Will Hydrinos Save the World - An evaluation of Randell Mills by ixp95504

VIEWS: 13 PAGES: 68

									             Introduction: What is CQM
             The Theory: Does it Work?
                  Some other objections
                             Summary




          Will Hydrinos Save the World?
An evaluation of Randell Mills’ Classical Quantum Mechanics
                by a skeptical mathematician


                            Willie W. Wong

                        Department of Mathematics
                           Princeton University


      September 16, 2006 meeting of the Philadelphia
             Association for Critical Thinking


                        Willie W. Wong    Mathematical Evaluation of CQM
                  Introduction: What is CQM
                  The Theory: Does it Work?
                       Some other objections
                                  Summary


Outline

  1   Introduction: What is CQM
         A bit of history
         Overview of the claims
         Overview: what this talk is and isn’t about.

  2   The Theory: Does it Work?
        Problem 1: The Classical Wave Equation
        Problem 2: The δ Function Solution
        Problem 3: The Haus Condition

  3   Some other objections



                             Willie W. Wong    Mathematical Evaluation of CQM
                  Introduction: What is CQM
                  The Theory: Does it Work?
                       Some other objections
                                  Summary


Outline

  1   Introduction: What is CQM
         A bit of history
         Overview of the claims
         Overview: what this talk is and isn’t about.

  2   The Theory: Does it Work?
        Problem 1: The Classical Wave Equation
        Problem 2: The δ Function Solution
        Problem 3: The Haus Condition

  3   Some other objections



                             Willie W. Wong    Mathematical Evaluation of CQM
                  Introduction: What is CQM
                  The Theory: Does it Work?
                       Some other objections
                                  Summary


Outline

  1   Introduction: What is CQM
         A bit of history
         Overview of the claims
         Overview: what this talk is and isn’t about.

  2   The Theory: Does it Work?
        Problem 1: The Classical Wave Equation
        Problem 2: The δ Function Solution
        Problem 3: The Haus Condition

  3   Some other objections



                             Willie W. Wong    Mathematical Evaluation of CQM
                Introduction: What is CQM
                                             A bit of history
                The Theory: Does it Work?
                                             Overview of the claims
                     Some other objections
                                             Overview
                                Summary


What is it and why do we care?


     Since the industrial revolution there’s a large market for
     “energy”. From the steam engine, ICE, to modern
     electricity, we have a need to tap into natural energy
     reserves. So energy research = $$$
     The unobtainable holy grail, energy conservation,
     magnetics.
     Slightly more mainstream: ZPE, cold fusion.
     Experiments are not accessible to layman.
     BLP + CQM: experiment and theory. Accessible to
     armchair scientists.


                           Willie W. Wong    Mathematical Evaluation of CQM
                Introduction: What is CQM
                                             A bit of history
                The Theory: Does it Work?
                                             Overview of the claims
                     Some other objections
                                             Overview
                                Summary


What is it and why do we care?


     Since the industrial revolution there’s a large market for
     “energy”. From the steam engine, ICE, to modern
     electricity, we have a need to tap into natural energy
     reserves. So energy research = $$$
     The unobtainable holy grail, energy conservation,
     magnetics.
     Slightly more mainstream: ZPE, cold fusion.
     Experiments are not accessible to layman.
     BLP + CQM: experiment and theory. Accessible to
     armchair scientists.


                           Willie W. Wong    Mathematical Evaluation of CQM
                Introduction: What is CQM
                                             A bit of history
                The Theory: Does it Work?
                                             Overview of the claims
                     Some other objections
                                             Overview
                                Summary


What is it and why do we care?


     Since the industrial revolution there’s a large market for
     “energy”. From the steam engine, ICE, to modern
     electricity, we have a need to tap into natural energy
     reserves. So energy research = $$$
     The unobtainable holy grail, energy conservation,
     magnetics.
     Slightly more mainstream: ZPE, cold fusion.
     Experiments are not accessible to layman.
     BLP + CQM: experiment and theory. Accessible to
     armchair scientists.


                           Willie W. Wong    Mathematical Evaluation of CQM
                Introduction: What is CQM
                                             A bit of history
                The Theory: Does it Work?
                                             Overview of the claims
                     Some other objections
                                             Overview
                                Summary


What is it and why do we care?


     Since the industrial revolution there’s a large market for
     “energy”. From the steam engine, ICE, to modern
     electricity, we have a need to tap into natural energy
     reserves. So energy research = $$$
     The unobtainable holy grail, energy conservation,
     magnetics.
     Slightly more mainstream: ZPE, cold fusion.
     Experiments are not accessible to layman.
     BLP + CQM: experiment and theory. Accessible to
     armchair scientists.


                           Willie W. Wong    Mathematical Evaluation of CQM
                Introduction: What is CQM
                                             A bit of history
                The Theory: Does it Work?
                                             Overview of the claims
                     Some other objections
                                             Overview
                                Summary


What is it and why do we care?


     Since the industrial revolution there’s a large market for
     “energy”. From the steam engine, ICE, to modern
     electricity, we have a need to tap into natural energy
     reserves. So energy research = $$$
     The unobtainable holy grail, energy conservation,
     magnetics.
     Slightly more mainstream: ZPE, cold fusion.
     Experiments are not accessible to layman.
     BLP + CQM: experiment and theory. Accessible to
     armchair scientists.


