Welcome to this week’s installment of the From Eternity to Here book club. This is a fun but crucial part of the book: Chapter Ten, “Recurrent Nightmares.”
Excerpt:
Fortunately, we (and Boltzmann) only need a judicious medium-strength version of the anthropic principle. Namely, imagine that the real universe is much bigger (in space, or in time, or both) than the part we directly observe. And imagine further that different parts of this bigger universe exist in very different conditions. Perhaps the density of matter is different, or even something as dramatic as different local laws of physics. We can label each distinct region a “universe,” and the whole collection is the “multiverse.” The different universes within the multiverse may or may not be physically connected; for our present purposes it doesn’t matter. Finally, imagine that some of these different regions are hospitable to the existence of life, and some are not. (That part is inevitably a bit fuzzy, given how little we know about “life” in a wider context.) Then—and this part is pretty much unimpeachable—we will always find ourselves existing in one of the parts of the universe where life is allowed to exist, and not in the other parts. That sounds completely empty, but it’s not. It represents a selection effect that distorts our view of the universe as a whole—we don’t see the entire thing, we only see one of the parts, and that part might not be representative. Boltzmann appeals to exactly this logic.
After the amusing diversions of the last chapter, here we resume again the main thread of argument. In Chapter Eight we talked a bit about the “reversibility objection” of Lohschmidt to Boltzmann’s attempts to derive the Second Law from kinetic theory in the 1870’s; now we pick up the historical thread in the 1890’s, when a similar controversy broke out over Zermelo’s “recurrence objection.” The underlying ideas are similar, but people have become a bit more sophisticated over the ensuing 20 years, and the arguments have become a bit more pointed. More importantly, they are still haunting us today.
One of the fun things about this chapter is the extent to which it is driven by direct quotations from great thinkers — Boltzmann, of course, but also Poincare, Nietzsche, Lucretius, Eddington, Feynman. That’s because the arguments they were making seem perfectly relevant to our present concerns, which isn’t always the case. Boltzmann tried very hard to defend his derivation of the Second Law, but by now it had sunk in that some additional ingredient was going to be needed — here we’re calling it the Past Hypothesis, but certainly you need something. He was driven to float the idea that the universe we see around us (which, to him, would have been our galaxy) was not representative of the wider whole, but was simply a local fluctuation away from equilibrium. It’s very educational to learn that ideas like “the multiverse” and “the anthropic principle” aren’t recent inventions of a new generation of postmodern physicists, but in fact have been part of respectable scientific discourse for over a century.
It’s in this chapter that we get to bring up the haunting idea of Boltzmann Brains — observers that fluctuate randomly out of thermal equilibrium, rather than arising naturally in the course of a gradual increase of entropy over billions of years. I tried my best to explain how such monstrosities would be the correct prediction of a model of an eternal universe with thermal fluctuations, but certainly are not observers like ourselves, which lets us conclude that that’s not the kind of world we live in. Hopefully the arguments made sense. One question people often ask is “how do we know we’re not Boltzmann Brains?” The realistic answer is that we can never prove that we’re not; but there is no reliable chain of argument that could ever convince us that we are, so the only sensible way to act is as if we are not. That’s the kind of radical foundational uncertainty that has been with us since Descartes, but most of us manage to get through the day without being overwhelmed by existential anxiety.
On page 226 you have the following sentence:
“Those memories will generally be false, and fluctuating into them is very unlikely, but it’s still much more unlikely than fluctuating the entire universe.”
I believe you meant to say “…much less unlikely than fluctuating the entire universe.” Or possibly “…much more unlikely to have fluctuated the entire universe.”
I have to agree that this is a fun part, and I am glad I don’t have to worry about being a lonesome fluctuation floating in chaos (with my own bogus memories).
Yep, that’s a typo. Thanks.
A look for a pleasure.
Silently, in
my mind, a
little desire
and the warm
atmosphere
of a sullen
romance……
Francesco Sinibaldi
Dr. Carroll, it was toward the end of this chapter that I believe that I finally understood your entire thesis — to paraphrase: We macroscopic beings remember the past but not the future because our memories rely on “macrostates” which have a 1-to-many correspondence with the fundamental “microstates” which defines an entropy for the brain which increases only because the entropy of the universe is increasing due to a relatively recently low entropy initial condition in the past.
