External discussion: Jacques Distler will write a few critical sentences about the Boddy-Carroll paper tomorrow. I completely agree with Distler – as he will reproduce some ideas from the text below (and others). It's not possible for hypothetical future events to influence the present; and there is no particular framework of probability theory into which sentences of the kind "we're likely Boltzmann Brains" may be justifiably embedded. Each of these two bugs is enough to identify the paper as crap and the authors as nuts.On his blog, the Preposterous Universe, Sean Carroll promoted a paper by himself and Kimberly Boddy:
The Higgs Boson vs. Boltzmann Brains (his blog)Last week, I was giving a popular physics talk in a planetarium in Northern Bohemia. It clearly turned out to be too complicated for the bulk of the audience (philosophers are sometimes annoying but a group of philosophers is more ready to listen to some almost real physics than a selected 1/1,000 fraction of the general public in a medium-size town!) but we've had some fun, anyway.
Can the Higgs Boson Save Us From the Menace of the Boltzmann Brains? (arXiv)
One of the longest discussions was dedicated to the phase transition that may destroy the Universe; the Higgs field instability is the most ordinary example of such a scenario. In a "seed of doom", the Higgs field (or, more generally, another usually scalar field) may penetrate to a new, lower energy state that is incompatible with life. This "seed of the new lifeless Universe" starts to expand almost by the speed of light and devour everything. You won't feel the pain because your nerves are slower than the inflating nothingness.
I wanted to calm the public. The Universe won't collapse anytime soon. At the end, however, I just couldn't tell them anything else than the truth. And the truth is that empirically, we only know that the approximate lifetime of the Universe after which the "seed of doom" starts to grow somewhere is unlikely to be much shorter than the current age of the Universe, 13.8 billion years. It may be comparable, it may be a bit shorter but it may also be much longer and infinite. If it is finite, it sounds sort of unlikely that it would be comparable to the current age of the Universe which means that it's probably much longer. Don't worry. But there's really no "solid" argument that would prove that the Universe won't start to disappear in the next 1 billion years.
You may find the "Higgs decay" scenario frightening. The Universe may die long before the Sun runs out of fuel in 7.5 billion AD and goes red giant. What a waste! It may be tomorrow. We're not able to present any solid enough proof that it won't happen. However, Boddy and Carroll are scared of something else: that the Universe won't die soon. So they claim that the unstable Higgs field is our savior from the genuine threat: the Boltzmann Brains. This fear is utterly irrational because the Boltzmann Brains aren't endangering us. They aren't endangering physics, either. The won't ever appear on the Earth (much like Category 6 hurricanes which are nothing else than another proof that Al Gore is a liar without any scruples). There's no reason to sacrifice the world (or billions of dollars).
Similar explanations have repeatedly occurred on this blog but here we go again.
Boddy and Carroll – and others – are scared of a competing theory that may "explain" all the observations we have had. It's a theory that doesn't require the usual prehistory that has led to our life – including the Big Bang, the formation of the galaxies, the Solar System, and the lengthy path of evolution, not to mention many less fundamental parts of our life story.
Instead, one may say that there will be infinitely many opportunities in our soon-to-be-almost-empty de Sitter space where brains locally indistinguishable from ours may be created out of pure thermal fluctuations. Carroll and others believe that because the number of such "freak brains" is infinite (when integrated over the whole infinite future of the Universe), they are predicted to be more likely to be "us" than anything else (i.e. the well-behaved brains that have evolved from the Big Bang and evolution).
But this just ain't the case.
If there is an infinite number of something, this infinite number doesn't mean that it "has to be us". For example, \(\pi\) has infinitely many digits in its decimal form but that doesn't mean that you are any of them. The probability that you are just a digit of \(\pi\) is zero which means that not even the infinite number of these digits may force you to become a digit. Even if the probability that you were a digit of \(\pi\) were nonzero, it may still decrease with the location in \(\pi\) so quickly that the overall probability that you are a digit will be tiny.
Let me hope that the previous paragraph sounds trivial to you but be sure that Sean Carroll and others don't understand this simple claim. They confuse the "number of some objects" with "their probability" which are completely different quantities (and in a general situation, completely uncorrelated quantities) because the probability that "you are something" is in no way uniform for all these "somethings".
That's one way to describe the fundamental mistakes in his reasoning.
