitely many de• grees of freedom, whereas a dressed particle's degrees of freedom are much more reduced by the particle's "confinement" in the solid state. Therefore, the more "complicated" (from the Latin "com-plicare," i.e., folding together) an object is (as opposed to "simple" or unrestricted with regard to EPR correlations), the fewer degrees of freedom of interaction with the environment there are, that is, the less "complex" such an ob• ject is. Thus, it is more appropriate to describe evolutionary processes in terms of the emergence and development of autonomous units with ever fewer EPR correlations: viewed quantum-mechanically, then, evolution is a process of de-complexification into states of ever higher forms of autonomy [Grossing 1993a]. To obtain a deeper understanding of the implications of quantum cyber• netics, it is essential to re-introduce modes of thinking based on continuum models for some "medium," i.e., to explicitly renounce an "atomistic" strat• egy. In this regard, the approach of quantum cybernetics is just one in a series of slightly differing attempts to provide a causal description of quan• tum processes, their common underlying assumption being the existence of some subquantum medium. One can only speculate what this medium consists of, but there may well be further "smallest units" constituting it. What we today call "elementary particles" may therefore some day appear as nonlinear modifications of an apparently continuous medium that only Coda: On the Meaning of Nonlocality 137 upon further resolution would decompose into the "atoms" of the aether. Thus, there may arise a new kind of atomism in the 21 st century, with the atoms then being the "discrete" elements of the "continuous" sub-quantum medium. Again, one would be entitled to say with Democritus of Abdera that " ... in truth there only exist atoms and the void." However, we might also realize that thereby we would only spin the wheel of controversies be• tween adherents of the discrete versus adherents of the continuous by one more turn, thus fulfilling another cycle in the dynamic process of "scientific cognition" that spirals along the axis of time. One particularly intriguing implication of quantum theory is, as we have seen, that "objects" in the common sense of the word cannot exist, or rather: whenever we define our "object," it must be clear that we also co• define a context in which the meaning of the "object" is operational, but which also excludes other meanings. In particular, "objects" can only be defined if certain EPR-type correlations are ignored. However, what about "subjects," then? Would not the same type of definitory restrictions have to hold for "subjects" as we1l3? In fact, as causal approaches to quantum theory are "objective" theories excluding the observer, said "objectivity" is subject to the same type of limitations: choosing a particular scientific approach is a "subjective" (or better "inter-subjective") decision which is, of course, also context-dependent.4 Thus, it is also interesting to explore other possible contexts, like, for example: what are the consequences that we as "subjects" consist of quan• tum systems with their characteristic nonlocal features? Furthermore, it is no more justified to describe subjects at the most basic physical level as a mere collection of atoms. Rather, the emerging new picture of space• time and matter as manifestations of a "medium" entail that also we are modulations of the aether. What are the consequences of such a viewpoint? Naturally, such questions touch upon a whole gamut of different topics and thus are definitely beyond the scope of quantum theory per se, but they are nevertheless legitimate ones in the pursuit of curiosity driven research. Moreover, in reaching beyond the borders of conventional dis• ciplinary boundaries, they may develop into whole new fields of research which today we can only vaguely circumscribe as "transdisciplinary" ones. Even within the domain of physics, the relations between issues on the quantum and on other (classical) levels can be seen in a new light, once

