Time as non‐observational knowledge: How to straighten out ΔEΔt≥h

Abstract

The Energy‐Time Uncertainty (ETU) has always been a problem‐ridden relation, its problems stemming uniquely from the perplexing question of how to understand this mysterious Δt. On the face of it (and, indeed, far deeper than that), we always know what time it is. Few theorists were ignorant of the fact that time in quantum mechanics is exogenously defined, in no ways intrinsically related to the system. Time in quantum theory is an independent parameter, which simply means independently known. In the early 1960s Aharonov (1961–64) and Bohm (1961–64) mounted a spirited attack against the ETU, which sealed its fate to the present date. By emphasising that time is always “well‐defined” in quantum theory, they were led to the conclusion that no ETU should exist, a view shared by many in the 1990s, if Busch (1990) is to be believed. In a similar vein, I emphasize that (a) physical systems occupy a particular energy state at a particular instant of time, if at all; (b) even in absence of all time‐measuring instruments, it is still trivially warranted that one can measure a system's energy as accurately as one pleases, and simply announce “The system's energy is exactly E NOW!”, a possibility which no quantum mechanics of any sort, or any physical theory whatsoever, can afford to tamper with or change, except circularly. One never loses one's own perception of time, when one measures the energy, a fact which no measurement conceivable can interfere with or affect. Both (a) and (b) uniquely entail that energy and time are compatible, if not indeed intimately interconnected, contrary to what the relevant uncertainty seems to affirm. In response to Aharonov's and Bohm's initial problem, I reinterpret ΔEΔt ≥ h, as directly derived from authentic quantum principles, without however having to assume a direct incompatibility between its related concepts, attributing their complementarity to conditions other than ordinarily assumed.