Maybe, I’m being too skeptical, but I still don’t think any of the arguments you put forth in this chapter eliminates the possibility of a universal fluctuation in entropy. Couldn’t the so-called initial conditions simply be a local fluctuation in the multiverse? I suspect you will discuss the role of gravity in universal evolution later because I am curious as to how gravitation must throw a monkey wrench into entropy.
Clifford, it’s certainly possible that a downward fluctuation in entropy could create conditions like we see in the early universe. However, it would create much smaller fluctuations much more often. So this theory predicts very strongly that we should be in a tiny fluctuation, not a large one. Therefore, it’s ruled out.
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Sean,
I ran into one of your papers on Internet (What if Time Really Exists?) and was amused with similarities of our approaches to the subject. Don’t want to be intrusive, so will try to be brief. Here are some thoughts you may already went through:
1. I think we both agree that the non-equilibrium state of infinite space is defined by some tiny, currently undetectable, quantum entropy gain (or, maybe, energy loss for clarity); this process defines time direction (from past to future, never back). What will happens if infinite space of higher power or dimension “overlaps” our infinite space and injects quantum units of energy equal or larger then energy losses that define our arrow of time? Will it reverse time arrow? On what conditions it may happens and will it be boundary surface effects or multidimensional wave effects? A wild field for speculations…
2. As for time recurrences I have some ideas, but stop here on just two simple scenarios:
– evolution of universe after Big Bang can be roughly illustrated as a charged particle movement along the magnetic flux ropes that, at any moment after the Bang, have radii of curvature orders larger then universe diameter. This common approach gives firm foundation to fundamental speed of light postulate. Also, it allows to link “dark matter” issue to sort of magnetic flux reconnection phenomena (placing black holes about a reconnection vicinity).
– another approach is strictly for atheists. Life on our planet most probably develops because we exist at the very middle of dimensional curve. All we know now is about 50 dimensional orders up (to macro space) and 50 dimensional orders down (into micro space). Anyway, we are pretty average, that’s why we exist. But who told that our universe ends up at dimensional values 50 orders of magnitude up or down? We should talk about infinity or near infinity dimensional values. So, most probably, our universe and our existence is just a tiny fluctuation (Boltzmann-type or Herodotus-type, who cares), another words, our universe is an energy quantum itself. That way, our universe as a singular statistical fluctuation in an infinite space, does not follow any other physical rules, that exist only within our very twisted singularity and will not exist elsewhere. So, this will be no space/time for our universe when the energy is gone, like it will be nothing left of soap bubble when it expands beyond film’s tensile strength.
I would be interested to know how trivial my ideas are.
Thanks,
Ivan Kuznetsov
(few words about myself: currently I am at NASA/GSFC. I am not a theorist anymore, my job is strictly projects-oriented. In my native country I worked at Lebedev Physics Institute, Moscow. I also beg forgiveness for my poor English, my literary ability is monolingual).
Hi Ivan– I’m afraid this description isn’t really enough for me to follow what you’re suggesting. Have you published any papers about the scenario?
Sean,
No, I haven’t publish anything on that. I did make some simple math – but it’s trivial and easily subject to criticism, cause introductions of quantum entropy and quantum time are too easy. The physics are now deep into it – building of a new dimension or quantification instead of continuity can relatively easy break most of visible discrepancies and paradoxes. So, I never dig the subject seriously. Any subject where one can argue upon or against without experimental or strong theoretical prove is simple, aren’t you agree?.
If you incline to do some serious job on that and if you are interested in any of my thoughts, you always welcome to use what you think is feasible, no obligations.
Sean: “Clifford, it’s certainly possible that a downward fluctuation in entropy could create conditions like we see in the early universe. However, it would create much smaller fluctuations much more often. So this theory predicts very strongly that we should be in a tiny fluctuation, not a large one. Therefore, it’s ruled out.”
That’s a very weak argument, which certainly cannot rule it out. Whose to say our fluctuation is “large” and not “tiny”? There is no such thing as an universal scale, the visible universe can be the whole there is or it can be an infinitesimal part of some superstructure.
“Large” refers to the size of the entropy fluctuation, which does have a scale — the maximum entropy of our observable patch is something like 10^120, and the actual entropy is something like 10^103, which is enormously smaller. Put another way: to explain us, you don’t need 100 billion other galaxies.
