# Boltzmann’s Universe

CV readers, ahead of the curve as usual, are well aware of the notion of Boltzmann’s Brains — see e.g. here, here, and even the original paper here. Now Dennis Overbye has brought the idea to the hoi polloi by way of the New York Times. It’s a good article, but I wanted to emphasize something Dennis says quite explicitly, but (from experience) I know that people tend to jump right past in their enthusiasm:

Nobody in the field believes that this is the way things really work, however.

The point about Boltzmann’s Brains is not that they are a fascinating prediction of an exciting new picture of the multiverse. On the contrary, the point is that they constitute a reductio ad absurdum that is meant to show the silliness of a certain kind of cosmology — one in which the low-entropy universe we see is a statistical fluctuation around an equilibrium state of maximal entropy. According to this argument, in such a universe you would see every kind of statistical fluctuation, and small fluctuations in entropy would be enormously more frequent than large fluctuations. Our universe is a very large fluctuation (see previous post!) but a single brain would only require a relatively small fluctuation. In the set of all such fluctuations, some brains would be embedded in universes like ours, but an enormously larger number would be all by themselves. This theory, therefore, predicts that a typical conscious observer is overwhelmingly likely to be such a brain. But we (or at least I, not sure about you) are not individual Boltzmann brains. So the prediction has been falsified, and that kind of theory is not true. (For arguments along these lines, see papers by Dyson, Kleban, and Susskind, or Albrecht and Sorbo.)

I tend to find this kind of argument fairly persuasive. But the bit about “a typical observer” does raise red flags. In fact, folks like Hartle and Srednicki have explicitly argued that the assumption of our own “typicality” is completely unwarranted. Imagine, they say, two theories of life in the universe, which are basically indistinguishable, except that in one theory there is no life on Jupiter and in the other theory the Jovian atmosphere is inhabited by six trillion intelligent floating Saganite organisms.

In the second theory, a “typical” intelligent observer in the Solar System is a Jovian, not a human. But I’m a human. Have we therefore ruled out this theory? Pretty clearly not. Hartle and Srednicki conclude that it’s incorrect to imagine that we are necessarily typical; we are who we observe ourselves to be, and any theory of the universe that is compatible with observers like ourselves is just as good as any other such theory.

This is an interesting perspective, and the argument is ongoing. But it’s important to recognize that there is a much stronger argument against the idea that Boltzmann’s Brains were originally invented to counter — that our universe is just a statistical fluctuation around an equilibrium background. We might call this the “Boltzmann’s Universe” argument.

Here’s how it goes. Forget that we are “typical” or any such thing. Take for granted that we are exactly who we are — in other words, that the macrostate of the universe is exactly what it appears to be, with all the stars and galaxies etc. By the “macrostate of the universe,” we mean everything we can observe about it, but not the precise position and momentum of every atom and photon. Now, you might be tempted to think that you reliably know something about the past history of our local universe — your first kiss, the French Revolution, the formation of the cosmic microwave background, etc. But you don’t really know those things — you reconstruct them from your records and memories right here and now, using some basic rules of thumb and your belief in certain laws of physics.

The point is that, within this hypothetical thermal equilibrium universe from which we are purportedly a fluctuation, there are many fluctuations that reach exactly this macrostate — one with a hundred billion galaxies, a Solar System just like ours, and a person just like you with exactly the memories you have. And in the hugely overwhelming majority of them, all of your memories and reconstructions of the past are false. In almost every fluctuation that creates universes like the ones we see, both the past and the future have a higher entropy than the present — downward fluctuations in entropy are unlikely, and the larger the fluctuation the more unlikely it is, so the vast majority of fluctuations to any particular low-entropy configuration never go lower than that.

Therefore, this hypothesis — that our universe, complete with all of our records and memories, is a thermal fluctuation around a thermal equilibrium state — makes a very strong prediction: that our past is nothing like what we reconstruct it to be, but rather that all of our memories and records are simply statistical flukes created by an unlikely conspiracy of random motions. In this view, the photograph you see before you used to be yellow and wrinkled, and before that was just a dispersed collection of dust, before miraculously forming itself out of the chaos.

Note that this scenario makes no assumptions about our typicality — it assumes, to the contrary, that we are exactly who we (presently) perceive ourselves to be, no more and no less. But in this scenario, we have absolutely no right to trust any of our memories or reconstructions of the past; they are all just a mirage. And the assumptions that we make to derive that conclusion are exactly the assumptions we really do make to do conventional statistical mechanics! Boltzmann taught us long ago that it’s possible for heat to flow from cold objects to hot ones, or for cream to spontaneously segregate itself away from a surrounding cup of coffee — it’s just very unlikely. But when we say “unlikely” we have in mind some measure on the space of possibilities. And it’s exactly that assumed measure that would lead us to conclude, in this crazy fluctuation-world, that all of our notions of the past are chimeric.

