In the Dark

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 of h_* across plasmas, we find a very similar value of h_* ≈ (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 ½h_*=ε_ct_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)u², 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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