Re: OM measure and universe size

[Russell Standish]

'twas perfectly readable to me, since it was bog-standard LaTeX
notation which is a defacto standard for mathematical notation in
email.

Until someone figures out a way of getting all email clients to read
and write mathML (which will probably be never), this is as good as it
gets.

Cheers

On Mon, Nov 05, 2007 at 03:34:52PM -0800, George Levy wrote:
> Sorry the nice equation formats did not make it past the server. Anyone 
> interested in the equations can find them at the associated wiki links.
> 
> George
> 
> Russell Standish wrote:
> 
> >On Fri, Nov 02, 2007 at 12:20:35PM -0700, George Levy wrote:
> >  
> >
> >>Russel,
> >>
> >>We are trying to related the expansion of the universe to decreasing 
> >>measure. You have presented the interesting equation:
> >>
> >>H = C + S
> >>
> >>Let's try to assign some numbers.
> >>1) Recently an article 
> >>
> >> 
> >>appeared in New Scientist stating that we may be living "inside" a black 
> >>hole, with the event horizon being located at the limit of what we can 
> >>observe ie the radius of the current observable universe.
> >>2) Stephen Hawking 
> >> showed that the 
> >>entropy of a black hole is proportional to its surface area.
> >>
> >>S_{BH} = \frac{kA}{4l_{\mathrm{P}}^2}
> >>
> >>where where k is Boltzmann's constant 
> >>, and 
> >>l_{\mathrm{P}}=\sqrt{G\hbar / c^3} is the Planck length 
> >>.
> >>
> >>Thus we can say that a change in the Universe's radius corresponds to a 
> >>change in entropy dS. Therefore, dS/dt is proportional to dA/dt and to 
> >>8PR(dR/dt)  R being the radius of the Universe and P = Pi. Let's assume 
> >>that dR/dt = c
> >>Therefore
> >>
> >>dS/dt = (k/4 L^2) 8PRc = 2kPRc/ L^2
> >>
> >>Since Hubble constant  is 
> >>71 ± 4 (km /s 
> >>)/Mpc 
> >>
> >>
> >>which gives a size of the Universe 
> >> from the Earth to the 
> >>edge of the visible universe. Thus R = 46.5 billion light-years in any 
> >>direction; this is the comoving radius 
> >> of the visible universe. (Not the 
> >>same as the age of the Universe because of Relativity considerations)
> >>
> >>Now I have trouble relating these facts to your equation H = C + S or 
> >>maybe to the differential version dH = dC + dS. What do you  think? Can 
> >>we push this further?
> >>
> >>George
> >>
> >>
> >>
> >
> >I think that the formula you have above for S_{BH} is the value that
> >should be taken for the H above. It is the maximum value that entropy
> >can take for a volume the size of the universe. 
> >
> >The internal observed entropy S, will of course, be much lower. I
> >don't have a formula for it off-hand, but it probably involves the
> >microwave background temperature.
> >
> >Cheers
> >
> >
> >  
> >
> 
> 
> > 

-- 


A/Prof Russell Standish  Phone 0425 253119 (mobile)
Mathematics  
UNSW SYDNEY 2052 [EMAIL PROTECTED]
Australiahttp://www.hpcoders.com.au


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Re: OM measure and universe size

[George Levy]

Sorry the nice equation formats did not make it past the server. Anyone 
interested in the equations can find them at the associated wiki links.

George

Russell Standish wrote:

>On Fri, Nov 02, 2007 at 12:20:35PM -0700, George Levy wrote:
>  
>
>>Russel,
>>
>>We are trying to related the expansion of the universe to decreasing 
>>measure. You have presented the interesting equation:
>>
>>H = C + S
>>
>>Let's try to assign some numbers.
>>1) Recently an article 
>>
>> 
>>appeared in New Scientist stating that we may be living "inside" a black 
>>hole, with the event horizon being located at the limit of what we can 
>>observe ie the radius of the current observable universe.
>>2) Stephen Hawking 
>> showed that the 
>>entropy of a black hole is proportional to its surface area.
>>
>>S_{BH} = \frac{kA}{4l_{\mathrm{P}}^2}
>>
>>where where k is Boltzmann's constant 
>>, and 
>>l_{\mathrm{P}}=\sqrt{G\hbar / c^3} is the Planck length 
>>.
>>
>>Thus we can say that a change in the Universe's radius corresponds to a 
>>change in entropy dS. Therefore, dS/dt is proportional to dA/dt and to 
>>8PR(dR/dt)  R being the radius of the Universe and P = Pi. Let's assume 
>>that dR/dt = c
>>Therefore
>>
>>dS/dt = (k/4 L^2) 8PRc = 2kPRc/ L^2
>>
>>Since Hubble constant  is 
>>71 ± 4 (km /s 
>>)/Mpc 
>>
>>
>>which gives a size of the Universe 
>> from the Earth to the 
>>edge of the visible universe. Thus R = 46.5 billion light-years in any 
>>direction; this is the comoving radius 
>> of the visible universe. (Not the 
>>same as the age of the Universe because of Relativity considerations)
>>
>>Now I have trouble relating these facts to your equation H = C + S or 
>>maybe to the differential version dH = dC + dS. What do you  think? Can 
>>we push this further?
>>
>>George
>>
>>
>>
>
>I think that the formula you have above for S_{BH} is the value that
>should be taken for the H above. It is the maximum value that entropy
>can take for a volume the size of the universe. 
>
>The internal observed entropy S, will of course, be much lower. I
>don't have a formula for it off-hand, but it probably involves the
>microwave background temperature.
>
>Cheers
>
>
>  
>


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Re: OM measure and universe size

[Russell Standish]

On Fri, Nov 02, 2007 at 12:20:35PM -0700, George Levy wrote:
> Russel,
> 
> We are trying to related the expansion of the universe to decreasing 
> measure. You have presented the interesting equation:
> 
> H = C + S
> 
> Let's try to assign some numbers.
> 1) Recently an article 
> 
>  
> appeared in New Scientist stating that we may be living "inside" a black 
> hole, with the event horizon being located at the limit of what we can 
> observe ie the radius of the current observable universe.
> 2) Stephen Hawking 
>  showed that the 
> entropy of a black hole is proportional to its surface area.
> 
> S_{BH} = \frac{kA}{4l_{\mathrm{P}}^2}
> 
> where where k is Boltzmann's constant 
> , and 
> l_{\mathrm{P}}=\sqrt{G\hbar / c^3} is the Planck length 
> .
> 
> Thus we can say that a change in the Universe's radius corresponds to a 
> change in entropy dS. Therefore, dS/dt is proportional to dA/dt and to 
> 8PR(dR/dt)  R being the radius of the Universe and P = Pi. Let's assume 
> that dR/dt = c
> Therefore
> 
> dS/dt = (k/4 L^2) 8PRc = 2kPRc/ L^2
> 
> Since Hubble constant  is 
> 71 ± 4 (km /s 
> )/Mpc 
> 
> 
> which gives a size of the Universe 
>  from the Earth to the 
> edge of the visible universe. Thus R = 46.5 billion light-years in any 
> direction; this is the comoving radius 
>  of the visible universe. (Not the 
> same as the age of the Universe because of Relativity considerations)
> 
> Now I have trouble relating these facts to your equation H = C + S or 
> maybe to the differential version dH = dC + dS. What do you  think? Can 
> we push this further?
> 
> George
> 

I think that the formula you have above for S_{BH} is the value that
should be taken for the H above. It is the maximum value that entropy
can take for a volume the size of the universe. 

The internal observed entropy S, will of course, be much lower. I
don't have a formula for it off-hand, but it probably involves the
microwave background temperature.

Cheers


-- 


A/Prof Russell Standish  Phone 0425 253119 (mobile)
Mathematics  
UNSW SYDNEY 2052 [EMAIL PROTECTED]
Australiahttp://www.hpcoders.com.au


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Re: OM measure and universe size

[George Levy]

Russel,

We are trying to related the expansion of the universe to decreasing
measure. You have presented the interesting equation:

H = C + S

Let's try to assign some numbers. 
1) Recently an article
appeared in New Scientist stating that we may be living "inside" a
black hole, with the event horizon being located at the limit of what
we can observe ie the radius of the current observable universe.
2) Stephen
Hawking showed that the entropy of a black hole is proportional to
its surface area. 


  

where where k is Boltzmann's constant, and  is the Planck
length.

