Download Quantum Fields and Fundamental Geometry

VII International Symposium : Meeting the Unknown
Industrial Physics Engineering, Monterrey Campus, Monterrey, Mexico
Quantum Fields and Fundamental
Geometry
Daniel Galehouse
17-19 February 2005
[email protected]
Introduction
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Basic concept — fields and geometry
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Quantum mechanics — interpretations
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Gravitation — structure and interaction
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Spin theory — eight dimensions
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Ongoing studies — higher interactions and theoretical issues
What is Field theory?
Quantum field concepts
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Point Classical Particles and countability
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Particle fields in classical physics
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Experimental point particles and wave particles
Quantum field:
A description of physical objects based on countable wave fields.
The justification of the constructs, which represent “reality” for us, lies
alone in their quality of making intelligible what is sensorially given . . .
-- A. Einstein
What is Quantization?
quantbox.pdf
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Is there a way to be sure that classical physics is right?
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Is there a verifiable starting point?
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Study values of 0<β<1.
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Is the process mathematically justified?
Essential quantum terms from
geometry
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Quantum terms can appear without quantization
Intrinsic Quantization:
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Weyl theories — gauge invariance + general covariance
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Kaluza and Klein theories — intrinsically quantum
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Implicit for curvilinear formalism
All quantum terms can come from geometry
Twin paradox and accelerated motion
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Twin paradox of general relativity
0:00
0:00
2:03
2:02
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Requires a curvilinear theory
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Equivalence implies the same problem for quantum motion
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Any failure of Lorentz invariance requires a curvilinear theory
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Special relativity fails for and real interaction.
Conformal Transformations
Curvilinear representation
of the wave function:
Expansion plus rotation
• Two dimensions
• More dimensions
• Conformal factor
g
g
 
g .  g
Quantum
Mechanics?
Quantum Measurements
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A source emits particles which are diffracted by a screen and detected.
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An explicit model of the detector models the basis of measurement.
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Wave particles are captured on target nuclei remaining as localized.
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Radiation is emitted as the capture occurs.
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Radiation details match the transition of the wave particle.
A sequence of refinements
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A particle traverses several slits in order, and is deflected at each
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The implied selection of the initial trajectory is refined at each step
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The argument for point like character fails.
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Radiation is emitted at each refinement.
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Information is carried away by the radiation.
Radiation Forces
E
I0
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For one antenna, the field is E ~ I0 and the power is P ~ E2 ~ I02
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For two antennas, the total field is E ~ 2I0 and the power is P ~ 4E2 ~ 4I02
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Double the expected energy from input excitation voltage to tower
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Increased force of radiation reaction to first tower from second.
Radiation symmetry
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Emitter and absorber one system
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Time symmetric interaction
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B
Forces of emission equivalent to
absorption
Time reversal exchanges emitter and
absorber
hυ
Interaction of universe assumed
fundamentally symmetrical.
Advanced forces essential to state
change of emitter
A
Entanglements
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Two wave particles interact
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Covariant interactions are light-like.
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Near field forces are symmetric
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Far field forces taken symmetric
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Absorption and emission symmetrical
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Complexity of connections implies
space-like forces indirectly.
Delayed Correlations
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Two photon emitter
No stable intermediate
Both photons required to force final
state transition.
detector
detector
“Double” radiation reaction forces
required
Polarization correlation also required
Detected correlations present for
any time
source
Determinism
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Cat in box with spontaneous trigger.
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Can cat be in a superposition state?
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Statistics depend on distant
absorbers
Determinism requires a closed system
Box not perfectly closed in quantum
statistical sense
Universe is a determined system
Evolution is determined if box
isolates from the distant absorber
hυ
How does geometry work?
Gravitational fields
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Universal field assumption for point particles
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Motion described by one field or metric
Individual field assumption for quantum particles
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Interactions must be separated on overlap.
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Each quantum wave particle must have
Q
P
separate electromagnetic, gravitational and
quantum fields.
P
Q
Geometrical Quantum Theory
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Use a separate tensor for each particle
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Essential quantum terms appear automatically
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Electromagnetic interactions
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Gravitational interactions
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Quantum effects
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All invariants come from the Riemann tensor
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Electron and neutrino spin
Some common difficulties in field theory
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Avoid double quantization.
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Justify from experiment, never classical theory.
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General relativity contains essential quantum terms .
and cannot be actively quantized.
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Quantization of a classical theory may or may not work.
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A quantum theory that is only Lorentz covariant (such as Q.E.D.)
is an approximation and cannot be written in closed form.
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Use geometrical quantization.
