Research Interests 2007: John L. Fry

Research Supported BY: Air Force Office of Scientific Research Air Force Office of Scientific Research R. A. Welch Foundation R. A. Welch Foundation National Research Council National Research Council Texas Advanced Research Texas Advanced Research Texas Advanced Technology Texas Advanced Technology Lockheed Martin Lockheed Martin Marilyn G. Cox (wife) Marilyn G. Cox (wife)

Current Research Interests Antimatter- matter interactions Antimatter- matter interactions Dielectric response in solids Dielectric response in solids Feynman-Kac quantum theory Feynman-Kac quantum theory Group theory in quantum mechanics: derivation of fundamental laws from symmetry of metric of space and time Group theory in quantum mechanics: derivation of fundamental laws from symmetry of metric of space and time Wave function “collapse” in qm. Wave function “collapse” in qm.

Preclusion I: Feynman’s Uncertainty Principle Anybody who thinks that they understand quantum theory doesn't.

Preclusion II: Feynman’s Certainty Principle Anybody who knows EVERYTHING EVERYTHING about NOTHING knows EVERYTHING

Motivation for Research I. Conflict between quantum theory and theory of relativity (collapse of qm state) II. Unexplained matter and energy A) Only 4% of matter and energy seen B) 23% of total is “dark matter” C) 73% of total is “dark energy”

Classifying Physical Laws A model for physics helps to understand a process or situation A model for physics helps to understand a process or situation A theory may explain the model in a special frame of reference only A theory may explain the model in a special frame of reference only A law is a theory always agreed upon by a defined set of observers (you pick them) A law is a theory always agreed upon by a defined set of observers (you pick them) A universal law is one agreed upon by all observers that have the same metric A universal law is one agreed upon by all observers that have the same metric

Mechanical Universe 1. Relativistic quantum mechanics (RQM) 1. Relativistic quantum mechanics (RQM) 2. Relativistic classical mechanics (RCM) 2. Relativistic classical mechanics (RCM) 3. Quantum mechanics (QM) 3. Quantum mechanics (QM) 4. Classical mechanics (CM) 4. Classical mechanics (CM) 5. Quantized general relativity? 5. Quantized general relativity?

Origin of Laws of Mechanics Define a (universal) law as any relationship for physical observables that is independent of an isometric transformation of coordinates Define a (universal) law as any relationship for physical observables that is independent of an isometric transformation of coordinates Then two fundamental postulates about our universe constrain the kinds of laws possible Then two fundamental postulates about our universe constrain the kinds of laws possible 1. Physical theories must be based upon analytic (possibly complex) functions 1. Physical theories must be based upon analytic (possibly complex) functions 2. Equations determining these functions must be expressible in a covariant form 2. Equations determining these functions must be expressible in a covariant form

Theoretical Constructions Quantum theories assume mechanics can be explained by a complex function ψ(x,t) in Hilbert space defined on a real carrier space (x, t) Quantum theories assume mechanics can be explained by a complex function ψ(x,t) in Hilbert space defined on a real carrier space (x, t) Classical theories assume that real quantities x, p and t are sufficient Classical theories assume that real quantities x, p and t are sufficient Care must be used in defining a “particle” to be consistent with Postulate II: isometric observers must agree on what the particle is since different types of particles have different laws! Care must be used in defining a “particle” to be consistent with Postulate II: isometric observers must agree on what the particle is since different types of particles have different laws!

Einstein (1915) Carrier Space Metrics

Physical laws are restricted by assumptions made in constructing a theory and postulates I and II Physical laws are restricted by assumptions made in constructing a theory and postulates I and II Postulate I implies physical functions can be expanded in a Taylor series on the carrier space Postulate I implies physical functions can be expanded in a Taylor series on the carrier space Postulate II requires knowledge of the group of the metric G for the carrier space and defines a “particle” as an irrep of G Postulate II requires knowledge of the group of the metric G for the carrier space and defines a “particle” as an irrep of G

Metrics Employed 1. Euclidean: (3+1)dim (non-relativistic) 1. Euclidean: (3+1)dim (non-relativistic) 2. Minkowski: 4dim (special relativity) 2. Minkowski: 4dim (special relativity)

Group of Metric Non-relativistic mechanics: Non-relativistic mechanics: Galilean group, Relativistic mechanics: Relativistic mechanics: Poincare group, 1. All unitary irreducible representations of these groups are known (needed for quantum theory) 2.Semi-direct product structure simplifies irreps 3. Invariant subgroup of 4-translations gives eigenvalue eqn. 4. Covariant eigenvalue equations give functions belonging to irreps of G(M) and fully describe elementary particles 5. These eigenvalue equations give the form of laws of physics but not the constants

Free Particle Equations T(4) gives a necessary condition for an irrep labeled by real 4-vector k For an analytic function: So a necessary, but not sufficient, condition for an irrep is

Free Particle Equations The last equation (actually 4 equations) is an eigenvalue equation; the solution transforms like irrep of T(4) but not P(3+1) or G(3+1) Manipulating the eigenvalue equations in various ways to yield covariant eigenvalue equations for each metric ensures that a full irrep of the group of the metric is found

Other Equations It is possible to use this technique to derive all dynamical equations of CM, QM, RCM, RQM, Maxwell’s equations, etc. Other equations may also exist, consistent with postulates I and II Each irrep (type of particle) has its own dynamical equation We are trying to find new equations or prove the existing ones are unique We will examine new metrics in the search for dark matter and dark energy

Conclusions Two postulates account for the laws of mechanics in flat space (also curved?) The origin of Hamilton’s principle is found in these two postulates Carrier space metrics play a central role in dynamical laws of any universe With only 4% of matter and energy seen in the universe there is plenty of room for new theories: we hope to find them.