Planeamento
Aulas do tipo Teórico-Prático
Lecture1: Introduction to the philosophy of quantum mechanics
Presentation of the module: main topics, syllabus, references.
1. The structure of a physical theory: system state, state space, dynamics.
2. What is quantum mechanics about?
3. Newtonian mechanics, Maxwell's electromagnetism and quantum mechanics.
4. Introduction to the wave function: problems with a realistic interpretation.
5. The standard view and Born's statistical interpretation of the wave function.
6. Introduction to vectors: polar and Cartesian representations, superpositions.
Lecture 2: the formalism of quantum mechanics, the uncertainty principle, the measurement problem
1 The formalism of quantum mechanics
- the system state as a vector in Hilbert space
- the state vector and the Schrõdinger equation
- Dirac notation, superpositions of states
- observables and eigenstates
- theory of measurement: the collapse postulate and the Born rule
2. The position-momentum uncertainty relation (Heisenberg uncertainty principle)
- derivation of the uncertainty principle from the canonical commutator and Robertson relation
- meaning of the uncertainty principle: ontological interpretation and epistemic interpretation
2. The measurement problem
- interaction between system and apparatus: superposition of classically incompatible states
- three measurement problems:
a. What is a measurement?
b. Why the measurement? (why is the measurement interaction different from ordinary physical interactions and why does it trigger the collapse of the wave function?);
c. what's before the measurement? (can quantum mechanics provide an objective description of systems independently from measurement?)
Lecture 3_The measurement problem
1. The measurement problem
- interaction between a system and a measurement apparatus
- entangled states and wave function collapse
- philosophical problems included in the measurement problem
2. What is a quantum superposition?
- The two-slit experiment
- The Schrödinger cat paradox
3. Introduction to quantum non-locality
- The EPR paper (1935)
Lecture 4_Interpretations of the wave function
Presentation and discussion of the assigned papers on the interpretation of the wave function:
1. Nomological interpretation (S. Goldstein and N. Zanghì)
2. Primitive ontology (V. Allori)
3. Quantum state (T. Maudlin)
4. Real field in configuration space (D. Albert)
5. Multi-field in 3D space (M. Hubert and D. Romano)
6. Everett/Many Worlds interpretation (D. Wallace)