LIGO's Approach: The Antithesis of Planck's
Updated: Mar 23, 2019
Science is all about explaining the results of experiments and observations. But, that's not LIGO's approach. It's like going into an exam with the answers; all you need are the questions.
When Planck took up the chair in Berlin, there was an active group of experimentalists studying black body radiation.
Such a radiation is form by heating a cavity to any given temperature and inserting a speck of charcoal. The speck has the job of absorbing and re-emitting all frequencies of radiation that the Planck oscillators in the cavity emit. A small hole is drilled out in the cavity so that some radiation may escape, but nowhere near enough that it disturbs the thermal radiation that has been reached between the walls of the cavity and the radiation itself. In fact, the thermal equilibrium that has been reached has been likened to a first order phase transition.
No other theoretician was interested in deriving the thermal spectrum of such radiation, so Planck had more or less a free hand. Working from Wien's distribution, which we derived from Maxwell's distribution, and Wien's displacement law relating the temperature to the frequency at which the radiation curve peaks, Planck was able to obtain the entropy associated with the distribution through a subtle application of the Second law. Had Planck known what that entropy corresponded to, he would have known that it corresponds to a limiting distribution, known as the Poisson distribution. And since it was a limiting distribution, Planck would have known that his search was not over.
But Planck had to wait until the experimentalists told him that there were deviations from his spectral density in the near infra-red limit of the spectrum. Armed with only thermodynamics, Planck succeeded in deriving his famous spectral density in a matter of hours. All this shows is that theory follows experiment, not the other way around.
Not so with LIGO. LIGO began with a template bank and matched filtering computes the cross correlation between detector output and template wave form. Because the signal's parameters are unknown, the detector output must correlate with the a set of template waveforms. So we have the shoe and all we have to do is find the right foot to fit it.
The templates are computer run calculations based on what is known as numerical relativity and post-Newtonian models. Since Einstein's field equations are nonlinear it is impossible to obtain analytic solutions so one resorts to modeling. Numerical relativity uses a (3+1) decomposition of spacetime for the three spatial and one temporal coordinates. However, there is no unique "time-slicing" in general relativity so that a unique instantaneous direction of time doesn't exist.
Yet, we are told that numerical relativity can describe the merger of binary stars, whether they be neutron stars or black holes. This is indeed surprising since the theory on which numerical relativity is based cannot even solve the two-body problem. Moreover, since potentials and forces are completely foreign to general relativity, it is indeed strange that the classical Newtonian limit pops up in the asymptotic limit of large distances. The post-Newtonian approximation deals with the weak-field limit, but it the two-body problem cannot, or has not, been solved, what is the post-Newtonian approximation of?
So LIGO is stuck with a bank of ad-hoc spectra that has been obtained from models that have nothing to do with general relativity. Is it a miracle then that some of the spectra correlate to "signals" that LIGO has picked up. Then there are the problems with noise, stray electromagnetic fields that can affect the tiny magnetics used to register the signal as the gravitational wave bounces off 40 kg suspended mirrors. And if that weren't enough, there is always the problem of the uncertainty of measurement over such small distances.
To obviate such problems there has been invented QND: quantum non-demolition measurements. Since conjugate variables like momentum and position, energy and time, amplitude and phase, etc. are "conjugate" variables, a measurement of one necessarily perturbs the other. Only on the scale where Planck's constant tends to zero, do such effects become unnoticeable. However, on the scale LIGO is making its measurements, there should definitely be a lower limit on the experimental precision of measurement.
First, and foremost, the wavelength of a gravitational wave must be smaller than the uncertainty in its position. Since gravitational waves are extremely low frequency of the order of 60 Hz, their wavelengths far exceed the 4 km interferometer arms that LIGO has constructed. With respect to the gravitational waves, the interferometer is a mere speck, so how the arms of the interferometer distinguish between the type of polarizations?
QND seeming gets around such problems by claiming that the position measurements of the mirrors does not disturb their momenta. According to Braginsky and Thorne, in Quantum Measurement, "A central feature of gravitational waves is their extremely weak interactions with matter...the weakness of the interaction guarantees that there is almost no back reaction of the probe on the gravitational wave field. As a result, the gravitational wave acts on the probe as though it were a classical force."
The analogy with radiation pressure is used--with disastrous consequences. The claim is that by taking a long enough time, and a weak enough force that one can measured to any "desired sensibility." It is therefore "necessary to register the pressure produced by a few quanta, and this is an extremely small pressure..." Have these authors ever tried to measure the pressure of a single molecule in a closed box?
The long time limit is also a double-edge sword since in such a long time, thermal equilibrium will have certainly been secured and with it all the effects created by thermal, white noise. There is no way of beating the roulette table, for in the long run, the odds are with the house. As with all of LIGO's inventions to avoid the inevitable consequences of flaws in its measurements, you can beat first principles.
In "Noise residuals for GW150914 using maximum likelihood and numerical relativity templates," (arXiv: 1903.02401) authors A D Jackson, H Liu, and P Naselsky conclude:
Finally, we wish to stress that the present manuscript should not be regarded as either an endorsement of or a challenge to the interpretation of GW150914 as a BBH merger or any other manifestation of gravitational waves. In our view, the physical interpretation of this event remains open. In this sense, we remain convinced that data must be analyzed and a best common signal determined without a priori biases and preconceptions before theoretical models are invoked. It is a truism that, if gravitational waves are all you look for, gravitational waves are all you will ever find.
Never has a truer word been spoken
They as us to keep in mind
The presence of statistically significant correlations in the Hanford and Livingston residuals is sufficient to eliminate any proposed waveform (e.g., the NR [numerical relativity] template of ) from further consideration. The absence of such residual correlations does not provide any evidence that the proposed waveform is correct.