Physical Constants

[Dirk Bruere]

...exist because they cannot be calculated from more fundamental
entities. Given the number of existing constants, which might reasonably
be expected to be truly fundamental and which can likely be derived in a
putative TOE?

[ Mod. note: John Baez has a nice article on this topic on his website.

http://math.ucr.edu/home/baez/constants.html

-ik ]

Dirk

[Dirk Bruere]

Dirk Bruere wrote:
> ..exist because they cannot be calculated from more fundamental
> entities. Given the number of existing constants, which might reasonably
> be expected to be truly fundamental and which can likely be derived in a
> putative TOE?
>
> [ Mod. note: John Baez has a nice article on this topic on his website.
>
> http://math.ucr.edu/home/baez/constants.html
>
> -ik ]

Interesting.
So might it be assumed that all those different masses might eventually
be reduced to one mass (derived from, say, the Planck Mass) in a TOE?

Dirk

[robert bristow-johnson]

Dirk Bruere wrote:
> ..exist because they cannot be calculated from more fundamental
> entities. Given the number of existing constants, which might reasonably
> be expected to be truly fundamental and which can likely be derived in a
> putative TOE?
>
> [ Mod. note: John Baez has a nice article on this topic on his website.
>
> http://math.ucr.edu/home/baez/constants.html
>
> -ik ]

nice website and page, but:

(1) i would *still* like to see these 26+ dimensionless universal
constants have a numerical value published somewhere (i know i had
asked about this in the past).

(2) and i would *still* like to know (or have confirmed) what
reference mass or equivalent energy the masses of fundamental particles
are expressed against. is it the Planck Mass?

(3) and lastly, i would like to see an expression that relates the
the U(1) coupling constant or the SU(2) coupling constant or whatever
to the Fine-structure constant, alpha (and whatever else is related).

sorry to be so pendantic, but you would think that these would be
defined and tabulated somewhere in a single place. John's site gets
close, but doesn't "go all the way". i can't see why NIST doesn't have
it down somewhere.

r b-j

[richard miller]

"Dirk Bruere" <dirk.bruere@gmail.com> wrote in message
news:4734o9Fdjli8U1@individual.net...
> ..exist because they cannot be calculated from more fundamental entities.
> Given the number of existing constants, which might reasonably be expected
> to be truly fundamental and which can likely be derived in a putative TOE?
>
> [ Mod. note: John Baez has a nice article on this topic on his website.
>
> http://math.ucr.edu/home/baez/constants.html
>
> -ik ]
>
> Dirk
>

Indeed, the Baez article is an excellent description. So, a pity about the
pious claptrap quote from JAW about 'How could we have been so stupid for so
long'. Why put that there? Its not a deep quote, it is not profound.
Hindsight always has been and always will be a wonderful thing.

Nice article though, and that's what counts.

Dick M.

[ebunn@lfa221051.richmond.edu]

In article <1141751220.341905.85640@j52g2000cwj.googlegroups.c om>,
robert bristow-johnson <rbj@audioimagination.com> wrote:

> (1) i would *still* like to see these 26+ dimensionless universal
>constants have a numerical value published somewhere (i know i had
>asked about this in the past).

You might check
out:

"Dimensionless constants, cosmology, and other dark matters,"
Tegmark, Aguirre, Rees, and Wilczek, Phys. Rev. D 73, 023505 (2006).

It has a great big table that might be the sort of thing you're
lookoing for.

-Ted

--
[E-mail me at name@domain.edu, as opposed to name@machine.domain.edu.]

[Ben Rudiak-Gould]

robert bristow-johnson wrote:
> (1) i would *still* like to see these 26+ dimensionless universal
> constants have a numerical value published somewhere (i know i had
> asked about this in the past).

The number of parameters has physical (or at least mathematical)
significance, but the values don't. The "26 constants" are coordinates of
the point in a 26-dimensional parameter space that corresponds to the world
we live in. They don't have particular values because there's no single
correct coordinate system.

If you really want numbers, the PDG website should have best estimates for
the constants mentioned in John Baez's article, and it's easy to convert
them into Planck units. E.g. they report the e mass as 548.57991 x 10^-6
amu, and Google Calculator says that 548.57991 * 10^-6 amu / sqrt(hbar*c/G)
= 4.18505 * 10^-23. But even the Planck units are only well-defined up to
about an order of magnitude, because you can use either h or hbar, and
either G or 8 pi G (the latter being the constant that actually shows up in
the GR field equations).

