IRREVERENT QUANTUM MECHANICS

1. IRREVERENT QUANTUM MECHANICS Giancarlo Borgonovi May 2004

2. MOTIVATION

3. What is irreverent quantum mechanics? • A discipline for OFs to keep involved with QM: • Develop allegories/metaphors about QM • Design/build models/representations of QM effects • Investigate QM trivia • Explore connection between science and art • Write fiction around QM subjects/characters • Develop humor about QM subjects/characters • Quantum mechanical cooking? • Give presentations to other OFs.

4. GENERAL PRINCIPLES

5. Classical and quantum mechanics comparison Classical Quantum System State vector Represented by real numbers Possible states Definite state Deterministic transition from one state to another System State vector Represented by complex numbers Possible states Superposition of states Probabilistic transition from one state to another

6. Abstract state vector Abstract state vector in dual space Probability amplitude for going from state A to state B Operator Matrix element of operator The formal elements of quantum mechanics

7. The great law of quantum mechanics From The Feynman Lectures on Physics, Vol. 3

8. Are there any questions? I have not understood how you passed from A to B That is a statement, not a question The unforgiving logic of P. A. M. Dirac

9. Observables in Quantum Mechanics • Represented by real operators • Describe possible states (eigenvectors) which are associated with possible outcomes of measurements (eigenvalues) • Before the measurement: calculate probabilities of different outcomes • After the measurement: only one outcomeExampleExpectation values for different cases

10. ? Hilbert space and human life

11. Human life according to Classical Mechanics Hamilton’s Equations

12. Human life according to Quantum Mechanics Schroedinger Equation

13. The different forms of quantum mechanics Matrix Mechanics Wave Function Schroedinger Heisenberg B A Symbolic Method Path Integral Dirac Feynman

14. h 1900 - Max Planck, studying the black body radiation, discovers the “brick”. Planck’s constant h = 6.55 x 10-27 erg sec can be considered as the building block of quantum mechanics.

15. h = 2π A new, downsized model of the ‘brick’ is introduced

16. 1925 - The ‘brick’ is split in half (Uhlenbeck and Goudsmit introduce the spin).

17. Particles position and momentum and Heisenberg uncertainty principle

18. BOSONSandFERMIONS

19. A wrong representation of the hands of God building matter A more realistic representation of the hands of God building matter Identical particles are not distinguishable

20. Quantum Mechanics divides the Universe into two Categories • Every particle in the universe is either a boson or a fermion, that is to say everything in the universe is made up of bosons and fermions. • What distinguishes a boson from a fermion? • What are the effects of this categorization?

21. What distinguishes a boson from a fermion 1) Bosons have spin integer, fermions have spin semi-integer 2) The possible states for a system of bosons (at least two) are symmetric 3) The possible states for a system of fermions (at least two) are antisymmetric 4) Two bosons interfere with the same phase 5) Two fermions interfere with the opposite phase.

22. + Boson + + Fermion - + Pauli or ExclusionPrinciple - Shapes represent quantum states, colors represent particles (Symmetric under exchange) (Antisymmetric under exchange) (Null for fermions under exchange)

23. Effects due to boson like features • Bosons are very gregarious and tend to congregate together. If bosons exist in a state, there is a tendency for another boson to enter that state. • The laser is an example of this tendency of the bosons to come together • Superfluidity of Helium-4 (not Helium-3 which emulates a fermion) at low temperature is a macroscopic example of the result of the tendency of bosons to get into the same state of motion.

24. Effects due to fermion like featuresFermions tend to avoid each other. If a fermion exists in a state, another fermion will not want to enter that state. • Pauli’s Exclusion Principle • What if electrons were bosons

25. Electrons as fermions (real) Electrons as bosons (imagined) Matter under different assumptions From The Feynman Lectures on Physics, Vol. 3

26. Classical and Quantum Statistics

27. The different nature of bosons and fermions Everyone in my army of fermions will occupy his place and defend the empire Unknown Roman Emperor My army of bosons will move and attack as one man Unknown Barbarian King Bosons Fermi sphere Fermions

28. New States of Matter

29. THE PERIODIC TABLE(Ability and Weirdness)

30. Quantum Mechanics and Weirdness - Thoughts about the periodic table

32. FORMATION OF THE PERIODIC TABLE

33. Spherical symmetry, angular momentum, and weirdness Low Angular Momentum High Angular Momentum

34. Sociological implications of the periodic table • Consider the order of the states as some kind of social order, or rank, or job position. In a rigid, hierarchical society, positions would be occupied according to certain parameters (e.g. diplomas, family connections, religious or ethnical factors, etc.). In a more intelligent society, people of higher ability pass in front of others and acquire a higher social status. This process has some similarity to the buildup of the periodic table. Thus nature rewards ability. • The external shells, which are responsible for the chemical behavior of the elements, consist of s and p electrons only. The “weirder” d and f electrons are left behind, and are used to fill incomplete shells, so in a sense they hide behind less weird electrons at a higher level. Thus, nature tends to hide weirdness.,

35. SECOND QUANTIZATION and QUANTUM FIELDS

36. Second Quantization Fixed number of particles Occupation number representation This operator creates or destroys particles

37. QUANTUM MECHANICAL SPACES Many particle space (Fock space) Collection of n-particle states N- particle space Symmetric or antisymmetric states One- particle space (Hilbert space} Principle of symmetrization

38. VIRTUAL PARTICLES • Virtual particles are like words, they can result in attraction or repulsion • Virtual particles have a very short lifetime • An exchange of momentum can be interpreted as the action of a force over a time interval • Photons Electromagnetic field • Phonons Cooper pairs, superconductivity • Mesons Nucleons • Gluons Quarks Hideki Yukawa

39. Quantum Fields • A classical field is easy to visualize and understand • A quantum field is an operator which is a function of position • To understand a quantum field one needs to understand the local creation and annihilation operators • Everything (energy, number of particles, total momentum, etc.) can be expressed in terms of the creation and annihilation operators • A quantum field is expressed in terms of creation and annihilation operators • A quantum field is a nice way to express the duality particle wave that pervades QM • What are the eigenvalues and eigenvectors of a quantum field?

40. Leon Brillouin, 1927 Quantum Cooking - Potatoes a la Brillouin

41. THANK YOU AND MAY YOU HAVE A HAPPY TRANSITION TO A STATE OF HIGHER ANGULAR MOMENTUM