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Predictions of Special Relativity More Predictions Pair Production General Predictions of Special Relativity More Predictions • The speed of the light is the same value • The speed of the light is the same value for all non-accelerating observers implies for all non-accelerating observers implies • Moving clocks run slowly implies • Speeds do not add according to our • Object lengths are contracted along their common sense implies direction of motion implies • Mass increases with speed implies • Two events that are simultaneous for an •E = mc2 observer may not be simultaneous for another observer. Pair Production General Theory of Relativity • Antimatter particle • Equivalence Principle (aka Principle of – Same as particle but opposite charge General Relativity): accelerating observers • Produced in pairs with the particle are equivalent to gravitational fields – Energy supplied by a “photon” according to • There is no force due to gravity: E = mc2 – Masses distort the geometry of spacetime • Eventually collides with a regular particle, – Everything moves in “straight lines” in this annihilating both non-flat geometry 1 Standard Hot Big Bang Model of Chaos Cosmology • Universe created in a “Big Bang” some 14 • Sensitive Dependence on Initial billion years ago Conditions (“Butterfly Effect”) – Has been expanding since • Trajectory never repeats • Question: will the expansion stop and reverse? • Transition to chaos preceded by infinite bifurcations • Problems: – Characterised by the “Feigenbaum number” – Dark matter and dark energy – The rate of expansion is increasing • Non-integer dimensions (“fractal”) – and more … Order From Disorder Conductors e.g. Metals • Requires a system that is open • Some electrons not tightly bound to the –Example: Vivarium conductor • Depends critically on the “rule set” • Can leave the metal by acquiring some – Cellular Automata energy • Energy sources on Earth • Energy can be supplied by: – Heat (“thermionic emission”) – Light (“photoelectric effect”) 2 Double Slit Experiment (photons or Photoelectric Effect electrons) • Light must have a minimum frequency • Interference pattern – Even for 1 particle at a time • Energy of photoelectrons proportional to – When we don’t look to see what is happening the light frequency at the slits • To explain: • When we look at the slits: – Light is a particle (“photon”) – Each particle goes through the upper or the – Energy of photon = h x frequency of wave lower slit – The measurement destroys the interference • h is very very small pattern • “Wave Particle duality” • Heisenberg: “The path comes into existence only when we observe it.” First Interpretation of Quantum • Line spectra for pure elements Theory – Identifies the element – Hydrogen appears to have some regularity • “Wave Function” aka “State Vector” aka • Standing Waves “Psi Field” aka Ψ – Born (1930): a wave of probability – Waves that “fit” • Einstein: “God does not play dice with the • Strings universe” • Drum Heads • Bohr: “Quit telling God what to do!” – Quantised • Heisenberg: “The wave function represents partly a fact, and partly our knowledge of the fact.” 3 de Broglie (1923) • Bohr Model for Hydrogen – “Allowed Orbits” characterised by an integer n • Electrons have a wave aspect – Absorbs a photon and “quantum jumps” to a – i.e. The Double Slit Experiment for electrons higher energy higher n orbital • Explains Bohr Model – When in a higher energy orbital “quantum jumps” to a lower energy one, emitting a • Basis for Quantum Theory photon. – Totally ad hoc Uncertainty (Indeterminacy) Bohr’s Interpretations of Quantum Principle Theory • Follows from de Broglie’s idea • Complementarity • Explains the Double Slit Experiments – Opposites are complements ΔE Δt also a minimum value • Copenhagen Interpretation Conservation of Energy can be briefly violated – Built on Complementarity “Virtual Pair Production” – Separation of observer and observed arbitrary • Wheeler: no “observers” only “participators” – “There is no quantum world” 4 Electron “Spin” Correlation Experiments • Only two states: “up” and “down” • Twins separated at birth • Beam from electron gun half up and half – Choice of profession down – Taste in music – Which is the case for a particular electron is • Electron pairs with total spin zero random • Direction for “up” defined by the apparatus – If one up, the other down, and vice versa that does the measurement – Pairs are “entangled” • Measurement destroys any previous • Is there “local causality”? definition of up Radioactive Decay Bell’s Theorem • Three types: Alpha, Beta, Gamma • Einstein-Podolsky-Rosen (1935) → Bohm (1950’s) → Bell (1964) • Half-life • Assume local hidden variables • Decay of a single radioactive atom – Derive a result for correlations of entangled – Schrödinger’s Cat electron pairs that is wrong – Is there a “hidden variable” influencing when – Either there are no hidden variables or they the atom decays? are not local • “Holographic” universe? – Is there a similar hidden variable influencing an electron’s spin? – Quantum Theory predicts the observed correlations 5 Types of Interactions Describing Interactions •Gravity –Newton Two Complementary Descriptions –Einstein 1. Fields •Electric 2. Particle Exchange • Magnetic “Quantum Field Theory” – Unified into “Electromagnetic” in 19th century Simplest electromagnetic interaction: an • Weak electron and a photon scatter – Radioactive Decay • Strong – Holds nucleus together Antimatter Redux Elementary Particles • Photon • Feynman (1949): a positron is an electron going backwards in time •Electron • Pair production and annihilation are just an •Proton extreme form of electromagnetic scattering • Neutron • Speculation: There is only one electron in the universe! • Speculation: protons and neutrons are made of each other – There are no “elementary particles” Plus their antimatter pairs 6 Neutrino Elementary Particles • Photon • Introduced to conserve energy in •Electron radioactive decays •Proton • Only interact via Weak and Gravitation • Neutron • Zero charge • Neutrino • Very small but non-zero mass Plus their antimatter pairs Exchange Particles Elementary Particles • Photon • Electromagnetic – Photons •Electron • Weak – W, Z •Proton • Neutron • Neutrino •W, Z Plus their antimatter pairs 7 Exchange Particles Elementary Particles • Photon • Electromagnetic – Photons •Electron • Weak – W, Z •Proton • Strong – “Mesons” • Neutron – Protons and Neutrons in nucleus exchange • Neutrino mesons •W, Z • Mesons Plus their antimatter pairs Exchange Particles Elementary Particles • Photon • Electromagnetic – Photons •Electron • Weak – W, Z •Proton • Strong – “Mesons” • Neutron – Protons and Neutrons in nucleus exchange • Neutrino mesons •W, Z • Gravitation – “Graviton” • Mesons – A Quantum Field Theory involving graviton • Graviton? exchange does not exist Plus their antimatter pairs 8 Elementary Particles String Theory • Photon •Electron • There is no such thing as String Theory (yet) •Proton Quarks • Neutron • Replaces “elementary particles” with strings • Neutrino – Vibrate with standing waves •W, Z – 11 dimensions or more • Mesons Quarks – Size ~ the size of the “quantum foam” of • Graviton? virtual pair production • Gluon Plus their antimatter pairs 9.
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