Complementary Paradigms in Physics

EPR Experiment and Complementary Paradigms in Physics

Since Einstein, Podolsky and Rosen have published their famous paper in 1935, there has been much speculation around the thought experiment they suggested to illustrate the issues of compatibility between quantum theory and relativism. The problem is certainly nontrivial. There are many relativistic theories of quantum systems, and, in a few cases, such theories allow rather accurate predictions. However, we are still far from a consistent theory incorporating both quantum behavior and relativism in a logically satisfactory way. To proceed, any doubts are just "swept under the carpet" and all we have is mere a posteriori justifications comparing the results of calculations with experiment. This would cause no problems for a semiempirical theory, but a fundamental science cannot stop seeking for a uniform description of phenomenological diversity, which would provide the formal criteria of the theory's applicability.

With time, discussions around the EPR experiment have outgrown the limits of the physical problem, inducing an extensive philosophical controversy related to methodology of science and mind-matter relations in general. Numerous interpreters brought the ideas underlying EPR-type experiments to the wide public, incidentally promoting various ideological distortions and utterly unphysical visions; today, it may be difficult to restate the problem in a scientifically productive manner.

A few examples of common prejudice around the EPR experiment and the relationship between quantum and relativistic paradigms are presented below.

Prejudice 1: Classical mechanics differs from both relativity theory and quantum mechanics in that it treats physical systems as independent of the observer, describing them in the absolute terms.

This is a misconception. No science can deal with isolated things, regardless of their participation in human activity. Formal structures developed in science reflect the common ways of our operating with things, and hence they always refer to the fragments of nature that have already been involved in cultural processes, and primarily, in industry and agriculture. A scientific concept is a concentrated expression of a scheme of activity, which entirely determines the scope of the concept’s applicability. Consequently, any theory is bound to incorporate a model of the subject of the underlying activity. In classical mechanics, such a model is provided by the concept of frame of reference. The Galilean principle of relativity states that all the inertial frames of reference are equivalent in respect to dynamics, that is, mass, acceleration and force; the observers that move with a constant speed in respect to each other will see the same physical picture. This means that each observer must be large enough to correlate different spatial points at the same time; more specifically, the observer is said to be able perceive the state of all the objects within the frame of reference "at a glance"; on the other hand, the observer must be small enough to be able to discern the details of the system, individual bodies constituting it. Roughly speaking, the size of observer must be comparable with the size of the system observed.

Alternatively, one could consider a frame of reference as a continuum of observers located in different spatial points, on the condition that the speed of communication between observers would be much greater than the speeds of the bodies within the system, as well as the speeds of the relative motion of the reference frames. In the dynamic aspect, observation is thought to be non-destructive, so that the energy transfer between the system and the observer is always negligible compared to the energy transfer between the parts of the system.

The observer of relativity theory is much smaller, being comparable in size with the individual bodies constituting the physical system (the frame of reference), rather than with the whole system, like in the classical case. Alternatively, the speed of communication between observers is comparable with the speeds within the system.

On the contrary, the observer of quantum mechanics is extremely large, much greater than the system observed, so that the fine details of the system get lost in observation. Quantum observer can only control the system’s behavior through boundary conditions, never directly interacting with any of the system’s constituents.

To summarize, classical mechanics implies a quite definite model of the observer, different from the observer of relativity theory, or quantum mechanics. However, the observer’s interference with the system’s behavior (measured by energy transfer between the observer and the system, as compared to any "internal" energy transfer) is assumed negligible in all the three cases; otherwise, there could be no physical measurement, and no physical science. The consistency of the physical description of nature is ensured by treating the observer on the same footing as any other physical system; the observer enters a physical theory as a kind of constraint entirely describable in terms of the same theory. For instance, in physics, one does not need to consider the observer’s consciousness, or economic position, which would be more appropriate to psychology or political economy. However, formal analogies are quite possible, and one could say, for instance, that K. Marx’s demand to account, in a social theory, for the class roots of the historian is a close match of the paradigm change in the transition from classical to relativistic physics.