31 have written two books in German on these issues, centering around a proposed polar relationship between "subjectuals" and "objectuals," rather than subject-object duality: in [Grossing 1993b], 1 concentrate on "objectlike" ("ob• jectual") determinants of theory building in physics, whereas in [Grossing 1997], 1 discuss "subjectlike" ("subjectual") organizations of knowledge, with physics being one of them. 4However, this does not make the approaches arbitrary or dependent on one's taste only - as with an artistic style, for example. 138 Coda: On the Meaning of Nonlocality systemic approaches are considered. For example, H. C. von Baeyer has reported on the discovery by Randall Hulet of a previously unexpected mirroring of microphysics in macrophysics in the behavior of Bose-Einstein condensates. For gases in which the interatomic force is attractive, it had recently turned out that Bose-Einstein condensates can be achieved only in well defined small accumulations of matter: if the condensed cloud in• cludes more than about 1,000 atoms, it becomes too large and collapses into a liquid. In other words, the attractive force and the gas pressure then cease to balance each other. Now, von Baeyer notes that all stars are ac• cumulations of particles in equilibrium between competing attractive and repulsive forces, where the equilibrium persists only for fixed, well-known ranges in the number of constituents: "In this light it is exciting to see similar limitations arising in the realm of the very small. Hulet, for exam• ple, compares the collapse of his little lithium clouds to 'what happens in a supernova,' when gravity finally overcomes the outward pressure of the stellar plasma and the star falls in on itself. The image provides a wonder• fullink between quantum theory and astrophysics." Von Baeyer concludes with the interesting conjecture that ''the replication of behavior is more momentous than the mere replication of form" [von Baeyer]. It is well known that similarities of form in different areas of the natural world, though very suggestive at first sight, do not imply any deeper con• nection at the physical level. 5 However, when it comes to comparing similar• ities in the dynamical behavior of different systems, one still may carefully enquire whether or not there does exist a more abstract common ground. To give another example, I just remind the reader of the familiar didactic practice to illustrate the self-interference of a quantum at a double-slit by a corresponding interference pattern produced by water waves. To the extent that one can ignore the particlelike aspects of quantum systems, the dy• namics of water waves around a double slit is even mathematically identical to the corresponding dynamics of light, for example. In this way, Huygens' principle provides the common ground for both phenomena - a fact, which in a rudimentary form was already known to Leonardo da Vinci. fda Vinci] Thus, one can also consider the interference of water waves as representing an "echo" during the evolution of the universe of the interference of quan• tum systems, just as the dynamics of Bose-Einstein condensates echoes the dynamics of stars. It is possible that many more such "echoes" exist in the physical world. In fact, systemic behaviors like self-organized critical• ity or fractal evolution indicate that certain dynamical processes are scale invariant over a wide range of scales. Under an evolutionary perspective, then, the emergence of novel organizational entities may represent a more general, perhaps even universal, pattern of iteratively produced recursive

5For example, simple analogies of form have often mislead the practitioners of alchemy to utterly wrong conclusions. Coda: On the Meaning of Nonlocality 139 dynamics. Thus, the science of the outgoing 20th century has provided radically new perspectives on what will be studied as "quasiobjects" (or "objec• tuals") in the 21 st century. With respect to spatial extension, quantum• mechanical nonlocality has rendered an "atomistic" approach obsolete. Regarding evolution in time, recursive dynamics points at an irreducible history-dependence of the behavior of nontrivial systems, which may well turn out to exhibit "universal" fractal properties. A future world-view in the physical sciences will then very likely aim at bringing the phenomena of nonlocality and recursive behavior together into a single, more coherent picture. The approach of quantum cybernetics may be considered in this regard as a contribution to such attempts. References

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absorption 18,25,26,126 Cramer's transactional interpre• algebraic quantum mechanics 81 tation 82 atomism 3,4,10,16,18,73,136-139 cybernetic description of a quan• atoms 2-4,56,90-93,102,135-138 tum system 59 autonomous system 58,59,130,136 cybernetics xiii,2, 7 ,8,33,53,54,57, 59,65,69,80,124,130,131

Bell's inequalities 3,83 de Broglie waves 18,28 Bohr-Sommerfeld condition 37 delayed-choice experiment 90,94 Born's rule 7,21,32 Dirac equation 45,46,50,81 Bose-Einstein condensates 138 double slit experiment 22,38,57, boundary conditions 22,41,51,56,57,71, 61,138 95,96,97,101,104,126 dressed particles 136