-- Ben

[Richard Saam]

Ben Rudiak-Gould wrote:
> robert bristow-johnson wrote:
>
>> (1) i would *still* like to see these 26+ dimensionless universal
>> constants have a numerical value published somewhere (i know i had
>> asked about this in the past).
>
>
> The number of parameters has physical (or at least mathematical)
> significance, but the values don't. The "26 constants" are coordinates
> of the point in a 26-dimensional parameter space that corresponds to the
> world we live in. They don't have particular values because there's no
> single correct coordinate system.
>
> If you really want numbers, the PDG website should have best estimates
> for the constants mentioned in John Baez's article, and it's easy to
> convert them into Planck units. E.g. they report the e mass as 548.57991
> x 10^-6 amu, and Google Calculator says that 548.57991 * 10^-6 amu /
> sqrt(hbar*c/G) = 4.18505 * 10^-23. But even the Planck units are only
> well-defined up to about an order of magnitude, because you can use
> either h or hbar, and either G or 8 pi G (the latter being the constant
> that actually shows up in the GR field equations).
>
> -- Ben
>

Why can't unit charge 'q'
be brought into the picture
in terms of fundamental dimensional relationships

with charge units dictated by E = q^2 / R

q cm^(3/2) g^(1/2) sec^(-1)
hb g cm^2 sec^-1
c cm sec^-1
G cm^3 sec^-2 g^-1

Dimensionally, the following
dimensional relationships must be satisfied.

q^A * c^B * hb^C * G^D = mass

q^A * c^B * hb^C * G^D = length

q^A * c^B * hb^C * G^D = time

An infinite number of Mass, Length & Time values
can be dimensionally calculated
based on exponents A,B,C&D
some of which are listed below
and including the conventionally expressed
Planck Mass, Length & Time values

I would like to know
if there is some way to choose
the 'right' A,B,C&D case?
Maybe there is a maximum or minimum
over some type of dimensional space.


q c hb G

A B C D Mass (g)
-8.00 4.50 4.50 -0.50 7.68E+03
-7.00 4.00 4.00 -0.50 6.56E+02
-6.00 3.50 3.50 -0.50 5.60E+01
-5.00 3.00 3.00 -0.50 4.78E+00
-4.00 2.50 2.50 -0.50 4.09E-01
-3.00 2.00 2.00 -0.50 3.49E-02
-2.00 1.50 1.50 -0.50 2.98E-03
-1.00 1.00 1.00 -0.50 2.55E-04
0.00 0.50 0.50 -0.50 2.18E-05 - Planck Mass
1.00 0.00 0.00 -0.50 1.86E-06
2.00 -0.50 -0.50 -0.50 1.59E-07
3.00 -1.00 -1.00 -0.50 1.36E-08
4.00 -1.50 -1.50 -0.50 1.16E-09
5.00 -2.00 -2.00 -0.50 9.90E-11
6.00 -2.50 -2.50 -0.50 8.46E-12
7.00 -3.00 -3.00 -0.50 7.22E-13
8.00 -3.50 -3.50 -0.50 6.17E-14


q c hb G

A B C D Length (cm)
-8.00 2.50 4.50 0.50 5.70E-25
-7.00 2.00 4.00 0.50 4.87E-26
-6.00 1.50 3.50 0.50 4.16E-27
-5.00 1.00 3.00 0.50 3.55E-28
-4.00 0.50 2.50 0.50 3.04E-29
-3.00 0.00 2.00 0.50 2.59E-30
-2.00 -0.50 1.50 0.50 2.21E-31
-1.00 -1.00 1.00 0.50 1.89E-32
0.00 -1.50 0.50 0.50 1.62E-33 Planck Length
1.00 -2.00 0.00 0.50 1.38E-34
2.00 -2.50 -0.50 0.50 1.18E-35
3.00 -3.00 -1.00 0.50 1.01E-36
4.00 -3.50 -1.50 0.50 8.61E-38
5.00 -4.00 -2.00 0.50 7.35E-39
6.00 -4.50 -2.50 0.50 6.28E-40
7.00 -5.00 -3.00 0.50 5.37E-41
8.00 -5.50 -3.50 0.50 4.58E-42



q c hb G

A B C D Time (sec)
-8.00 1.50 4.50 0.50 1.90E-35
-7.00 1.00 4.00 0.50 1.62E-36
-6.00 0.50 3.50 0.50 1.39E-37
-5.00 0.00 3.00 0.50 1.19E-38
-4.00 -0.50 2.50 0.50 1.01E-39
-3.00 -1.00 2.00 0.50 8.65E-41
-2.00 -1.50 1.50 0.50 7.39E-42
-1.00 -2.00 1.00 0.50 6.31E-43
0.00 -2.50 0.50 0.50 5.39E-44 Planck Time
1.00 -3.00 0.00 0.50 4.61E-45
2.00 -3.50 -0.50 0.50 3.93E-46
3.00 -4.00 -1.00 0.50 3.36E-47
4.00 -4.50 -1.50 0.50 2.87E-48
5.00 -5.00 -2.00 0.50 2.45E-49
6.00 -5.50 -2.50 0.50 2.09E-50
7.00 -6.00 -3.00 0.50 1.79E-51
8.00 -6.50 -3.50 0.50 1.53E-52