                           Willie W. Wong    Mathematical Evaluation of CQM
                Introduction: What is CQM
                                             A bit of history
                The Theory: Does it Work?
                                             Overview of the claims
                     Some other objections
                                             Overview
                                Summary


BlackLight Power and Dr. Randell Mills
  Randell Mills, MD
      B.A. chemistry summa cum laude and Phi Betta Kappa
      from Franklin and Marshall ’82
      M.D. Harvard Medical School ’86
      One year of graduate work in electrical engineering at MIT,
      where he read the work of H.A. Haus
  BlackLight Power, Inc. of Cranbury, NJ
      Founded by Randell Mills, the current president, director,
      and chairman of the board.
      Performs research to exploit the BlackLight Process of
      hydrino theory for energy generation.
      Claims to have over $50M in venture capital as of this year.

                           Willie W. Wong    Mathematical Evaluation of CQM
                Introduction: What is CQM
                                             A bit of history
                The Theory: Does it Work?
                                             Overview of the claims
                     Some other objections
                                             Overview
                                Summary


BlackLight Power and Dr. Randell Mills
  Randell Mills, MD
      B.A. chemistry summa cum laude and Phi Betta Kappa
      from Franklin and Marshall ’82
      M.D. Harvard Medical School ’86
      One year of graduate work in electrical engineering at MIT,
      where he read the work of H.A. Haus
  BlackLight Power, Inc. of Cranbury, NJ
      Founded by Randell Mills, the current president, director,
      and chairman of the board.
      Performs research to exploit the BlackLight Process of
      hydrino theory for energy generation.
      Claims to have over $50M in venture capital as of this year.

                           Willie W. Wong    Mathematical Evaluation of CQM
                Introduction: What is CQM
                                             A bit of history
                The Theory: Does it Work?
                                             Overview of the claims
                     Some other objections
                                             Overview
                                Summary


BlackLight Power and Dr. Randell Mills
  Randell Mills, MD
      B.A. chemistry summa cum laude and Phi Betta Kappa
      from Franklin and Marshall ’82
      M.D. Harvard Medical School ’86
      One year of graduate work in electrical engineering at MIT,
      where he read the work of H.A. Haus
  BlackLight Power, Inc. of Cranbury, NJ
      Founded by Randell Mills, the current president, director,
      and chairman of the board.
      Performs research to exploit the BlackLight Process of
      hydrino theory for energy generation.
      Claims to have over $50M in venture capital as of this year.

                           Willie W. Wong    Mathematical Evaluation of CQM
                Introduction: What is CQM
                                             A bit of history
                The Theory: Does it Work?
                                             Overview of the claims
                     Some other objections
                                             Overview
                                Summary


BlackLight Power and Dr. Randell Mills
  Randell Mills, MD
      B.A. chemistry summa cum laude and Phi Betta Kappa
      from Franklin and Marshall ’82
      M.D. Harvard Medical School ’86
      One year of graduate work in electrical engineering at MIT,
      where he read the work of H.A. Haus
  BlackLight Power, Inc. of Cranbury, NJ
      Founded by Randell Mills, the current president, director,
      and chairman of the board.
      Performs research to exploit the BlackLight Process of
      hydrino theory for energy generation.
      Claims to have over $50M in venture capital as of this year.

                           Willie W. Wong    Mathematical Evaluation of CQM
                Introduction: What is CQM
                                             A bit of history
                The Theory: Does it Work?
                                             Overview of the claims
                     Some other objections
                                             Overview
                                Summary


BlackLight Power and Dr. Randell Mills
  Randell Mills, MD
      B.A. chemistry summa cum laude and Phi Betta Kappa
      from Franklin and Marshall ’82
      M.D. Harvard Medical School ’86
      One year of graduate work in electrical engineering at MIT,
      where he read the work of H.A. Haus
  BlackLight Power, Inc. of Cranbury, NJ
      Founded by Randell Mills, the current president, director,
      and chairman of the board.
      Performs research to exploit the BlackLight Process of
      hydrino theory for energy generation.
      Claims to have over $50M in venture capital as of this year.

                           Willie W. Wong    Mathematical Evaluation of CQM
                Introduction: What is CQM
                                             A bit of history
                The Theory: Does it Work?
                                             Overview of the claims
                     Some other objections
                                             Overview
                                Summary


BlackLight Power and Dr. Randell Mills
  Randell Mills, MD
      B.A. chemistry summa cum laude and Phi Betta Kappa
      from Franklin and Marshall ’82
      M.D. Harvard Medical School ’86
      One year of graduate work in electrical engineering at MIT,
      where he read the work of H.A. Haus
  BlackLight Power, Inc. of Cranbury, NJ
      Founded by Randell Mills, the current president, director,
      and chairman of the board.
      Performs research to exploit the BlackLight Process of
      hydrino theory for energy generation.
      Claims to have over $50M in venture capital as of this year.

                           Willie W. Wong    Mathematical Evaluation of CQM
                 Introduction: What is CQM
                                              A bit of history
                 The Theory: Does it Work?
                                              Overview of the claims
                      Some other objections
                                              Overview
                                 Summary


CQM: A Classical Theory


  CQM is a classical theory that can be derived from “first
  principles”.
      Accepts Newtonian/relativistic mechanics, Maxwell’s
      equations, thermodynamics, etc.
      Also accepts some tenets of quantum mechanics (QM):
      quantization of energy levels, de Broglie wavelength.
      Macroscopic physics and Microscopic physics should
      correspond.




                            Willie W. Wong    Mathematical Evaluation of CQM
                 Introduction: What is CQM
                                              A bit of history
                 The Theory: Does it Work?
                                              Overview of the claims
                      Some other objections
                                              Overview
                                 Summary


CQM: A Classical Theory


  CQM is a classical theory that can be derived from “first
  principles”.
      Accepts Newtonian/relativistic mechanics, Maxwell’s
      equations, thermodynamics, etc.
      Also accepts some tenets of quantum mechanics (QM):
      quantization of energy levels, de Broglie wavelength.
      Macroscopic physics and Microscopic physics should
      correspond.