Now, just like Boltzmann’s Brain, nobody believes this is true. In fact, you can’t believe it’s true, by any right. All of the logic you used to tell that story, and all of your ideas about the laws of physics, depend on your ability to reliably reconstruct the past. This scenario, in other words, is cognitively unstable; useful as a rebuke to the original hypothesis, but not something that can stand on its own.

So what are we to conclude? That our observed universe is not a statistical fluctuation around a thermal equilibrium state. That’s very important to know, but doesn’t pin down the truth. If the universe is eternal, and has a maximum value for its entropy, then we it would (almost always) be in thermal equilibrium. Therefore, either it’s not eternal, or there is no state of maximum entropy. I personally believe the latter, but there’s plenty of work to be done before we have any of this pinned down.

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### 100 Responses to Boltzmann’s Universe

1. Sho Kuwamoto says:

Interesting discussion!

Before this set of articles, I’d never encountered the Boltzmann’s Brain thought experiment, which seems to put the nail in the coffin for theories that postulate that the initial state of the universe can be explained as a statistical fluctuation.

For those who want another stab at explaining this line of thinking, I wrote a short article here.

That having been said, I think the argument is not 100% definitive.

If the hypothesis is that there is a larger “world out there” which is literally a world that follows the laws of physics as we know it, and that this world is in thermal equilibrium and that the universe as we know it is literally a thermal fluctuation of stuff within this gigantic larger world… well… the BB argument wins.

But the hypothesis, I think, is that none of us knows what the “world out there” looks like, and no one knows exactly the laws under which it operates. As we fumble around trying to guess at what it might be like, could we postulate that there is some larger world of stuff that follows certain laws that are similar to ours, and that there are fluctuations (quantum? statistical?) within this larger world?

And depending on the laws of this larger world out there, perhaps even small fluctuations could be greatly magnified into large systems with low entropy, such as the state of our universe at the time of the big bang.

Of course, once you get into this realm of thinking, it’s hard to call it science. More like metaphysics or pseudoscience.

2. Hal S says:

I was wondering if anyone has ever attempted to derive an equation based on the following:

If we accept that the universe is expanding and accelerating, what happens when that expansion impacts the maximal entropy event horizon of a black hole? Suppose we took the position that a black hole represents a seed mass for a new universe and the mass of the new universe is not equal to that black hole mass but proportional or a function of that seed mass?

In this scenario the expansion of the old universe when it encounters the event horizon causes inflation of a new universe, which can not be stopped by the mass of the black hole, but only after a sufficient amount of new mass and energy is created out of the vaccuum.

Is there an equation that would tell us the mass of the new universe based on the seed mass of the black hole?

Any comments would be appreciated.

3. Lawrence B. Crowell says:

Hal S on Jan 17th, 2008 at 8:54 pm
In response to Lawrence B Crowell

I think the disconnect is that equilibrium only has meaning in a closed finite system. If our universe resides in an infinite open space, then we can abandon notions of equilibrium of that larger space altogether, which is a pretty exciting idea.

———————

General relativity is based on the Lorentz group on local regions. The group has 3 ordinary rotations plus 3 boosts. The boosts are hyperbolic instead of elliptical or “circular,” or more precisesly compact. A symmetry which is compact is guaranteed to return on itself, so to speak. For instance a set of rotations about some angle @ and another about a some angle @’ are when both repeated in an infinite series guaranteed to converge — A Cauchy convergence condition. This is a closure condition. A noncompact group, such as that which underlies relativity, will in many cases fail to converge as such. A hyperbola approaches and asymptote, instead of closing up. The “infinite” convergence points means a group theoretic closure is not possible. The group theoretic structure of gravitation fails to obey this sort of closure. In a fundamental sense this is why gravitation fails to “close up,” which is a reason it has a strange form of thermodynamics.

A hydrogen atom might be considered to be a computer, even naively we might think that by putting the electron in a superposition of an infinite number of states as possible by Rydberg’s formula a hydrogen atom could be an infinte Turing machine or quantum computer. There is one problem called the Bekenstein bound. There is an upper limit on the amount of quantum information you can in any system with a size or surface area A. As A goes down the amount of information that could be put on the system decreases by a convex function.