Another, closely related way to describe the fallacy is to point out that a hypothesis in science is something that explains our observations. To do so, it must not only make assumptions about "how the world works" but also about "where and when we are located or living" i.e. essentially "who we are" (I mean primarily who we are relatively to the rest of the world, not who we are internally and structurally).
Different assumptions about "where we are" and "when we are living" obviously lead to different predictions of what we should be seeing (the world looks different if you manage to live inside the Sun, inside the Moon, or million of light years from the nearest galaxy). So these assumptions distinguish different scientific hypotheses and they may be tested and falsified separately from each other. As a hardcore Marxist, Sean Carroll clearly wants to confirm or falsify all these different hypotheses simultaneously, as a collective, but science just can't work like that.
This simple point has been discussed using many different words on this blog. Several years ago, Hartle and Srednicki introduced the catchy term "xerographic distribution" to emphasize that the assumptions about our location within the spacetime incorporated in a theory is a part of the hypothesis that is being tested i.e. validated or falsified.
Imagine that our Universe will converge to an empty de Sitter space – everything indicates it is so (the world is already dominated by the cosmological constant and each 11 billion years of the cosmic time or so, the linear distances will double which means that the particle-based mass density of the Universe will decrease by a factor of 8 or so). This de Sitter space has a certain Poincaré recurrence time comparable to \(\exp(S_{dS})R_{dS}\) after which it has to repeat up to arbitrarily small errors and people have said many things about the question whether the repetitions should be viewed as independent episodes (the ER-EPR correspondence is surely another conceptual reason to think that these repeated stories should be thought of as being "in the same region of the spacetime" i.e. not independent).
But I don't really think that such questions about the identification influence how science chooses the valid hypotheses.
Fine. The Universe will continue as a nearly empty de Sitter space which is still filled with the thermal radiation at the temperature which is tiny (the typical thermal wavelength is comparable to the curvature radius of the de Sitter space) but nonzero. And because it's nonzero, every state of matter has a nonzero probability and when it's given infinitely many opportunities to be realized, it will be realized. In particular, freaky Boltzmann Brains that perceive the same things as we do even though they haven't evolved through the nice scientific big-bang-evolution path are guaranteed to appear at some very distant moment in the future.
But that doesn't mean that our best theories (assuming that the de Sitter space won't collapse) actually predict that we are the Boltzmann Brains. Even though the Boltzmann Brains will be repeated infinitely many times, science can say – and actually does say – that we're not belonging to their transtemporal society. Again, the number of objects is a different thing than the probability that you are one of these things, stupid!
The usual physical theories with the Big Bang and an infinitely long-lived empty de Sitter space are compatible with our having evolved by the "almost straightforward history" involving the usual events after the Big Bang and evolution, among others, without some exponentially unlikely events. Why? Because these assumptions are a part of the standard physical theory combining cosmology and particle physics! Like most good theories in science, the standard cosmology says that life has evolved without a dependence on some super-unlikely fluctuations or events. As a good scientific theory, our Big Bang cosmology explicitly says that we are not Boltzmann Brains. This claim isn't incompatible with any other assumption of the theory just like the claim that you are not a digit of \(\pi\) (even though there are infinitely many such digits) is not incompatible with the biology of mammals.
So the standard cosmological theory is a different theory than any theory that claims that we are Boltzmann Brains. They are totally incompatible with each other because the standard cosmological theory says that everything we see is a result of a nearly inevitable evolution that was picking the most likely outcomes almost all the time – and that depended on no "super-unlikely" events or fluctuations.
Different hypotheses may be compared with each other. You may compare the standard cosmological theory with the Boltzmann Brain hypothesis of any kind. Needless to say, the standard cosmological theory wins because the Boltzmann Brain hypothesis predicts that whenever you look a bit further than before, you should almost certainly see a disorder that will leak the fact that your brain and its vicinity is just a giant thermal fluctuation. (By the Boltzmann Brain hypothesis, I mean the hypothesis that our brains/civilization etc. appeared from a thermal fluctuation that only began to resemble the usual evolution at times much shorter than the usual age of the Universe or in a region much smaller than the usual size of the visible Universe but is truly thermal elsewhere; if you include large fluctuations that have evolved "ordinarily" in the whole visible Universe for 13.8 billion years, then such a "generalized Boltzmann Brain" hypothesis isn't falsified and may in fact be a good description or philosophical incarnation of our observations.)
