How LIGO Redefines the Meaning of Quantum Uncertainty

To avoid the negative consequences of Heisenberg's Uncertainty Relations (HUP), LIGO borrows from Braginsky et. al. to introduce what is supposed to be novel developments like the Standard Quantum Limit (SQL) and Quantum Non-Demolition (QND) experiments that supposedly beat the HUP. Yet, we know that HUP stands in the "defense" of quantum mechanics, to use a colorful expression borrowed from Feynman. When we get down to the quantum limit, the measuring device interacts with what is being measured to create unavoidable disturbances to transform what was the system prior to measurement into an entirely new system after measurement. Shining light on an electron imparts a velocity to it so that the more precisely we measure its position that less we know about its speed. This is summarized by HUP: $$S_xS_v=\hbar/m$$ where the spectral density for position measurements is $S_x=\sqrt{\overline{\Delta x)^2}/\Delta t}=\sqrt{\hbar}$, and velocity measurements $S_v=\sqrt{\overline{\Delta v^2}\Delta t}=\sqrt{\hbar}/m$. To "beat" the quantum limit, we must live in a world where the unit of action, $\hbar$ is small or the mass we are measuring is large enough so that it will be impervious to the impulses that photons subject it to. HUP says that measurements in position and speed are perfectly, negatively, correlated: the increase in the variance of one leads to a corresponding decrease in the other. It is therefore inaccurate to claim that a "fundamental premise of SQL is that the optical noise sources--radiation pressure nose and photon shot noise--together enforce SQL \it{only if they are uncorrelated}." (T Corbitt \& N Mavalvala, "Quantum noise in gravitational-wave interferometers" LIGO-P030067-00-R) This mistaken premise allows "the SQL [to] be overcome by creating correlations between radiation pressure and shot noise.,,,QND interferometers are achieved by creating correlations between radiation pressure and shot noise." If anything, such correlations will transform the above equality into an inequality so that there will be no direct relationship between the variances in the radiation pressure and shot noise. If fluctuations in phase are associated with those in position, while fluctuations in amplitude are associated with those in velocity, then such an analogy leads to two orthogonal quadratures of the radiation field where reducing one leads to a corresponding increase in the other. This is supposedly the origin of "squeezed" light. But such correlations will destroy the equality in HUP leading to an inequality so that the direct relations ship between the two uncertainties is lost. Moreover, it is contended that the spectral density of shot noise if flat, where $S_x\propto I_0$, the initial intensity of the beam, while radiation pressure has a spectral density $S_v\propto 1/I_0\omega^2$ "showing that radiation pressure falls off as $1/\omega^2$", where $\omega$ id the angular frequency at which the measurement is made. Consequently, their product will also fall off as $1/\omega^2$, and will not be a universal constant as in HUP. This says the variance of the radiation pressure can be reduced to zero merely by increasing the frequency of the laser beam---something that contradicts all logic. In statistics, HUP go under the name of Cramer-Rao. Non-perfect correlations convert the equality into an inequality which is none other than the Schwarz inequality between correlations in conjugate variables and their standard deviations. In thermodynamics the go under the name of thermodynamic uncertainty relations (TUR) where the inequality is a measure of irreversibility (B H Lavenda, \it{Statistical Physics: A Probabilistic Approach} (Dover, 2016)). Irreversibility is seen to decrease the "information" between conjugate thermodynamic variables, like energy and inverse temperature. They cannot beat the standard thermodynamic limit (STL) in which they are perfectly negative correlated. Finally, any modification of the nature of the laser beam will have unavoidable consequences on the measurement of the displacement of the masses. Here, again, there is an \it{ad hoc} mixture of quantum (photon) and classical measurements (displacement of the 40 kg mirrors). LIGO has first to overcome what ails it before it can say that it has beaten the HUP limit. And it is starting from a disadvantage because a Michelson interferometer do not mix the macroscopic and the microscopic. Moreover, to attempt to convert position into speed measurements, via a Michelson interferometer, because the latter at not acted upon by "kicks" the produce "back action" is to change entirely what the basic principles of a Michelson interferometer are. In fact, "back action", which is sort of a reaction to an action is completely foreign to quantum mechanics which knows no definition of a force (cf. D Bohm, \it{Quantum Theory} (Dover, 1989)).