Exclusion of standard $\hbar\omega$ gravitons by LIGO observation

Abstract

Dyson (2013) argued that the extraordinarily large number of gravitons in a gravitational wave makes them impossible to be resolved as individual particles. While true, it is shown in this paper that a LIGO interferometric detector also undergoes frequent and {\it discrete} quantum interactions with an incident gravitational wave, in such a way as to allow the exchange of energy and momentum between the wave and the detector. This opens the door to another way of finding gravitons. The most basic form of an interaction is the first order Fermi acceleration (deceleration) of a laser photon as it is reflected by a test mass mirror oscillating in the gravitational wave, resulting in a frequency blueshift (redshift) of the photon depending on whether the mirror is advancing towards (receding from) the photon before the reflection. If e.g. a blueshift occurred, wave energy is absorbed and the oscillation will be damped. It is suggested that such energy exchanging interactions are responsible for the observed radiation reaction noise of LIGO (although the more common way of calculating the same amplitude for this noise is based on momentum considerations). Most importantly, in each interaction the detector absorbs or emits wave energy in amounts far smaller than the standard graviton energy $\hbar\omega$ where $\omega$ is the angular frequency of the gravitational wave. This sets a very tight upper limit on the quantization of the wave energy, viz. it must be at least $\approx 10^{11}$ times below $\hbar\omega$, independently of the value of $\omega$ itself.