Absolute Planck Values:

Moving Beyond the Arbitrary Assignment of Unity

John R. LaubensteinIWPD Research Center

2008 APS March MeetingNew 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) 0.0855 fundamental charges Should these be normalized – that is, is an electron an electron?

2310184 .

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 .

.

2

2

mkg

22

21

dMM

mkg ee

)Force(

The relative strength of the electrostatic force may be expressed using the same units of force

established for Gravity .

2

422

2101664

dMM

.mkg ee

)Force(

2

2

mkg

For equal gravitational and

electrostatic forces it follows that:

110166.4

2

242

dMM

k

dMM

G

ee

ee

Resulting in:

G.k 42101664

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

1372 2

kehc

Through substitution it can be shown that:

1371016642 242

Ge.hc

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

1371016642 2422

2

e.ch

h/piG 2

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

11h

cMh

lfundamentamass lfundamenta

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

Gh

cMh

lfundamentalfundamenta

211

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

kcMh

chargecharge

2

This results in a relationship between G, k and e

42101664 .eGk

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

137

1016641016642242422

2

..

ch

Resulting in a Fundamental Mass of:

137106111016642

102122353422

242

m..

mkg.

Simplifying to an Absolute Fundamental Mass of:

110182 73 kg.