## Saturday, February 09, 2019

### Michael Mann's quantum climate pseudoscience

Michael Mann is the most notorious fraudster in the global warming scam. He was the key man in the team that constructed the "hockey stick graph" of temperatures in the recent millennium or two.

This is the politically correct version of the original video "Hide the Decline" that roughly describes what Mann did. Given it's just a song, the explanation is very accurate but I still prefer more accurate explanations than songs.

The hockey stick graph has claimed that the temperatures were nearly constant in 1000-1900 AD or so, and then began their clear increasing trend after 1900 AD. There were many problems with the individual steps that led to this outcome but the most important sinister trick was as follows: Mann basically connected (spliced) two graphs from the two periods.

The two pieces were obtained by different methods. The method for the distant past diluted and understated all temperature variations while the method for the 20th century kept them or amplified them. So you have to do get this result.

To make this cheap trick less transparent, Mann has employed the principal component analysis in a logically and statistically invalid way. From the temperature proxies (mostly tree rings), he picked those that showed some warming trend in the 20th century, and declared them good proxies; quantitatively speaking, they got a "big weight" proportional to their correlation with the thermometer-era series. (A 20th century cooling trend indicated by the proxies was also OK for him, he also took the trees that had the physically implausible sign of the correlation, but I don't want to enumerate all the problems with those papers.)

Then he effectively averaged these "good proxies". However, this is guaranteed to produce the hockey stick graph if you insert "random walk" proxies as the input. Why? Because some of those "random walk" proxies will unavoidably look like "global warming in the 20th century". Accidentally, they will show a pretty good correlation with the thermometer era measurements. However, they're still intrinsically random walk series. If you average many of them, you will get a near-constant function for the years 1000-1900 because that's where they are just "generic random walk" datasets! But in the period 1900-2000, only some of the trees were selected by a condition, so they will look like the thermometer data.

To make the analysis sensible, you would need to estimate the number of the "wrong proxies" that got into your dataset of "good proxies" by chance, and subtract their contribution. It's hard or impossible to do so with the tree ring data only which is why you can't really deduce anything about the relative magnitude of the temperature variability in the 20th century and the previous centuries.

The latest reconstructions of the temperature that avoid similar mistakes don't look like a hockey stick – the variability didn't qualitatively change in the 20th century.

The 2009 Climategate e-mails showed that Michael Mann, along with Phil Jones and others, were almost certainly producing this fabricated pseudoscientific research deliberately. Donald Trump has improved many things but the fact that Michael Mann hasn't been jailed or executed yet is one of the terrible disappointments of Donald Trump's tenure so far.

OK, so this Mann remains at large. He realized that the climate is neither hot nor cool so he must insert some cooler and hotter topics into his talks to sound attractive. Clearly, things related to quantum mechanics are cooler and more scientifically prestigious than climatology, everyone has always known it, and people still know it.

He is simply giving talks whose titles combine the climate and quantum mechanics. On Wednesday, February 13th, he is giving a talk about, well...

The adjective is spelled "influential", comrades, and the word that you actually wanted to use was "fraudulent".

Holy crap. The "quantum weirdness" deluded pop science about quantum mechanics has teamed up with "climate change" and "extreme weather" fearmongering!

Now, everyone who has completed at least some physics-related undergraduate degree knows very well that there are people who pretend that quantum mechanics, relativity, and other "impressive" topics may be found in everyday life observations such as the weather. All these competent people know that classical physics describes the weather just fine and the claims that these long-distance phenomena show the quantum behavior is just hogwash.

Careless and sensational combinations of ambitious claims about quantum mechanics with mundane situations such as the weather is one of the most straightforward signatures of a crackpot. Michael Mann is unquestionably a crackpot.

Does he have some justification for these bizarre claims about the "quantum weather"? What is it supposed to mean? With the help of W.S., I looked at their October 2018 paper
Projected changes in persistent extreme summer weather events: The role of quasi-resonant amplification
First, you may see that the authors – which include RealClimate.org charlatans Mann and Rahmstorf – are still spreading irrational fear, by esoteric comments about "extreme weather". But where do the quantum mechanical claims come from?

