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) Planck Masses  The charge of the electron represents (is counted as) 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 using consistent units of..

The relative strength of the electrostatic force may be expressed using the same units of force established for Gravity.

For equal gravitational and electrostatic forces it follows that:

Resulting in:

The inverse fine structure number can be derived h-bar, c, k and e.

Through substitution it can be shown that:

Through further manipulation using the relationship between G and h ( ) it can be shown that:

It is also known that a fundamental mass will have a Compton wavelength equal to h.

It is known that the Fundamental Mass is related to the Gravitational Constant

When mass and charge are normalized it follows that the fundamental charge is related to Coulomb’s Constant

This results in a relationship between G, k and e

This results in an opportunity to solve for the dimensionless intrinsic value of h

Resulting in a Fundamental Mass of:

Simplifying to an Absolute Fundamental Mass of: