BB #88: Boltsmann Brains

An article in a recent issue of New Scientist caught my attention on two counts: firstly, in what it said about my old friend wavefunction collapse and the measurement problem; and secondly, in mentioning Boltzmann Brains. Both set off my “Yeah, but!” reaction.

I’ll touch (as briefly as possible) on the first point, but this little Bubble is mainly about the second one.

Boltzmann Brains bug me.

Unfortunately, the article, A bold new take on quantum theory could reveal how reality emerges, by Tom Rivlin (postdoctoral researcher at the Vienna University of Technology in Austria), is behind a subscriber wall. I’ll quote sections relevant to this post.

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With regard to the measurement problem, Rivlin writes:

… Somehow, the act of measurement snaps the wave-like cloud of possibilities into a point-like reality with a defined position.

We call this process decoherence, and it explains why we don’t see quantum effects at everyday scales: once something gets big enough, there are too many other objects flying around that can “measure” it and upset its delicate quantum properties. But the same question still applies: how precisely does this process happen?

As an aside, some might argue that, while decoherence clearly plays a role, we don’t know quite what to call the process — collapse, reduction, decoherence, Many Worlds branching — because we don’t understand it. It’s a central mystery in quantum mechanics. (Of course, the point of the article is that they think they’re on track to solving it.) But decoherence definitely plays a major role — granting that wavefunction reduction actually does happen [see Wavefunction Collapse].

The article continues:

In the 2000s, physicists Robin Blume-Kohout […] and Wojciech Zurek […] took the idea of decoherence one step further. They argued that during this process, all the information in a system, including the quantum kind, spreads into the surrounding environment.

To that point, that’s pretty much a standard description of decoherence. It’s the next bit that raised my eyebrows:

This quantum information includes the system’s “two-places-at-once” property, or its superposition. But it also accounts for other intrinsically quantum features, like the bizarre, long-range “entanglement” that appears to allow instantaneous interaction between two quantum objects.

This seems to suggest some coherence in the information that’s lost into the environment during decoherence. [See Quantum Decoherence for more.]

What surprised me was the notion that the lost information was recoverable:

In a 2018 study, Jörg Schmiedmayer […] and his colleagues showed that quantum decoherence can also undo itself. They observed a few thousand ultracold atoms in a box and saw how the atoms’ positions became less correlated with each other through random collisions. The amount of correlation eventually reached a low, “equilibrium” value. But, after a few milliseconds, the correlation went back to almost its initial value.

But did the atoms randomly fall into that correlation? There seems an implication that they recovered their previous correlation but is it really the same one? A better question is whether the decohered information was taken (removed!) from the environment and restored to the atoms. Or was it lost, and a new correlation occurred due to probability?

Concerning this lost information, Rivlin writes:

Before a detector measures that particle’s position, there is information about all of the potential places it could have been detected. When the detector comes into contact with the particle, these pieces of information mix into the particles of the detector. We think this spreading process somehow “broadcasts” information from the system, making the information about its classical position available to read but its “two-places-at-once” information harder to spot.

The phrase “two-places-at-once” masks that, in many cases, it’s infinitely-many-positions-at-once. The position of an electron in a hydrogen atom, for example, can be literally anywhere (but with vanishing odds in most places), though the myriad positions near the nucleus are the “electron cloud” of most probable locations. Even the likely positions are infinite in the sense that position is a continuum.

So, I’m dubious about the claim this information is actually part of what decoheres. Even if a case can be made, I’m dubious about its ability to be recovered. I suspect, at the least, it dilutes and falls below Planck levels and is forever lost in the underlying static of reality.

[Far off the mainstream, I do not take conservation of information as axiomatic. I think it can be both created and destroyed.]

Rivlin continues:

The mathematics behind this process is complicated, so the first two papers on the framework, still in peer review, are heavy on calculations.

Which makes me wonder if they have become Lost in Math.

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But that was really just an opening aside. What inspired this Bubble was this bit:

…some have speculated that, in the ludicrously distant future, long after the last stars die out, random fluctuations away from equilibrium will happen, resulting in sentient beings spontaneously – and very briefly – flickering into existence. This thought experiment, known as the “Boltzmann brain”, suggests that equilibration isn’t the end of the story for a big, dynamic system.

Note that earlier he wrote:

The laws of thermodynamics, however, say that, given long enough, the milk and coffee will spontaneously separate back into the original, unmixed state. We would probably never see this happen because it would take far longer than the age of the universe.

Indeed. And “far longer than the age of the universe” is just for a cup of coffee. A working brain is a much more complicated proposition — “ludicrously distant future” seems a vast under-estimate.

And there’s an aspect to this I haven’t really seen addressed (not that I necessarily would have).

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There is the implication that particles just wander around and, given enough time, randomly arrange themselves into a complex structure. As if things jump from a mostly random state to a suddenly coherent state. Because probability.

The thing is, consider a human brain: 100 billion neurons with hundreds of trillions of connections. And the parts, the neurons and synapses, are extremely complicated all on their own. Incredibly more structure than a cup of coffee.

So, consider the particles wandering around randomly just a moment before the Boltzmann Brain forms. They are in an almost Boltzmann Brain state. A moment prior to that they were in an almost-almost B.B. state. And before that, almost-almost-almost, and so on.

The point is, these almost states are, as their name says, are almost as complex as the brain itself. A moment later, they would be the brain. But entropy always pushes back. At each almost stage, the overwhelming probability is for the configuration to become less ordered. Accomplishing the Boltzmann Brain requires a long series of increasingly unlikely configurations with each point along the way being pushed back more and more by entropy.

Further, without life support such a brain would perish quickly, so it’s not just the complicated structure of the brain that must spring into being but some sort of support structure as well.

Bottom line, Boltzmann Brains, far from being in any sense likely, are a ridiculous proposition — definitely a case of being lost in abstract idealized scenarios with no connection to reality. It’s the kind of science fiction that seems to have invaded science — an unfortunate co-effect of modern society’s general loss of connection with physical reality. The problem is epidemic.

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In closing: One thing about the mixed cup of coffee separating back into coffee and a glob of cream is that there are many configurations of coffee and a glob of cream, so we can’t really say the cup recovered its earlier information. I’d say the original configuration of coffee and a glob of cream has been lost.

But in far longer than the age of the universe it’s possible for the configuration to evolve to something indistinguishably similar. Note that the coffee mixture faces the same uphill battle as the B.B. configuration. At each step along the way to a state of coffee-cream separation, entropy pushes back.

Stay thermodynamic, my friends! Go forth and spread beauty and light.

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