Math and Physics

"Dr. Albert" at the Wesleyan University Graduation Ceremonies
May,2006

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April 7,2011
A new research article in Physics and Epistemology

On spontaneous changes in the speed of light (pdf); (docx); (doc)

Many consequences are drawn from this basic thesis:

"It is impossible by any means to design an experiment, within the universe described by Special Relativity, that can detect any change in the speed of light".

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1. Irreversible Motion in One Dimension:
   An exercise in teleogeometry

   Irreversibility (doc file)
   Irreversibility(pdf file)

2. Dynamical Systems and Ordinal Arithmetic:
   The classification of general functions on the real line

   Ordinal Maps (doc)
   Ordinal Maps (pdf)

3. Dynamics of Iterate sets of real numbers in basis representations (1983)
   n-cimals (pdf)

4. A Model for a Double-Intersection Projective Geometry
   Geometry (doc)
   Geometry(pdf)

Postscript, March 21:2010. A few paragraphs have been adjoined at the end, suggesting ways in which this construction could be extended to variants in elliptic and hyperbolic non-Euclidean spaces.

Lecture notes from a seminar on
The Dirac Equation of the Electron
Dirac Equation (doc)
Dirac Equation(pdf)

Lecture notes from a seminar on Spinors
Rotation Groups of Physics

Lecture notes from a seminar on Vector Fields
Vector Fields

Set Theory, the Zermelo-Fraenkel Axioms, and Form in Science and Art
(Updated December 21,2007):
Zermelo-Fraenkel(pdf)

Time measurement in empirical and conceptual Space-time models:
Non-Metrizable Time

Generalizing Set Theory:
Russell's Paradox and the Isostructure Theorem

Framing Questions in Quantum Physics:

• Quantum Question Theory
  
• Time Derivatives and Uncertainty

Descartes/Huyghens from an advanced standpoint:

• Two Trains and a Fly
  
• The Restricted Collision Theorem
  
• The General Collision Theorem

Mechanics in special manifolds:

• Gravity on the 2-Cone

• 3-Cone Gravity, the Hubble field and dark energy

• Relativity on 2-Manifolds (pdf);(doc); (docx)

• On Inertial Paths, Frames and Groups (docx);(doc);(pdf)

• Galilean Relativity and the group structure of Inertia (docx) ;(doc);(pdf)

By David Clark, Mathematics, SUNY-New Paltz:
The Consecutive Integer Game

On random versus systematic Uncertainty:
Quantum Astronomy and the Big Bang (html);(pdf)

The Paradoxes of Zeno, as seen by:
Peter Lynds

Knot Theory in the:
Hydrodynamics of Bus Boarding(html);(pdf)

Logical finitism in physics:
Barrier Theory(pdf)

Measuring irreversible time in irreversible time, with consequences:
Topological Paradoxes of Time Measurement

Speculations on Kuhnian relativism:
On Counter-Intuitive Science(.pdf)
Table (.pdf)

Heraclitus versus Empedocles revisited:
Thoughts on Gravitation

Book Review: The Road to Reality
Roger Penrose, Alfred Knopf.2005

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