A Revised Planck Scale?

The standard paradigm for the cosmos is composed of 3 main parts: (1)
the standard model of particle physics, (2) the standard Big Bang
model, and (3) the Inflationary Scenario. To be sure there are other
components, but these three main components are interwoven and together
they constitute our general paradigm for understanding nature.

This post concerns identifying ways in which to clearly distinguish
between the standard paradigm and the Discrete Fractal paradigm (see
www.amherst.edu/~rloldershaw for details). I believe that I have found
another major, and promising, distinction between these two paradigms.

Within the context of the standard model of particle physics, there is
virtually no question about the Planck Scale, at which General
Relativity plays an equally important dynamical role with QED. The
conventional Planck length is about 1.6 x 10^-33 cm and the Planck mass
is about 2 x 10^-5 g.

According to the Discrete Fractal paradigm, nature has a discrete
spacetime structure and each of the fundamental scales in nature's
unbounded discrete hierarchy has its own unique value for the
gravitational "constant".

Numerically the relationship between G values on neighboring scales is:
G(n-1) = 3.27 x 10^38 G(n), where G(n) = 6.67 x 10^-8 cgs.
That means G(n-1) for the atomic scale would be equal to 2.31 x 10^31
cgs.
When you put G(n-1) into the conventional equations for the Planck
length and the Planck mass, because you want all atomic scale
"constants" for uniformity, you get:

Planck length = 3 x 10^-14 cm (= 0.4 times the proton radius)

Planck mass = 1.2 x 10^-24 g (= 0.8 times the proton mass).

Parenthetically, the revised Schwarschild radius for the proton is
about 0.8 x 10^-13 cm, which is about equal to the charge radius of the
proton and the revised Planck length.

So we have identified another example of a fundamental, very large,
difference between the two paradigms. Unlike the definitive Dark Matter
Test, the reality of the two differing Planck Scales is not so easily
tested empirically. However, if the radically different revised Planck
Scale of the DF paradigm should lead to promising new ideas in quantum
field theory, that could lead to a re-examination of the standard
particle physics model's Planck Scale, and, in turn, to a
re-examination of the foundations of the standard cosmological
paradigm.

Robert L. Oldershaw

wrote:

Perceptive readers who see the connection between this thread and the
one entitled "Critical Test Of The Discrete Fractal And Big Bang
Paradigms" will likely think: 'what motivates us to seriously consider
discrete self-similarity between elementary particles and astrophysical
objects like stellar-mass Kerr-Newman black holes?'.

Both elementary particles and stellar-mass Kerr-Newman black holes
share the following properties:

1. Nearly complete characterization in terms of mass, charge and
angular momentum.

2. Gyromagnetic ratios = 2.

3. Magnetic moments, but no electric dipole moments.

4. Similar mass formulae.

5. Cross-sections that increase in collisions.

The detailed physics of these arguments for meaningful discrete
self-similarity can be found in Sivaram, C. and Sinha, K.P., Physics
Reports 51, 111-187, 1979. It is an old paper, but well worth the
effort to find and read.

With the advent of the Discrete Fractal paradigm, it is now clear why
'strong gravity' is confined to very small spacetime scales, although a
considerable amount of work needs to be done in terms of elaborating on
this largely conceptual/empirical result.

Robert L. Oldershaw

Thus spake "
Parenthetically, the revised Schwarschild radius for the proton is
about 0.8 x 10^-13 cm, which is about equal to the charge radius of the
proton and the revised Planck length.

I should just like to add that the Schwarzschild radius of the proton
is not something which appears in standard physical models, the reason
being that a classical massive point particle is not a consistent idea
in general relativity. In fact a proton must be treated quantum
mechanically, and we do not have an accepted theory on that, but if the
Schwarzschild radius of the proton were considered then it would have a
magnitude given by

2Gm/c^3 =3D 8.28 x 10 e^-63 m

Planck length also has a formal definition

l_p =3D sqrt(hbar*G/c^3) =3D 1.61605e-35 =B1 1.0e-39 m

Neither of these figures is open to revision beyond that allowed by
experimental margins of error. If you are defining other quantities, you
should give them other names.







Regards

--=20

Oh No wrote:
Thus spake "

Parenthetically, the revised Schwarschild radius for the proton is
about 0.8 x 10^-13 cm, which is about equal to the charge radius of the
proton and the revised Planck length.


I should just like to add that the Schwarzschild radius of the proton
is not something which appears in standard physical models, the reason
being that a classical massive point particle is not a consistent idea
in general relativity. In fact a proton must be treated quantum
mechanically, and we do not have an accepted theory on that, but if the
Schwarzschild radius of the proton were considered then it would have a
magnitude given by

2Gm/c^3 =3D 8.28 x 10 e^-63 m

Planck length also has a formal definition

l_p =3D sqrt(hbar*G/c^3) =3D 1.61605e-35 =B1 1.0e-39 m

Neither of these figures is open to revision beyond that allowed by
experimental margins of error. If you are defining other quantities, you
should give them other names.


Gentlemen:

Given:

Planck's constant hb 1.054572675E-27 g cm^2 sec^-1
gravitational constant G 6.6725985E-8 cm^3 sec^-2 g^-1
speed of light c 2.997924580E10 cm sec^-1

The following is list of some of the Planck scale parameters:

Planck length (hb G/c^3)^(1/2) 1.61605E-35 cm
Planck time (hb G/c^5)^(1/2) 5.39056E-44 sec
Planck mass (hb c/G)^(1/2) 2.17671E-08 g
Planck energy (hb c^5/G)^(1/2) 1.95610E-16 g cm^2 sec^-2
Planck momentum (hb c^3/G)^(1/2) 6.52483E+05 g cm sec^-1
Planck force (c^4/G) 1.21027E+49 g cm sec^-2
Planck density (c^5/(hb G^2) 5.15500E+93 g/cm^3
Planck acceleration (c^6/(hb G)) 1.03145E+97 cm/sec^2
Planck kinematic viscosity (c^7/(hb G))^(1/2) 5.56077E+53 cm^2/sec
Planck absolute viscosity (c^9/(hb G^3))^(1/2) 2.49779E+71 g cm^-1 sec^-1

It is difficult to say which has a 'physical meaning'.

Using dimensional units of mass, length & time
the constants hb, G, c can be arranged in an infinite number of possibilities.

Richard

Richard Saam wrote:






Gentlemen:

Given:

Planck's constant hb 1.054572675E-27 g cm^2 sec^-1
gravitational constant G 6.6725985E-8 cm^3 sec^-2 g^-1
speed of light c 2.997924580E10 cm sec^-1

The following is list of some of the Planck scale parameters:

Planck length (hb G/c^3)^(1/2) 1.61605E-35 cm
Planck time (hb G/c^5)^(1/2) 5.39056E-44 sec
Planck mass (hb c/G)^(1/2) 2.17671E-08 g
Planck energy (hb c^5/G)^(1/2) 1.95610E-16 g cm^2 sec^-2
Planck momentum (hb c^3/G)^(1/2) 6.52483E+05 g cm sec^-1
Planck force (c^4/G) 1.21027E+49 g cm sec^-2
Planck density (c^5/(hb G^2) 5.15500E+93 g/cm^3
Planck acceleration (c^6/(hb G)) 1.03145E+97 cm/sec^2
Planck kinematic viscosity (c^7/(hb G))^(1/2) 5.56077E+53 cm^2/sec
Planck absolute viscosity (c^9/(hb G^3))^(1/2) 2.49779E+71 g cm^-1 sec^-1

It is difficult to say which has a 'physical meaning'.

Using dimensional units of mass, length & time
the constants hb, G, c can be arranged in an infinite number of possibilities.

Richard


hb = 1.054572675*10^(-27)
1.054572675`*^-27
G = 6.6725985*10^(-8 )
6.672598500000001`*^-8
c = 2.997924580*10^10
2.99792458`*^10
(hb G/c^3)^(1/2)
1.6160496497524128`*^-33
(hb G/c^5)^(1/2)
5.390561392149541`*^-44
(hb c/G)^(1/2)
0.000021767127031707378`
Two out of three wrong isn't bad?

Roger Bagula wrote:
Richard Saam wrote:





Gentlemen:

Given:

Planck's constant hb 1.054572675E-27 g cm^2 sec^-1
gravitational constant G 6.6725985E-8 cm^3 sec^-2 g^-1
speed of light c 2.997924580E10 cm sec^-1

The following is list of some of the Planck scale parameters:

Planck length (hb G/c^3)^(1/2) 1.61605E-35 cm
Planck time (hb G/c^5)^(1/2) 5.39056E-44 sec
Planck mass (hb c/G)^(1/2) 2.17671E-08 g
Planck energy (hb c^5/G)^(1/2) 1.95610E-16 g cm^2 sec^-2
Planck momentum (hb c^3/G)^(1/2) 6.52483E+05 g cm sec^-1
Planck force (c^4/G) 1.21027E+49 g cm sec^-2
Planck density (c^5/(hb G^2) 5.15500E+93 g/cm^3
Planck acceleration (c^6/(hb G)) 1.03145E+97 cm/sec^2
Planck kinematic viscosity (c^7/(hb G))^(1/2) 5.56077E+53 cm^2/sec
Planck absolute viscosity (c^9/(hb G^3))^(1/2) 2.49779E+71 g cm^-1 sec^-1

It is difficult to say which has a 'physical meaning'.

Using dimensional units of mass, length & time
the constants hb, G, c can be arranged in an infinite number of possibilities.

Richard



hb = 1.054572675*10^(-27)
1.054572675`*^-27
G = 6.6725985*10^(-8 )
6.672598500000001`*^-8
c = 2.997924580*10^10
2.99792458`*^10
(hb G/c^3)^(1/2)
1.6160496497524128`*^-33
(hb G/c^5)^(1/2)
5.390561392149541`*^-44
(hb c/G)^(1/2)
0.000021767127031707378`
Two out of three wrong isn't bad?

Roger:
Thank you for the obvious corrections
Updated list as follows:

The following is list of some of the Planck scale parameters:

Planck length (hb G/c3)^(1/2) 1.61624E-33 cm
Planck time (hb G/c5)^(1/2) 5.39121E-44 sec
Planck mass (hb c/G)^(1/2) 2.17645E-05 g
Planck energy (hb c5/G)^(1/2) 1.95610E+16 g cm2 sec^-2
Planck momentum (hb c3/G)^(1/2) 6.52483E+05 g cm sec^-1
Planck force (c4/G) 1.21027E+49 g cm sec^-2
Planck density (c5/(hb G2) 5.15500E+93 g/cm3
Planck acceleration (c6/(hb G)) 1.03145E+97 cm/sec2
Planck kinematic viscosity (c7/(hb G))^(1/2) 5.56077E+53 cm2/sec
Planck absolute viscosity (c9/(hb G3))^(1/2) 2.49779E+71 g cm^-1 sec^-1


Richard

"re" == rloldershaw@amherst edu writes:

re This post concerns identifying ways in which to clearly
re distinguish between the standard paradigm and the Discrete Fractal
re paradigm (...). I believe that I have found another major, and
re promising, distinction between these two paradigms.

re Within the context of the standard model of particle physics,
re there is virtually no question about the Planck Scale, at which
re General Relativity plays an equally important dynamical role with
re QED. The conventional Planck length is about 1.6 x 10^-33 cm and
re the Planck mass is about 2 x 10^-5 g.

It is likely that quantum effects do become important on scales of
order the Planck scale, but, not having a unified theory, I think your
statement of certainty is too strong.

[...]
re Numerically the relationship between G values on neighboring
re scales is: G(n-1) = 3.27 x 10^38 G(n), where G(n) = 6.67 x 10^-8
re cgs. That means G(n-1) for the atomic scale would be equal to
re 2.31 x 10^31 cgs. When you put G(n-1) into the conventional
re equations for the Planck length and the Planck mass, because you
re want all atomic scale "constants" for uniformity, you get:

re Planck length = 3 x 10^-14 cm (= 0.4 times the proton radius)

re Planck mass = 1.2 x 10^-24 g (= 0.8 times the proton mass).

Is this analysis consistent with observations that distant sources are
not fuzzy? e.g., URL:
http://adsabs.harvard.edu/cgi-bin/np...pJ...585L..77L
and similar papers.

--
Lt. Lazio, HTML police | e-mail:
No means no, stop rape. | http://patriot.net/%7Ejlazio/
sci.astro FAQ at http://sciastro.astronomy.net/sci.astro.html

Oh No wrote:

Schwarzschild radius of the proton were considered then it would have a
magnitude given by

2Gm/c^3 =3D 8.28 x 10 e^-63 m

Planck length also has a formal definition

l_p =3D sqrt(hbar*G/c^3) =3D 1.61605e-35 =B1 1.0e-39 m

Neither of these figures is open to revision beyond that allowed by
experimental margins of error. If you are defining other quantities, you
should give them other names.


Perhaps, I did not make myself clear, so I will try again.

