A Boltzmann Brain is (very roughly) a "brain", i.e. self-aware entity, that appears spontaneously in the middle of the universe due to random quantum fluctuations. In an infinitely old and infinitely large universe this should actually be a common occurrence. So why are we not Boltzmann Brains ourselves? Why are we all here observing the universe clustered together on this one planet a mere 15 billion years since it came into being? Why is there so much structure?
I believe the concept is a little different than what you stated. It starts with the assumption that the Universe is actually in or very close to a maximal entropy state, which is orders and orders of magnitudes more likely than the low entropy state we perceive. The idea of a Boltzmann brain is that a downward fluctuation in entropy from this maximum entropy state could result in forming a consciousness with our associated memories and experiences and this is more likely, statistically speaking, than the alternative possibility: that we actually live in an extremely low entropy state of the Universe.
> "In an infinitely old and infinitely large universe this should actually be a common occurrence. So why are we not Boltzmann Brains ourselves?"
Because our Universe is neither infinitely old (is about ~14 thousand millions years old) nor infinitely large (is about 90 thousand millions ly in diameter).
Now this might seem big for you, but it's actually infinitesimal when compared to the number of necessary permutations in order for higher intelligence to appear solely by a quantum fluctuation.
This means that the only scientific possibility for higher intelligence to appear, is then that only a very small set of universe conditions must occur so that atoms then stars then planets then life then intelligent life has the time and conditions to form.
This is the diameter of the observable universe. We don't know if the universe is infinitely big, but all signs (e.g. the flatness of space as far as we can measure it) point to it being infinite, or very very much larger than our observable sphere.
I don't understand why I'm constantly having to inform smart people of this very basic fact. Is there something wrong with the way we teach astronomy? Can you help me spread the word?
Could you expand on the "all signs" bit please? I was under the impression that there was little to no evidence of anything much outside the observable universe.
Read about measurements of the flatness of space. To the precision we're capable of measuring, it appears completely flat.
Then picture us as ants on a surface that appears flat as far as we can see. Are we on an infinitely sized surface? Either we are, or it's a sphere but the surface is curved but so slightly that it appears flat. This implies the sphere is much bigger than our observable area.
Note, we're assuming the universe doesn't just end we arbitrary boundaries. It either is infinite or it curves back on itself.
> ""90 thousand millions ly in diameter"
This is the diameter of the observable universe. We don't know if the universe is infinitely big, but all signs (e.g. the flatness of space as far as we can measure it) point to it being infinite, or very very much larger than our observable sphere."
Our observable sphere is nowhere near 90 thousand million ly in diameter since that would violate relativity. Our observable sphere in ly is always smaller than the age of the universe in years (so ~14 thousand million years).
Also, what you said is no fact, basic or not, it's just some misconception you have about cosmology so you should stop spreading that word since you are misinforming people you talk to.
In a nutshell: A Universe that begins in a singularity cannot have an infinite diameter and while it's true that we do calculate the size of the Universe by assuming the expansion rate right after the Big Bang and that rate might be wrong, it still cannot be infinite without violating the major principles of physics and the all big bang theory.
My "fact" doesn't refer to the universe being flat. I would never call this a fact. The "fact" I referred to is that the universe appears to us to be flat as far as we can tell.
Our observable sphere in ly is always smaller than the age of the universe in years (so ~14 thousand million years)
This ignores the basic fact that the universe is expanding at an accelerating rate. I'm comfortable calling this one a fact. Many 9s behind that confidence percentage (even if the number of nines was recently lowered).
A Universe that begins in a singularity cannot have an infinite diameter
Based on what logic? You are probably imagining an infinitesimally small sphere expanding out and becoming the universe. This is a good description of only our observable universe. There's no reason not to think that point wasn't part of an infinitely large manifold. This would point to an infinitely large universe.
I'm not an expert, but in my curiosity I've spoken to Dr. Don Lincoln from Fermilab about this very topic, so that's the source of my confidence. Along with my own subsequent (armchair) research. I've since followed up and done my best to understand why this misconception is so prevalent. I'm convinced it's because many sources say "universe" when they mean "observable universe", leading to many misconceptions.
> "This ignores the basic fact that the universe is expanding at an accelerating rate."
And that ignores the basic fact that information about those parts of the Universe didn't have time to arrive yet (that is where relativity is violated). You are mixing the concept of "observable universe" with "observed universe". At a given time, given the expansion rate of the universe you have an "observable universe" (those ~90E9 ly), but it will only be fully observable somewhere in the future, in the present you only get to observe ~14E9 ly). In a nutshell what you are proposing is that we are observing particles with infinite redshift. Or perhaps in a simpler way: You can be observing today parts of the universe that are (for instance) 25E9 ly away today, but you are observing particles of light that left that part of the universe a long time ago so that the c x t condition was never violated.
