Sho, OK I think I see what you (and all those cosmologists) are saying a little clearer now but to clarify even more, am I correct in thinking that the theoretical Boltzmann Brains Universe is just that, simply an abstract infinite space with an infinite number of floating brains in it? No planets, no galaxies, no black holes etc… On the other side we have “our” universe with it’s annoyingly unlikely low entropic initial state.

Am I right? If so then I guess I can start to agree, or at least properly comprehend.

The only thing that still bugs me is, okay our universe’s initial low entropy big-bang state is super unlikely, but what kind of initial state would a Boltzmann Brains universe need to pop into existence? Would it not also be radically unlikely? Or is this entirely beside the point! ;-)

Anyway, thanks for the clarification!

]]>To be clear, we are comparing the uniqueness of A: a universe with many Boltzmann Brains, and B: a universe consisting of the initial state of the big bang. We are not comparing it with the complexity of the universe today.

We know that the initial state of the big bang was placed in a highly improbable low entropy state. As an analogy, let’s imagine that a large stack of individual grains of sand had been placed on top of one another in perfect balance, and that this stack of sand reached to the moon.

Meanwhile, let’s imagine that “a human brain” is represented by another improbable state, say, a perfect pyramid of sand 1 foot tall.

Now, let’s say that someone comes up with a theory that says that the initial state of the universe might have been created through random fluctuations due to the wind. Maybe this stack of sand grains is part of a much, much bigger sandbox, and given infinite time, a stack like this is *bound* to come up sooner or later, right?

Yes, it’s true that given an infinite amount of time of observing random configurations of sand, that we would probably observe a stack of individual grains of sand that reached up to the moon. However, it is infinitely more likely that a 1 foot tall pyramid would appear. Both are unlikely configurations, but the 1 foot tall pyramid is much more more likely than the stack of sand that reaches to the moon.

Again, we are talking about the “specialness” of the initial state of the universe, not the “specialness” of the current state of the universe.

]]>I must admit, this is where I get troubled in all the discussion around Boltzmann’s Brains and it’s disproving of the statistical fluctuation model of the big bang’s entropic state.

What troubles me specifically is that when you compare the uniqueness of A: a universe with many Boltzmann Brains, and B: a universe with us in our galaxy in it, it seems wrong to calculate the uniqueness of each simply by how much more complicated our galaxy/solar system/planet is compared to a floating brain of x trillion atoms. Surely one should compare the uniqueness of each system that lead to the final instance of A or B, and when you compare the systems then I fail to see how a system that ends with floating brains is any less complex than one that ends in a planet with scientists observing all and sundry!

Know what I mean?

Anyway, great post, interesting thoughts.

]]>So it’s a fool’s errand, but one can try. :-)

It’s as if the universe were made of jillions of grains of sand, and we happened to know that at the beginning of the universe, all the grains of sand were stacked vertically on top of each other. It might not make sense to talk about “the probability” that this happened, but you could certainly talk about how unique this configuration was relative to all the other possible configurations.

To be a little more precise, the estimate for the 10^10^123 probability of the initial state of the universe being “just so” comes from a book by Penrose called “The Road to Reality”. On the one hand, he’s a well respected mathematician who dabbles in physics (having co-authored papers by Hawking, etc.) On the other hand, he’s kind of a nutball, so people have differing opinions about him.

Anyway, Penrose’s formulation of the 10^10^123 estimate is pretty solid, I think, and it comes from the following:

1) Our best picture of the early universe comes from the so-called 2.7K background radiation, which is a remnant of the big bang. By observing it, we know that the early universe was extremely homogeneous.

2) We can approximate the mass of the universe as having ~ 10^80 baryons (particles) in it.

3) Based on our measurments of (1) and our count of (2), we can estimate the entropy of the early universe as ~ 10^8 per baryon, which is 10^88. A staggeringly huge number.

4) Now, let’s estimate the entropy of the final days of the universe. Assume the universe is closed, and will ultimately collapse on itself. The argument doesn’t require that the universe actually does this, but calculating the entropy of black holes is easy, so let’s go with that for now.

5) As the entire universe swallows itself into a gigantic black hole, the entropy can be estimated using the Bekenstein-Hawking formula at 10^123.

6) When it comes to probabilities, what matters is not the entropy but the number of accessible states, so we’re really talking about e^10^88 and e^10^123.

7) For large numbers, e^x ~ 10^x, and powers of 10 are a lot easier to work with, so let’s use them instead.

8) By these estimates, the final macro-state of the universe (a singularity) contains ~10^10^123 accessible states. The initial macro-state of the universe (also a singularity, roughly) contained ~10^10^88 accessible states.

9) The ratio between 10^10^123 and 10^10^88 is roughly 10^10^123, so you can see that there are vastly, vastly more singularities that look like an unordered mess than our initial universe.

So to be precise, we are talking about the observed entropy of the early universe and the volume of phase space that it occupies relative to the total space of all available states.

Now you can’t compute “the probability of a floating brain appearing”, because you need to have some kind of hypothesis of a physical process behind that. But you can talk about the “uniqueness” of that state relative to the “uniqueness” of the state of the big bang. And since there are vastly fewer particles in a human brain than there are in the universe, any theory that attempts to explain the initial state of the universe as a “statistical fluctuation” is going to have to explain why other “special configurations” of the universe (such as a human brain that just “thinks” it is observing the universe) can’t occur through the same statistical process.

]]>And please … the floating brain stuff, what are your probabilistic estimations deriving from anyway? WAY WAY what ???? WTF are you talking about ???? please elabourate … i would love to read through. ]]>