Well, they use an equation that is said to be analogous to Schrödinger's equation – and they even claim to solve it by the WKB approximation. People have derived various things from that mathematics, especially the "quasi-resonant amplification (QRA)".

Let's slow down a little bit, Gentlemen, OK? ;-)

First, "quasi-resonant amplification". You may click and search for the "seemingly nice experts' term" on Google Scholar. You will find 54 papers, starting with a 1967 article by De Martini. You will also find a paper by Richard Lindzen and a co-author and a 2013 paper by Petoukhov, Rahmstorf, Petri, and Schellnhuber. (The last man is a German Nazi skinhead who wants to save the Earth by eliminating most of the mankind. For these ambitious plans, he has been given quite some power by a successor of the German Führer.)

Sorry, Richard, but already the term "quasi-resonant amplification" is an example of silly terminology. Why? Because at least the word "amplification" is redundant. Resonance already describes any phenomenon in which the amplitude of oscillations is amplified when the frequency is close enough to the right one. The term "resonance" is very tolerant so when we talk about a "similar" phenomenon, it's either a resonance or it is not! When it is resonant, there is some amplification of the oscillations (increase of the amplitudes) associated with the precise enough choice of the frequencies or wave numbers. And such a resonant amplification may be deduced by presenting the relevant equation as a small deformation of the resonant equation.

Incidentally, I think that the Chapter I/23 of Feynman's Lectures on Physics is a brilliant introduction to resonance. It solves the canonical simplest equation that has resonance – and Feynman introduced his students to complex numbers because it's a rather wonderful context where they are really helpful. And he describes the mechanical and electromagnetic-circuit examples of resonance and their mathematical equivalence.

So the QRA should have been called "someone's resonance" or "resonance with some adjective", the "quasi-" and "amplification" fog suggests that someone wanted to sound smarter but he ended up sounding stupid to those who actually understand what "resonance" means. OK, let me not be difficult and let us accept that some resonant phenomenon is called QRA.

QRA appears in some equation but there is a totally cute sentence in the 2018 paper by Mann et al.:
Starting with the linearized quasi-geostrophic barotropic potential vorticity equation, we have, in the weak perturbation (“WKB”) limit, the approximate description of...
Wow, they believe that the "WKB approximation" is a "weak perturbation limit". To make things worse, Michael Mann basically markets himself as a quantum mechanics expert but he believes that the "WKB limit" is a "weak perturbation limit".

Every undergraduate student who deserves a passing grade in the first quantum mechanical course at least knows that the "WKB approximation" and "perturbation theory" are two totally different and unequivalent approaches to solve Schrödinger's equation of quantum mechanics and they're applicable in different limits.

Perturbation theory is actually used for "weak perturbations". Perturbation theory means that the Hamiltonian – an operator encapsulating the laws of physics and describing the evolution in time – may be written as$H = H_0 + \lambda V$ where the simplified Hamiltonian $$H_0$$ can be solved exactly or it is understood but we add a new term, $$\lambda V$$, where $$V$$ has "comparable matrix entries" as $$H_0$$ but $$\lambda \ll 1$$. The condition $$\lambda \ll 1$$ means that the perturbation is weak and the behavior (eigenstates, eigenvalues, time evolution) governed by the Hamiltonian $$H$$ is extracted as a perturbed treatment of the corresponding answers linked to $$H_0$$ where all the corrections are written down as appropriate Taylor expansions in the parameter $$\lambda$$.

That's perturbation theory – and it has several pieces that are normally taught in the first year of quantum mechanics, time-dependent and time-independent perturbation theory and degenerate perturbation theory, not to mention the particular machinery to apply perturbation theory in quantum field theory which is really the computational cornerstone of particle physics.

But the WKB approximation is something completely different. First of all, the words "weak perturbation ('WKB') limit" suggest that Mann et al. think that WKB stands for "WeaK Berturbation" or something like that. Mann is a German name so maybe he imagines it's a German acronym of a "German" phrase such as "Die WeaKheste Berturbatung". Not really, WKB stands for Wentzel–Kramers–Brillouin, the three authors (sometimes Jeffreys is added to make it JWKB). And the inequality required for the WKB approximation to work has nothing to do with the weak perturbations!