                            Willie W. Wong    Mathematical Evaluation of CQM
                 Introduction: What is CQM
                                              A bit of history
                 The Theory: Does it Work?
                                              Overview of the claims
                      Some other objections
                                              Overview
                                 Summary


CQM: A Classical Theory


  CQM is a classical theory that can be derived from “first
  principles”.
      Accepts Newtonian/relativistic mechanics, Maxwell’s
      equations, thermodynamics, etc.
      Also accepts some tenets of quantum mechanics (QM):
      quantization of energy levels, de Broglie wavelength.
      Macroscopic physics and Microscopic physics should
      correspond.




                            Willie W. Wong    Mathematical Evaluation of CQM
                 Introduction: What is CQM
                                              A bit of history
                 The Theory: Does it Work?
                                              Overview of the claims
                      Some other objections
                                              Overview
                                 Summary


CQM: A Classical Theory


  CQM is a classical theory that can be derived from “first
  principles”.
      Accepts Newtonian/relativistic mechanics, Maxwell’s
      equations, thermodynamics, etc.
      Also accepts some tenets of quantum mechanics (QM):
      quantization of energy levels, de Broglie wavelength.
      Macroscopic physics and Microscopic physics should
      correspond.




                            Willie W. Wong    Mathematical Evaluation of CQM
                  Introduction: What is CQM
                                               A bit of history
                  The Theory: Does it Work?
                                               Overview of the claims
                       Some other objections
                                               Overview
                                  Summary


CQM’s (alleged) Advantages Over QM

      Lorentz-invariant
      Deterministic
      Gives exact solutions, rather than approximations
      Explains non-radiation of electrons in orbit
      Agrees with current observations
      Is self-consistent (?!)
      ...
  and the list goes on. c.f. the “Introduction” of Randall Mills’ The
  Grand Unified Theory of Classical Quantum Mechanics for a
  list of objections of Schrödinger’s wave mechanics that
  underlies QM.

                             Willie W. Wong    Mathematical Evaluation of CQM
                  Introduction: What is CQM
                                               A bit of history
                  The Theory: Does it Work?
                                               Overview of the claims
                       Some other objections
                                               Overview
                                  Summary


CQM’s (alleged) Advantages Over QM

      Lorentz-invariant
      Deterministic
      Gives exact solutions, rather than approximations
      Explains non-radiation of electrons in orbit
      Agrees with current observations
      Is self-consistent (?!)
      ...
  and the list goes on. c.f. the “Introduction” of Randall Mills’ The
  Grand Unified Theory of Classical Quantum Mechanics for a
  list of objections of Schrödinger’s wave mechanics that
  underlies QM.

                             Willie W. Wong    Mathematical Evaluation of CQM
                  Introduction: What is CQM
                                               A bit of history
                  The Theory: Does it Work?
                                               Overview of the claims
                       Some other objections
                                               Overview
                                  Summary


CQM’s (alleged) Advantages Over QM

      Lorentz-invariant
      Deterministic
      Gives exact solutions, rather than approximations
      Explains non-radiation of electrons in orbit
      Agrees with current observations
      Is self-consistent (?!)
      ...
  and the list goes on. c.f. the “Introduction” of Randall Mills’ The
  Grand Unified Theory of Classical Quantum Mechanics for a
  list of objections of Schrödinger’s wave mechanics that
  underlies QM.

                             Willie W. Wong    Mathematical Evaluation of CQM
                  Introduction: What is CQM
                                               A bit of history
                  The Theory: Does it Work?
                                               Overview of the claims
                       Some other objections
                                               Overview
                                  Summary


CQM’s (alleged) Advantages Over QM

      Lorentz-invariant
      Deterministic
      Gives exact solutions, rather than approximations
      Explains non-radiation of electrons in orbit
      Agrees with current observations
      Is self-consistent (?!)
      ...
  and the list goes on. c.f. the “Introduction” of Randall Mills’ The
  Grand Unified Theory of Classical Quantum Mechanics for a
  list of objections of Schrödinger’s wave mechanics that
  underlies QM.

                             Willie W. Wong    Mathematical Evaluation of CQM
                  Introduction: What is CQM
                                               A bit of history
                  The Theory: Does it Work?
                                               Overview of the claims
                       Some other objections
                                               Overview
                                  Summary


CQM’s (alleged) Advantages Over QM

      Lorentz-invariant
      Deterministic
      Gives exact solutions, rather than approximations
      Explains non-radiation of electrons in orbit
      Agrees with current observations
      Is self-consistent (?!)
      ...
  and the list goes on. c.f. the “Introduction” of Randall Mills’ The
  Grand Unified Theory of Classical Quantum Mechanics for a
  list of objections of Schrödinger’s wave mechanics that
  underlies QM.

                             Willie W. Wong    Mathematical Evaluation of CQM
                  Introduction: What is CQM
                                               A bit of history
                  The Theory: Does it Work?
                                               Overview of the claims
                       Some other objections
                                               Overview
                                  Summary


CQM’s (alleged) Advantages Over QM

      Lorentz-invariant
      Deterministic
      Gives exact solutions, rather than approximations
      Explains non-radiation of electrons in orbit
      Agrees with current observations
      Is self-consistent (?!)
      ...
  and the list goes on. c.f. the “Introduction” of Randall Mills’ The
  Grand Unified Theory of Classical Quantum Mechanics for a
  list of objections of Schrödinger’s wave mechanics that
  underlies QM.

