Over the past years the author has developed a quantum language going beyond the concepts used by Bohr and Heisenberg. The simple formal algebraic language is designed to be consistent with quantum theory. It differs from natural languages in its epistemology, modal structure, logical connections, and copulatives. Starting from ideas of John von Neumann and in part also as a response to his fundamental work, the author bases his approach on what one really observes when studying quantum processes. This way the new language can be seen as a clue to a deeper understanding of the concepts of quantum physics, at the same time avoiding those paradoxes which arise when using natural languages. The work is organized didactically: The reader learns in fairly concrete form about the language and its structure as well as about its use for physics.
Act 1 One.-
1. Quantum Action.- 1.1 The Quantum Evolution.- 1.2 Quantum
Concepts.- 1.2.1 Initial and Final Modes.- 1.2.2 Quantum Relativity.- 1.2.3
Time.- 1.2.4 Being, Becoming and Doing.- 1.2.5 Ontism and Praxism.- 1.3
Quantum Entities.- 1.3.1 Sharp Actions.- 1.3.2 Complete Actions.- 1.3.3
Quantum Acts.- 1.3.4 Quantum Activity.- 1.3.5 Quantum Superposition.- 1.4 The
Quantum Project.- 1.4.1 Understanding Quantum Theory.- 1.4.2 The
Quantum-Relativity Analogy.- 1.5 Quantum Nomenclature.- 1.6 Summary.-
2.
Elementary Quantum Experiments.- 2.1 Malusian Experiments.- 2.2 Adjoint.- 2.3
Action Vector Semantics.- 2.3.1 General Actions.- 2.3.2 Action Vectors of
Classical Systems.- 2.3.3 Equivalent Actions.- 2.3.4 Semantics and
Ensembles.- 2.3.5 Logic, Kinematics, and Dynamics.- 2.3.6 Complex Vectors.-
2.3.7 Adjoint and Time Reversals.- 2.4 Quantum and Classical Kinematics.-
2.4.1 Classical Kinematics.- 2.4.2 Bohr Quantum Principle.- 2.4.3 Quantum
Kinematics.- 2.4.4 Logical Modes.- 2.4.5 Causes.- 2.4.6 Completeness.- 2.4.7
Connectedness.- 2.5 Quantum and Classical Relativities.- 2.6 Sums Over
Paths.- 2.7 Discrete Quantum Theory.- 2.8 Summary.-
3. Classical Matrix
Mechanics.- 3.1 Operations and Cooperations.- 3.1.1 Classical Operators.-
3.1.2 Classical Cooperations and Coarrows.- 3.1.3 Linearization.- 3.1.4
Vacuum.- 3.2 Ordinates and Coordinates.- 3.2.1 Classical Eigenvalue
Principle.- 3.2.2 Spectral Analysis.- 3.2.3 Complete Coordinates.- 3.2.4 OR,
XOR, and POR.- 3.2.5 Averages.- 3.2.6 Framed Algebras.- 3.3 Some Classical
Systems.- 3.3.1 Bit.- 3.3.2 N-ring.- 3.3.3 Bin and Commuting Calculus.- 3.3.4
Bits and Anticommuting Calculus.- 3.3.5 Top Bin.- 3.3.6 Extended Bin.- 3.4
Summary.- 3.5 References.-
4. Quantum Jumps.- 4.1 Quantum Arrows and
Coarrows.- 4.1.1 Quantum Operations.- 4.1.2 Quantum Systems Are Not
Categories.- 4.2 Adjoints and Metrics.- 4.2.1 Quantum Types.- 4.2.2 Negative
Norms.- 4.2.3 Projections.- 4.2.4 Quantum Coordinates.- 4.2.5 Interpretations
of Coordinates.- 4.2.6 Projective Coordinates.- 4.2.7 Non-numerical
Coordinates.- 4.3 Transformation Theory.- 4.3.1 Frames.- 4.3.2 Operator
Kinematics, Quantum and Classical.- 4.3.3 Quantum Entity.- 4.4 Quantizing.-
4.4.1 Re-relativizing.- 4.4.2 Rephasing.- 4.4.3 Quantization and
