Bekenstein Bound (was: Crypto and new computing strategies)

The Deutsch paper I quoted before was where I first heard of the Bekenstein
Bound which Eric Hughes mentioned.  According to Deutsch:

"If the theory of the thermodynamics of black holes is trustworthy, no
system enclosed by a surface with an appropriately defined area A can have
more than a finite number

        N(A) = exp(A c^3 / 4 hbar G)

of distinguishable accessible states (hbar is the Planck reduced constant,
G is the gravitational constant, and c is the speed of light.)"

The reference he gives is:

Bekenstein, J.D. 1981 Phys Rev D v23, p287

For those with calculators,  c is approximately 3.00*10^10 cm/s, G is
6.67*10^-8 cm^3/g s^2, and hbar is 1.05*10^-27 g cm^2/s.  N comes out
to be pretty darn big by our standards!

Hal

> 
> The Deutsch paper I quoted before was where I first heard of the Bekenstein
> Bound which Eric Hughes mentioned.  According to Deutsch:
> 
> "If the theory of the thermodynamics of black holes is trustworthy, no
> system enclosed by a surface with an appropriately defined area A can have
> more than a finite number
> 
>         N(A) = exp(A c^3 / 4 hbar G)
> 
> of distinguishable accessible states (hbar is the Planck reduced constant,
> G is the gravitational constant, and c is the speed of light.)"
> 
> The reference he gives is:
> 
> Bekenstein, J.D. 1981 Phys Rev D v23, p287
> 
> For those with calculators,  c is approximately 3.00*10^10 cm/s, G is
> 6.67*10^-8 cm^3/g s^2, and hbar is 1.05*10^-27 g cm^2/s.  N comes out
> to be pretty darn big by our standards!
> 
> Hal
> 
> 
The problem I see with this is that there is no connection between a black holes
mass and surface area (it doesn't have one). In reference to the 'A' in the    
above, is it the event horizon? A funny thing about black holes is that as the
mass increases the event horizon gets larger not smaller (ie gravitational
contraction).

Jim Choate writes:
>> 
>> The Deutsch paper I quoted before was where I first heard of the Bekenstein
>> Bound which Eric Hughes mentioned.  According to Deutsch:
>> 
>> "If the theory of the thermodynamics of black holes is trustworthy, no
>> system enclosed by a surface with an appropriately defined area A can have
>> more than a finite number ...

> The problem I see with this is that there is no connection between a
> black holes mass and surface area (it doesn't have one). In
> reference to the 'A' in the above, is it the event horizon? A funny
> thing about black holes is that as the mass increases the event
> horizon gets larger not smaller (ie gravitational contraction).

If I read the quote correctly, the surface area of the black hole
itself is not under discussion.  Rather, whether it can be contained
in a surface with some area, which it can be.

Peter

> 
> 
> Jim Choate writes:
> >> 
> >> The Deutsch paper I quoted before was where I first heard of the Bekenstein
> >> Bound which Eric Hughes mentioned.  According to Deutsch:
> >> 
> >> "If the theory of the thermodynamics of black holes is trustworthy, no
> >> system enclosed by a surface with an appropriately defined area A can have
> >> more than a finite number ...
> 
> > The problem I see with this is that there is no connection between a
> > black holes mass and surface area (it doesn't have one). In
> > reference to the 'A' in the above, is it the event horizon? A funny
> > thing about black holes is that as the mass increases the event
> > horizon gets larger not smaller (ie gravitational contraction).
> 
> If I read the quote correctly, the surface area of the black hole
> itself is not under discussion.  Rather, whether it can be contained
> in a surface with some area, which it can be.
> 
> Peter
> 
Of course a singularity can be contained in a volume (not shure what you mean
by surface), it is in the universe after all.

I fail to see how this solves anything.

Jim Choate writes:
>> Jim Choate writes:
>>>> 
>>>> The Deutsch paper I quoted before was where I first heard of the Bekenstein
>>>> Bound which Eric Hughes mentioned.  According to Deutsch:
>>>> 
>>>> "If the theory of the thermodynamics of black holes is trustworthy, no
>>>> system enclosed by a surface with an appropriately defined area A can have
>>>> more than a finite number ...
>> 
>>> The problem I see with this is that there is no connection between a
>>> black holes mass and surface area (it doesn't have one). In
>>> reference to the 'A' in the above, is it the event horizon? A funny
>>> thing about black holes is that as the mass increases the event
>>> horizon gets larger not smaller (ie gravitational contraction).
>> 
>> If I read the quote correctly, the surface area of the black hole
>> itself is not under discussion.  Rather, whether it can be contained
>> in a surface with some area, which it can be.

> Of course a singularity can be contained in a volume (not shure what you mean
> by surface), it is in the universe after all.

> I fail to see how this solves anything.

When I read the quote being discussed, it seems to say that no system
which can be contained in a surface with an appropriate area A can
have more than a finite number of states.

I don't think that volume is discussed at all, just a surface.  If you
are happy to contain the singularity in an imaginary cube with a
million light years on each side, I'm happy to call the surface the
sides of that cube.

This may seem pointless, because, as you point out, everything in the
universe can be contained in a surface (or volume).  It is not
pointless if we can imagine systems which cannot be contained in a
surface.  I'm guessing that a very large system, say everything in the
universe, might not be containable in a surface.  If the quote is
correct that would imply that the universe may not have a finite
number states.

The cryptography tie in: if the quote is correct, then any computer we
build is going to have a finite number of states which implies that
the number of computrons is theoretically limited.  And this implies
that there may be RSA keys of sufficient size that they cannot be
broken with brute force, which doesn't seem that surprising.

Peter

You made the assertion in your rebuttal about area -v- volume in relation
to black holes and event horizons about the entire universe not being   
containable in a volumn, if you accept this premice then you have to accept
the premice that the universe is unbouded and hence not containable. This 
leads the bounds on the B-equation to be infinitly large number of possible
states.