EPR experiment and complementary paradigms in physics

After the famous 1935 paper by Einstein, Podolsky and Rosen, there has been much speculation around the thought experiment suggested by the authors to illustrate the problem of the compatibility of quantum theory and relativism. The problem is in no way trivial, since, though there are numerous relativistic theories of quantum systems, and, in a few cases, such theories can be used to obtain rather accurate predictions, there is no consistent theory incorporating both quantum nature and relativism in a logically satisfactory way; as a rule, any doubts are being "swept under the carpet", and the calculations get justified a posteriori, by comparison of their results with experiment. This cannot be considered a satisfactory way of theory development, since it cannot be thus elevated above the semi-empirical level, and no indication of the range of the theory's applicability can be made.

However, discussions around the EPR experiment have extended beyond the limits of the physical problem, inducing a kind of philosophical controversy related to methodology of science and mind-matter speculation in general. Numerous interpreters trying to convey the ideas underlying EPR-type experiments to common public have introduced many misconceptions and unphysical statements, so that it may be difficult to re-state 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 in this paper.

Predjudice 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 absolute terms.

This opinion is unjustified. No science deals with nature on itself, without any relation to human activity. Formal structures developed in science reflect nothing but the common ways of people's operating with things, and hence they refer to the sides of nature that have already been involved in cultural processes, and in industry and agriculture first of all. A scientific concept is a concentrated expression of a scheme of activity, and it can only be applicable within the scope of this underlying activity. Consequently, any theory has to incorporate a model of the subject of activity described by that theory. In classical mechanics, such a model is provided by the concept of frame of reference. The Galilean principle of relativity states that all the observers represented by inertial frames of reference are equivalent in respect to dynamics, that is, mass, acceleration and force. This means that the observer is large enough to correlate different spatial points at the same time; more specifically, the observer must be large enough to reflect the state of the system observed, so that it could be observed "at a glance"—however, the observer must be small enough to be able to discern the details of the system, individual bodies constituting it. That is, the size of observer must be comparable with the size of the system observed.

Alternatively, one could consider a frame of reference as a number of observers located in different spatial points—one must demand that the speed of communication between observers be much greater than the speeds of the bodies within the system, as well as the speeds of the relative motion of the observers. In the dynamic aspect, energy transfer between the system and the observer must be much less than the energies transferred between the parts of the system.

The observer of relativity theory is much smaller, being comparable with the individual bodies of the system observed, 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 very large, much greater than the system observed, so that the fine details of the system get lost in observation. Quantum observed controls the behavior of the system through boundary conditions only, an never through direct interaction with it.

To summarize, classical mechanics implies a quite definite model of the observer, though different from those of relativity theory or quantum mechanics. However, the observer's interference with the system's behavior (measured by energy transfer from observer to the system, as compared to "internal" energy transfers) is assumed negligible in all the three cases—no physical measurement could be performed otherwise. It should also be noted that the observer can be included in a physical theory only as a physical constraint, being entirely describable in the same terms as the rest of the system. For instance, one does not need considering the observer's consciousness or economic position in physics, which would be quite normal in psychology or sociology, respectively. Thus, minding this analogy, one could say that the transition from classical social theories to K. Marx's demand to account for the class roots of a historian in assessing his works completely matches the paradigm change in the transition from classical to relativistic physics.

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

Generally this statement is associated with the well-known correspondence principle, demanding that older theories must be derivable from the newer ones as special cases. However, the two principles are essentially different. There may well be complementary aspects in describing a physical system, so that theoretical description of one aspect of the system's behavior does not need to be correlated with another aspect, developing in a relatively independent way. Thus, thermodynamic approach is different from kinetic description, and one can never reduce one to another: all such attempts are bound to contain conceptual strains and hidden logical loops.

It might be more productive to consider such independent paradigms as qualitatively different and irreducible to each other, treating any mixed cases as requiring a new model, a boundary science different from the original ones.

This is a manifestation of the diversity of activities in common life, and the significant difference of their schemes. Certainly, the general line of human development leads to growing unification of activities, so that formerly incompatible activities become quite compatible in the same person. For instance, computerization lead to that many things can be done with a mouse click, though formerly they might require specialists of quite different qualification. However, such a unification is only possible on the level of simple standardized solutions—professional work will still require special training depending on the peculiar field. For instance, WWW pages can be easily generated by MS FrontPage or any other HTML authoring tool—however, such pages will be generally less efficient and less attractive than those designed by a professional Web specialist, with low-level adjustment. Similarly, different physical theories may be absorbed by a more general treatment—however, each special case will require a special model, which does not need to be compatible with other special models. To illustrate this, 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.

Predjudice 3: In relativistic theory, there can be no synchronized events separated by a space-like interval.

In popular literature, this statement takes even more striking form: there can be no synchronized distant events. This vulgar form is obviously absurd, since two material points moving in different directions from the same point will finally be very far 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. For instance, the two particles in the EPR experiment will always be correlated; another example: a spherical wave with the phases of very distant points correlated at any moment.

However, there may also exist synchronized events separated by a space-like interval: if such a synchronization has once occurred, it will pertain in any frame of reference, being relativistically invariant. No reference frame could exist in relativistic theory otherwise, since any frame of reference implies synchronization of clocks located at space-like intervals between each other. The most common example from relativistic field theory is a plane wave: phases of all the points in all the space-time are correlated by the plane wave—not only inside the light cone. This inherent nonlocality of plane waves makes them so valuable in quantum field theory, allowing to describe quantum states in a covariant manner.