Non-Commutativity.- 4.5 Born-Malus Law.- 4.6 Quantum Logic.- 4.6.1 Quantum
Binary Variables.- 4.6.2 Quantum OR, POR, and XOR.- 4.6.3 Quantum
Cooperations.- 4.7 Indefinite Quantum Kinematics.- 4.8 Simple Quantum
Systems.- 4.8.1 Bit.- 4.8.2 Bin.- 4.8.3 Projective Quantum Bin.- 4.8.4
Indeterminacy Principle.- 4.8.5 Hydrogen Atom.- 4.8.6 Photon and Ghost.- 4.9
Summary.-
5. Non-Objective Physics.- 5.1 Descartes' Mathesis.- 5.2 Newton's
Aether.- 5.2.1 Partial Reflection and Interference.- 5.2.2 Polarization.-
5.2.3 Diffraction.- 5.2.4 Quantum Principle.- 5.3 Planck's Constants.- 5.3.1
k is for Thermodynamics.- 5.3.2 c is for Special Relativity.- 5.3.3 G is for
Gravity.- 5.3.4 h is for Quantum Theory.- 5.3.5 Planck Units.- 5.4 Einstein's
Quantum.- 5.4.1 Photoelectric Effect.- 5.4.2 Unified Fields.- 5.4.3 How Did
Newton Know?.- 5.5 Bohr's Atom.- 5.5.1 Correspondence Principle.- 5.6
Post-quantum Theories.- 5.6.1 Theory S.- 5.6.2 Theory N.- 5.6.3 Theory O.-
5.6.4 Theory E.- 5.6.5 Why So Many Theories?.-
6. Why Vectors?.- 6.1
Fundamental Theorem (Weak Form).- 6.2 Galois Lattices and Galois Connection.-
6.3 Multiplicity.- 6.4 Logic-based Arithmetic.- 6.4.1 Quantum-Logical
Addition.- 6.4.2 Quantum-Logical Multiplication.- 6.5 Fundamental Theorem
(Strong Form).- 6.5.1 Occlusion.- 6.5.2 Identification.- 6.5.3 Adjoint.-
6.5.4 Modularity.- 6.5.5 Irreducibility.- 6.5.6 Desarguesian Postulate.-
6.5.7 Proofs.- 6.6 Generators.- 6.7 Critique of the Lattice Logic.- 6.8
Summary.- Act 2 Many.-
7. Many Quanta.- 7.1 Classical Combinatorics.- 7.1.1
Ordered Pairs of Units.- 7.1.2 Unordered Pairs of Units.- 7.1.3 Symmetry and
Duality.- 7.1.4 Sequence.- 7.1.5 Series.- 7.1.6 Sib.- 7.1.7 Set.- 7.2 Quantum
Combinatorics.- 7.2.1 Quantum Sequence.- 7.2.2 Quantum Series.- 7.2.3 Quantum
Sib.- 7.2.4 Quantum Set.- 7.3 Singleton.- 7.4 Why Tensors?.- 7.5 Summary.-
8.
Quantum Probability and Improbability.- 8.1 Quantum Law of Large Numbers.-
8.1.1 Weak Law of Large Numbers.- 8.1.2 Strong Law of Large Numbers.- 8.2
Mixed Operations.- 8.2.1 Superpositions and Mixtures.- 8.2.2 Diffuse Initial
Actions.- 8.2.3 Diffuse Final Actions.- 8.2.4 Diffuse Medial Actions.- 8.2.5
Coherent Cooperators.- 8.3 Classical Limit.- 8.3.1 Coherent States.- 8.3.2
Macroscopic Measurement.- 8.3.3 Equatorial Bulge.- 8.3.4 Coherent Plane.-
8.3.5 The ?qcs Process.- 8.4 Hidden States.-
9. The Search for Pangloss.- 9.1
Aristotle.- 9.2 Llull and Bruno.- 9.3 Leibniz.- 9.4 Grassmann.- 9.4.1
Extensors.- 9.4.2 Extensor Terminology.- 9.5 Boole.- 9.6 Peirce.- 9.6.1
Tychistic Logical Algebra.- 9.6.2 Synechism and Quantum Condensation.- 9.6.3
Nomic Evolution.- 9.7 Peano.- 9.8 Clifford.- 9.9 Summary.-
10. Quantum Set
Algebra.- 10.1 Remarks on Set Algebra.- 10.2 Tensor Algebra of Sets.- 10.2.1
Opposite.- 10.2.2 Degree.- 10.2.3 Extensor Structure.- 10.2.4 Bases.- 10.2.5
Products.- 10.2.6 Complement.- 10.3 Recursive Construction.- 10.4 Infinite
Sets.- 10.5 Classical, Mixed and Fully Quantum Set Algebras.- 10.6 Clifford
Algebra.- 10.6.1 Classes as Clifford Extensors.- 10.6.2 Real Quantum Theory.-
10.6.3 Episystemic Variables.- 10.6.4 The Real World.- 10.7 Quantum