The way you have calculated the Schwarschild radius for the proton and
the Planck length *assumes* that it is correct to use the conventional
Newtonian value for G in your calculations. That might not be valid.
In fact the Discrete Fractal paradigm ( www.amherst.edu/~rloldershaw )
says that for atomic scale systems you must use G(n-1), which is 10^38
times larger. Note that Sivaram and Sinha also derive a 'strong
gravity' G(f) that is about 10^38 times G.

A much more compact discussion (4 pages vs 76 pages) of the remarkable
self-similarity between elementary particles and Kerr-Newman black
holes by Sivaram and Sinha can be found at Physical Review D, vol.16,
no. 6, pp. 1975-1978, 1977.

In science, virtually anything is open to revsion. Scientists do not
deal in absolute knowledge, which is the province of religion.

Robert L. Oldershaw

Thus spake "
Oh No wrote:

Schwarzschild radius of the proton were considered then it would have a
magnitude given by

2Gm/c^3 =3D 8.28 x 10 e^-63 m

Planck length also has a formal definition

l_p =3D sqrt(hbar*G/c^3) =3D 1.61605e-35 =B1 1.0e-39 m

Neither of these figures is open to revision beyond that allowed by
experimental margins of error. If you are defining other quantities, you
should give them other names.


Perhaps, I did not make myself clear, so I will try again.

The way you have calculated the Schwarschild radius for the proton and
the Planck length *assumes* that it is correct to use the conventional
Newtonian value for G in your calculations. That might not be valid.
In fact the Discrete Fractal paradigm ( www.amherst.edu/~rloldershaw )
says that for atomic scale systems you must use G(n-1), which is 10^38
times larger. Note that Sivaram and Sinha also derive a 'strong
gravity' G(f) that is about 10^38 times G.

A much more compact discussion (4 pages vs 76 pages) of the remarkable
self-similarity between elementary particles and Kerr-Newman black
holes by Sivaram and Sinha can be found at Physical Review D, vol.16,
no. 6, pp. 1975-1978, 1977.

In science, virtually anything is open to revsion. Scientists do not
deal in absolute knowledge, which is the province of religion.


I think in fact that I did not make myself clear. This is not how
Schwarzschild radius and Planck length are *calculated*, it is how they
are *defined*. A definition is a truism and cannot be incorrect unless
it is inconsistent..

This is a matter of semantics, not one of the physical properties of the
universe. One uses, in so far as is possible, accepted definitions for
the simple reason that if one does not do so, one is talking a different
language from other people, and because that tends to make communication
difficult. It will appear to others that one is talking gibberish, even
if one is not. "A rose by any other name, would smell as sweet". But a
horticulturalist would think one an idiot for calling a rose an apple.

Certainly definitions can be changed. It may be that a defined quantity
turns out not to be useful, and that definition falls into disuse. Then
one is free to redefine the quantity. But if a quantity is in general
use, it is unwise to redefine it since no one will understand what you
are talking about.

Sivaram and Sinha, for example, have taken note. They wish to use
another value for the gravitational constant. But they have not called
it G. They have defined a new quantity, clearly related to G, but they
have also given it a new name, G(f).



Regards

--
Charles Francis
substitute charles for NotI to email

Thus spake Oh No
Thus spake "
Parenthetically, the revised Schwarschild radius for the proton is
about 0.8 x 10^-13 cm, which is about equal to the charge radius of the
proton and the revised Planck length.

I should just like to add that the Schwarzschild radius of the proton
is not something which appears in standard physical models, the reason
being that a classical massive point particle is not a consistent idea
in general relativity. In fact a proton must be treated quantum
mechanically, and we do not have an accepted theory on that, but if the
Schwarzschild radius of the proton were considered then it would have a
magnitude given by

2Gm/c^3 =3D 8.28 x 10 e^-63 m

Planck length also has a formal definition

l_p =3D sqrt(hbar*G/c^3) =3D 1.61605e-35 =B1 1.0e-39 m

Neither of these figures is open to revision beyond that allowed by
experimental margins of error. If you are defining other quantities, you
should give them other names.

With apologies, I copy pasted those figures from another source. The
equations looked all right when I posted, but obviously they did not
contain pure ASCII and they appear to have been corrupted by one of the
gateways used by s.a.r. = has come out as =3D and +- has come out as
=B1. They should read

Schwarzschild radius of the proton

2Gm/c^3 = 8.28 x 10 e^-63 m

Planck length

l_p = sqrt(hbar*G/c^3) = 1.61605e-35 +- 1.0e-39 m



Regards

--
Charles Francis
substitute charles for NotI to email