Observation of a Time Interval by a Single Observer

Bernhard F. Rothenstein, Ioan Damian

A method of measuring time intervals by a single observer proposed by Crowell is extended to the more general case when the events separated by the time interval take place at two points characterized by the same y=y' space coordinates. We show that time dilation and time contraction can take place or even an inversion in the time succession can be detected

Cheolhoon Cheong

Paul A. Benioff

Abstract Here, some difficulties resulting from the application of any empirical acceptability conditions on sequences of single measurements are investigated. In particular, the often used acceptability requirement that each single measurement be made under the "same conditions" is discussed. In quantum mechanics, this means that each single measurement is made of the same physical quantity on a system in a ensemble of identically prepared systems. One of the resultant difficulties is that such an application leads to an infinite regression of sequences of single measurements. That is, it does not account for the fact that an observer must start the process of measurement or knowledge acquisition. Furthermore, it is seen that there are some basic sequences of single measurements for which an observer can not possibly know at the outset that the "same condition" requirements are satisfied. These include those measurements by which the homogeneity of space-time is tested. The possible relevance of these difficulties to physics is shown by first considering two possi­bilities of avoiding these difficulties. One is that the "same condition" requirements can be given the weaker interpretation that there be no physical principle forbidding an observer from knowing in terms of limit empirical means, that they are satisfied at the outset of any sequence. This gets rid of the infinite regression problem as it does not mean that an observer must know in fact that these requirements are satisfied. The other possibility is that if physics does not forbid one in principle from measuring an expectation value in an arbitrarily small time interval then both the basic sequence as well as those by which one knows the "same" requirements are satisfied can be relegated to arbitrarily small time intervals. As far as physics is concerned, then the epistemological difficulties while existing in these small intervals, do not exist for other times, or almost all time. It is then shown that quantum mechanics, as distinct from classical mechanics, and the special relativity require that an infinite time interval is necessary to measure, as a limit mean, any expectation value. Thus physics denies both the above possibilities as it forbids an observer from knowing even in principle, by any finite time that the "same" requirements are satisfied. Also, physics forbids the relegation of the epistemological problems to arbitrarily small time intervals.

Andreas Schlatter

Dmitry A. Varshalovich

Gesualdo Delfino A

We previously showed that a quantum quench in a one-dimensional translation invariant system produces undamped oscillations of a local observable when the post-quench state includes a single-quasiparticle mode and the observable couples to that mode [J. Phys. A 47 (2014) 402001]. Here we consider quenches that break initial translation invariance. Focusing on quenches performed only on an interval of the whole system, we analytically determine the time evolution of local observables, which occurs inside a truncated light cone spreading away from the quenched interval as time increases. If the quench excites a single-quasiparticle mode, oscillations with the frequency of the quasiparticle mass stay undamped until a time increasing with the length of the quenched interval, before eventually decaying as t−1/2. The translation invariant case with no damping is recovered as the length of the interval goes to infinity.