Prejudice 2: Different physical paradigms must be compatible within a unified theory.

This statement is commonly related to the well-known correspondence principle, demanding that new theories must include their predecessors as special cases. However, the two principles are essentially different. A physical system may admit complementary descriptions referring to uncorrelated aspects of the system’s behavior; such "parallel" theories can develop in a relatively independent way. For instance, a thermodynamic picture is qualitatively different from the kinetic description, and one can never be reduced to another without conceptual strains and hidden logical circularity. The correspondence principle is only valid for the theories of the same kind, and it may be broken in an entirely new theory suggesting a complementary description of the same physical area.

One could consider such independent paradigms as separate theories, despite the fact that they apparently apply to the same observable things. That is, the definition of the object will include, in addition to the specification of the material scope, a reference to the range of the physical phenomena selected by this particular approach; a physical system viewed from a different angle is a different physical system. In this view, any mixed model (combining different paradigms) can develop into a boundary science well distinct from the original theories, and possibly treated as more fundamental.

The hierarchy of paradigms in science reflects the diversity of our everyday activities and the objectively different types of their organization. However, the general line of cultural development is directed towards a wider unification of activities; operations that formerly required professional differentiation can be naturally combined in a uniform activity of the same person. For instance, the universal computerization has introduced yet another intermediate level between the idea and its implementation; the principles of control are the same for all kinds of software, and an average user can do, in a mouse click, what earlier required several specialists of an advanced qualification. Of course, this is the level of simple standardized solutions; still, with a wider availability of universal tools, the boundary between unqualified and professional work will shift up, also influencing the organization of special training. Thus, Web pages can be easily generated by anybody using any of the numerous HTML authoring tools, or right from a regular office document; industrial Web designers will probably stick to special development platforms, with minimum knowledge about the underlying technologies; the low-level optimization will still require mastering a number of programing languages and the intricacies of their implementation. Similarly, different physical theories can be absorbed by a more general approach describing the related phenomena in a simpler and more elegant way; this does not remove the necessity of special models adapted to some particular cases, and such "derivative" models do not need to be compatible with each other. For illustration, one could observe that, say, the technical skills in ballet and ball dances are based on the same laws of the dynamics of human body; but a ballet dancer can hardly compete with a professional ball dancer, and a ball dancer cannot be expected to professionally dance ballet.

Prejudice 3: A relativistic theory does not admit any synchronization across a space-like interval.

In the popular literature, this statement takes an even more striking form: there can be no synchronized distant events. This vulgar formulation is obviously absurd, since two material points moving in different directions from the same point will finally be far away from each other, but the interval between them will remain time-like, since material points cannot move faster than light; the movement of such diverging points will remain synchronized if it was synchronized in the starting point (provided the synchronicity is not broken by local interactions). For instance, the two particles in the EPR experiment will always be correlated; for another example consider a spherical wave, with the phases of very distant points remaining correlated at any moment.

Synchronized events separated by a space-like interval are also possible: if such a synchronization has once occurred, it will pertain in any frame of reference, according to the principle of relativity. The very notion of a reference frame is based on this possibility, since any frame of reference implies synchronization of the clocks located at any (including space-like) intervals from each other. A plane wave is, probably, the most common example from relativistic field theory: the phases of all the points in all the space-time are correlated in the plane wave, including the points outside the light cone. This inherent nonlocality of plane waves makes them so valuable in quantum field theory, allowing a covariant description of quantum states.

Obviously, the existence of a plane wave implies an infinite source, which would not obey the laws of relativity theory. All local events (the only ones possible in a consistently relativistic theory) would only produce outgoing spherical waves, and never plane waves. The handbooks on physics often treat a plane wave as a small part of a spherical wave far from the source. This approximation is only possible in the non-relativistic limit, and hence it cannot justify the usage of plane (or incoming spherical) waves in relativistic field theories. The inconsistency of introducing nonlocal objects in a local theory manifests itself in a number of conceptual and formal difficulties; renormalizable singularities are among the most common. However, while the nonlocal objects thus introduced do not enter any interactions, they can exist in theory without raising any contradictions, in a covariant way.

