Interaction of a wave with an accelerating object and the equivalence principle

Abstract

A new look at the so-called effect of an accelerating matter is presented. It was previously stated that the effect is optical in nature and consists in changing the frequency of the wave passing through a refractive sample moving with acceleration. However, from a simple consideration based on the principle of equivalence, it follows that the idea of the connection of the effect only with the refraction phenomenon is unreasonably narrow, and a change in the wave frequency should inevitably occur during scattering by any object moving with acceleration. Such an object can be either an elementary scatterer or any device transmitting a narrowband signal.For the first time the phenomenon that later became known as the accelerating matter effect was briefly mentioned in the PhD thesis by V.I. Mikerov [1]. Analyzing the possibility of filling a trap for ultracold neutrons (UCN) without its depressurization, he proposed using a thin membrane moving in harmonic law with and against the UCN motion. At the same time, he found that the energy of UCNs, after their passing through an oscillating foil, should change. Being unpublished, this result has remained unknown for a long time.In 1982 K. Tanaka [2] found a solution to the problem of an electromagnetic wave passing through a linearly accelerating dielectric plate and predicted that the frequency of a wave transmitted through such a sample differs from the frequency of an incident wave. With a single passage of a wave through the plate, the frequency change is determined as follows:where ω is the incident wave frequency, n is the refraction index, d is the plate thickness, a is the acceleration, and c is the speed of light. The possibility of observing this optical effect was discussed in [3], but, as far as we know, due to the smallness of the effect, the experiment was never performed. In 1993 the work of F.V. Kowalski [4] appeared, where he proposed to verify the equivalence principle in a new type of neutron experiment. His theoretical approach was based on the concept of the group and phase velocities of the neutron. He also calculated the time of wave propagation between the corresponding points in the laboratory coordinate system and in a system moving with acceleration. In both cases, the wave passed through a refracting sample. As an intermediate result, the author concluded that the neutron energy changes as it passes through a sample moving with a not too much acceleration. The energy change was deter- * frank@nf.jinr.ru mined as:where m is the neutron mass. Later, the same issue was considered by V.G. Nosov and A.I. Frank [5]. The analysis aimed at sequential calculation of the velocity of neutrons at their entering the sample, propagating in the medium, and escaping through another surface, was in fact based on the classical approach. To estimate the magnitude of the effect, the authors obtained a formula that coincided with the result by F.V. Kowalski (2).It should be noted that in [5] the formula (2) was obtained under two important assumptions. Firstly, i...

Interaction of a wave packet with potential structures moving with acceleration

“…The results obtained are consistent with the qualitative prediction [13] concerning changes in the frequency of the wave and in the energy of the particle as a result of its interaction with an accelerating object not only in the case of optical but also in the case of essentially quantum phenomena. Consequently, the hypothesis that the acceleration effect supplementing the usual Doppler effect is of a very general nature is confirmed.…”

“…A comparison of the curves in figure 5 shows that the change of the neutron velocity qualitatively repeats the GDT curve behaviour, which is quite consistent with the prediction in Ref. [13].…”

“…where E n and U are the neutron energy and the potential, respectively. According to the hypothesis [13] in the case of accelerated motion of the potential region one should expect, in addition to the conventional Doppler change in neutron velocity, some additional effect due to acceleration. The results of the numerical calculation of the evolution of the wave packet at reflection from a potential step moving with acceleration allow such interpretation.…”

“…If the prediction made in Ref. [13] is true, the result of interaction of a particle with any object moving with acceleration is a change in its energy and frequency. Here we are speaking about some effect that complements the conventional Doppler shift and is proportional not to speed, but to acceleration.…”

“…In the recent work [13], attention was drawn to an important fact that the conclusion about the change of the frequency of the wave passing through an accelerating sample was made in [7] just on the assumption of different propagation times of the wave in the sample and in vacuum, but, in no way, on the assumption that the difference ∆t is due to refraction in matter. Consequently, this conclusion holds if, instead of a refracting sample, we speak about an object moving with acceleration and transmitting a signal with a delay in time.…”