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 generate only outgoing spherical waves, and never plane waves. The courses of physics often say that a plane wave is a small part of a spherical wave far from the source. However, this approximation can only be possible in the non-relativistic limit, and hence 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 introduced do not enter any interactions, they can exist in theory without any contradictions, in a covariant way.

Predjudice 4: There may be independent quantum mechanical measurements.

This is a logical contradiction, since the quantum observer occupies all the space, so that any two measurements are bound to be correlated. However, energy transfer from the observer to the system can be minimized if the observer does not interact with the system under study itself, but rather with some other microscopic systems serving as "probes". The typical quantum experiment is scattering, with the observer detecting the results of a projectile (the probing particle) scattered on a target (quantum system of interest) only at "infinity". The interaction of a probing particles 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 said to little influence the state of the quantum system—however, this is not exactly so, and there may be cases when macroscopic events get 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. One could recall the well-known result of special relativity theory, that there can be no absolutely rigid bodies, as an analogy. As the time of measurement becomes comparable or smaller than the internal ticks of the system, energy transfers implied prevent distant measurements from being performable by the same observer; if two observers perform measurements in different spatial points, their communication has to be accounted in analyzing the results of experiment, introducing significant corrections.

Predjudice 5: EPR-type experiments could serve as tests of the validity of quantum mechanics against local theories, including relativity theory.

The falsity of this statement follows from the above treatment. The experiment is to be staged either locally—in which case measurements on one outgoing particle are not correlated with measurements in the other, and hence their correlation would require a special process, which would significantly interfere with measurement—or it will be an essentially nonlocal quantum experiment—in which case it must be adiabatic, so that the particles will effectively be always in the same point, the interval between them being equal to zero. For quantum approach, there are no two distinct particles that could be probed independently—rather, there is a quantum system consisting of the two particles plus, possibly, some other objects, representing the interference of the observer.

If local measurements happen to be correlated, that 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 frames of reference. Quantum physics is based on the concept of "system preparation", implying specification of the observer's involvement in the system's motion. Formally, this means eliminating a number of coordinates and momenta using constraints imposed and various 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 eliminate three coordinates and three momenta and effectively deal with only one particle, so that there is no problem of measurement on one particle reflected on the other violating relativistic locality. It is the phases of the same wave that are observed, and no wonder that they have to be correlated. To make relativism important, 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 "simultaneous" measurement of coordinates and momenta, as described by the uncertainty principle.

Predjudice 6: Bell theorems can be used to experimentally falsify hidden-variables theories and justify quantum mechanics.

Bell theorems, as any other formal results in science, do not deal with general principles, but rather with specific models. If experimental results satisfy Bell theorems, it does not mean that that will always be the case, and it is only one particular class of hidden-variables theories that might be put in question. If there are results not satisfying Bell theorems, this neither supports the model of an independent variable incorporated in the derivation, nor indicates the incompleteness of quantum mechanics, but rather the presence of some deviation from the quantum-mechanical staging in the experiment.

Predjudice 7: Quantum mechanics needs interpretation.

There have been numerous attempts to give quantum mechanics an interpretation in terms other than physical. The Copenhagen interpretation is one of the most famous, representing a "mystical" camp of interpreters, claiming that consciousness plays a decisive role in quantum measurement, producing a kind of "state reduction" or "quantum collapse". Since the adherents of that camp do not exactly specify 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 more productive group of interpretations suggest various semi-physical models to explain the probabilistic nature of quantum mechanics, nonlocal correlations, complementarity or uncertainty principles. One could mention hidden-variable theories, semiclassical interpretations, many-world interpretations or advanced-action and transactional models. However, interpretations of that kind have no relevance to the problems of quantum physics proper, or relativity theory—no actual calculation or derivation really needs them. It is in the search for new paradigms explicating new aspects of reality, different from both quantum behavior and relativity, that these interpretations can be useful, being a specific form of creativity in theoretical physics.

Quantum mechanics, as well as relativity theory, does not need any interpretation. On the contrary, such general theories serve as a framework for interpreting physical experiments and observations, regulating construction of specific 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 may be as many such aspects as one likes, and there is always possibility for yet another paradigm to arise.

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

Life cannot be reduced to physical or chemical processes, and consciousness cannot be reduced to neither physics nor biology. It would be naïve to expect that more understanding of human mind could be obtained from studying interaction of particles and fields within the brain. No physical experiment can have any relation to studying consciousness, since it is physical data that are registered in such an experiment, and the possible influence of the observer has to be accounted for on the physical level, in physical terms. To study life and consciousness, one have to perform experiments of the appropriate kind, and use conceptualizations of the same level. Any usage of physical terms in, say, psychology can only be metaphorical.

However, this does not mean that the formal models originally built in physics cannot be applied in other sciences. One can describe psychological phenomena using the formalism of classical mechanics, quantum mechanics or relativity theory—if all the variables of the model have been reinterpreted in psychological terms. Thus, 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 by the interplay of various motives, rather than in terms of physical forces.

Obviously, the application of similar formalism in different sciences is only possible when there is similarity in the modes of activity implied. This similarity may be not evident. 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 described with the same model of harmonic oscillator. However, one would not assert that the planet's motion is caused by the same mechanism as the motion of an electron in a wire. Different processes can have identical schemes—this is directly related to ways of their involvement in human activity.