The standard cosmological theory predicts that the next galaxy you are going to observe with your next-generation telescopes will be similar to those you already know. And of course that the standard cosmological theory's predictions are pretty much right while the totally different predictions of the Boltzmann Brain hypothesis are falsified.
A scientific hypothesis working with the assumption that we are Boltzmann Brains is empirically falsified – by totally elementary observations, in fact. Simple observations (combined with simple logic) are the easiest ways to falsify a hypothesis in science. But it shouldn't be shocking that one needs at least some empirical data to falsify a hypothesis. That's how science has always worked. Science chooses the right and wrong hypotheses by looking at the empirical data. There's no reason to be ashamed of this fact. It is true and it has to be true, otherwise it wouldn't be science.
So we don't need to assume that our Universe will die in a few billion years if we want to protect our physical theories from the Boltzmann Brains' being us. The empirical evidence is overwhelming that we are not Boltzmann Brains. Because we know that we're not Boltzmann Brains, we may immediately eliminate every hypothesis or its part that would force us to believe that we are Boltzmann Brains. It's that simple. That's why we just don't have to be afraid of "being" Boltzmann Brains or postulate some "liberating doomsday" to protect the good feelings about our identity against some crazy ideas.
At the end, I really think that Carroll's totally wrong reasoning is tightly linked to an ideology that blinds his eyes. As a hardcore leftist (or at least a person pretending to be one in order to improve his social status in a hard left-wing environment), he believes in various forms of egalitarianism. Every "object" has the same probability. Also, much like climate "scientists" (and I am only talking about "scientists" in the quotation marks here, not about genuine scientists), he wants to "collectively test" (and "collectively trust") models (e.g. climate models) whether they are right. But none of these things is scientifically true. Objects, people, and their categories are created unequal, probabilities aren't proportional to the numbers of objects in any reasonable sense, and hypotheses must be validated individually and not "in collectives" because at most one of the inequivalent theories or models may be right at the very end and it's just wrong to clump a right theory with the wrong ones because the very purpose of science is to be disentangling the right ones from the wrong ones.
Let me offer you an analogy that should hopefully clarify why Boddy's and Carroll's way of thinking is totally silly.
Imagine that we discover a stone that looks like a display and it displays one decimal digit every hour. Such a stone looks like a result of Intelligent Design but it doesn't matter whether it's man-made, UFO-made (OK, I meant ET-made), or natural. Assume it's natural but your task is to predict what the object will do. Once people begin to watch the digits and remember them, they record the following sequence:
4,1,5,9,2,6,5,3,5,8,9,7,9,...It looks like a random sequence of digits. However, someone realizes that they look like digits (starting from the third one) of \(\pi\):\[
\pi\approx 3.1415926535897932384626\dots
\] This person will predict that the next digits will be 3,2,3,8 and the prediction is confirmed. It's great. Note that by now, 17 hours after the records began, people have recorded 17 digits from the stone so far.
But someone will start to claim that there is no reason why the digits should be taken from the beginning of \(\pi\). The same sequence of 17 digits appears roughly once in a sequence of \(10^{17}\) digits of \(\pi\) and because \(\pi\) has infinitely many digits, the same 17-digit sequence is bound to appear infinitely many times somewhere.
In fact, someone else will change the statement and say that they will appear somewhere in\[
e\approx 2.718281828459045235360\dots\qquad\\
\qquad \dots 28747135266249775724709369995\dots
\] or somewhere in its powers \(e^n\) where \(n\) is a nonzero integer. Because there are infinitely many numbers of the form \(e^n\) and just one number \(\pi\), someone else may even claim that it's more likely that the stone emits random digits from a number of the form \(e^n\) and not from \(\pi\).
Needless to say, such a claim is unjustified because there's no reason why the \(e^n\)-based explanation should be "equally likely" as an explanation based on \(\pi\). And indeed, the empirical evidence will keep on accumulating (new digits are coming every hour!) that the \(\pi\)-based explanation is the right one while the other hypotheses are just wrong.
