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Mathematical Proceedings of the Cambridge Philosophical Society

A suggested experiment on the clock paradox

William D. Cochran

Published Jul 1, 1957• 0 citations
Publisher

Abstract

ABSTRACT An experiment is suggested to settle the question whether two clocks which are synchronized and subsequently separated must necessarily show identical readings on being brought together again. Charged π-mesons play the role of a clock travelling with a velocity comparable with c, this clock being read by passing the mesons through a scintillation counter or counters. It is pointed out that the experiment can be designed in a way which makes it technically feasible for a laboratory possessing an accelerating machine capable of producing mesons in the 100 Me V. energy range. Some considerations suggested by the proposed experiment are examined, and it is concluded that only the orthodox result—that in general the two clocks will record the passage of different time intervals between successive coincidences—is consistent with the result of an experiment which has already been made, or with the special theory of relativity.

DOI
10.1017/s0305004100032709

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ABSTRACT An experiment is suggested to settle the question whether two clocks which are synchronized and subsequently separated must necessarily show identical readings on being brought together again. Charged π-mesons play the role of a clock travelling with a velocity comparable with c, this clock being read by passing the mesons through a scintillation counter or counters. It is pointed out that the experiment can be designed in a way which makes it technically feasible for a laboratory possessing an accelerating machine capable of producing mesons in the 100 Me V. energy range. Some considerations suggested by the proposed experiment are examined, and it is concluded that only the orthodox result—that in general the two clocks will record the passage of different time intervals between successive coincidences—is consistent with the result of an experiment which has already been made, or with the special theory of relativity.
Entangled states of light exhibit measurable correlations between light detections at separated locations. These correlations are exploited in entangled-state quantum key distribution. To do so involves setting up and maintaining a rhythm of communication among clocks at separated locations. Here, we try to disentangle our thinking about clocks as used in actual experiments from theories of time, such as special relativity or general relativity, which already differ between each other. Special relativity intertwines the concept of time with a particular definition of the synchronization of clocks, which precludes synchronizing every clock to every other clock. General relativity imposes additional barriers to synchronization, barriers that invite seeking an alternative depending on any global concept of time. To this end, we focus on how clocks are actually used in some experimental situations. We show how working with clocks without worrying about time makes it possible to generalize some designs for quantum key distribution and also clarifies the need for alternatives to the special-relativistic definition of synchronization.
Abstract In the twin paradox of special relativity, an observer that travels along an accelerated trajectory at a high velocity will experience a smaller amount of elapsed time than an observer that remains at rest. This illustrates the fact that time is relative unlike the situation in classical physics where time is absolute. In a recent paper, Bushev et al (2016 New J. Phys. 18 093050 ) showed that the twin paradox can also be demonstrated using a single electron that functions as a quantum-mechanical clock. The wave function of the electron can travel along two different paths simultaneously, which allows a measurement of the difference in proper times along the two trajectories using a single particle. Quantum interference effects show that time cannot be thought of as a classical parameter even when associated with a single clock or observer.
Abstract Time plays a fundamental role in our ability to make sense of the physical laws in the world around us. The nature of time has puzzled people — from the ancient Greeks to the present day — resulting in a long running debate between philosophers and physicists alike to whether time needs change to exist (the so-called relatival theory), or whether time flows regardless of change (the so-called substantival theory). One way to decide between the two is to attempt to measure the flow of time with a stationary clock, since if time were substantival, the flow of time would manifest itself in the experiment. Alas, conventional wisdom suggests that in order for a clock to function, it cannot be a static object, thus rendering this experiment seemingly impossible. Here we show, with the aid of counterfactual measurements, the surprising result that a quantum clock can measure the passage of time even while being switched off, thus lending constructive support for the substantival theory of time.
With Einstein’s interpretation, “everything is relative”, the so-called twin experiment discloses what is called a paradox, when the travelling twin returns and they compare watches (and aging). Some assign the solution to acceleration, which they claim should be taken into account so that the paradox evaporates. However, it’s easy to construct an experiment in which any acceleration lays outside the considered part of the experiment, so that within the measured part we have only constant velocities. We can then have one observer at rest, and two travelers who run through the travelling twin’s route, but without acceleration. Within a hypothetical absolute underlying medium, particles oscillate slower for an observer who moves through the Aether than they do for an observer at rest. An acceleration free experiment can be made in which all three agree on that. The conflict appears if the traveling ‘twins’ measure how fast the first observers clock runs, based on their respective lines of simultaneity, because then the travelling ‘twins’ then insist that A’s particles oscillate slower than their own. Even without the physical experiment, the thought experiment itself discloses that the twin-paradox is a product of the “everything is relative” interpretation.
The conceptual foundations of the special and general theories of relativity differ greatly from those of quantum mechanics. Yet in all cases investigated so far, quantum mechanics seems to be consistent with the principles of relativity theory, when interpreted carefully. In this paper I report on a new investigation of this consistency using a model of a quantum clock to measure time intervals; a topic central to all metric theories of gravitation, and to cosmology. Results are presented for two important scenarios related to the foundations of relativity theory: the speed of light as a limiting velocity and the weak equivalence principle (WEP). These topics are investigated in the light of claims of superluminal propagation in quantum tunnelling and possible violations of WEP. Special attention is given to the role of highly non-classical states. I find that by using a definition of time intervals based on a precise model of a quantum clock, ambiguities are avoided and, at least in the scenarios investigated, there is consistency with the theory of relativity, albeit with some subtleties.