                             Willie W. Wong    Mathematical Evaluation of CQM
                  Introduction: What is CQM
                                               A bit of history
                  The Theory: Does it Work?
                                               Overview of the claims
                       Some other objections
                                               Overview
                                  Summary


CQM’s (alleged) Advantages Over QM

      Lorentz-invariant
      Deterministic
      Gives exact solutions, rather than approximations
      Explains non-radiation of electrons in orbit
      Agrees with current observations
      Is self-consistent (?!)
      ...
  and the list goes on. c.f. the “Introduction” of Randall Mills’ The
  Grand Unified Theory of Classical Quantum Mechanics for a
  list of objections of Schrödinger’s wave mechanics that
  underlies QM.

                             Willie W. Wong    Mathematical Evaluation of CQM
                Introduction: What is CQM
                                             A bit of history
                The Theory: Does it Work?
                                             Overview of the claims
                     Some other objections
                                             Overview
                                Summary


Hydrino Theory

     There exists states with fractional principle quantum
               1
     numbers n where n is an integer–hydrogen atoms in such
     states are called hydrinos.
     n is limited by the fact that the electron in orbit cannot
     exceed the speed of light.
     n = 1 (QM ground state) is metastable: transition to the
     fractional states can only occur by non-radiative energy
     transfers, i.e. collisions of hydrogen atoms with catalyst.
     BlackLight Process: the catalyst should release the energy
     obtained from the hydrogen atom in the collision by
     photo-emission—which would be in the ultraviolet, a.k.a.
     “black light”, regime.

                           Willie W. Wong    Mathematical Evaluation of CQM
                Introduction: What is CQM
                                             A bit of history
                The Theory: Does it Work?
                                             Overview of the claims
                     Some other objections
                                             Overview
                                Summary


Hydrino Theory

     There exists states with fractional principle quantum
               1
     numbers n where n is an integer–hydrogen atoms in such
     states are called hydrinos.
     n is limited by the fact that the electron in orbit cannot
     exceed the speed of light.
     n = 1 (QM ground state) is metastable: transition to the
     fractional states can only occur by non-radiative energy
     transfers, i.e. collisions of hydrogen atoms with catalyst.
     BlackLight Process: the catalyst should release the energy
     obtained from the hydrogen atom in the collision by
     photo-emission—which would be in the ultraviolet, a.k.a.
     “black light”, regime.

                           Willie W. Wong    Mathematical Evaluation of CQM
                Introduction: What is CQM
                                             A bit of history
                The Theory: Does it Work?
                                             Overview of the claims
                     Some other objections
                                             Overview
                                Summary


Hydrino Theory

     There exists states with fractional principle quantum
               1
     numbers n where n is an integer–hydrogen atoms in such
     states are called hydrinos.
     n is limited by the fact that the electron in orbit cannot
     exceed the speed of light.
     n = 1 (QM ground state) is metastable: transition to the
     fractional states can only occur by non-radiative energy
     transfers, i.e. collisions of hydrogen atoms with catalyst.
     BlackLight Process: the catalyst should release the energy
     obtained from the hydrogen atom in the collision by
     photo-emission—which would be in the ultraviolet, a.k.a.
     “black light”, regime.

                           Willie W. Wong    Mathematical Evaluation of CQM
                Introduction: What is CQM
                                             A bit of history
                The Theory: Does it Work?
                                             Overview of the claims
                     Some other objections
                                             Overview
                                Summary


Hydrino Theory

     There exists states with fractional principle quantum
               1
     numbers n where n is an integer–hydrogen atoms in such
     states are called hydrinos.
     n is limited by the fact that the electron in orbit cannot
     exceed the speed of light.
     n = 1 (QM ground state) is metastable: transition to the
     fractional states can only occur by non-radiative energy
     transfers, i.e. collisions of hydrogen atoms with catalyst.
     BlackLight Process: the catalyst should release the energy
     obtained from the hydrogen atom in the collision by
     photo-emission—which would be in the ultraviolet, a.k.a.
     “black light”, regime.

                           Willie W. Wong    Mathematical Evaluation of CQM
               Introduction: What is CQM
                                            A bit of history
               The Theory: Does it Work?
                                            Overview of the claims
                    Some other objections
                                            Overview
                               Summary


What I Won’t Talk About



     Experimental evidence and their interpretations
     The collision model of energy transfer
     The various “exact solutions” for atoms and molecules that
     BLP research claimed to have found
     The inner functionings of the orbitsphere model and the
     notion of the trap photon.




                          Willie W. Wong    Mathematical Evaluation of CQM
               Introduction: What is CQM
                                            A bit of history
               The Theory: Does it Work?
                                            Overview of the claims
                    Some other objections
                                            Overview
                               Summary


What I Won’t Talk About



     Experimental evidence and their interpretations
     The collision model of energy transfer
     The various “exact solutions” for atoms and molecules that
     BLP research claimed to have found
     The inner functionings of the orbitsphere model and the
     notion of the trap photon.




                          Willie W. Wong    Mathematical Evaluation of CQM
               Introduction: What is CQM
                                            A bit of history
               The Theory: Does it Work?
                                            Overview of the claims
                    Some other objections
                                            Overview
                               Summary


What I Won’t Talk About



     Experimental evidence and their interpretations
     The collision model of energy transfer
     The various “exact solutions” for atoms and molecules that
     BLP research claimed to have found
     The inner functionings of the orbitsphere model and the
     notion of the trap photon.




                          Willie W. Wong    Mathematical Evaluation of CQM
               Introduction: What is CQM
                                            A bit of history
               The Theory: Does it Work?
                                            Overview of the claims
                    Some other objections
                                            Overview
                               Summary


What I Won’t Talk About



     Experimental evidence and their interpretations
     The collision model of energy transfer
     The various “exact solutions” for atoms and molecules that
     BLP research claimed to have found
     The inner functionings of the orbitsphere model and the
     notion of the trap photon.




