This is why ever since I learned QM properly I thought Boltzmann Brains based purely on quantum fluctuations were silly. Just because you can dice the vacuum state up so it looks like things are going on until you finish off the math, doesn't mean that anything is actually going on. It just means you chose a silly coordinate system for the problem.
Consider a wavefunction X that contains a mind. Clearly, if we take -X, that will also have a mind. But X+(-X) does not have a mind. I'm not sure whether this concept has been given a name, but "quantum zombie" seems like a good term. Is the mind in X not conscious? X fully describes a mind that is capable of thinking about its existence and wondering whether there is a -X branch. If a conscious being exists before your finish off the math, how can it cease to exist after you finish off the math? What if the universal wavefunction has a negative of our branch? Can we say for certain that it doesn't?
What do you mean by "a negative of our branch"? The idea seems confused to me. Specifically, if the universal wavefunction is a function Psi on config. space, and "our branch" is the portion of the wavefunction whose domain is the config. space region Q, then what is the negative of our branch? Is it -Psi(Q)? Is it Psi(-Q)? In neither of these cases does your point hold, I think. Were you thinking of something else?
To zero in on the part of this line of questions that's relevant to the above...
1) The vacuum state is orthogonal to any states which represent minds, because no component of a mind is the empty state.
2) Even some mind has some tiny sliver of amplitude of |0> in it somehow, then if you apply the retarded Green function to it to extract how it got into that situation, the result isn't going to look like |0>, so you're violating the assumptions of the hypothetical. At best, it's going to look like converging radiation, i.e. a conventional Boltzmann Brain.
3) IF the conscious being had existed before finishing off the math, then it would still be there afterwards. But when the cancellation comes up, we instead are finding out that we'd been wasting our time considering it because it wasn't there after all.
Interesting, reading this I just realized how incomplete the Schrodinger equations is without a corresponding theory of what Eliezer once called "reality fluid".
Quantum fluctuations are not dynamical processes inherent to a system, but instead reflect the statistical nature of measurement outcomes.
I'm no expert at all, but while that sounds agreeable on an intuitive level, I've read that the opposite is true - ie that QM processed are inherently fuzzy. Is there a consensus on this?
edit: Reading further into the blog post clarified the claim they were making, though I still don't know how mainstream this is.
Quantum fluctuations are not dynamical processes inherent to a system, but instead reflect the statistical nature of measurement outcomes.
I'm no expert at all, but while that sounds agreeable on an intuitive level, I've read that the opposite is true - ie that QM processed are inherently fuzzy
I don't quite understand why you think that this is the opposite of what you quoted. The point is that the "inherent fuzziness" is there, but it is not because of literal unobserved "fluctuations" of the system over time. Speaking of "fluctuations" as if they were actual processes happening in time is poetic language (and all physicists understand that it is poetic language. The process of trying to explain QM to lay audiences generates a huge number of attractive but incomplete oversimplifications like this one).
String theorist Luboš Motl strongly disagrees with the analysis writing "Sean Carroll has no clue about physics and is helping to bury the good name of 2 graduate students".
P=NP would be good for the environment, though. Think of all the gas the travelling salesmen would save.
Calling Luboš Motl a string theorist is reaching. He hasn't done any research in forever. His contrarian opinions have more chance of being wrong than right and so can be safely ignored. His blog is mostly of entertainment value if you enjoy reading putdowns. I would wait until real QFT/GR/Cosmology experts chime in.
Motl with his immature style and his political extremism is very easy to mock, but I don't think he's intentionally contrarian. When he writes about physics at least his opinions agree with the mainstream view as far as I can tell. Three examples
Some time around 2005 Motl frequently exchanged hostilities with another blogger, Peter Woit of Not Even Wrong (that's actually how I first heard of LM: I was following NEW which frequently linked to Molt's blog to mock him). The disagreement was that Woit was a critic of the String Theory whereas Motl was a defender of it. The latter view is much more common in the academia.
In January last year, Motl criticized Sean Carroll's blog post about the interpretations of Quantum Mechanics. Here again Motl is defending the most popular view.