Extensors.- 10.8 Summary.- Act 3 One.-
11. Classical Spacetime.- 11.1 Flat
Spacetime.- 11.1.1 Chronometry.- 11.1.2 Causal Symmetry Implies Minkowski.-
11.1.3 Spinors and Minkowski.- 11.2 Causal Symmetries.- 11.2.1 Null Symmetric
Metric.- 11.2.2 Poincare.- 11.2.3 Lorentz.- 11.2.4 Infinitesimal Lorentz.-
11.3 Einstein Locality.- 11.3.1 Equivalence Principle.- 11.3.2 General
Relativization.- 11.4 The Idea of Gauge.- 11.5 Tensor Differential Calculus.-
11.5.1 Covariant Derivative.- 11.5.2 Distortion.- 11.5.3 Curvature.- 11.5.4
Ricci Tensor.- 11.5.5 Torsion Tensor.- 11.6 Gravity.- 11.6.1 Special
Relativistic Gravity.- 11.6.2 Einstein Gravity.- 11.7 Spin.- 11.7.1 Spinors
and Polyspinors.- 11.7.2 Spin Algebra.- 11.7.3 Sesquispinors.- 11.7.4 Spin
Adjoint.- 11.7.5 Spacetime Decomposition of Spin.- 11.7.6 Dirac Spinors.-
11.8 Spin Gauge.- 11.9 Summary.-
12. Semi-quantum Dynamics.- 12.1
Propagator.- 12.1.1 Forward Propagation.- 12.1.2 Classical Propagation.-
12.1.3 Quantum Propagation.- 12.1.4 Backward Propagation.- 12.1.5 The
Measurement Problem.- 12.1.6 Generators.- 12.2 Classical Dynamics.- 12.2.1
Phase Space.- 12.2.2 Least Time Principle.- 12.2.3 Endpoint Variations.-
12.2.4 Variational Derivative.- 12.2.5 Stationary Phase.- 12.2.6 Action
Principle.- 12.2.7 Hamiltonian Dynamics.- 12.3 Canonical Quantization.-
12.3.1 Quantum Energy.- 12.3.2 Coherent states.- 12.4 Quantum Dynamics.-
12.4.1 Real Time and Sample Time.- 12.4.2 Quantum Connection.- 12.4.3
Heisenberg Picture.- 12.4.4 Schrodinger Picture.- 12.4.5 Time-dependent
Dynamics.- 12.5 Quantum Action Principle.- 12.5.1 Path Amplitude.- 12.5.2
Path Tensor.- 12.5.3 Hamiltonian and Lagrangian Theories.- 12.5.4 Schwinger
Variational Principle.- 12.5.5 Superquantum Theory.- 12.5.6 What do
Physicists Want?.- 12.6 Summary.-
13. Local Dynamics.- 13.1 Local Fields.-
13.2 Gauge Physics.- 13.2.1 Gauge History.- 13.2.2 Standard Model.- 13.2.3
Measuring the Gauge Connection.- 13.3 Odd Fields.- 13.4 Energy.- 13.5 Quantum
Locality.-
14. Quantum Set Calculus.- 14.1 Why Set Calculus?.- 14.1.1
Interpretations of Set Theory.- 14.1.2 Activated Set Theory.- 14.1.3
Classical Pure Sets.- 14.2 Random Sets.- 14.2.1 First-Order Random Sets.-
14.2.2 Grassmann Algebra of the Random Set.- 14.3 The Quantum Set.- 14.3.1
Higher-Order Quantum Set.- 14.3.2 Operators of the Quantum Set.- 14.3.3 Does
Unitizing Respect Degree?.- 14.3.4 Tensor Set Theory.- 14.3.5 Order.- 14.3.6
Metastatistics.- 14.3.7 Quantum Lambda Calculus.- 14.4 Act Algebra.- 14.5
Quantum Mapping.- 14.6 Summary.-
15. Quantum Groups and Operons.- 15.1
Motivations.- 15.2 Double Operations.- 15.2.1 Algebraic Preliminaries.-
15.2.2 Classical Double Arrows.- 15.2.3 Classical Double Semigroup and
Algebra.- 15.3 The Operon Concept.- 15.4 Quantum Operon.- 15.5 Quantum Double
Arrows.- 15.5.1 Unit and Inversor.- 15.6 Examples.- 15.6.1 Quantum Plane.-
15.6.2 Quantum Four-group.- 15.6.3 Operation Semigroup.- 15.6.4 Operon
Diagrams.- 15.6.5 Pair Monoids.- 15.6.6 Projective Quantum Groups.- 15.7
Coherent Group of a Quantum Monoid.- 15.8 Summary.- Act 4 Nothing.-
16.