                          Willie W. Wong    Mathematical Evaluation of CQM
                 Introduction: What is CQM
                                              A bit of history
                 The Theory: Does it Work?
                                              Overview of the claims
                      Some other objections
                                              Overview
                                 Summary


What I Will Present


  A critical analysis of the foundations of CQM with regards to:
      inner consistency of the theory
      the mathematical derivation of the electron model
      the mathematical intuition behind the theory
  Unless otherwise stated, material below pertaining to CQM is
  all taken from Randell Mills’ book, The Grand Unified Theory of
  Classical Quantum Mechanics, available free for download on
  BlackLight Power’s website.




                            Willie W. Wong    Mathematical Evaluation of CQM
                 Introduction: What is CQM
                                              A bit of history
                 The Theory: Does it Work?
                                              Overview of the claims
                      Some other objections
                                              Overview
                                 Summary


What I Will Present


  A critical analysis of the foundations of CQM with regards to:
      inner consistency of the theory
      the mathematical derivation of the electron model
      the mathematical intuition behind the theory
  Unless otherwise stated, material below pertaining to CQM is
  all taken from Randell Mills’ book, The Grand Unified Theory of
  Classical Quantum Mechanics, available free for download on
  BlackLight Power’s website.




                            Willie W. Wong    Mathematical Evaluation of CQM
                 Introduction: What is CQM
                                              A bit of history
                 The Theory: Does it Work?
                                              Overview of the claims
                      Some other objections
                                              Overview
                                 Summary


What I Will Present


  A critical analysis of the foundations of CQM with regards to:
      inner consistency of the theory
      the mathematical derivation of the electron model
      the mathematical intuition behind the theory
  Unless otherwise stated, material below pertaining to CQM is
  all taken from Randell Mills’ book, The Grand Unified Theory of
  Classical Quantum Mechanics, available free for download on
  BlackLight Power’s website.




                            Willie W. Wong    Mathematical Evaluation of CQM
                 Introduction: What is CQM
                                              A bit of history
                 The Theory: Does it Work?
                                              Overview of the claims
                      Some other objections
                                              Overview
                                 Summary


What I Will Present


  A critical analysis of the foundations of CQM with regards to:
      inner consistency of the theory
      the mathematical derivation of the electron model
      the mathematical intuition behind the theory
  Unless otherwise stated, material below pertaining to CQM is
  all taken from Randell Mills’ book, The Grand Unified Theory of
  Classical Quantum Mechanics, available free for download on
  BlackLight Power’s website.




                            Willie W. Wong    Mathematical Evaluation of CQM
                  Introduction: What is CQM
                                               Wave equation
                  The Theory: Does it Work?
                                               δ function
                       Some other objections
                                               Haus condition
                                  Summary


The Equation of Motion?!

  Some sophisticated mumble-jumble and jargon throwing:
  From The Grand Unified Theory of CQM, Chapter 1
  One-electron atoms include the hydrogen atom. . . The mass-
  energy and angular momentum of the electron are constant; this
  requires that the equation of motion of the electron be tempo-
  rally and spatially harmonic. Thus, the classical wave equation
  applies and
                       2   1 ∂2
                         − 2 2 ρ(r , θ, φ, t) = 0              (1)
                          v ∂t
  where ρ(r , θ, φ, t) is the function of the electron in time and space
  . . . All forces are central and Special Relativity applies.


                             Willie W. Wong    Mathematical Evaluation of CQM
                 Introduction: What is CQM
                                              Wave equation
                 The Theory: Does it Work?
                                              δ function
                      Some other objections
                                              Haus condition
                                 Summary


The Equation of Motion?!

  He includes two helpful footnotes:
  Footnote 1
  The equation of motion of an extended electron is postulated
  based on first principles and should not be confused with the en-
  ergy equation of a point-particle-probability-density wave such
  as the Schrödinger equation of quantum mechanics.
  and another about the classical wave equation
  Footnote 2
  This is not to be confused with the Schrödinger equation which
  is not a proper wave equation.



                            Willie W. Wong    Mathematical Evaluation of CQM
                 Introduction: What is CQM
                                              Wave equation
                 The Theory: Does it Work?
                                              δ function
                      Some other objections
                                              Haus condition
                                 Summary


The Equation of Motion?! Two specific objections
  Contrary to the claims, there is no Lorentz invariance of the
  equation of motion.
      The phase velocity v in his equation would undergo a
      classical Lorentz transform in a new coordinate system:
      v → (v − w)c 2 /(c 2 − wv )
      Hence the equation is only invariant if v = c.
  Furthermore, just conservation of energy and angular momenta
  doesn’t guarantee a classical wave equation:
      The trajectory of Newton’s first law, x = x0 + vt perfectly
      conserves both.
  So from the very start, the theoretical underpinning of this
  theory is suspect. But we’ll take the leap of faith here and
  suppose the equation of motion a priori.
                            Willie W. Wong    Mathematical Evaluation of CQM
                 Introduction: What is CQM
                                              Wave equation
                 The Theory: Does it Work?
                                              δ function
                      Some other objections
                                              Haus condition
                                 Summary


The Equation of Motion?! Two specific objections
  Contrary to the claims, there is no Lorentz invariance of the
  equation of motion.
      The phase velocity v in his equation would undergo a
      classical Lorentz transform in a new coordinate system:
      v → (v − w)c 2 /(c 2 − wv )
      Hence the equation is only invariant if v = c.
  Furthermore, just conservation of energy and angular momenta
  doesn’t guarantee a classical wave equation:
      The trajectory of Newton’s first law, x = x0 + vt perfectly
      conserves both.
  So from the very start, the theoretical underpinning of this
  theory is suspect. But we’ll take the leap of faith here and
  suppose the equation of motion a priori.
                            Willie W. Wong    Mathematical Evaluation of CQM
                 Introduction: What is CQM
                                              Wave equation
                 The Theory: Does it Work?
                                              δ function
                      Some other objections
                                              Haus condition
                                 Summary