This is much less clear cut but, if you continue reading despite the political raving (which I realize is not easy), everything he says in this review about discrete and continuous mathematics and how it relates to the foundations of physics is eminently reasonable and what I'd expect to hear from a physicist.
These are not cherry-picked examples, it's all I recollect reading of Motl about physics, since I don't follow his blog regularly. In all these cases the vibe I'm getting is not contrarianism, but exasperation with people who pretend they have deep insights into his field when he feels all they have is a nice turn of phrase and the ability to please the audience.
I agree that Motl has an occasional keen insight, but it is usually and unfortunately buried under a mountain of opinionated nonsense. And I don't mean his political opinions, whatever they are, which I never pay attention to. Given that there are bloggers out there who are consistently insightful, like Baez, Aaronson, Carroll and others, I find that life is too short to look for nuggets of wisdom in his piles of garbage. Incidentally, I used to like Woit's writings before, but I find them a bit lower quality lately. Sometimes he sounds like Motl, only more respectful. Anyway, if you like we could discuss the merits of a particular point Motl makes, dissociated from the source of it. Unfortunately, I am not qualified to decide whether vacuum fluctuations in vacuum are "real" enough to eventually produce Boltzmann brains, but I tend to agree that, even if they are, they dissipate too fast in a de Sitter space to produce Boltzmann brains in any quantity.
Motl with his immature style and his political extremism is very easy to mock, but I don't think he's intentionally contrarian. When he writes about physics at least his opinions agree with the mainstream view as far as I can tell. Three examples
Some time around 2005 Motl frequently exchanged hostilities with another blogger, Peter Woit of Not Even Wrong (that's actually how I first heard of LM: I was following NEW which frequently linked to Molt's blog to mock him). The disagreement was that Woit was a critic of the String Theory whereas Motl was a defender of it. The latter view is much more common in the academia.
In January last year, Motl criticized Sean Carroll's blog post about the interpretations of Quantum Mechanics. Here again Motl is defending the most popular view.
This is much less clear cut but, if you continue reading despite the political raving (which I realize is not easy), everything he says in this review about discrete and continuous mathematics and how it relates to the foundations of physics is eminently reasonable and what I'd expect to hear from a physicist.
These are not cherry-picked examples, it's all I recollect reading of Motl about physics, since I don't follow his blog regularly. In all these cases the vibe I'm getting is not contrarianism, but exasperation with people who pretend they have deep insights into his field when he feels all they have is a nice turn of phrase and the ability to please the audience.
Another link to Sean Carroll's blog: Squelching Boltzmann Brains (And Maybe Eternal Inflation). The discussion of Boltzmann brains has come up many times on LW, starting from this Eliezer's post. Now Sean and his collaborators argue that in an empty expanding universe:
Quantum fluctuations are not dynamical processes inherent to a system, but instead reflect the statistical nature of measurement outcomes. Making a de nite measurement requires an out-of-equilibrium, low-entropy detection apparatus that interacts with an environment to induce decoherence. Quantum variables are not equivalent to classical stochastic variables. They may behave similarly when measured repeatedly over time, in which case it is sensible to identify the nonzero variance of a quantum-mechanical observable with the physical fluctuations of a classical variable. In a truly stationary state, however, there are no fluctuations that decohere. We conclude that systems in such a state|including, in particular, the Hartle-Hawking vacuum never fluctuate into lower-entropy states, including false vacua or con gurations with Boltzmann brains.
Although our universe, today or during inflation, is of course not in the vacuum, the cosmic no-hair theorem implies that any patch in an expanding universe with a positive cosmological constant will asymptote to the vacuum. Within QFT in curved spacetime, the Boltzmann brain problem is thus eliminated: a patch in eternal de Sitter can form only a finite (and small) number of brains on its way to the vacuum.
In other words, in an empty universe no macroscopic areas of low entropy can form. And a non-vacuum expanding universe like ours becomes vacuum after a time too short to form more than a few Boltzmann brains.