This reminded me of my least favorite parts of a philosophy class in that I took in college – the subject of how do we know we aren’t a disembodied brain. Although I was a bit worried about where the book was going, I was happy to see that ultimately there is a good reason why we can conclude that our universe and laws of physics are real and not just a random fluctuation.
While reading this, I also thought about how virtual particles pop in and out of existence. This would also negate any theory that depends upon a finite set of particles.
Hi Sean,
Thank you very much for providing the first satisfactory expalnation for the cause of the Big Bang, namely your idea of breakaway Black Holes, as expalined in both your book and in Part Two of your talk in Australia on Entropy, and the Arrow of Time. As I understand what you’re saying, our universe could have started from vacuum fluctuations causing virtual particles to form a Black Hole, which expanded to became our universe.
A Question please: could you please explain one question about our universe starting as a Black Hole:
(Math Question)
If the mass of the observable universe is about 2×10(55) gm estimated
from the cosmic expansion (including dark matter and everything). We
would not be living inside a black hole because it requires a mass of
about 6.5×10(55) gm to create one with the radius of the observable
universe (~ 10(28) cm). Perhaps Inflation changes the Black-Hole-starting-density into the less than Black Hole density in the universe we see now? Please explain, thanks.
Regards,
Joe Sullivan
Joe– The simple answer is that the requirements to make a black hole are very different when the whole universe is expanding. Basically, the equivalent of “making a black hole” becomes “having the universe recollapse to a Big Crunch.” Our universe isn’t in danger of doing that, because it’s actually accelerating.
There is some sense in which our universe is analogous to a white hole, as it has a spacelike singularity in the past.
Sean: “Large” refers to the size of the entropy fluctuation, which does have a scale — the maximum entropy of our observable patch is something like 10^120, and the actual entropy is something like 10^103, which is enormously smaller. Put another way: to explain us, you don’t need 100 billion other galaxies.
But why is entropy of observable patch a useful scale? Observable patch is not the whole Universe so it’s size is irrelevant. Whose to say if 100 billion other galaxies is small or large when compared to the whole? What if the whole Universe contains 10^10^10^10^10^….^10 and so on 10000000000 times galaxies? Then 10 billion is a negligible number.
It’s somewhat like the argument ancient Greek used to prove that stars were immobile – since they couldn’t see movement due to parallax they stars had to either be immobile or extremely far away but the distance involved was just to large for them to accept it so they settled on immobile.
For what it’s worth, all of these eternity to here pages have an HTML error:
a href=””http://eternitytohere.com
Thanks for catching that! Shows just how many people were clicking.
Sean,
Since a dead brain has much higher entropy than a live one, would a Boltzmann Brain with the ability to ignore the equilibrated soup and see only highly ordered anomalies find itself surrounded by dead brains and fragments thereof?
Doesn’t seem like much of a lifestyle…
There would be a lot more dead brains than live brains, and a lot more half-brains than whole brains. But the expected value of either would be zero; almost all brains would find themselves surrounded by thermal equilibrium.
Assuming arbitrarily large telescopes, wouldn’t Boltzmann-brains arising in the arbitrarily distant future have light cones so huge they can beat those odds?
Sean,
If I understand correctly, you bring up the claim: “In an eternal universe, there would be an infinite number of low-entropy fluctuations, and we must be in one of those since otherwise we would not be here to wonder about our universe” and then reject it by saying: “Sure, but under this model, we would expect the maximum-entropy arrangement that would support such a mind wondering about itself and the universe, which is an absolute maximum-entropy mess anywhere but in the immediate environment of a lonely Boltzmann brain”.
My question is: what if a fluctuation that creates the *conditions* under which a brain can evolve is far more likely than the fluctuation into existence of a “ready-made Boltzmann brain”? Then, given that we are here to ask questions, we would expect the universe around us to be consistent with a past which supports the evolution of life, not just its existence at a particular moment, since this is more likely (far more possible configurations) than a particular Boltzmann brain existing out of context.
In other words, does it not make sense that the fluctuation into existence of the conditions for intelligent life to evolve is more likely than the fluctuation into existence of a lonely Boltzmann brain, complete with all the complexity required for intelligence? And, continuing on the same line of thought, isn’t that also likely that such conditions would constrain all the observable universe around us to be relatively ordered rather than just a small low-entropy pocket around us?