Prejudice 4: Independent measurements are possible in quantum mechanics.

This is a logical contradiction, since a quantum observer occupies all the space, so that any two measurements will necessarily be correlated. However, the energy transfer from the observer to the system can be minimized if the observer does not directly interact with the system to study, but rather with some other microscopic systems serving as "probes". Quantum experiments typically employ the scattering setup, with the observer controlling the state of the projectile (the probing particle) and any outgoing (scattered) particles only at "infinity", far from the target (the quantum system of interest). The interaction of a probing particle with the target can be made weak, that is, comparable with interactions within the target or weaker. The interaction of the observer with the scattered projectile at "infinity" is believed to little influence the state of the quantum system just because it is "too far"; this is a very strong assumption that fails to hold, for instance, when macroscopic events are globally synchronized and one cannot disentangle the observer from the system even asymptotically. Still, the model of an "asymptotic" observer remains one of the fundamental parts of the formalism of quantum mechanics.

Considering the relations between quantum theory and relativity, one could note that the two outgoing particles in the EPR experiment will be always correlated if detected by the same observer; this implies that measurement can only be "adiabatic", that is, the time of measurement must be much greater than the characteristic times of relaxation processes within the system. For an analogy, recall the well-known result about the absence of absolutely rigid bodies in special relativity theory. As the time of measurement becomes comparable or smaller than the internal ticks of the system, energy transfers thus implied will prevent any distant measurements performed by the same observer; if two observers perform measurements in different spatial points their communication will take an additional time, which has to be accounted for in analyzing experimental data, with the necessarily introduced significant corrections.

Prejudice 5: EPR-type experiments could be a test of the validity of quantum mechanics against local theories, including relativity theory.

The falsity of this statement follows from the above. Any possible experiment is either local (compatible with classical dynamics), or it will be an essentially nonlocal quantum experiment. In the first case, any measurements on one outgoing particle do not depend on the measurements on the other, and hence putting them in sync would require a special process significantly modifying the scheme of measurement. On the other hand, to stage a quantum experiment, we need to keep within adiabatic limits, so that the particles would effectively always remain in the same point, with the zero interval between them. In the quantum scheme, there are no separate particles that could be distinguished in observation and probed independently; rather, there is a quantum system consisting of the incident two particles plus, possibly, some other objects, representing the interference of the observer.

If local measurements happen to be correlated, this only means that the system has been prepared that way, and global correlations have been introduced in a nonlocal process, after which they can pertain in all the frames of reference. Quantum physics is entirely based on the concept of "system preparation", implying a kind of the observer’s involvement in the system’s motion. Formally, this means eliminating a number of dynamic variables through imposing various constraints (including pre-supposed symmetries and the corresponding conservation laws). Thus, in the EPR experiment, we do not deal with two independent particles, with three coordinates and three momenta needed to describe the state of each particle; we can effectively eliminate three coordinates and three momenta (or any other six variables) and effectively deal with a single particle. Consequently, there is no particle synchronization violating relativistic locality, and no problem at all. All we observe is the phases of the same wave; no wonder that they are perfectly correlated. To introduce relativism in an essential manner, one has to consider two independent (separated by a space-like interval) observers; such observers cannot communicate their results to each other, and hence there is no restriction on the "simultaneous" measurement of coordinates and momenta, as imposed by the uncertainty principle.

Prejudice 6: Bell’s theorem allows experimental falsification of the hidden variables approach in favor of quantum mechanical treatment.

Bell’s theorem and its reformulations (like CHSH), like any other formal results in science, are based on very special models, so that all the implications would apply to these original models, without touching any universal principles. Hidden variables (or other classical models for quantum experiments) can be introduced in many ways, and no theorem can cover all the possibilities. If the results of some experimenting happen to violate Bell’s (or CHSH) inequality, this can only put in question the premises of a particular derivation, and possibly, the adequacy of interpretation. If some other results lie within the formal limits, this can neither prove the validity of the model, nor indicate any incompleteness of quantum mechanics; all we can is to suspect some inconsistency in the experimental setup violating the "pure" quantum-mechanical scheme. From the philosophical standpoint, the hierarchy of the world will certainly reveal an infinity of cases intermediate between classical and quantum physics and additional levels can be found "below" quantum physics and "above" the classical scheme.