I am not a big fan of anthropic principles. I will say I think the weak anthropic principle is useful as a sort of guiding question. A century ago the age of the Earth was known to be in the hundreds of millions of years. Ideas about solar light and energy involved gravitational contraction, which predicted a much shorter life for the sun. So geology, evolution and the fact we emerged from this jostled physics of the day to find a better theory. Along came quantum mechanics, nuclear physics and Hans Bethe who came up with the answer. Similarly the fine tuning issue and anthropic ideas are likely a similar question posed to us. The Polchinski-Bousso (2000) worked on how the cosmological constant / was due to a large bare term which is corrected by oscillator terms associated with a D7-brane dual to the D4-brane in the ‘bulk.” The exact / came about from a specialized condition or a sort of transversality of p-forms on these branes. Nice, and particularly nice since it raises a big question in the form of an anthropic implication.

The Boltzmann brain idea has to be taken in light of biology. What really matters on this planet are prokaryotes or bacteria. All the rest is fluff, and even plants are just photosynthetic machines meant to grab energy for bacteria. Eukaryotic cells (those with nuclei, organelles etc) evolved from ancient associations of prokaryotic cells, and all the rest of life we see ordinarily are just energy generating machines that are food for bacteria. This includes us. Prokarotic communities, which can involve a wide range of species, appear to exist in large webs that extend around the planet. They really run this place, not us. So to juxtapose Boltzmann’s brain against the great Bard

“Life’s but like a walking shadow, a poor player that struts and frets upon the stage, and then is heard no more; It’s a tale told by an idiot, filled with sound and fury, signifying nothing.” —- MacBeth, Shakespeare

The idea that the universe is a set of fluctuations that bring about a brain with various perceptions or internal conscious ideations, but with nothing else “out there” seems to pose more of a question, rather than being any idea which should be taken seriously. It is a sort of anthropic realization, which are entertaining over a scotch and cigar.

Finally, human beings should not take themselves that seriously. We have too much history of that, and it all seems to lead to the same eating of dust. Everyone should ponder what it is that we actually manage to accomplish here, even in our personal lives. You might find that everything you have ever made, bought, borrowed or stole ends up in the landfill. We humans at the end of the day appear to be little more than a terminator species turning everything we can get our hand on into trash.

Lawrence B. Crowell

4. Hal S says:

Lawrence B. Crowell

“General relativity is based on the Lorentz group on local regions. The group has 3 ordinary rotations plus 3 boosts. The boosts are hyperbolic instead of elliptical or “circular,” or more precisesly compact. A symmetry which is compact is guaranteed to return on itself, so to speak. For instance a set of rotations about some angle @ and another about a some angle @’ are when both repeated in an infinite series guaranteed to converge — A Cauchy convergence condition. This is a closure condition. A noncompact group, such as that which underlies relativity, will in many cases fail to converge as such. A hyperbola approaches and asymptote, instead of closing up. The “infinite” convergence points means a group theoretic closure is not possible. The group theoretic structure of gravitation fails to obey this sort of closure. In a fundamental sense this is why gravitation fails to “close up,” which is a reason it has a strange form of thermodynamics.”

I have a suspicion that we aren’t to far off our thinking on this, however, current understanding is that a massive object can not reach the speed of light traveling in a straight line. This is absolutely true, and I do not dispute that.

However, there shouldn’t be any problem for a massive object to reach the speed of light if it follows a continuous closed curve.

I base this on the following logic:

As a massive object approaches the speed of light, its effective acceleration in the direction of travel approaches zero. However, there is nothing prohibiting an acceleration in a perpendicular direction.

An acceleration perpendicular to the direction of travel will cause a change in velocity perpendicular to the orginal direction of travel.

In this case, you have two component velocity vectors, both less than the speed of light, that combine to produce a velocity vector equal to the speed of light. Mass along the closed curve has now stabilized at a finite value, depending on the initial mass and velocity of the object when it was moving in a straight line.

In this regard we can get relativity to close up.

5. Sean says:

Guys — this is not the place for discussing your ideas about general relativity. Keep the comments short and on topic. We don’t have time to edit or negotiate, so we will just delete.

6. Albatross says:

Although I don’t think that he had Botzmann’s Brain in mind when he wrote it, Steven Brust’s short novel, “To Reign in Hell postulates a universe created almost exactly under the conditions of Boltzmann’s Brain. The first being to spring into existence and not immediately redissolve into Chaos? Yahweh. Then he reached into the chaos and pulled out Lucifer, and the fun began…

7. Hal S says:

Apologies, I didn’t realize I was doing anything wrong. I just wanted to help.

