Re: Computability in principle

From: Jerzy Karczmarczuk (karczma_at_info.unicaen.fr)
Date: 11/05/03 

Date: Wed, 05 Nov 2003 08:58:00 +0100

Ray Blaak wrote:
> gat@jpl.nasa.gov (Erann Gat) writes:
>
>>There are about 10^80 particles in the known Universe.
>>The universe is about 10^18 seconds old.
>>The Planck time, the time that it takes light to travel the diameter of a
>>proton, believed to be the smallest possible time scale on which physical
>>processes can occur, is 10^-43 seconds.
>>
>>So if you turned the entire universe into a computer and had it do nothing
>>but count it could enumerate about 10^141 = 2^468 states.
>
>
> Well, the universe is not dead yet. If you are *really* willing to wait you
> could count as much as you need to.

And, anyway all this is *rubbish*. Perhaps Erann Gatt should read something on
cosmology. The "known universe" is not the full universe, the universe is -- in
belief of almost all astrophysicists and "fundamental" physicists -- OPEN.
Infinite, if you wish. Our "Hubble sector" might be finite *for local obser-
vations*, but it doesn't matter.

The time to get through a proton has *nothing* to do with the Planck length (and
related Planck time = length/c). Planck length is constructed with the aid of
gravitational constant, which has nothing to do with protons.

Then, "smallest possible scale on which physical processes can occur" being the
Planck length is another untruth. Certainly awfully speculative at the level
of high-school and science popularizers. NOT for string theorists.

===

Fergus noted that the world is quantum, and Erann Gatt summarized that he will
wait until quantum computers appear. This is methodologically a position impos-
sible to defend. The "computability in principle" deals with the number of
quantum states independently of any "realistic" model of quantum devices, the
Turing machine "in general" does not exist either... And, perhaps you should
be aware that we don't really know how to count quantum states in the universe.
In a curved, potentially infinite space, the spectra may be whatever, so all
this counting has a very, very weak sense.

EG:
> It is not yet clear whether quantum computation can really be made to
> work. It may be that the practical difficulty of keeping N qbits mutually
> entangled grows exponentially with N, in which case the same argument may
> well apply. We just don't know yet.

First, the problem is *NOT* with "keeping the qubits entangled". They entangle
themselves quite fast, and they got entangled with the environment, which is
called the "decoherence". It is the other way round, the keeping of coherence
which is delicate. If Eran Gatt wants really to use savant words, perhaps he
should do it after having verified the meaning of them. Of course, there are
several known bounds on the efficiency of quantum information transfer etc.,
but the story is much more complicated and ambiguous that sketched above,
moreover all these theorems, bounds, etc., are weakly related (read: at all...)
to the computability in principle.

(But, besides, it is KNOWN that quantum computation works in toy cases.)

I suggest moving this thread to some .alt. limbo independently of its ambitions,
since it is not based on any qualified knowledge.

Jerzy Karczmarczuk
Caen, France

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