Relational Approach To Quantum Physics - Analysis of The Concept of Localizability

Analysis of The Concept of Localizability

One can continue to consider an object's position measurement, in order to see more clearly what this hypothesis implies with regard to the notion of localizability in physics, similar to the discussion of simultaneity in Einstein's theory of special relativity.

In Newtonian mechanics, one can measure an object's position with the aid of a detector. The outcome of a detection event (resulting from the interaction between a detector and the object), or the occurrence of a detection event at a point in space, indicates the position of the object. But as far as Newtonian mechanics is concerned, it is assumed that there is only one position corresponding to an object. This implies that given any detection event at a position (as registered by an accurate detector), similar procedures will produce other detection outcomes in which the measurements will all be co-located at the same point in space as the first event. As a result, no detector carrying out proper position measurements on the object will ever produce results that are different from each other. If this is the case, then it makes sense to ascribe a definite (or "absolute") position to the object, and to say that the object is localized at a point in space.

This is not what is found in quantum theory, however. For instance, the detection of light is described by the measurement of one-photon states. From a general property of Fourier transforms, the wave packet at a given time, with a spectrum width, indicates that the detection of an event can no longer be localized to a specific point in space — i.e., a definite position for the photon — but instead covers a range specified by, where

This is a major break with older ideas, because different detection events do not agree on the position of a photon. It must be emphasized, however, that whether localizability can be established is based only on an indirect deduction, the result of a statistical analysis, which expresses the deviation for the detection. Localizability is therefore not an immediate fact by which an object can be described simply as a point mass condensed at a spot in space. Instead, it is seen to depend largely on a purely conventional means of taking into account the deviation of the detected signals. This convention seems natural to our common sense, but it leads to unambiguous results — a definite position for a physical object — only in cases where Newtonian mechanics is a good approximation. When the characteristic widths of and can no longer be regarded as effectively infinite, then the results of empirical experiment make it clear that the measurements depend on the characteristic deviations for the problem in question.

It follows from the above discussion that localizability is not an absolute quality of objects; rather, its significance is dependent upon objects' characteristic deviations, for example the widths of and .

Consequently, although the mathematical structure of the above approach is equivalent to that of the Heisenberg theory (which leads to the uncertainty principle), the underlying conceptual framework is vastly different. In the Heisenberg theory, one deduces the uncertainty relation as a consequence of the disturbance of observing instruments, as they irreducibly participate in the observation process; subsequently, this infers that a causal description is impossible for quantum theory, and is therefore interpreted as the uncertainty of position. On the contrary, by adopting a relational approach, one begins with the experimentally well-confirmed hypothesis of the probability of detection events, as actually observed. With this starting point, the above inequality implies that the concept of absolute position is no longer meaningful in quantum theory, where specifies the deviation of detection. Indeed, once it is clear that the absolute position underlying localizability is not valid in quantum mechanics, it immediately follows that new concepts are needed to describe quantum processes, which contain the particle as a limiting case.