8. Lawrence B. Crowell says:

Yahweh (Yod Hey Vov Hey) is an example of what Max Tegmark calls an observer with a “bird’s eye view” of the world. Of course there are theological quibbles here, for most religions regard God as outside the world or universe. The Be’raysheet (Genesis) story does have an interesting component to it, for light is separated from dark, dry land from sea, things that swim and things that fly and so forth. It reflects a cornerstone of Jewish thought of Kodesh or separation. So the face of God was upon the deep, here the waters signifying chaos or void, and He then imposed a dichotomy of distinct categories. Since God is a Tegmarkian bird’s eye observer He can do all of this on a fine grained scale without making a mess, or in other words generating entropy. Then of course there is the question I asked at an early age, “Where did God come from?” Boltzmann’s brain?

I don’t think the universe is fundamentally thermodynamic. Thermodynamics is what might be called an effective theory. Penrose thinks that quantum state reductions are an “Objective Reduction,” which are fundamental. These then destroy information and quantum information and impose a fundamental time asymmetry to the universe. A fundamental time asymmetry to the universe implies that quantum information is lost. This means it is difficult to attach an endpoint to the cosmological path integral based on solid physics. The universe may well be “void to void,” with an initial point being a set of inequivalent vacua and the final point the AdS conformal infinity, an empty M^4. Everything in between is just a holographic way that these two nothingness voids are connected together. Existence is just nothingess rearranged, or maybe what we see locally as “something” is just a way that nothingness is rearranging itself from an unstable nothingness to a stable nothingness along this illusion we call time.

But then is that a sort of fluctuation in an equilibrium bath? If you have a universe that globally is an equilibrium bath, there is no time. Time is something measured by a clock, which is a heat engine that requires a free energy source. In a grand world of equilibrium there is no clock, so operationally maybe there is no time. So everything is nothingess, Jean Paul Sartre is laughing, and if God is Boltzmann’s brain then it must go back into the soup of maximal entropy, Nietzsche declared “God is Dead.”

Lawrence B. Crowell

9. go back to 4 says:

“My one cent” (comment #4) summarized my thoughts on this. Creating a brain (or anything complex) from essentially uniform nothing is much harder (less likely) than allowing more common physical processes to act over long times. Indeed the notion that time+ordinary events produces extraordinary outcomes is the basis of the theory of evolution, our best way of understanding how brains came about.

10. Hal S says:

Sean

“Guys — this is not the place for discussing your ideas about general relativity. Keep the comments short and on topic. We don’t have time to edit or negotiate, so we will just delete.”

Please don’t delete this last comment, I want to make it and then I’ll let it go.

Boltzmann’s Brains and other ideas challenge our notion of probability and statistics, things that are intimately related to quantum mechanics.

Various authors make statements about how we should view the universe as a field of finite volumed points.

When it comes to the speed of light and mass, what is the difference between jumping from point to point in a straight line and jumping from point to point in a circle?

The distance traveled moving point to point along line segments approximating a circle is less than the circumference of that circle.

Under these circumstances, a massive object moving in a circle could appear to be moving at the speed of light, when in reality it isn’t.

The mass should then be equivalent to the relativistic mass related to the speed of the object moving along the line segments.

Very respectfully,

Hal S.

11. Lawrence B. Crowell says:

go back to 4 on Jan 18th, 2008 at 5:25 pm
“My one cent” (comment #4) summarized my thoughts on this.
————

Exactly. This is the old argument by creationists that natural science says that life and humans came about spontaneously from clouds of hydrogen. No, it didn’t happen that way. Life, brains and iPODS came about through a long protracted process and not some spontaneous assembly of bits.

Lawrence B. Crowell

12. Hal S says:

Lawrence B. Crowell (#61)

I agree with your statement, I get confused sometimes about how people interpret the anthropic principle.

I tend to like the idea of infinities simply because a natural infinity is not an argument for the creationist view, but an argument against it. We should expect conditions in our natural world to be such that we don’t require some intelligent agent in order to get things started.

Nothingness should be an unattainable state. It would be a state that would be both consistent and complete, which should not be possible. Nothingness should require an agent to keep stable; which contradicts our concept of nothingness.