Five dimensional quantum geometry
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Fifth coordinate from proper time
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Null displacements
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Electromagnetic potential and wave function placed offdiagonal
Precise relationship with quantum fields
Geodetic currents
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Electrodynamic-gravitational motion
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Quantum scaling of coefficients
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Accelerations from quantum forces
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Probability current trajectories
Null displacements along trajectory
Quantum Field Equation
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Gives the wave function, including
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Diffraction and interference
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Electromagnetic effects
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Gravitational fields
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Arbitrary coordinate systems
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Geometrical mass corrections
Positrons and electrons
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•
•
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e-p pairs are connected at the point of
origination
They may start with an acute angle or
they may curve around
The sharp angular representation is
common but studies following the
perspective of G.R. are smooth
Five dimensional terms suggest a
connection of the spaces following the
Riemannian theory
Experimental tests are difficult
Calculations may be affected in some
detail
Mass corrections
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Energy density correction
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Integral to in 5-d theory
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Part of 5-covariance
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Simple of mass theory
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Electron correction beyond
measurement
Neutrino correction may be within
range
Numerical factors for more
dimensions
Quantum gravitational source terms
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Source currents from five dimensional conformal effects.
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Quantum relativistic corrections
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Essential quantum gravitational effects
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Densities for electromagnetic sources
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Constants and interactions
Black holes?
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Quantum-gravitational corrections may bring the horizon into the star
surface
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Quantum information may persist
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Gravitational pair production
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Pressure term may affect cosmological constant
Field quantization
Electrodynamics
Quantum
electrodynamics
Feynman,
Schwinger
Tomonaga
Classical
electrodynamics
Quantum
gravitational
waves
Wheeler,
Feynman
Davies
Time
symmetric
quantum
electrodynamic
s
Gravitation
Hoyle,
Narlikar
Time symmetric
classical
electrodynamics
Ashtekar,. . .
Classical
gravitational
waves
Kilmister
Time symmetric
quantum
gravitational
waves
Time symmetric
classical
gravitational
waves
What
is
spin?
Dirac Equation in 5-symmetric form
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Dirac equation converts to symmetric form suitable for five dimensions
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A similarity transformation is used to include the mass symmetrically
Spin Matrices and Geometry
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Standard gamma matrices relate to general metric
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Fifth anti-commuting Dirac matrix completes the set for five dimensions.
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Dotted values for observers' space
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Un-dotted values for particle space.
Eight dimensional spinor basis.
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Eight real coordinates are combined into four complex pairs
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Standard spinor metric is used
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Transformation to the five dimensional space depends on gamma
matrices
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Spinor type Lorentz transformations
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Delta parametrizes local frame orientation
Spinor space curvature invariant
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Zero curvature scalar corresponds to eight dimensional D'Alembertian
Local conformal parameter equal to the two thirds power of the wave
function
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Conformal transformations are sufficient
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All spaces taken conformally flat
Spin from the gradient of a scalar
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8-Gradient of scalar wave function space gives Dirac spinor
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Standard transformation properties follow from local coordinate relation.
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Characteristic equation becomes first order
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Use chain rule to get differential equation in five space
Spinor wave by differentiation
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Scalar plane wave in five dimensional form
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Spinor differentiation gives related Dirac wave function
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General solutions are locally of the Dirac form
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Parameterization is in five dimensional spinor basis with arbitrary orientation
Pluecker-Klein correspondence
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General bilinear spinor combination
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Six pair-wise combinations
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Quadratic invariant for any spinors
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Algebraic identity
Spinor invariants in five-space
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Single spinor invariant
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Known similarity transformation
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Energy-momentum in classical limit
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Extra physical quantities
Lepton mass
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Mass is generated from two of the six quantities in the sum
Mass zero quantities constrain allowable spinor wave
functions
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Positive or negative helicities required
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Neutrinos and electrons satisfy same equation
Types of field theory
G.R.
E.D.
Q.M.
Spin
Standard Model
Weak
Strong
Q.C.D
Q.E.D
5-D Theory
8-D Theory
?
What is next?
Ongoing studies and physical implications
General mass theory
● Propagating mass and rest mass
● Inertia, gravity and the Higgs
● Geometries for weak and strong interactions
● Curvilinear description of elementary particles
● Particle transmutation
● Regularization requirements
● Renormalization
● Theory of the vacuum
● Black holes
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Summary
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Basic concepts
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Quantum mechanics
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Metrics, geodesy, wave equations, source equations, five dimensions
Spin theory
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Refinements, entanglements, measurements, radiation, correlations, cats
Gravitation
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Fields, quantization, geometry, waves, conformal transformations
Matrices, Dirac equation, eight dimensions, waves, invariants, lepton mass
Ongoing studies
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Field quantization, applications, conflicts to study
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