The Heisenberg Limit and the Speed of Light

Sang Y and Kennes D

Published on: 2023-06-10

Abstract

In quantum metrology, the Heisenberg Limit constrains the precision of quantum measurements. Here it is shown that modern experiments which measure the speed of light in a vacuum such asinterferometry, cavity resonance, and other similar techniques do not fully encapsulate the uncertainty associated with the Heisenberg Limit. Although the constancy of the speed of light in a vacuum is a necessary axiom in electromagnetism and relativistic mechanics, maintaining that it is invariant on all scales is fallacious quantum-mechanically. This paper shows that the speed of light in a vacuum must conform to the Heisenberg Limit in order to remain consistent with quantum mechanics.

Keywords

Heisenberg limit; Quantum metrology; Quantum mechanics

Introduction

Modern measurements of the speed of light in a vacuum are typically macroscopic in nature. Examples of these approaches include observing the variations in synchronized clocks through the Global Positioning System (GPS), cavity resonance, and interferometry, with the most precise of which being the latter. These methods are primarily classical and are inconsistent with the sensitivity of quantum theory. Comparatively, modern reviews of experimental approaches invariably admit degrees of uncertainty associated with the measurements [1-9]. Of the aforementioned experiments, interferometry remains the soundest method of measuring the speed of light in a vacuum [5,8], and was used to determine the most experimentally accepted value at the 17th conference of the CPGM [9].

In experiments which rely on interferometry, such as the one at the CPGM, a laser is fired at a mirror which splits the light ray into perpendicular rays which reciprocate between two other mirrors. The mirrors are equidistant from the initial mirror, so the two light rays return simultaneously. When the beams meet in the middle, they constructively interfere, resulting in a wave that has twice the amplitude of the initial one. The same experiment is repeated, however one of the mirrors is moved back so the distance between it and the initial mirror is increased. When the mirror is moved back by half the wavelength of the light wave, the waves will destructively interfere. Consequently, nothing arrives at the detector.

Thereafter, the wavelength of the laser is measured by determining the distance by which the stationary mirror needs to be moved to cause destructive interference. The speed of light is then calculated by multiplying the initial frequency and the distance of the mirror. Clearly, the calculation assumes a time invariant frequency, although in quantum mechanics frequency is considered indeterministic [10]. Here, it is shown that due to the uncertainty in wave mechanics, there is a fundamental degree of indeterminacy associated with measuring the speed of light, that is not accounted for in experiments.

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