## Universality in Space Plasmas?

It’s been a while since I posted anything reasonably technical, largely because I’ve been too busy, so I thought I’d spend a bit of time today on a paper (by Livadiotis & McComas in the journal *Entropy*) that provoked a Nature News item a couple of weeks ago and caused a mild flutter around the internet.

Here’s the abstract of the paper:

In plasmas, Debye screening structures the possible correlations between particles. We identify a phase space minimum

h_{*}in non-equilibrium space plasmas that connects the energy of particles in a Debye sphere to an equivalent wave frequency. In particular, while there is no a priori reason to expect a single value ofh_{*}across plasmas, we find a very similar value ofh≈ (7.5 ± 2.4)×10_{*}^{−22 }J·s using four independent methods: (1) Ulysses solar wind measurements, (2) space plasmas that typically reside in stationary states out of thermal equilibrium and spanning a broad range of physical properties, (3) an entropic limit emerging from statistical mechanics, (4) waiting-time distributions of explosive events in space plasmas. Finding a quasi-constant value for the phase space minimum in a variety of different plasmas, similar to the classical Planck constant but 12 orders of magnitude larger may be revealing a new type of quantization in many plasmas and correlated systems more generally.

It looks an interesting claim, so I thought I’d have a look at the paper in a little more detail to see whether it holds up, and perhaps to explain a little to others who haven’t got time to wade through it themselves. I will assume a basic background knowledge of plasma physics, though, so turn away now if that puts you off!

For a start it’s probably a good idea to explain what this mysterious *h*_{*} is. The authors define it via ½*h*_{*}=ε_{c}t_{c}, where ε_{c} is defined to be “the smallest particle energy that can transfer information” and t_{c} is “the correlation lifetime of Debye Sphere (i.e. volumes of radius the Debye Length for the plasma in question). The second of these can be straightforwardly defined in terms of the ratio between the Debye Length and the thermal sound speed; the authors argue that the first is given by ε_{c}=½(m_{i}+m_{e})u^{2}, involving the electron and ion masses in the plasma and the information speed u which is taken to be the speed of a magnetosonic wave.

You might wonder why the authors decided to call their baby *h*_{*}. Perhaps it’s because the definition looks a bit like the energy-time version of Heisenberg’s Uncertainty Principle, but I can’t be sure of that. In any case the resulting quantity has the same dimensions as Planck’s constant and is therefore measured in the same units (Js in the SI system).

Anyway, the claim is that *h*_{*} is constant across a wide range of astrophysical plasmas. I’ve taken the liberty of copying the relevant Figure here:

I have to say at this point I had the distinct sense of damp squib going off. The panel on the right purports to show the constancy of *h*_{*} (y-axis) for plasmas of a wide range of number-densities (x-axis). However, but are shown on logarithmic scales and have enormously large error bars. To be sure, the behaviour looks *roughly* constant but to use this as a basis for claims of universality is, in my opinion, rather unjustified, especially since there may also be some sort of selection effect arising from the specific observational data used.

One of the authors is quoted in the Nature piece:

“We went into this thinking we’d find one value in one plasma, and another value in another plasma,” says McComas. “We were shocked and slightly horrified to find the same value across all of them. This is really a major deal.”

Perhaps it will turn out to be a major deal. But I’d like to see a lot more evidence first.

Plasma (astro)physics is a fascinating but very difficult subject, not because the underlying requations governing plasmas are especially complicated, but because the resulting behaviour is so sensitively dependent on small details; plasma therefore provide an excellent exemplar of what we mean by a *complex* physical system. As is the case in other situations where we lack the ability to do detailed calculations at the microscopic level, we do have to rely on more coarse=grained descriptions, so looking for patterns like this is a good thing to do, but I think the Jury is out.

Finally, I have to say I don’t approve of the authors talking about this in terms of “quantization”. Plasma physics is confusing enough as classical physics without confusing it with quantum theory. Opening the door to that is a big mistake, in my view. Who knows what sort of new age crankery might result?

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June 17, 2013 at 10:49 am

The Russian school has been using a ‘quantised formulation’ of elementary excitations (aka waves) in plasmas for several decades, including the usual creation and annihilation operators of many-body theory, and they would surely have some interesting comments on this. Various books by Vadim Tsytovich as I recall.

Separately, I have heard it said that the Higgs mechanism is simply the quantum-field analogue of the classical phenomenon of mutual Debye screening among particles. That demystified it for me.

June 17, 2013 at 11:27 am

Yes, Debye screening did make me think of the Higgs mechanism as I was writing it, but it must have popped out of my mind as quickly as it popped in as I didn’t mention it in the post…

June 17, 2013 at 6:55 pm

I haven’t read the paper, so I shan’t comment on it or its results. However, I’ll issue a general warning about hidden selection effects when interpreting observational data from diverse sources.

Did I really type that? I love Big Brother.

June 18, 2013 at 10:22 pm

Reblogged this on Observational Astronomy.