The Equation of Motion?! Two specific objections
  Contrary to the claims, there is no Lorentz invariance of the
  equation of motion.
      The phase velocity v in his equation would undergo a
      classical Lorentz transform in a new coordinate system:
      v → (v − w)c 2 /(c 2 − wv )
      Hence the equation is only invariant if v = c.
  Furthermore, just conservation of energy and angular momenta
  doesn’t guarantee a classical wave equation:
      The trajectory of Newton’s first law, x = x0 + vt perfectly
      conserves both.
  So from the very start, the theoretical underpinning of this
  theory is suspect. But we’ll take the leap of faith here and
  suppose the equation of motion a priori.
                            Willie W. Wong    Mathematical Evaluation of CQM
                 Introduction: What is CQM
                                              Wave equation
                 The Theory: Does it Work?
                                              δ function
                      Some other objections
                                              Haus condition
                                 Summary


The Equation of Motion?! Two specific objections
  Contrary to the claims, there is no Lorentz invariance of the
  equation of motion.
      The phase velocity v in his equation would undergo a
      classical Lorentz transform in a new coordinate system:
      v → (v − w)c 2 /(c 2 − wv )
      Hence the equation is only invariant if v = c.
  Furthermore, just conservation of energy and angular momenta
  doesn’t guarantee a classical wave equation:
      The trajectory of Newton’s first law, x = x0 + vt perfectly
      conserves both.
  So from the very start, the theoretical underpinning of this
  theory is suspect. But we’ll take the leap of faith here and
  suppose the equation of motion a priori.
                            Willie W. Wong    Mathematical Evaluation of CQM
                 Introduction: What is CQM
                                              Wave equation
                 The Theory: Does it Work?
                                              δ function
                      Some other objections
                                              Haus condition
                                 Summary


The δ Function Ansatz
  From The Grand Unified Theory of CQM, Chapter 1
  In general, radial solutions of the Helmholtz wave equation are
  spherical Bessel functions, Neumann functions, Hankel func-
  tions, and associated Laguerre functions. It was found that any
  radial solution with radial motion results in radiation. Thus, a
  solution of the two-dimensional wave equation plus time is the
  proper stable, nonradiative equation of motion of the bound elec-
  tron. The corresponding radial function is the radial Dirac delta
  function.
  Which basically is an assertion that a solution for the wave
  equation exists in the form
                                  1
                 ρ(r , θ, φ, t) = 2 δ(r − rn )Ψ(θ, φ, t)                       (2)
                                 r

                            Willie W. Wong    Mathematical Evaluation of CQM
                 Introduction: What is CQM
                                                Wave equation
                 The Theory: Does it Work?
                                                δ function
                      Some other objections
                                                Haus condition
                                 Summary


The δ Function Ansatz: Some problems

  There are basically three problems with Mills’ reasoning:
      The various functions he cited are solutions to the
      Helmholtz differential equation
                                        2
                                            φ + k 2φ = 0

      and not the wave equation in general.
      A charge density with no radial motion does not imply a
      chanrge density with the radial part represented by a delta
      function.
      The assertion that the δ-function ansatz gives rise to a
      solution to the wave equation is false.


                            Willie W. Wong      Mathematical Evaluation of CQM
                 Introduction: What is CQM
                                                Wave equation
                 The Theory: Does it Work?
                                                δ function
                      Some other objections
                                                Haus condition
                                 Summary


The δ Function Ansatz: Some problems

  There are basically three problems with Mills’ reasoning:
      The various functions he cited are solutions to the
      Helmholtz differential equation
                                        2
                                            φ + k 2φ = 0

      and not the wave equation in general.
      A charge density with no radial motion does not imply a
      chanrge density with the radial part represented by a delta
      function.
      The assertion that the δ-function ansatz gives rise to a
      solution to the wave equation is false.


                            Willie W. Wong      Mathematical Evaluation of CQM
                 Introduction: What is CQM
                                                Wave equation
                 The Theory: Does it Work?
                                                δ function
                      Some other objections
                                                Haus condition
                                 Summary


The δ Function Ansatz: Some problems

  There are basically three problems with Mills’ reasoning:
      The various functions he cited are solutions to the
      Helmholtz differential equation
                                        2
                                            φ + k 2φ = 0

      and not the wave equation in general.
      A charge density with no radial motion does not imply a
      chanrge density with the radial part represented by a delta
      function.
      The assertion that the δ-function ansatz gives rise to a
      solution to the wave equation is false.


                            Willie W. Wong      Mathematical Evaluation of CQM
                 Introduction: What is CQM
                                              Wave equation
                 The Theory: Does it Work?
                                              δ function
                      Some other objections
                                              Haus condition
                                 Summary


The δ Function Ansatz: not actually a solution


      ρ(r , θ, φ, t) = (−v 2 ∂t2 +   )ρ(r , θ, φ, t)              (3)
                                         2          1
                    = (−v 2 ∂t2 + ∂r2 + ∂r + 2 θ,φ )ρ(r , θ, φ, t)(4)
                                          r        r
                                   2    2       1
                    = Ψ(θ, φ, t)(∂r + ∂r ) 2 δrn (r )             (5)
                                         r     r
                         1                       1
                      + 2 δrn (r )(−v 2 ∂t2 + 2 θ,φ )Ψ(θ, φ, t)   (6)
                        r                       r
  Next we use a well-known theorem in mathematics, that the
  various derivatives of the Dirac δ function are linearly
  independent, with which we can separate the above expression
  into three terms.

