Russell Standish writes, regarding
http://arxiv.org/abs/astro-ph/0607227 :
> Thanks for giving a digested explanation of the argument. This paper
> was discussed briefly on A-Void a few weeks ago, but I must admit to
> not following the argument too well, nor RTFA.
>
> My comment on the observer moment issue, is that in a Multiverse, the
> measure of older observer moments is less that younger ones. After a
> certain point in time, the measure probably decreases exponentially or
> faster, so there will be a mean observer moment age.
I had a similar thought. I am curious to know your reasoning or
justification for why this should be true.
I have not read the papers referenced by this one, but the authors allude
to previous work: "Given some a priori distribution of the values of
the fundamental constants across the ensemble, the probability for a
'typical' obserer to measure a certain value of one or more of these
constants is usually taken to be proportional to the number of observers
(or the number of observers per baryon)."
It is this last parenthetical comment I found interesting. Apparently
there has been a difference in previous work about whether the measure
should be proportional to observers vs observers per baryon. Consider
two cases: one observer in a universe of a given size, or one observer
in a universe twice that big. These would be considered the same by a
number-of-observers measure, but the first would have twice the measure
if it was observers per baryon.
I argued some time past, based on some hand-wavey arguments, that the
latter measure is better - we attribute a portion of a universe's measure
to an observer, proportional to the fraction of the universe that the
observer takes up. This came from the UDASSA concept I was describing
in detail last year. It amounts to the observers-per-baryon measure.
It's interesting that physicists have considered a similar idea.
In terms of time, like Russell I would say that ancient observer-moments
should get less measure than early ones, for the same basic reason -
it takes more information to specify the location of the "physical"
system that instantiates the OM within the universe. My reasoning
though would imply that measure should be inversely proportional to
age, rather than Russell's suggestion of an exponential decay. So I am
curious where he got that. I could describe my reasoning in more detail
if there is interest.
> So contra all these old OMs dominating the calculation, and giving
> rise to an expected value of Lambda close to zero, we should expect
> only a finite contribution, leading to an expected finite value of
> Lambda.
>
> We don't know what the mean age for an observer moment should be, but
> presumably one could argue anthropically that is around 10^{10}
> years. What does this give for an expected value of Lambda?
I don't know if I know enough physics to figure that out. I'll take
another look at the paper.
I see that I misstated the reason why the CC limits observation.
It's not that the universe becomes uninhabitable. Rather, computation
and observation is assumed to be proportional to internal energy divided
by external universe temperature. It turns out that the optimal strategy
is to accumulate and store up as much energy as you can, as the universe
expands and cools. Then, when the universe is all cooled down, you go
ahead and do all your observations and calculations.
In a universe with a high CC, you can't accumulate as much energy,
because it expands more quickly and hence mass-energy thins out faster.
It cools down sooner and you don't have as much stored up at that time,
so you can't do as much.
So what we would have to say is that that strategy is no longer optimal
because such distant observer-moments will have low measure, and we care
more about OMs which have high measure. (I admit that few people take
the idea seriously that seemingly undetectable OM measure changes should
matter, but I can assume that this is a super-advanced civilization and
everyone is smart, so of course they will agree with me!)
Instead, the optimal strategy maximizes the total measure of OM-
computations, and that requires doing more computations early. OTOH,
it is more efficient to wait until the universe is cooler, we can do more
computing with the same amount of energy. Maximizing the product of these
two effects would require a detailed model for how quickly measure decays
with time. (We'd also have to consider whether measure should change with
temperature, which it might in my model, I have to think about it more.)
> Of course their argument does sound plausible for a single universe -
> is this observational evidence in favour of a Multiverse?
I think what you're saying is that if this is the only universe, and if
civilizations adopt the strategies advocated in this paper, then most
OMs will be far in the future, hence by the ASSA we are unlikely to be
experiencing present-day OMs. This was the basic concept of a paper we
discussed back in 2002:
> Dyson, L., Kleban, M. & Susskind, L. Disturbing implications of a
> cosmological constant. Preprint <http://xxx.lanl.gov/abs/hep-th/0208013>,
> (2002).
They used a slightly different physics model but came up with the same
idea, that most OMs should be in the distant future, contradicting what
we call the ASSA, which I think they just considered an implication of
the anthropic principle.
You might be right that these papers could be read as an argument
against a single-universe model, if in fact we could come up with a
good justification within a multiverse model for decreasing OM measure
in the future. We'd probably have to have a pretty strong argument
in that regard, though.
Hal Finney
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Received on Fri Jul 28 2006 - 19:18:23 PDT