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 Poincaré.- 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 Schrödinger 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 Poincaré Group.- 16.6.2 Minkowski Spacetime.- 16.6.3 Quantum Poincaré 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.

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.