[Aetherist]

On Sat, 11 Mar 2006 00:21:40 +0000 (UTC), Richard Saam <rdsaam@att.net> wrote:

>Ben Rudiak-Gould wrote:
>> robert bristow-johnson wrote:
>>
>>> (1) i would *still* like to see these 26+ dimensionless universal
>>> constants have a numerical value published somewhere (i know i had
>>> asked about this in the past).
>>
>>
>> The number of parameters has physical (or at least mathematical)
>> significance, but the values don't. The "26 constants" are coordinates
>> of the point in a 26-dimensional parameter space that corresponds to the
>> world we live in. They don't have particular values because there's no
>> single correct coordinate system.
>>
>> If you really want numbers, the PDG website should have best estimates
>> for the constants mentioned in John Baez's article, and it's easy to
>> convert them into Planck units. E.g. they report the e mass as 548.57991
>> x 10^-6 amu, and Google Calculator says that 548.57991 * 10^-6 amu /
>> sqrt(hbar*c/G) = 4.18505 * 10^-23. But even the Planck units are only
>> well-defined up to about an order of magnitude, because you can use
>> either h or hbar, and either G or 8 pi G (the latter being the constant
>> that actually shows up in the GR field equations).
>>
>> -- Ben
>>
>
> Why can't unit charge 'q' be brought into the picture in terms of
> fundamental dimensional relationships
>
> with charge units dictated by E = q^2 / R
>
> q cm^(3/2) g^(1/2) sec^(-1)
> hb g cm^2 sec^-1
> c cm sec^-1
> G cm^3 sec^-2 g^-1

Ah, you're in the cgs system where permittivity is folded into
q. There's the problem, in the physical world you're actually
saying,

q = q'/Sqrt(4pi<eps>)

Where q' would represent actually charge and <eps> is permittivity.
If permittivity is not dimensionless you'll get screwy results
(irrational) for charge defined in this manner. Since we know
that in SI the relationship,

c = 1/Sqrt(<eps>µ) ... [1]

is true, and we also know that in this system charge is also
defined arbitrarily as C (Coulombs) and factors out, both µ
(Permeability) and <eps> cannot be dimensionless. Logic would
dictate that this is also so in cgs. Now we can indeed scale
the magnitudes of constants to resolve a set so that they are
unity, c = 1, h = 1 or h-bar = 1, etc. But the dimensions
involved cannot vanish even if the value is scaled to unity.
The same is true for charge in cgs.

Take a clue from Eq. 1 above. We've seen it before. Namely,

c^2 = Y/<eps>

Where, in this case, Y is Young's Modulus and <eps> is density.
Thus map the EM Permeability and Permittivity to be,

µ = 1/Y
<eps> = <eps> (Density)

Then use the Coulombic force approximation,

F = k(q/r)^2

But, instead of setting k = 1 diemsionless, set it to its
SI value, 1/4pi<eps>. Substuting in density as mapped above
we find that then, dimensionally, when solved, charge has
units of mass per time. To do this in cgs would require
significant redefinitions to make it equivalent to SI
in terms of Permittivity and Permeability. Many simply
will not go there.

There are some rather nifty side effects of looking at it
this way. Try thinking about 'if this is true, what
follows?'.

[Snip of rest...]

Paul Stowe

[robert bristow-johnson]

Richard Saam wrote:
>
> Ben Rudiak-Gould wrote:
> >
> > The number of parameters has physical (or at least mathematical)
> > significance, but the values don't. The "26 constants" are coordinates
> > of the point in a 26-dimensional parameter space that corresponds to the
> > world we live in. They don't have particular values because there's no
> > single correct coordinate system.

this doesn't make any sense to me, but i'll leave it to physikers to
evaluate.

> > If you really want numbers, the PDG website should have best estimates
> > for the constants mentioned in John Baez's article, and it's easy to
> > convert them into Planck units. E.g. they report the e mass as 548.57991
> > x 10^-6 amu, and Google Calculator says that 548.57991 * 10^-6 amu /
> > sqrt(hbar*c/G) = 4.18505 * 10^-23.

i can deal with m_e (it's well publicized at NIST) and converting it to
in terms of Planck Units (non-dimensionalizing it). i believe that out
of those 26 parameters (masses of quarks and other particles more
fundamental than the electon) that m_e can be constructed.

