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 | | From: | Lewis Mammel | | Subject: | Re: too much information! | | Date: | Sat, 15 Jan 2005 05:38:13 GMT |
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Mike wrote:
>
> John Baez wrote:
>
> [snip]
> >
> > But, I wasn't trying to explain this stuff in detail - just
> > compute the amount of information in a raindrop!
>
> [snip]
>
> Now that you "know" the amount of information, can you use it in any
> way to replicate the rain drop?
Well, you would have to have the actual information, not just
know the amount of it! Remember this would be 1E24 bits -
a trillion terabits. This is the problem of Maxwell's Demon
in spades.
Maxwell's Demon is an imagined demon of whatever sort that
operates a microscopic portal between two chambers
of a gas. It can cause one side to get hotter by opening
the portal to let through fast molecules in one direction,
and slow molecules in the other direction, creating a violation
of the Second Law.
It is Maxwell's Demon that stimulated the thought about the
relationship between information and entropy. The original
thought was that the demon would have to create more entropy
than he destroyed in carrying out its project, so an "entropy
cost" of information was postulated.
In the Quantum view, there are many reasons to think that
every raindrop at the same temperature and pressure, and
the same number of molecules, and other external conditions,
is equivalent to every other.
Certainly, there is no question of specifying the velocity
and position of the molecules. A lot of the energy of the
drop is tied up in hydrogen bonds and dissociation, which depend
on the motion of the electrons.
There's interesting info about this on the net if you search
for "water" "molecule" "structure" and the like.
Remember from basic chemistry that 1 in ten million of
each HOH is dissociated. ( 1E-7 provides the "7" in the
pH of water. ) I read that the average lifetime of an
intact HOH is 1 millisecond. Of course, these dissociations
and reassociations are quantum events, subject to uncertainty,
so I think we can safely say that there is no way to "prepare"
the quantum state of a water droplet in any meaningful sense.
Lew Mammel, Jr.
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| | From: | David Bernier | | Subject: | Re: too much information! | | Date: | Sat, 15 Jan 2005 09:26:26 -0500 |
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| Lewis Mammel wrote:
>
> Mike wrote:
>
>>John Baez wrote:
>>
>>[snip]
>>
>>>But, I wasn't trying to explain this stuff in detail - just
>>>compute the amount of information in a raindrop!
>>
>>[snip]
>>
>>Now that you "know" the amount of information, can you use it in any
>>way to replicate the rain drop?
>
>
> Well, you would have to have the actual information, not just
> know the amount of it! Remember this would be 1E24 bits -
> a trillion terabits. This is the problem of Maxwell's Demon
> in spades.
>
> Maxwell's Demon is an imagined demon of whatever sort that
> operates a microscopic portal between two chambers
> of a gas. It can cause one side to get hotter by opening
> the portal to let through fast molecules in one direction,
> and slow molecules in the other direction, creating a violation
> of the Second Law.
>
> It is Maxwell's Demon that stimulated the thought about the
> relationship between information and entropy. The original
> thought was that the demon would have to create more entropy
> than he destroyed in carrying out its project, so an "entropy
> cost" of information was postulated.
>
> In the Quantum view, there are many reasons to think that
> every raindrop at the same temperature and pressure, and
> the same number of molecules, and other external conditions,
> is equivalent to every other.
[...]
In quantum theory, a state is a linear composition of
eigenstates (say for the hydrogen atom).
From what I've read on the Internet, the coefficients are complex
numbers (and there are continuum many of these).
Naively, it would take about countably many bits to
represent a state vector...
Is that nonsense?
David Bernier
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| | From: | Lewis Mammel | | Subject: | Re: too much information! | | Date: | Sat, 15 Jan 2005 18:26:44 GMT |
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David Bernier wrote:
>
> Lewis Mammel wrote:
> >
> > Mike wrote:
> >
> >>John Baez wrote:
> >>
> >>[snip]
> >>
> >>>But, I wasn't trying to explain this stuff in detail - just
> >>>compute the amount of information in a raindrop!
> >>
> >>[snip]
> >>
> >>Now that you "know" the amount of information, can you use it in any
> >>way to replicate the rain drop?
> >
> >
> > Well, you would have to have the actual information, not just
> > know the amount of it! Remember this would be 1E24 bits -
> > a trillion terabits. This is the problem of Maxwell's Demon
> > in spades.
> >
> > Maxwell's Demon is an imagined demon of whatever sort that
> > operates a microscopic portal between two chambers
> > of a gas. It can cause one side to get hotter by opening
> > the portal to let through fast molecules in one direction,
> > and slow molecules in the other direction, creating a violation
> > of the Second Law.
> >
> > It is Maxwell's Demon that stimulated the thought about the
> > relationship between information and entropy. The original
> > thought was that the demon would have to create more entropy
> > than he destroyed in carrying out its project, so an "entropy
> > cost" of information was postulated.
> >
> > In the Quantum view, there are many reasons to think that
> > every raindrop at the same temperature and pressure, and
> > the same number of molecules, and other external conditions,
> > is equivalent to every other.
> [...]
>
> In quantum theory, a state is a linear composition of
> eigenstates (say for the hydrogen atom).
>
> From what I've read on the Internet, the coefficients are complex
> numbers (and there are continuum many of these).
>
> Naively, it would take about countably many bits to
> represent a state vector...
>
> Is that nonsense?
Here's from Schoedinger, Statistical Thermodynamics ( 1944 ) :
We shall always regard the state of the assembly as
determined by the indication that system No. 1 is in
state, say l1, No. 2 in state l2, ..., No. N in state
lN. We shall adhere to this, although the attitude is
altogether wrong. For a quantum-mechanical system is
not in this or that state to be described by a complete
set of commuting variables chosen once and for all.
[ Noooooooo, Dear Friends! ( sorry ) ] To adopt this
view is to think along severely 'classical' lines. With
the set of states chosen, the individual system can at best,
be relied upon as having a certain probability amplitude,
and so a certain probability, of being, on inspection,
found in state No.1 or No.2 or No.3 etc. [ your suggestion ]
I said: at best a probability amplitude. Not even that
much of determination of the single system need there be.
****** Indeed, there is no clear-cut argument for attributing to ******
****** the single system a 'pure state' at all. ******
The 'nonpure states" are expressed by a density matrix, which allows
for a sort of mixture of states. An example I like is the problem
of expressing the state of a Boron atom, which has configuration
1s2 2s2 2p1. Any combination of 2p state amplitudes has an orientation,
so there is no pure spherically symmetric 2p state. The density matrix
allows for the specification of a 'mixed state' which has no
preferred orientation.
Well, that's about as much as I can say about it.
Lew Mammel, Jr.
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