> "This is a good description of only our observable universe. There's no reason not to think that point wasn't part of an infinitely large manifold. This would point to an infinitely large universe."
Based on the theory of the Big Bang which is the de facto theory accepted by Cosmology. It is true that you could have an infinitely large manifold and that is a very interesting theory. But I was answering inside the actual theory that is the accepted one now-a-days the Big Bang (and I actually referred that in the answer). Also, even inside the manifold theory theory, our universe that is what is being discussed here, would still not have an infinite diameter.
There is a difference between the size of the observable Universe now and the size when the light was emitted. It does not violate relativity to state that objects that were 14 billion light years away when the light we see from them left are now much farther away due to expansion.
Furthermore, your reference to relativity is also incorrect. The expansion of the Universe is not caused by objects moving away from each other, which would be limited by the speed of light. The expansion of the Universe is actually an expansion of space itself, which is not limited by the speed of light. You should look up the "metric expansion of the universe".
In general, relativity is known to be incomplete on a cosmological scale. The situation is much more complicated due to the existence of dark energy and dark matter. You should read about the Lambda-CDM model if you want to learn more about the state of modern cosmology.
I didn't quote you or claim you said anything. I made some assumptions about why you made certain statements like the fact that you think the Universe being ~90 billion light years in diameter violates relativity (it doesn't and this is the currently accepted estimate for its size).
You could just clarify your statements/reasoning to try and progress the discussion instead of getting overly defensive.
> "you made certain statements like the fact that you think the Universe being ~90 billion light years in diameter violates relativity"
I was the one explaining to the OP of the thread that the universe is 90E9 ly in diameter (and also, just to clarify for the future so that it doesn't get mixed up yet again, that this is just an approach based on what we know about the history of the universe), it is therefore ridiculous that I also said that it violates relativity. So, sorry if I'm "overly defensive" about you mixing everything up and me having to use my time to answer you so that you don't twist everything I said on the thread.
You made the original claim that it violates relativity so why don't you take your own advice and be more explicit.
The current accepted size of the observable universe is ~90 billion light years in diameter. If you were referring to some other statement that you think violates relativity then feel free to clear things up.
if you're upset about people making assumptions about your comments then (calmly) address those and clarify your point(s). Don't make aggressive and pejorative assumptions of your own.
If you don't know what I was referring to, then why where you so sure that "it doesn't violate relativity" then?
The statement was made about the infinite size of the Universe and the OP (along the way) was talking about the observable Universe. He is mixing the extent of the Universe with the spatial dimensions of the Universe (so, the better word here is actually space). It is still an open debate if the dimensions of the Universe (space) are infinite (although what we knows seems to point that way), but the extent of the Universe is not infinite, if it was, that would violate relativity (or the standard model as I explained along the thread).
Because our Universe is neither infinitely old (is about ~14 thousand millions years old) nor infinitely large (is about 90 thousand millions ly in diameter)
You have just suggested the universe expands at roughly 6c, no?
In the early moments after the big bang, the metric of the universe expanded much faster than the speed of light increasing it's size way above the c x t linearity.
This doesn't violate relativity though, since what is expanding is the length of the spacial dimensions, but the particles between themselves are moving slower than the speed of light (imagine 2 points in the surface of a balloon when the ballon is inflating).
The acceleration of the Universe has not been constant. In the very early Universe there was a period called Inflation where the speed of expansion was much much much faster than the speed of light.
Is there any way to tell that you are not, in fact, a Boltzmann brain with simulated memories and inputs that just imagines everything else exists? I assume it's hard to refute, like Solipsism?
> In an infinitely old and infinitely large universe this should actually be a common occurrence. So why are we not Boltzmann Brains ourselves?
Our Universe of 13.8 Billion years (think: just 13.8 G years -- my fingernail-sized camera card has more bytes than that number) is infinitely younger than an infinitely old Universe.
I didn't word my post very well (I posted the "infinitely old" comment), but what I meant was that it should be more likely to be a Boltzmann Brain in an infinitely old universe than a human standing on Earth in a ~14 Billion year old universe. So why are we the latter rather than the former? That's basically what the anthropic principle is all about. The fact that we are the latter tells us a lot about how the universe, or universes as the case may be, work.
We can't forget that Boltzmann was purely thinking of (near) equilibrium structures. Structure emerges spontaneously minimizing free-energy, totally OK with LBs high entropy laws.
https://en.wikipedia.org/wiki/Boltzmann_brain
A Boltzmann Brain is (very roughly) a "brain", i.e. self-aware entity, that appears spontaneously in the middle of the universe due to random quantum fluctuations. In an infinitely old and infinitely large universe this should actually be a common occurrence. So why are we not Boltzmann Brains ourselves? Why are we all here observing the universe clustered together on this one planet a mere 15 billion years since it came into being? Why is there so much structure?