13. Neil B. says:

Hal, nothingness certainly wouldn’t require an agent to keep stable, after all it would have no process of time and therefore have to be stable since it couldn’t change. I think that for a universe to just be around with certain properties “and not others we can imagine” (as alternative self-consistent choices) is an absurd existential loose end flapping around. You can believe in many universes then, but where does that end? Is it modal realism, does it even include cartoon universes and things much weirder than Boltzmann Brains? Is there anything like “the chance” of the fine structure constant being certain values, etc? What are the laws behind the laws?

14. Hal S says:

Neil (#63)

I am trying to understand Godel’s incompleteness theorem, and I still have a very naive view; and with my naive interpretation, it seems that a state of nothingness must be self consistent, i.e. without external context. It must also be complete in that if it were incomplete, then the whole state collapses.

I just can’t escape the thought that nothingness needs context.

I guess my current thinking is that we continue to take on a more mathematical view of the universe. In the context of sets, how do we discern sets of things that can exist and sets of things that can’t.

In a sense, things which we define as not real (cartoons and such) do have an existance on “the surface” of our perceived reality. Is our ability to imagine these things constrained? What is the set of things we can not imagine?

To get back on track, “What are the laws behind the laws?” I think is the real question. I find the use of the term “anthropic principle” has been misused enough to really have no strong meaning anymore.

I think if it is used purely as a statement like, “In our natural state we must live on Earth and not on Jupiter because we evolved here on Earth; and this affects our view of things.”; then its perfectly okay. But I don’t even know if that is the correct interpretation anymore, and if it is, then there are a lot of bad interpretations out there.

When I think of a “multiverse” I tend to think along those lines. I think if it does exist, then there is a definite structure to it; and I think that structure should be discernible in our present universe (and if it doesn’t exist that’s fine too, I have no strong preference to live in any particular universe, just as long as it looks a lot like the one I’m in)

I don’t believe in ghosts or goblins or any of the other fairy like things people want to exist in a “multiverse”. I don’t believe that you can derive the “laws of morality” from the laws of physics. I do believe that discernable physical laws in our universe should be similar or identical to the ones in the “multiverse”.

I am fascinated by the fact that square pegs don’t fit in round holes, that we can’t square the circle, and that we live in a universe with straight lines, ellipses and hyperbolas. I think that indicates what kind of “laws behind the laws” might govern things.

15. Hal S says:

I think I figured #60 out.

It seems that the answer is that the object in question would occasionally have to jump to points outside the apparent circular path, this would give it the opportunity to “self correct” the distance traveled along the segments.

I think that would make the path look like a tube and not a circle…spaghetti anyone?

16. Lawrence B. Crowell says:

I think Neil B. indicates a problem with the whole many universe idea. In order to make our world probable you need to drag in all sorts of other worlds in an ensemble or set so that ours is somehow inevitable. I really think we can do better than that.

Godel’s theorem rests upon Cantor’s diagonalization of Godel numbers and showing that no formal system as defined by Church’s Lambda calculus or the Russell-Whitehead Principia is able to enumerate all of its Godel numbers. So any axiomatic system that is sufficiently powerful will contain sets which it is unable to enumerate, or any axiomatic system as non-RE (recursively enumerable) statements, theorems etc in them. These are also theorems which effectively state their own unprovability as predicates that act on their own Godel numbers. Godel showed this by demonstrating there existed solutions to Diophantine equations which could not be computed. Cohen and Bernays demonstrated that the continuum hypothesis was consistent in Zermalo Fraenkel set theory as an example of Godel’s theorem.

Does this have anything to do with physics? It might, but serious caution is in order. Penrose threw out some ideas about Godel’s theorem and quantum state reductions, quantum gravity and even consciousness. It basically flopped. Underlying physics at the Planck scale things might indeed by a chaos of quantum states which are self-referential. For instance some quantum states have Diophantine representations, and by Godel’s original argument maybe some quantum systems have states which exist, but are not dynamically computable because their quantum information content is self referential. Maybe? Chaitan argues that axiomatic mathematics, the math we prove, know and use is the result of self-referential accidents. Maybe by the same line of thought physical law which is understood mathematically is also an accident. Of course we have to ask, “What do we even mean by law?” In some ways these are human constructions.

So does Godel’s thoerem have anything to do with physics or cosmology? Well if so it might be at the “end of physics,” at the Planck scale where everything might come to some end. Of course this is all highly speculative.

Lawrence B. Crowell

17. Qubit says:

Its still Pinocchio.

18. The idea of macroscopic statistical fluctuations is fascinating, if bizarre. Here’s a smaller-scale version of the Boltzmann’s brain argument that’s applicable to a single room.