Thus we can say that a change in the Universe's radius corresponds to a
change in entropy dS. Therefore, dS/dt is proportional to dA/dt and to
8PR(dR/dt)  R being the radius of the Universe and P = Pi. Let's assume
that dR/dt = c 
Therefore 

dS/dt = (k/4 L^2) 8PRc = 2kPRc/ L^2 

Since Hubble
constant is 71 ± 4 (km/s)/Mpc

which gives a size of the
Universe from the Earth to the edge of the visible universe. Thus R
= 46.5 billion light-years in any direction; this is the
comoving radius
of the visible universe. (Not the same as the age of the Universe
because of Relativity considerations)

Now I have trouble relating these facts to your equation H = C + S or
maybe to the differential version dH = dC + dS. What do you  think? Can
we push this further?

George


Russell Standish wrote:

  On Wed, Oct 31, 2007 at 05:11:01PM -0700, George Levy wrote:
  
  
Could we relate the expansion of  the universe to the decrease in 
measure of a given observer? High measure corresponds to a small 
universe and conversely, low measure to a large one.  For the observer 
the decrease in his measure would be caused by all the possible mode of 
decay of all the nuclear particles necessary for his consciousness. 
Corresponding to this decrease, the radius of the observable universe 
increases to make the universe less likely.

This would provide an experimental way to measure absolute measure.

I am not a proponent of ASSA, rather I believe in RSSA and in a 
cosmological principle for measure: that measure is independent of when 
or where the observer makes an observation. However, I thought that 
tying cosmic expansion to measure may be an interesting avenue of inquiry.

George Levy


  
  
There is a relationship, though perhaps not quite what you think. The
measure of an OM will be 2^{-C_O}, where C_O is the amount of
information about the universe you know at that point in time
(measured in bits). The physical complexity C of the universe at a point
in time is in some sense the limit of all that is possible to know
about the universe, ie C_O <= C.

C is related to the size of the universe by the equation H = C + S,
where S is the entropy of the universe (measured in bits), and H is
the maximum possible entropy that would pertain if the universe were
in equilibrium. H is a monotonically increasing function of the size
of the universe - something like propertional to the volume (or
similar - I forget the details). S is also an increasing function (due
to the second law), but doesn't increase as fast as H. Consequently C
increases as a function of universe age, and so C_O can be larger now
than earlier in the universe, implying smaller OM measures.

However, it remains to be seen whether the anthropic reasons for
experiencing a universe 10^9 years and of large complexity we
currently see is necessary...

  

OM measure and universe size

[Russell Standish]

On Wed, Oct 31, 2007 at 05:11:01PM -0700, George Levy wrote:
> 
> Could we relate the expansion of  the universe to the decrease in 
> measure of a given observer? High measure corresponds to a small 
> universe and conversely, low measure to a large one.  For the observer 
> the decrease in his measure would be caused by all the possible mode of 
> decay of all the nuclear particles necessary for his consciousness. 
> Corresponding to this decrease, the radius of the observable universe 
> increases to make the universe less likely.
> 
> This would provide an experimental way to measure absolute measure.
> 
> I am not a proponent of ASSA, rather I believe in RSSA and in a 
> cosmological principle for measure: that measure is independent of when 
> or where the observer makes an observation. However, I thought that 
> tying cosmic expansion to measure may be an interesting avenue of inquiry.
> 
> George Levy
> 

There is a relationship, though perhaps not quite what you think. The
measure of an OM will be 2^{-C_O}, where C_O is the amount of
information about the universe you know at that point in time
(measured in bits). The physical complexity C of the universe at a point
in time is in some sense the limit of all that is possible to know
about the universe, ie C_O <= C.

C is related to the size of the universe by the equation H = C + S,
where S is the entropy of the universe (measured in bits), and H is
the maximum possible entropy that would pertain if the universe were
in equilibrium. H is a monotonically increasing function of the size
of the universe - something like propertional to the volume (or
similar - I forget the details). S is also an increasing function (due
to the second law), but doesn't increase as fast as H. Consequently C
increases as a function of universe age, and so C_O can be larger now
than earlier in the universe, implying smaller OM measures.

However, it remains to be seen whether the anthropic reasons for
experiencing a universe 10^9 years and of large complexity we
currently see is necessary...

-- 


A/Prof Russell Standish  Phone 0425 253119 (mobile)
Mathematics  
UNSW SYDNEY 2052 [EMAIL PROTECTED]
Australiahttp://www.hpcoders.com.au


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