                            Willie W. Wong    Mathematical Evaluation of CQM
                 Introduction: What is CQM
                                              Wave equation
                 The Theory: Does it Work?
                                              δ function
                      Some other objections
                                              Haus condition
                                 Summary


The δ Function Ansatz: not actually a solution



                                            1 ∂2
                                          Ψ(θ, φ, t)
                                                   δr (r ) = 0                 (7)
                                           r 2 ∂r 2 n
                                              2 ∂
                                  Ψ(θ, φ, t) 3 δrn (r ) = 0                    (8)
                                             r ∂r
                   2   1             1
        Ψ(θ, φ, t) 4 + 2 (−v 2 ∂t2 + 2 θ,φ )Ψ(θ, φ, t) = 0                     (9)
                  r   r             rn

  The first two of the above implies that Ψ = 0 throughout–quite
  different from what Mills obtained.



                            Willie W. Wong    Mathematical Evaluation of CQM
                Introduction: What is CQM
                                             Wave equation
                The Theory: Does it Work?
                                             δ function
                     Some other objections
                                             Haus condition
                                Summary


The Haus Condition: What is it?


     In 1985, H.A. Haus: alternate interpretation of radiation.
     Haus was unaware of earlier work by Goedecke,
     Sommerfield, Bohm, Weinstein, and more.
     The interpretation: radiation of charge/current distribution
     implies it has Fourier components synchronous with
     light-speed waves.
     The derivation is a simple exercise in taking Fourier
     transforms.




                           Willie W. Wong    Mathematical Evaluation of CQM
                Introduction: What is CQM
                                             Wave equation
                The Theory: Does it Work?
                                             δ function
                     Some other objections
                                             Haus condition
                                Summary


The Haus Condition: What is it?


     In 1985, H.A. Haus: alternate interpretation of radiation.
     Haus was unaware of earlier work by Goedecke,
     Sommerfield, Bohm, Weinstein, and more.
     The interpretation: radiation of charge/current distribution
     implies it has Fourier components synchronous with
     light-speed waves.
     The derivation is a simple exercise in taking Fourier
     transforms.




                           Willie W. Wong    Mathematical Evaluation of CQM
                Introduction: What is CQM
                                             Wave equation
                The Theory: Does it Work?
                                             δ function
                     Some other objections
                                             Haus condition
                                Summary


The Haus Condition: What is it?


     In 1985, H.A. Haus: alternate interpretation of radiation.
     Haus was unaware of earlier work by Goedecke,
     Sommerfield, Bohm, Weinstein, and more.
     The interpretation: radiation of charge/current distribution
     implies it has Fourier components synchronous with
     light-speed waves.
     The derivation is a simple exercise in taking Fourier
     transforms.




                           Willie W. Wong    Mathematical Evaluation of CQM
                Introduction: What is CQM
                                             Wave equation
                The Theory: Does it Work?
                                             δ function
                     Some other objections
                                             Haus condition
                                Summary


The Haus Condition: What is it?


     In 1985, H.A. Haus: alternate interpretation of radiation.
     Haus was unaware of earlier work by Goedecke,
     Sommerfield, Bohm, Weinstein, and more.
     The interpretation: radiation of charge/current distribution
     implies it has Fourier components synchronous with
     light-speed waves.
     The derivation is a simple exercise in taking Fourier
     transforms.




                           Willie W. Wong    Mathematical Evaluation of CQM
                  Introduction: What is CQM
                                               Wave equation
                  The Theory: Does it Work?
                                               δ function
                       Some other objections
                                               Haus condition
                                  Summary


The Haus Condition: What is it?


  Theorem (Goedecke 1964)
  Let J be the Fourier transform of a charge-current distribution
  (ρ, j). A sufficient condition for nonradiation is that

                              2πn
                         J(       ˆ        ˆ
                                  x , n) ∝ x ,         n>0
                               T
  where T is the period of the motion of the distribution (the
                                                     ˆ
  distribution is localised in space), n an integer, x a unit vector.




                              Willie W. Wong   Mathematical Evaluation of CQM
                Introduction: What is CQM
                                             Wave equation
                The Theory: Does it Work?
                                             δ function
                     Some other objections
                                             Haus condition
                                Summary


The Haus Condition: But is it enough?


     Pearle ’77 has an improved necessary and sufficient result
     that uses the condition as

                                k 0 J a (k ) = k a J 0 (k )                   (10)

     where k is null.
     Mills’ application of Goedecke’s result is consistent with
     Pearle’s result, so modulo a constant factor, gives his
     claimed “boundary condition”.
     Pearle’s condition is not consistent with Special relativity.



                           Willie W. Wong    Mathematical Evaluation of CQM
                Introduction: What is CQM
                                             Wave equation
                The Theory: Does it Work?
                                             δ function
                     Some other objections
                                             Haus condition
                                Summary


The Haus Condition: But is it enough?


     Pearle ’77 has an improved necessary and sufficient result
     that uses the condition as

                                k 0 J a (k ) = k a J 0 (k )                   (10)

     where k is null.
     Mills’ application of Goedecke’s result is consistent with
     Pearle’s result, so modulo a constant factor, gives his
     claimed “boundary condition”.
     Pearle’s condition is not consistent with Special relativity.



                           Willie W. Wong    Mathematical Evaluation of CQM
                Introduction: What is CQM
                                             Wave equation
                The Theory: Does it Work?
                                             δ function
                     Some other objections
                                             Haus condition
                                Summary


The Haus Condition: But is it enough?


     Pearle ’77 has an improved necessary and sufficient result
     that uses the condition as

                                k 0 J a (k ) = k a J 0 (k )                   (10)

     where k is null.
     Mills’ application of Goedecke’s result is consistent with
     Pearle’s result, so modulo a constant factor, gives his
     claimed “boundary condition”.
     Pearle’s condition is not consistent with Special relativity.