Suppose you have some small room that is completely closed off from the rest of the universe. No energy or matter gets in or out. The walls of the room are built to last a gazillion years (or even 10^10^10^gazillion). Before you close it off, you place into the room all the ingredients for a human being: Carbon, Hydrogen, Oxygen, trace minerals, etc. Now just wait.

Eventually (we’re talking a long time to wait) the material will assemble itself into a human being. Call him Random. Random will then age just like a normal human being. However, there is a big difference between Random and an ordinary human. With an ordinary human, whatever age that person is, you can bet he was younger in the past. With our macroscopic-fluctuation-produced human, that assumption is not warranted at all. The processes that lead to aging are driven by entropy, and they are time-symmetric. So the same argument that would lead us to conclude that Random will look older and more decrepit in 40 years will just as validly lead us to conclude that Random already looked older and more decrepit 40 years ago. In other words, the chances are overwhelming that Random is the youngest he ever was.

It’s very rare that living humans would appear in the room, but it is much more rare that you would ever see children or babies.

What this shows is that our notions of “common sense” are intrinsically bound up with the idea that the universe has not been around forever, and that entropy was much lower in the distant past than it is now.

19. Lawrence B. Crowell says:

Of course these thought experiments indicate that something is wrong with the whole theory. Thermodynamics is what might be called an effective theory. It works well in a proper domain of application and observation. It even works with black holes. But appealing to fluctuation theory to understand how the universe came about, something similar to the Boltzmann brain, appears inoperative. Then reducing this down to a fluctuation which gives rise to a brain that has sensations of an existing universe, but where these might be an illusion as well as memories is a sort of solipcism.

The universe is a path integral over a set of configurations, which under a Wick rotation is a partition function in thermodynamics. So there is a connection here. Yet the start of the path integral is some vacuum state, or set of vacua, that are unstable, and the end point is a Minkowski spacetime with maximal entropy and the simplest vacuum configuration. This is the conformal infinity of the Anti-deSitter spacetime. Everything else is how states or quantum information connect up the start and final conformal infinity points.

Lawrence B. Crowell

20. seriously says:

“But appealing to fluctuation theory to understand how the universe came about, something similar to the Boltzmann brain, appears inoperative. Then reducing this down to a fluctuation which gives rise to a brain that has sensations of an existing universe, but where these might be an illusion as well as memories is a sort of solipsism.”

The Boltzmann’s brains that are solipsists are actually the sane ones. But the overwhelming majority of Boltzmann’s brains will be completely insane. Appropriately, some fluctuations will give rise to entire asylums full of Boltzmann’s brains. Unfortunately, some of these asylums will be populated purely by sane Boltzmann’s brains (except for the staff).

21. Hal S says:

Daryl

please read entry 41 and 48

22. Hal S,

Sorry, I don’t see how your arguments address what I wrote.

23. Lawrence B. Crowell writes: Of course these thought experiments indicate that something is wrong with the whole theory.

How do they indicate that?

24. Hal S says:

Daryl

A human being will never self assemble in the scenario you propose. Ever.

25. Hal S.,

I think everyone agrees that in principle it will never happen (it would require a time period on the order of Poincare recurrence time, an ungodly large amount of time, much, much longer than the lifetime of the universe). However, such an assembly is not impossible. It doesn’t violate any of the laws of physics. So I don’t know why you are saying it will never happen.

26. Hal S,

Why do you think that Bose condensates are relevant here?

27. Hal S says:

“No energy or matter gets in or out”

and you provided no source of heat

28. Hal S says:

Of course you could argue that when the some of the elements combine chemically they will produce heat, you then have a question of how much, and how big is your room.

You also have a problem in that you are in an inertial frame of reference. If the temp does get high enough, all elements will gravitate into blobs.

This leaves out the question of electrical currents that will be caused in any of the atoms become ionized. How do you prevent a capacitance from forming?

29. Hal S says:

There will be an evolution to this process, and entropy will increase, but again as outlined in 48, you can never get rid of all the correlations, and there will be some finite record of this evolution

30. Hal S,

I don’t believe that you are correct. The laws of physics don’t in any way say that there must remain a record of past evolution.

31. Hal S says:
32. Hal S says:
33. Here’s a more mathematically precise claim about what is possible from fluctuations.

Let |Psi> and |Phi> be two different states of a quantum system involving many, many particles. Then the prediction of quantum mechanics is that the probability that the system, when put in state |Psi> at time 0 will be found in state |Phi> at a later time t is given by

P = |A|^2

where A = is the transition amplitude and where H is the Hamiltonian.