Bell-like inequalities are a special case of applicability conditions that are required from any sufficiently developed physical theory, regardless of its generality. Such inequalities can be formulated for any model at all, from the configuration interaction approximation in the physics of autoinization to general relativity and cosmology. It is important that applicability conditions be derived within the theory. If the derivation is to compare different theories, this is a logical fallacy; provided the deductive scheme is correct, we conclude that the derivation is applicable to neither of the original theories, but rather refers to another theory describing a boundary situation.

Prejudice 7: Quantum mechanics needs interpretation.

Quantum mechanics has always been a matter of philosophical speculation, and many people tried to "translate" it into the ordinary language, or a metaphysical slang, explaining its peculiarities by anything else. The Copenhagen interpretation is one of the most famous projects, representing the "mystical" camp; it claims that consciousness is to play a decisive role in quantum measurement, producing a kind of "state reduction" or "quantum collapse". Since the adherents of that school do not really know what they mean under consciousness, there is always enough room for idealistic speculation and pessimism about the people’s ability to comprehend anything at all.

A productive group of interpretations suggests various semi-physical models to explain the probabilistic nature of quantum mechanics, nonlocal correlations, complementarity or uncertainty principles. One could mention hidden variables theories, semi-classical interpretations, many-world interpretations, or advanced-action and transactional models. However, interpretations of that kind are irrelevant to the regular problems of quantum physics, or relativity theory, and no practical solution really needs them. Still, such interpretations could be useful as a specific form of creativity in theoretical physics, stimulating the search for new paradigms explicating new aspects of reality, different from both quantum world and relativity.

As a physical model, neither quantum mechanics not relativity theory needs any interpretation. On the contrary, such general theories serve as a framework for interpreting physical experiments and observations, regulating construction of special physical theories aimed to explaining particular classes of phenomena. It would be a logical error to speak about the "incompleteness" of quantum or other theory. They are not intended to be complete, since the very nature of science is analysis, characterizing the system of interest from different aspects, complementary (and hence irreducible) to each other. There are as many such aspects as one likes, and there is always room for yet another paradigm.

Prejudice 8: Physics can explain phenomena related to life or consciousness.

No, life can never be reduced to mere physical or chemical processes, and consciousness cannot be explained by mere physics or biology. It would be naïve to expect an insight into the nature of the human mind from a study of particles and fields within the brain. A physical experiment is to bring physical data, entirely interpretable within the physical science; otherwise, it would not be physics. And within physics, the possible influence of the observer can only be accounted for on the physical level, in physical terms. To study life and consciousness, one needs experimenting of an appropriate character, directed by the conceptualizations of the same level. Any usage of physical terminology in, say, psychology can only be metaphorical.

This does not mean that the formal models originally developed in physics are never applicable in other sciences. In particular, one can describe psychological phenomena using the formalism of classical mechanics, quantum mechanics or relativity theory, provided all the quantities thus introduced are reinterpreted in the psychological terms, referring to psychological processes rather than physical motion. For instance, one cannot speak about a mass of a thought; but one can consider psychological inertia as a specifically psychological phenomenon. Similarly, psychological dynamics will be described as an interplay of human motives, rather than the balance of physical forces. A similarity of the form does not imply the same content.

The applicability of the same formal scheme in many different sciences is primarily due to the commonality of the culturally established modes of activity, which may be difficult to perceive. Thus, a weight on a rope, electric current and a planet moving around a star may seem entirely different and having nothing in common; still, they all could be approximately modeled with the same notion of harmonic oscillation. With all that, the physics of a planet’s motion around the central star is quite unlike the dynamics of an electron in a wire. Physically different processes may have identical formal schemes; this is a consequence of their involvement in the integrity of human activity.

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