Can a charged decaying particle serve as an ideal clock in the presence of a magnetic field?

Abstract

We investigate a model of a supposedly ideal clock based on the decay rate of a charged particle in circular motion in a constant magnetic field. We show that the time measured by an ideal clock depends on the acceleration. However, the effect becomes visible at an order of magnitude of 10 28 g, therefore confirming the validity of the ideal clock hyphotesis for realistic accelerations.

Universality of quantum time dilation

“…That resulting difference quantifies the amount of quantum time dilation. Therefore, this quantum time dilation can be viewed as an effect of state discrimination procedure between a quantum-superposed clock state (10) and a classical mixture (12).…”

“…Let us notice that another possibility would be to take the classical counterpart to be (9) instead of (12), in which case the difference of clock rates would always be zero. This is because the expression (8) depends only on the diagonal elements of the density matrix in momentum space.…”

“…Specifically, it is known that every physical system reacts differently to proper acceleration: a pendulum clock and an atomic clock will certainly be affected differently by acceleration. It was shown that no 'ideal clock' that is completely insensitive to proper acceleration may exist [10][11][12]. Similarly, due to the equivalence principle, where the effects of proper acceleration are indistinguishable from gravitational effects, no realistic clock can measure proper time accurately in a gravitational field.…”

“…A pendulum clock will react differently to acceleration than an atomic clock. Moreover, it was shown [10][11][12] that no physical system acting as a clock can be insensitive to accelerations due to the Unruh effect [13] and therefore no ideal clocks 7 can exist. However, an idealized clock as a physical model is still commonly used and studied in physics.…”

Quantum and classical effects in a light-clock falling in Schwarzschild geometry

“…Using a clock model where timekeeping is defined by the ability to consistently order events [15], introducing the requirement that a clock runs autonomously has revealed the necessity of entropy generation in the process of keeping time [16]. In a relativistic quantum setting, the role of clock-mass in limiting time measurements has been revealed [17], and deviations from clock ideality have been predicted in experiments using decaying particles to keep time [18][19][20] as well as in a superconducting quantum interference device (due in part to relativistic particle creation) [21]. Moreover, an operational approach has also been used to shed light on the energy-time uncertainty relation in the context of the Bohr-Einstein gedankenexperiment [22].…”