Information entropy of physical fundamental constants

SBJ: Information entropy of physical fundamental constants

The fundamental constant can be measured increasingly accurate, it
does not seem (for me) that the  repetitive pattern of rational
numbers after some number of digits may take place; if it is the case
then there is not enough "room" in the universe / multiverse to
accommodate such information as exact representation of fundamental
constant - just in principle, there is no way to have it exact as
there is no way to write down an exact arbitrary irrational number and
it is not a technical limitation it is a fundamental limitation unless
it may be represented as a rational number ;o). Information Entropy
can be measured as an average number of bits per symbol/digit encoded
by rank-0 context model + entropy encoder (let say arithmetic
encoder). Therefore, there are two distinct possibilities: entropy
equals zero or Log2(10) (for decimal representation) or simply: ZERO
or NON-ZERO. I have my ideas how NON-ZERO case may workout but I'm
interested to listen others opinions.

Thanks,
Stefan


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[Brent Meeker-2]

stefanbanev@... wrote:
> SBJ: Information entropy of physical fundamental constants
>
> The fundamental constant can be measured increasingly accurate, it
> does not seem (for me) that the  repetitive pattern of rational
> numbers after some number of digits may take place;

Physical measurements are always relative, i.e. one quantify is measured in
units of another quantity.  It is generally thought that there is a smallest
possible unit, the Planck scale, so all physical measurements will be rational
numbers (integers in Planck units).


>if it is the case
> then there is not enough "room" in the universe / multiverse to
> accommodate such information as exact representation of fundamental
> constant - just in principle, there is no way to have it exact as
> there is no way to write down an exact arbitrary irrational number and
> it is not a technical limitation it is a fundamental limitation unless
> it may be represented as a rational number ;o).

There is no problem writing down irrational numbers: sqrt(2), pi,... See nothing
to it.  ;-)

Of course from an information standpoint you want to know their bits.  But it
also easy to write down a quite short program that will compute whatever bit you
want to know for those irrational numbers.  But you are right that for almost
all real numbers is impossible to give them a finite representation.  But why
believe in those numbers anyway, they are convenient fictions.

>Information Entropy
> can be measured as an average number of bits per symbol/digit encoded
> by rank-0 context model + entropy encoder (let say arithmetic
> encoder). Therefore, there are two distinct possibilities: entropy
> equals zero or Log2(10) (for decimal representation) or simply: ZERO
> or NON-ZERO. I have my ideas how NON-ZERO case may workout but I'm
> interested to listen others opinions.

Most cosmogonies assume the (microscopic) entropy of the universe is zero.  It
started at the Planck scale, where there is room for at most one bit and since
QM insists on unitary evolution the entropy cannot change (as measured at the
Planck scale).  The increase in entropy we see is due to our coarse graining, or
as Bruno would say, "above our substitution level".  It is impossible to however
to use the negative information to get back to local zero because the expansion
of the universe has carried the correlations beyond the relativistic horizon.
At least that's the common theory.

Brent

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Brent> all physical measurements will be rational numbers

Well, it is quite a statement ;o) so you may write down an exact
Planck constant (h), please illustrate that...
If you experience difficulty to do that for ( h ) please try write
down an exact gravitational constant ( G )...

Ref: Planck constant:  h = 4.135 667 33(10) × 10−15 eV s
(10) The two digits between the parentheses denote the standard
uncertainty in the last two digits of the value.

SB> there is no way to write down an exact arbitrary irrational number
Brent> There is no problem writing down irrational numbers:
Brent> sqrt(2), pi,... See nothing to it.  ;-)

You miss the key word "arbitrary", it is simple to show that the
number of irrational numbers which can be expressed/encoded with ZERO
entropy equals to number of rational numbers (sqrt(2) is one of such
examples).

--sb






On Jul 23, 4:30 pm, Brent Meeker <meeke...@...> wrote:

> stefanba...@... wrote:
> > SBJ: Information entropy of physical fundamental constants
>
> > The fundamental constant can be measured increasingly accurate, it
> > does not seem (for me) that the  repetitive pattern of rational
> > numbers after some number of digits may take place;
>
> Physical measurements are always relative, i.e. one quantify is measured in
> units of another quantity.  It is generally thought that there is a smallest
> possible unit, the Planck scale, so all physical measurements will be rational
> numbers (integers in Planck units).
>
> >if it is the case
> > then there is not enough "room" in the universe / multiverse to
> > accommodate such information as exact representation of fundamental
> > constant - just in principle, there is no way to have it exact as
> > there is no way to write down an exact arbitrary irrational number and
> > it is not a technical limitation it is a fundamental limitation unless
> > it may be represented as a rational number ;o).
>
> There is no problem writing down irrational numbers: sqrt(2), pi,... See nothing
> to it.  ;-)
>
> Of course from an information standpoint you want to know their bits.  But it
> also easy to write down a quite short program that will compute whatever bit you
> want to know for those irrational numbers.  But you are right that for almost
> all real numbers is impossible to give them a finite representation.  But why
> believe in those numbers anyway, they are convenient fictions.
>
> >Information Entropy
> > can be measured as an average number of bits per symbol/digit encoded
> > by rank-0 context model + entropy encoder (let say arithmetic
> > encoder). Therefore, there are two distinct possibilities: entropy
> > equals zero or Log2(10) (for decimal representation) or simply: ZERO
> > or NON-ZERO. I have my ideas how NON-ZERO case may workout but I'm
> > interested to listen others opinions.
>
> Most cosmogonies assume the (microscopic) entropy of the universe is zero.  It
> started at the Planck scale, where there is room for at most one bit and since
> QM insists on unitary evolution the entropy cannot change (as measured at the
> Planck scale).  The increase in entropy we see is due to our coarse graining, or
> as Bruno would say, "above our substitution level".  It is impossible to however
> to use the negative information to get back to local zero because the expansion
> of the universe has carried the correlations beyond the relativistic horizon.
> At least that's the common theory.
>
> Brent

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[Brent Meeker-2]

stefanbanev@... wrote:
>
> Brent> all physical measurements will be rational numbers
>
> Well, it is quite a statement ;o) so you may write down an exact
> Planck constant (h), please illustrate that...
> If you experience difficulty to do that for ( h ) please try write
> down an exact gravitational constant ( G )...

No, problem.  Like most physicists I write h=1, G=1, c=1.


>
> Ref: Planck constant:  h = 4.135 667 33(10) × 10−15 eV s
> (10) The two digits between the parentheses denote the standard
> uncertainty in the last two digits of the value.

The uncertainty is in the conversion to eVs.  It arises because different people
got different numbers when measuring, but each measurement was a rational number.

Brent

>
> SB> there is no way to write down an exact arbitrary irrational number
> Brent> There is no problem writing down irrational numbers:
> Brent> sqrt(2), pi,... See nothing to it.  ;-)
>
> You miss the key word "arbitrary", it is simple to show that the
> number of irrational numbers which can be expressed/encoded with ZERO
> entropy equals to number of rational numbers (sqrt(2) is one of such
> examples).
>
> --sb
>
>
>
>
>
>
> On Jul 23, 4:30 pm, Brent Meeker <meeke...@...> wrote:
>> stefanba...@... wrote:
>>> SBJ: Information entropy of physical fundamental constants
>>> The fundamental constant can be measured increasingly accurate, it
>>> does not seem (for me) that the  repetitive pattern of rational
>>> numbers after some number of digits may take place;
>> Physical measurements are always relative, i.e. one quantify is measured in
>> units of another quantity.  It is generally thought that there is a smallest
>> possible unit, the Planck scale, so all physical measurements will be rational
>> numbers (integers in Planck units).
>>
>>> if it is the case
>>> then there is not enough "room" in the universe / multiverse to
>>> accommodate such information as exact representation of fundamental
>>> constant - just in principle, there is no way to have it exact as
>>> there is no way to write down an exact arbitrary irrational number and
>>> it is not a technical limitation it is a fundamental limitation unless
>>> it may be represented as a rational number ;o).
>> There is no problem writing down irrational numbers: sqrt(2), pi,... See nothing
>> to it.  ;-)
>>
>> Of course from an information standpoint you want to know their bits.  But it
>> also easy to write down a quite short program that will compute whatever bit you
>> want to know for those irrational numbers.  But you are right that for almost
>> all real numbers is impossible to give them a finite representation.  But why
>> believe in those numbers anyway, they are convenient fictions.
>>
>>> Information Entropy
>>> can be measured as an average number of bits per symbol/digit encoded
>>> by rank-0 context model + entropy encoder (let say arithmetic
>>> encoder). Therefore, there are two distinct possibilities: entropy
>>> equals zero or Log2(10) (for decimal representation) or simply: ZERO
>>> or NON-ZERO. I have my ideas how NON-ZERO case may workout but I'm
>>> interested to listen others opinions.
>> Most cosmogonies assume the (microscopic) entropy of the universe is zero.  It
>> started at the Planck scale, where there is room for at most one bit and since
>> QM insists on unitary evolution the entropy cannot change (as measured at the
>> Planck scale).  The increase in entropy we see is due to our coarse graining, or
>> as Bruno would say, "above our substitution level".  It is impossible to however
>> to use the negative information to get back to local zero because the expansion
>> of the universe has carried the correlations beyond the relativistic horizon.
>> At least that's the common theory.
>>
>> Brent
> >
>

