On 19 Mar 2014, at 01:57, meekerdb wrote:
On 3/18/2014 5:07 PM, LizR wrote:
On 19 March 2014 12:47, meekerdb <[email protected]> wrote:
But in general that would mean knowing the state of everything the
system had interacted with in the past, since it is now entangled
with them. So even if you suppose there is no collapse of the
wavefunction, decoherence has the same effect.
I was only asking about the theoretical possibility, given
unrealistically perfect information about the state of the system.
The universe (assuming unitary QM) is reversible. In fact from the
standpoint of QM there is no arrow of time - it's deterministic,
just like Laplace's universe. So, as always, when the word
"possibility" is used there has to be some context. To *calculate*
a history of the universe from it's present state would require
knowing its *complete* present state, including your mental state.
Is that "theoretically possible"? I think it involves a paradox of
self-reference.
You are almost right. We might be able to know the complete present
state, but not the complete history leading that present. You can
build a completely self-referential machine capable to describe its
entire present state, but not its entire trace. You can go very near
that goal, and write a program capable of giving, not its complete
trace, but capable of giving a program, which when run, will give the
entire trace of the first problem.
It is like in arithmetic, we can't define V = arithmetical truth (the
set of Gödel numbers of all true sentences), but arithmetical can
defined the singleton {V}.
With comp, God has no name, but the singleton {God} might have a name.
It is counter-intuitive, and I have still some problem to figure out
how this is proved, but a proof is available in the Boolos and Jeffrey
book.
To put it another way, in the Game of Life, even with perfect
information, you can't trace the state of the system backwards
because it loses information. So even the laws of physics couldn't
work backwards in a universe based on the GOL. QM, I'm informed,
doesn't lose information, so (very much in theory) you could work
backwards - or (less in theory) the laws of physics could.
Yes the universe doesn't lose information like the GoL. But
relative to any point it loses information across spacetime
horizons. So there's no way to gather that information up into a
calculation unless you have some God's eye view from outside the
universe, in which case you could see the past anyway.
OK.
There's a couple of nice papers about this by Yasunori Nomura: arXiv:
1205.267v2 is a popular exposition and arXiv:1205.5550v2 is a more
technical paper.
Nomura is very interesting, and is going into the direction that QM
belongs to the core physical laws of comp, and that this leads to
different "geographical" cosmologies possible. If comp is true, the
multiverse = the many-worlds = the many comp dreams. It would entail
that "we" are very big numbers, which are very deep. The vast majority
of "our computations" below our subst level, would be gievn by our
electronic configurations. Our substitution level might be that low.
Bruno
Brent
I wasn't asking whether I could build a chronoscope and watch the
past happening on TV.
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