Gleason’s theorem can be used to derive born rule?
can we Model discrete physics as moving between eigenstates with unitary operators?
quantum mechanics now describes state as v, and then also Psi as state, and then defines Psi.v seems inconsistent?
physics big page: explicitly say qed, electroweak, quantum chromodynamics
quantum mechanics before qed non relativistic particles have wave like properties deriving born rule from many worlds qed virtual particles particles are excitation of underlying field renormalisation charge symmetry parity symmetry time symmetry chirality and helicity muon: electron but higher mass tau: higher mass again
neutrios: neutino (electron) muon neutrino (muon) tau neutrino (tau) why these number of electric particles? Unclear why only 3? Unclear why only -1,0,1. (reasons exist but complex?) parity symmetry exists energy density of empty space? fermion: half integer spin lepton: fermion without color
electroweak spontaneous symmetry breaking superconductivity? Related to breaking U(1), not sure if part of electroweak, or QED, or requires atoms therefore QCD? no parity symmetry. Gives way to define handedness of universe? charge symmetry? cp symmetry cp violations happens for some electroweak phenomena? cpt symmetry adds new gauge bosons. Qed just has photons W+̂, W-̂, Z0̂ gauge bosons have mass, unlike photon mediate weak force higgs boson and higgs field doesn’t predict why specific masses we see of particles though strong no cp violations? Unclear why, note there are for electroweak page on reconsiling quantum with general vacuum catastrophe singularities hawking radiation
Quantum systems Set of possible values Use these as eigenvalues and construct hermitian matrix State is vector. Vector being equal to eigen vector means at eigen state. Orthogonal states because only 1 at a time Do that on classical discrete before moving to quantum
quantum spin statistics theorem bose-einstein statistics (integer spin) fermi-dirac statistics (half integer spin)
concept of spin comes from quantum electromagnetism. spinning large object generates field in direction. so does electron
Quantum mechanics If discrete states sum of states, if continuous integral and coefficient is wave function
nuclear physics + nuclear binding energy + radioactive decay + exponential decay + half life + fusion + fission + fissile isotope. most common is 235U + enrichment. making ore into 235U from mix of that and 238U + critial mass decreses with more purity + control rods: absorb material + prompt critical neutrons vs delayed critical neutrons + effective neutron multiplication factor
number of pure states is the dimension of state vector. if there are 2 states, represent as 2 vector with 0 and 11.
for pauli matrices. start with one, then construct others such that prob = 0.5. so 2 state system results in 3 vector measurements. 3 dimensions
de broglie wavelength
link between hermit matrix and eigen vec val real?
on quantum computing: quantum fourier transform. quantum equivalent of discrete fourier transform. exponentially faster than discrete. quantum error correction in quantum computing. Quantum: Grover algorithm
quantum computers + shor’s algorithm + postBQP (BQP with post selection) + bounded-error polynomial time (BQP) (1/3 cut off) + Quantum Merlin Arthur (QMA) verify on quantum computer in poly time
quantum computing + turing machines can do all things quantum can do + but possibly different complexity classes + qubits
page on quantum computing? + classical memory: series of bits + quantum memory: superposition of classical bits + what do we do with these states? in classical apply logical gates. now, apply quantum logic gates + measuring state: in classical, simple, deterministic. in quantum, not. want high probability of correct answer + types of quantum gates: in classical, can create any using and, not, etc. what is equivalent for quantum? + measurement happens at end. otherwise interupts