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Brent>> all physical measurements will be rational numbers

SB> Well, it is quite a statement ;o) so you may write down an exact
SB> Planck constant (h), please illustrate that...
SB> If you experience difficulty to do that for ( h ) please try
write
SB> down an exact gravitational constant ( G )...

Brent>No, problem.  Like most physicists I write h=1, G=1, c=1.

Apparently no problem ;o)

--sb


On Jul 24, 9:29 pm, Brent Meeker <meeke...@...> wrote:

> stefanba...@... wrote:
>
> > Brent> all physical measurements will be rational numbers
>
> > Well, it is quite a statement ;o) so you may write down an exact
> > Planck constant (h), please illustrate that...
> > If you experience difficulty to do that for ( h ) please try write
> > down an exact gravitational constant ( G )...
>
> No, problem.  Like most physicists I write h=1, G=1, c=1.
>
>
>
> > Ref: Planck constant:  h = 4.135 667 33(10) × 10−15 eV s
> > (10) The two digits between the parentheses denote the standard
> > uncertainty in the last two digits of the value.
>
> The uncertainty is in the conversion to eVs.  It arises because different people
> got different numbers when measuring, but each measurement was a rational number.
>
> Brent
>
>
>
> > SB> there is no way to write down an exact arbitrary irrational number
> > Brent> There is no problem writing down irrational numbers:
> > Brent> sqrt(2), pi,... See nothing to it.  ;-)
>
> > You miss the key word "arbitrary", it is simple to show that the
> > number of irrational numbers which can be expressed/encoded with ZERO
> > entropy equals to number of rational numbers (sqrt(2) is one of such
> > examples).
>
> > --sb
>
> > On Jul 23, 4:30 pm, Brent Meeker <meeke...@...> wrote:
> >> stefanba...@... wrote:
> >>> SBJ: Information entropy of physical fundamental constants
> >>> The fundamental constant can be measured increasingly accurate, it
> >>> does not seem (for me) that the  repetitive pattern of rational
> >>> numbers after some number of digits may take place;
> >> Physical measurements are always relative, i.e. one quantify is measured in
> >> units of another quantity.  It is generally thought that there is a smallest
> >> possible unit, the Planck scale, so all physical measurements will be rational
> >> numbers (integers in Planck units).
>
> >>> if it is the case
> >>> then there is not enough "room" in the universe / multiverse to
> >>> accommodate such information as exact representation of fundamental
> >>> constant - just in principle, there is no way to have it exact as
> >>> there is no way to write down an exact arbitrary irrational number and
> >>> it is not a technical limitation it is a fundamental limitation unless
> >>> it may be represented as a rational number ;o).
> >> There is no problem writing down irrational numbers: sqrt(2), pi,... See nothing
> >> to it.  ;-)
>
> >> Of course from an information standpoint you want to know their bits.  But it
> >> also easy to write down a quite short program that will compute whatever bit you
> >> want to know for those irrational numbers.  But you are right that for almost
> >> all real numbers is impossible to give them a finite representation.  But why
> >> believe in those numbers anyway, they are convenient fictions.
>
> >>> Information Entropy
> >>> can be measured as an average number of bits per symbol/digit encoded
> >>> by rank-0 context model + entropy encoder (let say arithmetic
> >>> encoder). Therefore, there are two distinct possibilities: entropy
> >>> equals zero or Log2(10) (for decimal representation) or simply: ZERO
> >>> or NON-ZERO. I have my ideas how NON-ZERO case may workout but I'm
> >>> interested to listen others opinions.
> >> Most cosmogonies assume the (microscopic) entropy of the universe is zero.  It
> >> started at the Planck scale, where there is room for at most one bit and since
> >> QM insists on unitary evolution the entropy cannot change (as measured at the
> >> Planck scale).  The increase in entropy we see is due to our coarse graining, or
> >> as Bruno would say, "above our substitution level".  It is impossible to however
> >> to use the negative information to get back to local zero because the expansion
> >> of the universe has carried the correlations beyond the relativistic horizon.
> >> At least that's the common theory.
>
> >> Brent

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