The guy or babe who invented the \(\pi\) theory of the stone used \(\pi\) and not \(e^n\) and he or she did claim that the digits are taken almost from the beginning of \(\pi\), too. He or she isn't "obliged" to consider some faraway sequences in \(\pi\) (or even in other numbers) to be "equally justified" predictions of his or her theory because the theory includes the statement that the digits are taken almost from the beginning. The place in \(\pi\) from which the digits are being taken isn't "obliged" to be "typical" – on the contrary, it's a point of the explanation that it is a very special point, the beginning. So every inequivalent statement is a competing hypothesis and it will finally lose. Too specific theories based on specific enough locations in other numbers will be strictly falsified; theories explicitly or effectively claiming that the digits are random will be "fuzzily" (but increasingly robustly) falsified because they predict that (very/extremely) long \(\pi\)-like patterns are (very/extremely) unlikely. But they're being observed which makes these random explanations increasingly falsified.
In this analogy, Boddy's and Carroll's claim about the "desirable" Higgs decay of the Universe is analogous to the statement that \(e\) is a rational number. If the digits of \(e\) start to get repeated, then the same is true for \(e^n\) as well and the numbers \(e^n\) won't have the sufficient infinite diversity of sequences of digits to match the observed digits emitted by the stone. In this way, the analogous Boddy and Carroll will argue, the \(\pi\) theory is protected against the Boltzmann Brain explanation – the explanation assuming that the digits are being taken from a random faraway place of one of the numbers \(e^n\).
Indeed, academically speaking, the Boltzmann Brains-like \(e^n\) theory of the stone could be falsified in this way: if \(e\) were rational, it just couldn't generate an aperiodic sequence of digits. But what Boddy and Carroll (and others) don't understand is that it is not neccessary for \(e\) to be a rational number if we want to scientifically establish that the digits are actually being taken from \(\pi\). The empirical evidence is enough. And indeed, \(e^n\) for \(n\neq 0\) aren't rational numbers which means that the strategy to disprove the \(e^n\) theory of the stone is hopeless because it depends on propositions that are wrong. And indeed, the evidence from the stone keeps on arriving and confirming the \(\pi\) theory while falsifying any other simple enough hypothesis.
Also, I want to mention that we may know a reason or we may not know any reason why the stone prefers \(\pi\) over \(e^n\). But even if we don't know any such deeper reason, it doesn't mean that the \(\pi\) and \(e^n\) explanations are equally likely. Instead, the empirical data heavily break this symmetry and imply that \(\pi\) is vastly preferred. That observation really means that deeper theories about the inner workings of the stone are either "encouraged" or "totally required" to prefer \(\pi\) over \(e^n\). You may believe that \(\pi\) and \(e^n\) are equally good for the stone but much like any belief in science that has observable consequences, your belief may be proved to be wrong and indeed, it is proved to be wrong in this case, too. There's nothing "holy" or "infallible" about egalitarianism; in fact, it's one of the crappiest ideologies around.
We know that we aren't Boltzmann Brains and we don't need to assume a "doomsday scenario" – a Higgs vacuum decay or any other doomsday scenario one could talk about (the very fact that Boddy and Carroll single out the Higgs vacuum decay is a piece of demagogy or a hint that they're unable to localize the actual reasons that lead to certain conclusions) – to be sure that we aren't Boltzmann Brains because the observations we have already made are enough to be absolutely sure. The state-of-the-art scientific theories claim that we are results of a nearly inevitable evolution involving a very dense and hot Universe after the Big Bang, structure formation, and evolution of species and these scientific theories are explicitly stating that we are not random thermal fluctuations that would have to be super-exponentially unlikely.
Someone may think he has reasons to think that we should be Boltzmann Brains or it should be likely that we are Boltzmann Brains. But "where we are" represent a part of the scientific hypotheses – the xerographic distribution – that needs to be tested much like any other part of a scientific theory. The tests are very easy, have been done long before we became homo sapiens, and the result is that the Boltzmann Brain xerographic distribution is safely falsified. So why do people keep on talking about it? It's as safely falsified a scientific hypothesis as any other falsified scientific hypothesis. In fact, more so. It's one of the key principles of the scientific method that we are gradually ceasing to discuss scientific hypotheses and paradigms that have been falsified.
So Boddies and Carrolls of the world, please stop emitting this crap and attempting to raise the stakes by incorporating ever more irrational and ever more megalomaniac "requirements" concerning a doomsday. No doomsday is necessary for the science we have learned to work.
And that's the memo.
0 comments:
Post a Comment