Instead, the WKB approximation produces solutions to the Schrödinger's and analogous equations of the form$\psi(x,y,z,t) = \exp( i \Sigma(x,y,z,t) )$ where $$\Sigma$$ is some quickly changing function of the spacetime coordinates. In quantum mechanics, one may prove that $$\Sigma$$ may be calculated as $$S/\hbar$$ where $$S$$ is the classical (optimal) action evaluated on a trajectory that ends at the given point.

This zeroth-order solution is just an "extremely quickly oscillating wave function" with a fixed absolute value (one may add corrections that make the absolute value variable). When is such a solution a good enough approximation? It's a good enough approximation if the changes of the phase are much larger than the changes of the absolute value. When is it so? It's when the coefficient(s) of the highest-derivative term(s) (the second-derivative term in quantum mechanics) is (are) tiny.

Are they tiny in quantum mechanics? The one-particle Schrödinger's equation in an external potential says$i\hbar\frac{\partial \psi}{\partial t} = -\frac{\hbar^2}{2m} \nabla^2 \psi + V(\vec x,t) \psi.$ The term with the highest number of derivatives is the $$\nabla^2$$ term. And indeed, its coefficient is tiny because $$\hbar^2$$, the squared Planck's constant, is really tiny. That small value of Planck's constant, the defining dimensionful constant of quantum mechanics, is the reason why the quantum mechanical waves have extremely short wavelengths – and high frequencies – relatively to the macroscopic (and even mezzoscopic) timescales and distance scales from the everyday life. The $$\nabla^2$$ term cannot be called a "perturbation"; it is the most unavoidable, "constant" term in the equation. The conditions $$\hbar \to 0$$ and $$\lambda \to 0$$ are completely different.

Let's move to the climate. There is some $$\psi$$ which is clearly not the quantum mechanical wave function because it doesn't have the probabilistic interpretation. That's why all Mann's claims that his atmospheric mathematical masturbations have something to do with "quantum weirdness" are absolute hogwash.

But at least mathematically, is it right that the WKB approximation is relevant for the weather phenomenon? The WKB limit is basically equivalent to the condition that the number of wave periods (the number of maxima and minima) is very high in the other distance scales and length scales of the problem. For example, the spatial part would say that a huge number of waves, up and down, must be compressed if you go from one pole to the other pole and observe what is happening to $$\psi$$.

It doesn't seem plausible that "very many waves" are arranged along the Earth in the weather patterns. Well, you have many short-wavelength waves on Earth, the normal acoustic waves and ocean waves and electromagnetic waves. But if you describe things like the hurricanes or polar vortices, the "number of waves" that may be compressed inside the Earth is obviously of order one, it cannot be large, and therefore the WKB approximation in the normal interpretation of the acronym is not usable.

So the usage of the term "WKB approximation" – that goes back at least to the 2013 paper that I mentioned above – is deeply misleading. Some of their mathematics is "somewhat correct" but all the details are wrong. In particular, their "WKB Ansatz" starts with plane waves. But that's not really what we get in the WKB approximation. The WKB approximation is supposed to be useful for equations with the general potential and the equation isn't solved by a simple plane wave. It is $$\exp(iS)$$ in the zeroth approximation where $$S$$ is a more complicated function of the spacetime coordinates than just a linear function.

If a competent physicist just said that a (probably simple enough) equation has a plane wave solution, he would simply not use the term "WKB approximation".

Atmospheric physics doesn't have terribly smart folks in it and šitty terminology may be normal and justifiable – after all, it's šitty terminology. But Mann's claim that his papers have something to say about the "quantum weirdness" are absolute and total nonsense which shows that pseudoscientific scammers in the climate hysteria and the pop science delusions about quantum mechanics sell rather similar "sexy misconceptions" – and indeed, sometimes it's the very same people who do so.