Transcript the Planck mass is incredibly larger than

Absolute Planck Values:
Moving Beyond the Arbitrary
Assignment of Unity
John R. Laubenstein
IWPD Research Center
2008 APS March Meeting
New Orleans, Louisiana
Part 1
Dimensionless Values:
Do They Have Significance?
What are dimensionless
numbers telling us?

We know from the inverse-fine structure constant of
137 that dimensionless numbers have significance

A logical conclusion is that they represent the
“counting” of something

The potential exists for the counting of a fundamental
entity
In Current Theory

The mass of the electron represents (is counted as)
4.18  10 23 Planck Masses

The charge of the electron represents (is counted as)
0.0855 fundamental charges

Should these be normalized – that is, is an electron an
electron?
Are Current Planck Values
Absolute Units?

Derived from combinations of the fundamental
constants: c, h-bar, G

Require an arbitrary normalization that constrains
the fundamental constants to a value of unity:
c = h-bar = G = 1

No physical evidence supports these assumptions
Multiplying by Unity

Dimensional analysis is based on conversions by multiplying
by a factor of unity

Combining physical constants in different ways does not represent
Dimensional Analysis unless the factor is know to be unity

Planck Values represent a manipulation of fundamental constants
resulting in units for mass, distance and time for which – at best –
only an intuitive meaning may be assigned
The Price of Arbitrary
Assumptions



We conclude that if we all play by the same “rules”
that arbitrary assumptions are OK
This leads to outcomes that are consistent, but not
necessarily an accurate description of reality
Are we currently making a huge “end-run” around
a much simpler path to reality?
The Price for Unity

Planck Mass is large on a quantum scale

Questions on how mass is manifested: Higgs? etc.

Is the complexity of “mass” a requirement forced
on us by observation; or, an unnecessary consequence
of our arbitrary decisions?
A. Gleeson, University of Texas
“the Planck mass is incredibly larger than anything
we have been able to use to create a single particle.
Thus, in addition to the fact that the elementary
particles we know have masses with no obvious
relation to each other, if they have any particular
relation to the Planck mass, it is for now simply some
incredibly small fractional number to which we can
assign no particular significance.”
The Magnitude of
Planck Mass

Inversely changing the values of h-bar and G will
change the value of Planck Mass without changing
Planck Distance or Planck Time

Question: Is there an intrinsic value for all physical
constants that may be expressed as a dimensionless
number?
A Fundamental Entity

Dimensionless intrinsic values represent the counting
of a physically significant entity

This counting can represent mass, distance or time

This physical entity is a singular entity that may be
manifested as mass, distance or time
Absolute Planck Values

Unitless numbers exist that represent the true values
of c, h-bar and G.

As such, unity values of mass, distance and time may
be derived from the true dimensionless values of c,
h-bar and G.

This suggests the existence of Absolute Planck Values
Are Absolute Planck
Values Achievable?

If dimensionless numbers with universal intrinsic
meaning exist, are they attainable or hidden from
us from nature herself?

If hidden, is this for all time, or until we become
“smarter?”

Are we “smart” enough now?
Part 2
Calculating Absolute Planck
Values
If G is set to 1, then the relative
gravitational force
between an electron- electron pair
can be expressed
kg 2
using consistent units of 2 .
m
.
kg
m
2
2
 1
( Force )
M eM e
d
2
The relative strength of the
electrostatic force may be expressed
using the same units of force
2
kg
established for Gravity
.
m2
kg
m

2
2
 4.166  10
( Force )
42

M eM e
d
2
For equal gravitational and
electrostatic forces it follows that:
 M eM e 
4.166  10 G 

2
 d
 1
 M eM e 
k

2
 d

42
Resulting in:
k  4.166  10 G
42
The inverse fine structure number can be
derived h-bar, c, k and e.
hc

137
2
2ke
Through substitution it can be shown that:
hc
2 4.166 10
42
Ge
2
 137
Through further manipulation using the
relationship between G and h (G  2 pi / h )
it can be shown that:
2
h c
2 
2
4.166 10 e
42
2
 137
It is also known that a fundamental mass
will have a Compton wavelength equal to h.
 fundamenta l mass 
h
M fundamenta l
h

 c 11
It is known that the Fundamental Mass is
related to the Gravitational Constant
 fundamenta l 
h
M fundamenta l
h
2


 c 11 G
When mass and charge are normalized it
follows that the fundamental charge is
related to Coulomb’s Constant
charge
2


M charge  c
k
h
This results in a relationship between
G, k and e
k
42
 e  4.166 10
G
This results in an opportunity to solve for
the dimensionless intrinsic value of h
2
h c
2 
2
4.166 10 4.166 10 
42
42 2
 137
Resulting in a Fundamental Mass of:
2.21 10
2 
2
 42
kg  m

2
4.166  10  1.61 10
42 3
35
m

2
 137
Simplifying to an Absolute Fundamental
Mass of:
2.18  10
73
kg  1