> > But even the Planck units are only
> > well-defined up to about an order of magnitude, because you can use
> > either h or hbar, and either G or 8 pi G (the latter being the constant
> > that actually shows up in the GR field equations).

i've always felt that Planck missed a little in judiciously defining
units that normalize G instead of 4*pi*G or 8*pi*G or 16*pi*G. and in
the pseudo-definition of the Planck charge that normalizes
4*pi*epsilon_0 instead of just normalizing epsilon_0. i think there
needs to be more discussion by the heavyweights on what makes the most
natural

> Why can't unit charge 'q' be brought into the picture
> in terms of fundamental dimensional relationships
>
> with charge units dictated by E = q^2 / R

that's the most common definition of the Planck Charge that is
reflective of the way CGS defines the unit of charge (statcoulomb or
"esu of charge"). i still think it missed by 4*pi since factors like
that are left over in the CGS form of Maxwell's Eqs.

> q cm^(3/2) g^(1/2) sec^(-1)
> hb g cm^2 sec^-1
> c cm sec^-1
> G cm^3 sec^-2 g^-1
>
> Dimensionally, the following
> dimensional relationships must be satisfied.
>
> q^A * c^B * hb^C * G^D = mass
>
> q^A * c^B * hb^C * G^D = length
>
> q^A * c^B * hb^C * G^D = time
>
> An infinite number of Mass, Length & Time values
> can be dimensionally calculated
> based on exponents A,B,C&D

not if A=0, that unit of charge is equivalent to tossing in another
putting a 4th dimensional relationship

q^A * c^B * hb^C * G^D = charge

and the A's and B's and C's and D's have to be different in each row.

this is what is done to contrive Planck Units. the rest are small
adjustments (should h or hbar be normalized? G or 4*pi*G or 8*pi*G?
epsilon_0 or 4*pi*epsilon_0?) that do not change the order of
magnitude.

the questions remain, why are the sizes of atoms (about the Bohr
radius) about 10^25 times bigger than the natural unit of length
(whether it is the Planck Length or "rationalized" Planck Length)?
which is equivalent to asking: why is the mass of the electron about
10^25 times smaller than the natural unit of mass (times alpha)? why
is it that these particle dimensions are so far from the size of their
natural units and yet the amount of electric charge on particles with
charge are in the same ballpark as the natural unit of charge (which is
equivalent to asking why is gravity so weak compared to E&M)?

> some of which are listed below
> and including the conventionally expressed
> Planck Mass, Length & Time values
>
> I would like to know
> if there is some way to choose
> the 'right' A,B,C&D case?
> Maybe there is a maximum or minimum
> over some type of dimensional space.
>
> q c hb G
>
> A B C D Mass (g)
...

it's a little bit more philosophical and aesthetic, but i am convinced
that the units most inherent to nature are those that have definition
derived from free space without consideration of any prototype object
(kg or planet Earth), substance (density of H2O), particle (e or m_e),
or "thing", and those that naturally eliminate extraneous scaling
factors from fundamental equations of free space. this normalizes c.
hbar, epsilon_0, and (my preference) 4*pi*G. (i know there are
advocates for normalizing 8*pi*G or 15*pi*G instead.) but it isn't G
and 4*pi*epsilon_0 that are normalized as is done now with Planck
Units. in the units i advocate, the Elementary Charge, e, would be e =
sqrt(4*pi*alpha) = 0.302822 which is in the ballpark of unity.
currently, with the common definition of the Planck Charge (i noticed
the reference provided by Ted Bunn, they use the Elementary Charge, e,
as the natural unit of charge) then e = sqrt(alpha), an order of
magnitude smaller than unity.

r b-j

[Oz]

Aetherist <TheAetherist@best.net> writes
> But, instead of setting k = 1 diemsionless, set it to its
> SI value, 1/4pi<eps>. Substuting in density as mapped above
> we find that then, dimensionally, when solved, charge has
> units of mass per time.

and how about eps_0 and mu_0?

--
Oz
This post is worth absolutely nothing and is probably fallacious.

[FrediFizzx]

"Oz" <Oz@farmeroz.port995.com> wrote in message
news:VS1q8qHJtQFEFwgd@farmeroz.port995.com...
> Aetherist <TheAetherist@best.net> writes
> > But, instead of setting k = 1 diemsionless, set it to its
> > SI value, 1/4pi<eps>. Substuting in density as mapped above
> > we find that then, dimensionally, when solved, charge has
> > units of mass per time.

Or as we discussed before, charge = mass*frequency.

> and how about eps_0 and mu_0?

eps_0 becomes a mass density constant for the "vacuum" in Paul's unit
system and mu_0 would be meters*sec^2/kg constant of the "vacuum". A
magnetic field becomes dimensionless.

FrediFizzx

http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.pdf
or postscript
http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.ps

http://www.vacuum-physics.com