                           Willie W. Wong    Mathematical Evaluation of CQM
              Introduction: What is CQM
              The Theory: Does it Work?
                   Some other objections
                              Summary


Other objections




     Agreement with experiment?
     Closed form?




                         Willie W. Wong    Mathematical Evaluation of CQM
              Introduction: What is CQM
              The Theory: Does it Work?
                   Some other objections
                              Summary


Other objections




     Agreement with experiment?
     Closed form?




                         Willie W. Wong    Mathematical Evaluation of CQM
              Introduction: What is CQM
              The Theory: Does it Work?
                   Some other objections
                              Summary


Summary



    The theoretical foundation of CQM is shaky at best.
    The egregious “derivations” in the introductory chapters
    indicates that care must be taken to confirm the
    calculations in later chapters.
    Unclear whether Mills’ experiments have revealed some
    yet-unknown property of our universe.




                         Willie W. Wong    Mathematical Evaluation of CQM
              Introduction: What is CQM
              The Theory: Does it Work?
                   Some other objections
                              Summary


Summary



    The theoretical foundation of CQM is shaky at best.
    The egregious “derivations” in the introductory chapters
    indicates that care must be taken to confirm the
    calculations in later chapters.
    Unclear whether Mills’ experiments have revealed some
    yet-unknown property of our universe.




                         Willie W. Wong    Mathematical Evaluation of CQM
              Introduction: What is CQM
              The Theory: Does it Work?
                   Some other objections
                              Summary


Summary



    The theoretical foundation of CQM is shaky at best.
    The egregious “derivations” in the introductory chapters
    indicates that care must be taken to confirm the
    calculations in later chapters.
    Unclear whether Mills’ experiments have revealed some
    yet-unknown property of our universe.




                         Willie W. Wong    Mathematical Evaluation of CQM
               Introduction: What is CQM
               The Theory: Does it Work?
                    Some other objections
                               Summary


Further References and Resources

     http://www.blacklightpower.com/ (where the
     GUT-CQM is free for download)
     GH Goedecke, “Classically Radiationless Motions and
     Possible Implications for Quantum Theory”, Phys. Rev.
     135 (1B) July 1964, pB281
     HA Haus, “On the radiation from point charges”, Am. J.
     Phys. 54 (12), December 1986, p1126
     P Pearle, “Classical electron models” in Electromagnetism,
     Paths to Research, Plenum Press, NY, 1982; p211
     A Rathke, “A critical analysis of the hydrino model”, New J.
     Phys. 7 (2005) 127


                          Willie W. Wong    Mathematical Evaluation of CQM
               Introduction: What is CQM
               The Theory: Does it Work?
                    Some other objections
                               Summary


Further References and Resources

     http://www.blacklightpower.com/ (where the
     GUT-CQM is free for download)
     GH Goedecke, “Classically Radiationless Motions and
     Possible Implications for Quantum Theory”, Phys. Rev.
     135 (1B) July 1964, pB281
     HA Haus, “On the radiation from point charges”, Am. J.
     Phys. 54 (12), December 1986, p1126
     P Pearle, “Classical electron models” in Electromagnetism,
     Paths to Research, Plenum Press, NY, 1982; p211
     A Rathke, “A critical analysis of the hydrino model”, New J.
     Phys. 7 (2005) 127


                          Willie W. Wong    Mathematical Evaluation of CQM
               Introduction: What is CQM
               The Theory: Does it Work?
                    Some other objections
                               Summary


Further References and Resources

     http://www.blacklightpower.com/ (where the
     GUT-CQM is free for download)
     GH Goedecke, “Classically Radiationless Motions and
     Possible Implications for Quantum Theory”, Phys. Rev.
     135 (1B) July 1964, pB281
     HA Haus, “On the radiation from point charges”, Am. J.
     Phys. 54 (12), December 1986, p1126
     P Pearle, “Classical electron models” in Electromagnetism,
     Paths to Research, Plenum Press, NY, 1982; p211
     A Rathke, “A critical analysis of the hydrino model”, New J.
     Phys. 7 (2005) 127


                          Willie W. Wong    Mathematical Evaluation of CQM
               Introduction: What is CQM
               The Theory: Does it Work?
                    Some other objections
                               Summary


Further References and Resources

     http://www.blacklightpower.com/ (where the
     GUT-CQM is free for download)
     GH Goedecke, “Classically Radiationless Motions and
     Possible Implications for Quantum Theory”, Phys. Rev.
     135 (1B) July 1964, pB281
     HA Haus, “On the radiation from point charges”, Am. J.
     Phys. 54 (12), December 1986, p1126
     P Pearle, “Classical electron models” in Electromagnetism,
     Paths to Research, Plenum Press, NY, 1982; p211
     A Rathke, “A critical analysis of the hydrino model”, New J.
     Phys. 7 (2005) 127


                          Willie W. Wong    Mathematical Evaluation of CQM
               Introduction: What is CQM
               The Theory: Does it Work?
                    Some other objections
                               Summary


Further References and Resources

     http://www.blacklightpower.com/ (where the
     GUT-CQM is free for download)
     GH Goedecke, “Classically Radiationless Motions and
     Possible Implications for Quantum Theory”, Phys. Rev.
     135 (1B) July 1964, pB281
     HA Haus, “On the radiation from point charges”, Am. J.
     Phys. 54 (12), December 1986, p1126
     P Pearle, “Classical electron models” in Electromagnetism,
     Paths to Research, Plenum Press, NY, 1982; p211
     A Rathke, “A critical analysis of the hydrino model”, New J.
     Phys. 7 (2005) 127


                          Willie W. Wong    Mathematical Evaluation of CQM

								
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