Quantum Spacetime Net.- 16.1 Quantum Topology.- 16.2 Quantum Spacetime Past.-
16.2.1 Hyperspace.- 16.2.2 Infraspace.- 16.2.3 Microstructure.- 16.3 Quantum
Spacetime Present.- 16.3.1 Causal Spacetime Network.- 16.3.2 Causal Relation
and Successor Relation.- 16.3.3 Hyperalgebra.- 16.3.4 Simplicial Complex
Theory.- 16.3.5 Membership Theory.- 16.3.6 Vertex Theory.- 16.3.7 Graph
Theory.- 16.3.8 Inclusion Theory.- 16.3.9 Choosing a Spacetime Theory.- 16.4
Quantum Spacetime Nets.- 16.4.1 Correspondence.- 16.4.2 Net Diagrams.- 16.4.3
Quantizing Discrete Spacetimes.- 16.4.4 Net Notation.- 16.4.5 The
Supercrystalline Vacuum.- 16.5 Spin.- 16.5.1 Discrete Spin.- 16.5.2 Quantum
Spin.- 16.5.3 Indefinite Spin Metric.- 16.5.4 Coherent Spin.- 16.6 Flat
Spacetime.- 16.6.1 Discrete Poincare Group.- 16.6.2 Minkowski Spacetime.-
16.6.3 Quantum Poincare Group.- 16.6.4 Coherent Translation Group.- 16.7
Internal Groups.- 16.7.1 QND Gauge Symmetries.- 16.7.2 Commutation Relations
of the Standard Model.- 16.8 Quantum Network Dynamics.- 16.8.1 Network
Charges and Fluxes.- 16.8.2 The Unitary Groups.- 16.8.3 QND Action
Principle.- 16.9 Summary.-
17. Toolshed.- 17.1 Recursive Constructions.-
17.1.1 Logic and Sets.- 17.1.2 Acts.- 17.2 Algebra.- 17.2.1 Semigroup and
Group.- 17.2.2 Category.- 17.2.2.1 Graph.- 17.2.2.2 Complex.- 17.2.2.3
Diagram.- 17.2.3 Group.- 17.2.4 Ring, Algebra, Module, Vector Space.- 17.2.5
Group Representation.- 17.2.6 Involutions.- 17.2.7 Lie Algebra.- 17.2.8
Tensor.- 17.2.9 Manifold.- 17.2.9.1 Tensor Calculus.- 17.2.9.2 Gauge.- 17.3
Order Concepts.- 17.3.1 Projective Geometry.- 17.3.2 Order Structures.-
17.3.3 Relation.- 17.4 Topology.- 17.5 Perturbation Methods.- 17.5.1 Discrete
Perturbation Theory.- 17.5.2 Double Operators.- 17.5.3 Perturbation Series.-
17.5.4 Continuous Perturbation Theory.- 17.6 Hilbert Space and + Space.- 17.7
Notation.- 17.7.1 Indices.- 17.7.2 Mathematical Symbols and Abbreviations.