The question is: under what circumstances do we expect the transition amplitude A to be zero for all values of t? Well, certainly A will always be zero if Phi and Psi have different eignvalues for conserved quantities. But if that’s not the case; if Phi and Psi have the same values for charge, total momentum, total energy, total angular momentum, etc., then I would think that A would be nonzero for most values of t.

34. Hal S,

Please don’t post any more urls without explaining why you think that any of them are relevant. Why are any of those web pages relevant?

35. Hal S says:

This is actually rather neat.

We know that fundamental forces unify at higher energies, and we know the universe is expanding and energy density is decreasing. Thus we have a permanent record of the fact that the universe had a higher energy density early in its evolution

36. Somehow, my definition of the transition amplitude A disappeared. But it’s just the element: A(t) = .

37. Hal S says:

All stable heavy elements must have been produced in large stars through nucleosynthesis, therefore we have permanent record that there was some large star that existed before our own solar system

38. Hal S,

Your conclusion does not follow from that. The average energy density for the entire universe may be decreasing with time, but that doesn’t imply that local densities might not increase.

39. Hal S says:

The universe evolves through the process of diffusion…some bound states are only producable at energy scales larger than what we see today

40. Hal S says:

ie supermassive black holes and spiral galaxies

41. Sorry, I don’t see how any of your comments are relevant. To say that some reaction is only possible at such and such an energy scale is a probabilistic statement. What it means is that without that energy, the transition becomes much less likely. But the probability never goes to zero unless the transition violates a conserved quantity.

42. Qubit says:

I can live my life backwards through time, while every one else lives forwards through time and we can all see the exact same history of the world. I dont think am real enough and am probably dead already because my life is improbable.

What they dont tell you at school is that it is possable to produce an imaginary black hole in your mind, information on its own is enough to do this. This is called frame setting, it makes your life real and observed up to that point. While you live on like being born again; in other words you exist in every single point in the universe as a real object. Then you simply are a universe at that point. Everthing before it simply is your imagination, that has become real. You surround the universe like a dyson sphere; like around a star and then you take everthing you need to carry on you life as yourself and nothing more. Doing this is the same as an animal that has no concious ablity to understand that its giving birth.

If I got something wrong then its your fault, because you used me to do it! You cant expect me to get “everything” right. Your frame is the one I set and unless you are “Your” then you can dismiss this as nonsense.
Its not wrong anyway, its entropy is just too high at the begining to be right, it needs to be a lot lower. The universe is not real, its proably a simulation and that really does suck!

Look left see blue “Think way of the mushroom!”, “Eyes forward!”, “A cat see’s with two eyes”, look right? “I cant remember?”

Do it yourselves next time!

If you dont understand this, then ignore it! And don’t comment!

43. Lawrence B. Crowell says:

To discuss quantum fluctuations I am going to texify some here. I hope I make no errors. Often when I do this I have to repair errors I make in doing this, but there is no preview. So here goes.

If you have a state psi(t) it will evolve into a state psi(t + &t) by the Schrodinger equation
$ihbarfrac{partialpsi(t)}{partial t}~=~Hpsi(t)$
where I will from now set hbar to one. The Hamiltonian H defines a unitary time development operator U(t) with
$|psi(t_0~+~t)rangle~=~e^{-iH(t_0~+~t)}|psi(t_0)rangle$
where the unitary operator is the exponential term on the right. We then consider the overlap of a state and its time development some small increment of time
$langlepsi(t)|psi(t~+~delta t)rangle~=~langlepsi(t)|e^{-iHdelta t}|psi(t)rangle$
which with the Taylor theorem gives
$langlepsi(t)|psi(t~+~delta t)rangle~simeq~langlepsi(t)|(1~-~iHdelta t~-~frac{1}{2}H^2delta t^2|psi(t)rangle$
This is the overlap between a state and its time development into the future. Now what we do is to take the modulus square of this to get
$|langlepsi(t)|psi(t~+~delta t)rangle|^2~simeq~(1~-~Big(langlepsi(t)|H^2|psi(t)~-~|langlepsi(t)|H|psirangle^2Big)delta t^2$
The last two terms on the right are
$(langle~H^2~rangle~-~langle~H~rangle^2)delta t^2,$
with some compression of notation. The term in the parenthesis is the square of
$Delta H~=~sqrt{langle~H^2~rangle~-~langle~H~rangle^2}$
Now this is the Heisenberg uncertainty principle for the whole package in the modulus squared is
$Delta Hdelta t/hbar~=~sqrt{langle~H^2~rangle~-~langle~H~rangle^2})delta t/hbar.$
This says that if I sample the system in a short time I will get a range of possible values for the energy of the system.

