If the universe is extremely large, with effective physics and cosmological conditions varying widely from place to place, how can we predict the conditions we should expect to see? In principle we can use anthropic reasoning, by expecting to see conditions that give rise to observers, and perhaps expecting more conditions that give more observers. But how can we apply this theory when we know so little about the sorts of conditions that produce observers?
I just added to this post.
The causal diamond is the amount of stuff in the future light cone (taking into account the eventual disappearance of things over the horizon of accelerating expansion). But even if it weren't, the difference only matters to a small constant factor, which disappears in the noise in this context. What's important here is the big-O size, and that's the same for cones and diamonds.
Russell, cones and diamonds are different shapes, so integrals over them could be different.
Robin - I don't think I understand your reasoning. The causal entropic principle says a larger causal diamond gives higher weight because it contains more dust-produced entropy. I'm suggesting it gives higher weight because it increases the total number of observers resulting from each origin of intelligent life. I think the two give the same predictions at least for a causal diamond no larger than the one we observe, i.e. cosmological constant as low as 1e-123. Am I missing something?
Russell, your concept would suggest the chance to find observers at any one place would be the integrated entropy production in the back light cone from that place. While plausible, this would seem to make different predictions from the causal diamond used in the causal entropic principle.
God has chosen the world that is the most perfect, that is to say, the one that is at the same time the simplest in hypotheses and the richest in phenomena.-- Gottfried Von Liebniz
Final afterthought for tonight:
Why would the above reasoning not push, or at least float, the cosmological constant even lower than the observed value? The authors' reasoning is that additional galaxies reachable in later time are mostly "used up", so don't provide much additional weighting. However, it's been suggested that burnt-out stars retain most of their energy value to an advanced civilization (e.g. feeding helium etc into black holes for energy).
Suppose intelligent life is rare, but not that rare, and over distances substantially larger than our horizon, expanding bubbles of civilization are likely to bump into each other, thereby negating further weight bias.
By that interpretation - with additional disclaimer, obviously this is even more extremely tentative than my earlier comment - the above papers just might constitute the very first evidence for a lower bound on the frequency of intelligent life.
Oh, now this is interesting! Here's my interpretation after reading the first paper:
Prior distribution of cosmological constant is linear random. So observed value of 1e-123 is exponentially unlikely, expected value is near 1.But values higher than 1e-120 disrupt galaxy formation, hence unobservable.This leaves 3 orders of magnitude unaccounted for, because intelligent life could almost as easily appear with 1e-120 as 1e-123. The galaxies would rapidly vanish from each other's sight, but each would still evolve life.
Specifically, suppose possible values are weighted by number of observers per baryon (as previous authors have done). That weighting doesn't care to reduce cosmological constant much past 1e-120, on the assumption that intelligent life evolves in every galaxy, so it doesn't matter if the galaxies separate rapidly.
The above authors reproduce the observed value 1e-123 by weighting by number of observers per causal diamond (roughly speaking, per Hubble volume). In other words, their weighting cares to reduce it to 1e-123 on the assumption that it's important that the galaxies stay in contact with each other at least until a decent fraction of their energy reserves have been used up.
This makes sense (my interpretation, the authors talked only in terms of entropy production by dust heated by starlight) if we assume most galaxies don't evolve intelligent life. Therefore the actual number of observers per whatever divisor you choose, will be determined by the number of galaxies to which observers, once evolved, can spread. A typical observer will, therefore, find himself in a universe where the cosmological constant was small enough for intelligent life evolving in one galaxy to spread to many others before they disappeared from sight.
Therefore (with obvious disclaimer about extreme tentativeness of such conclusions) the above findings arguably constitute evidence that intelligent life is rare.
'As far as you can tell' doesn't go far enough. You're confusing the system that implements the observers with what they're observing - their experiences are necessarily low-entropy. The Anthropic Principle dicates the sorts of worlds that the observers will perceive themselves to be in.
Your inability to perceive order in the chaos is akin to complaining that most of the Library is nonsense static and ignoring the fact that it contains the Grand Unified Theory.
Chaotic observers born in the hearts of stars do not necessarily observe their surroundings.
Indeed they don't. Their observations are falsidical, random... and, so far as I can tell, maximum-entropy.
Our observations are highly ordered; a maximum-entropy probability distribution over observations would very strongly favor chaotic ones; so our observations are not selected from a maximum-entropy distribution.
You're confusing observers and observations. Chaotic observers born in the hearts of stars do not necessarily observe their surroundings.
By what rationale does anthropic reasoning count as "observers" all the humans ever living or ever to live, but not fluctuations in the stellar gases?
Our observations are highly ordered; a maximum-entropy probability distribution over observations would very strongly favor chaotic ones; so our observations are not selected from a maximum-entropy distribution. The observations of observers created momentarily by random fluctuations would follow something close to a maximum-entropy distribution; so such observers contribute only a tiny amount to the total measure of observations, so the overall distribution is still very far from maximum entropy.
Or so the argument goes, but I can't think of a good, rigorous, a priori reason not to count chaotic observers formed by stellar gas fluctuations or whatever (though David Chalmers has made a promising start). I'm very confused by this.
Tim and Recovering, the principle calculates entropy production over a very large volume, and so is not sensitive to detailed density variations or local derivatives.
Observers are not currently found where entropy production is highest [namely] inside stars and other massive objects.
They aren't? How could we know? Might not minds be constantly coming into existence within stars (albeit with very short existences)? By what rationale does anthropic reasoning count as "observers" all the humans ever living or ever to live, but not fluctuations in the stellar gases?
This seems odd. Wouldn't at least early observers be more likely to spawn within a range of entropy gain/volume? Not far too low, not far too high?
Surely that matches what we tend to observe regarding known life and physical quantities (heat, pressure, concentration of whatever substance) and remove the need for theory-complexifying specific exceptions for objects with huge entropy gain/volume like black holes.