Casimir effect 5,39,125,126 Einstein-Podolsky-Rosen exper• causal paradoxes 7,10,105,107,108,110 iment xii,5,69,83,87,90, circular causality 2,6,7,33,57,59,80,82, 95,101-103,106,110,135 125,129,130,133 EPR correlations 4,5,9,102, complementarity 45 136,137 complex conjugation 31,63 EPR simulator 83 configuration space 43,44 Einstein's field equations 7,115, continuity equation 35,36,64,66,113,122 119,120,123,127 control 3,7,59,83,84,124,130 electrons 2,3,36,38,39,44,50,85, cosmological constant 127 136 152 Index entanglement 3,4,45,94,104,135, Lorentz transformations 15,94,114,115 136 equation of motion 37 equivalence principle 115-118, Mach's principle 7,124-130 123 Michelson-Morley experiment 11 feedback 2,7,33,58-60,72,81,82, neutrons 3,24,88,90,95 124,126,130,131 Newtonian mechanics 12,38,55,124, Fermat's principle 49 127,129 fermions 32,45,75 Newton's third law 55,129 Feynman's General Rule 73 nonlinearity 6,10,1133,36,59,60,74,80- Feynman's Grand Principle 73 82,87,113,114,118,119,123,124, fractal evolution 133,138 136 "free particle" 51-54,85,95 nonlocalityxii,3-9,21,27-31,41,43,54- 59,68,72,74,78,80-87,94,96,99- Gaussian wave packet 28,31,40,90,120 102,111 ,114,120,125,127,131, gravitational field 4,116ff 135,137,139 Greenberger-Home-Zeilinger ex- nontrivial machines 131 periment 6,80,87,101 N-body system 43,44 guiding wave 6,10,37,43,44,50,57,65, 69,70,72 object 3,4,56,57,81,135-139 organizational coherence 74,79,87,131 Hamilton-Jacobi equation 35,49 orthogonality 20,22,28,31,32,49,50,63,65, Hamilton-Jacobi-Bohm equation 68,77,97,104,125 35- 37,43,46,64,120 Heisenberg's uncertainty relations partial reflection 75ff 40,45,54 particle in a box 41,51-53,96 Huygens' principle 66,114,116,138 path integrals 72 Pauli's principle 75 perception ix-xiii,34,57-59,124,130 imaginary stopwatch 73 phase locking 53,60,66,82 inertial system 11-14,94,115,119 phase space 28,88,95 see also: reference frame phase velocity 21,53,65,69,88,94,97,100 interferometry 24-27,51,52,75-78,87- phase waves 23,24,65,66,77-82,95,101, 91,95-100 104,108,110,114-117,124 photons 18,29,30,56,73,93-95,102,106 Klein-Gordon equation 46,47,62- principle of least action 49,71 67,82,120 principle of relativity 11-16,21,24,33,62, 114 generalized 115 Lagrangian 1,36,119-123 probability amplitudes 7,24,28,31- late-choice experiment 94-100,107,111 33,73,78,120 Index 153 quantum cellular automata 131 velocity of light, see: speed of light quantum eraser experiment 56,90- 94,102 quantum postselection experiment waves of simultaneity 16,19,53,105 56,57,88 quantum potential 6,10,35-44,53, zero-point energy 50,67,114,125 64,66,72,80,85,117,118,123 zero-point fluctuations 5,85,125 reference frame 15,16,28,52,103,105, 108,109,114,116 relativistic EPR-dilemma 16,102,105, 106 Ricci tensor 122,123 Riemannian geometry 119 rigged Hilbert space 104 rotating unit vectors 21,62,63,85

Schrodinger-cat-like states 90 Schrodinger equation 24,32,34,41- 44,52,63,81,85,97 nonlinear 81 self-organized criticality 2,138 semigroup time evolution 104 speed of light xii,9,12,15,42,55,56, 77,82,85,105,115 stochastic electrodynamics 125 subject 137 superluminal signaling 7,95,98- 102,107-111 superluminal velocities 7,107,110 superluminal causation 110 thermodynamics 18,69 two-particle system 27-30,42, 78,87 vacuum energy 5,39,41,67,70, 127 variable rest mass 54,64,67,82,120, 124 variational principle for macroscopic quantum cybernetics 120