As a digression this has some interesting properties, for this is the metric of the Fubini-Study space and the fibration over the projective Hilbert space.

The quantum fluctuation is physically the result of sampling or measuring the system. Quantum mechanics is contrary to popular belief a completely deterministic physics. The Schr{“o}dinger wave equation is completely deterministic. But since the wave is complex valued, and there is this fibration given by the unitary operator over the projective Hilbert space what we measure in real variables has this range of possible outcomes.

In thermodynamics there are also fluctuations, and a formula for them based on the deBroglie wavelength. It is analogous to this, but where one has to look at Fokker-Planck equations or Langevin processes. These are similar to quantum fluctuations, but are really different physics.

Lawrence B. Crowell

44. Qubit says:

Maybe there is a killer virus that lurks in the universe, one that makes the odds of a boltzmann brain popping out of the ether at any point almost impossible. Viruses don’t have brains, but they do a great job of killing them and are a hell of a lot more likely to pop into existence than a brain. It’s not unconceivable that a type of virus removes all none real boltzman brains, leaving only evolved life forms possible. The nature of the universe is extremely violent and unforgiving; the universe simply has no time for things that are not real! Of course there is a chance boltzman brain can get lucky, but you simply just have to look at conception in humans to realise that once in the egg, no other sperm can get in; then the odd of twins are statistically possible, but in universe terms very unlikely.

You could tell your self in the past this, if you found a way; but you would end up leading yourselves into an un-real universe, once you passed the point you sent the information to yourselves in the past, you would not know what to do next. Unless you told yourselves what to do and that would be like creating a big polo mint in space and driving through the hole! Where would that get you?

45. RedCharlie says:

Anybody read Huw Price’s “Time’s Arrow and Archimedes’ Point”?

To paraphrase Price, the mystery is not why entropy always increases but why entropy is always lower in the past. If we assume that physics is time symmetric, then not only can cream spontaneously jump out of a cup of coffee and pebbles leap out of ponds, but they do, regularly. To see this all one has to do is run the tape backwards.

Price’s argument against Boltzman goes something like this:

1) We are not now in thermal equilibrium.

2) The statistical basis of the 2nd law dictates all matter moves toward thermal equilibrium.

3) So, we have to explain why we are not in equilibrium now, in the present.

4) Boltzman’s solution was to allow random fluctations from equilibrium, which is certainly possible, even inevitable, given enough time.

5) So, maybe we are in a non-equilibrium state because of such a random fluctuation in a universe that is otherwise in thermal equilibrium (most of the time).

6) The past, however, appears to us to have been even further from equilibrium, in fact, as one goes back in time, the further from equilibrium the (observable) universe becomes. I.e. entropy paradoxically decreases going back into time. If this doesn’t seem like a problem, please understand that we want a physics that is time-symmetric, i.e. has rules that work going forward or backward in time. So it’s no good to just say the 2nd law only applies going forward in time.

7) If it is the case, however, that our current departure from thermal equilibrium is due to a random fluctuation, then it is quite likely that our past is “fake”, that is, it only appears to be lower in entropy (further from thermal equilibrium) than it is now. This is because the more a possible fluctuation moves away from equilibrium, the less likely it is to happen. Assuming our current state is due to such a fluctuation, it will always be a “cheaper” or a more likely solution, statistically, to say the past is fake than to say the past really was lower in entropy than now. If one admits that the past is fake, then the furthest departure from equilibrium one must account for is now. But the further you push the point of “reality” into the past, the further the explanatory fluctuation must have departed from equilibrium, and thus the less likely it is to have actually happened that way.

This really isn’t to say that I believe our brains spontaneously appeared out of the muck a nanosecond ago. It’s really a reductio ad absurdum argument. It just shows that Boltzman’s proposed fluctuation is really not a satisfactory explanation of why the (observable) universe has a low entropy in the past.

And I think Carroll is wrong about this too:
“Note that this scenario makes no assumptions about our typicality — it assumes, to the contrary, that we are exactly who we (presently) perceive ourselves to be, no more and no less.”

If statistically the past is more likely to be “fake” than “real” (i.e. only appearing to be lower in entropy than now), then why not the present also? It’s more likely that the monkeys only typed out the first page of Hamlet rather than waiting around to finally produce the whole thing. If just we popped out of the uniform muck a nanosecond ago, it’s more likely that what popped out was just an empty, ephemeral stage-set, and less likely to be the “real thing”, no?