Where Are We, Really? Parallel Universes, Fact or Fiction Lecture 3: Science’s Parallel Worlds – the Many-Worlds Interpretation of Quantum Reality Max Tegmark - Professor of Physics at MIT - Classified parallel universe theories into 4 major categories or “levels” Max Tegmark (1967 - ) Tegmark’s Parallel Universe Levels Level Description Assumptions 1 Regions beyond our Infinite space, same laws of physics cosmic horizon – subject of next lecture! 2 Multiple post-Big Bang Inflation, possibly different physical “bubbles” constants or dimensions in different “bubbles” – subject of next lecture! 3 The “many worlds” of Quantum physics, quantum quantum physics computing; can coexist with Level 1 or Level 2 – subject of this lecture! 4 Other mathematical String theory and M-theory; whatever structures is mathematically possible is physically realizable – subject of next lecture! Tegmark’s Parallel Universe Levels Level Description Assumptions 1 Regions beyond our Infinite space, same laws of physics cosmic horizon – subject of next lecture! 2 Multiple post-Big Bang Inflation, possibly different physical “bubbles” constants or dimensions in different “bubbles” – subject of next lecture! 3 The “many worlds” of Quantum physics, quantum quantum physics computing; can coexist with Level 1 or Level 2 – subject of this lecture! 4 Other mathematical String theory and M-theory; whatever structures is mathematically possible is physically realizable – subject of next lecture! Continuity vs. Quantization Truly Continuous Continuity vs. Quantization 1 2 3 4 5 6 7 8 9 … Discrete or Quantized Founders of Quantum Theory Max Planck (1858-1947) Albert Einstein (1879-1955) Niels Bohr (1885-1962) Planck: Blackbody Radiation - Box made of perfectly radiation-absorbing material - Box has a small hole - Put box in furnace, measure energy radiating out of hole Anatomy of a Wave - A = Wavelength of the wave - B = Amplitude of the wave - Frequency (n) of the wave = number of wavelengths / unit time - Wavelength = 1 / Frequency; Frequency = 1 / Wavelength Blackbody Radiation Spectrum Radiation intensity (E) measured at hole in box Box absorbs radiation perfectly, heating interior (E = f(n) – continuous =E function of frequency) Radiation escapes from hole in box = 1/frequency (1/n) Blackbody Radiation Spectrum Radiation intensity (E) measured at hole in box Planck: E = f(hn) – quantized function Box absorbs radiation perfectly, heating interior (E = f(n) – continuous =E function of frequency) Radiation escapes from hole in box = 1/frequency (1/n) Einstein: Photoelectric Effect Potassium – 2.0 eV needed to eject electron Bohr’s Atomic Model - Electron “orbits” nucleus of atom - When atom absorbs photon (E = hn), electron “jumps” to orbit farther away from nucleus - When atom emits photon, electron “jumps” back Transition N=2 to N=3 Founders of Quantum Mechanics Max Born (1882-1970) Werner Heisenberg Erwin Schrodinger (1901-1976) (1887-1961) Consequences of Quantization - Limits knowledge precision (Heisenberg’s Uncertainty Principle) … Example: position and momentum - Measurement unavoidably alters what is being measured - Particles in multiple states at once … until we measure them - Particles coordinate their properties instantaneously, regardless of distance in space and time - The universe at its most basic level is probabilistic instead of deterministic … Observed phenomena (e.g., interference) can only be described by wave-based mathematics I think it is safe to say that no one really understands quantum mechanics. Do not keep saying to yourself, if you can possibly avoid it, “How can it possibly be like that?” No one knows how it can possibly be like that. -- Richard Feynman Nobel Prize, 1965 Richard Feynman (1918-1988) The more success the quantum theory has had, the sillier it looks. -- Albert Einstein I do not like it, and I am sorry I ever had anything to do with it. -- Erwin Schrodinger Level 3: The Many Worlds of Quantum Physics - Key concepts: superpositions, entanglement, decoherence - Superpositions represent the results of events or actions in the world with more than one possible outcome - Entanglement occurs when the different elements involved in a superposition evolve unobserved over time – without interacting with anything else outside the superposition - Decoherence causes a superposition to break down due to interaction with the world outside the superposition Quantum Mechanics Notation |X> = a vector for the quantum state of some thing (X) y = the wavefunction representing how the quantum state changes over time Superposition: Schrodinger’s Cat The cat is in a superposition of two states: alive and dead Superposition: Schrodinger’s Cat The cat is in a superposition of two states: alive and dead Superposition: Schrodinger’s Cat The cat is in a superposition of two states: alive and dead Superposition: Schrodinger’s Cat a2 = probability that material does not decay The cat is in a superposition of two states: alive and dead Superposition: Schrodinger’s Cat 2 a = probability b2 = probability that material that material does not decay does decay The cat is in a superposition of two states: alive and dead Superposition: Schrodinger’s Cat 2 a = probability b2 = probability that material that material does not decay does decay The cat is in a superposition of two states: alive and dead Y = a(|Alive>Cat) + b(|Dead>Cat) Superposition Y = a(|Alive>Cat ) + b(|Dead>Cat ) - Hilbert space …Vectors for different outcome states are |Dead>Cat orthogonal coordinates |Alive>Cat Superposition Y = a(|Alive>Cat ) + b(|Dead>Cat ) - Hilbert space …Vectors for different outcome states are |Dead>Cat orthogonal coordinates ... a and b are amplitudes for b each outcome a |Alive>Cat Superposition Y = a(|Alive>Cat ) + b(|Dead>Cat ) Unitary: a2 + b2 = 1 |Dead>Cat b a |Alive>Cat Superposition Y = a(|Alive>Cat ) + b(|Dead>Cat ) Unitary: a2 + b2 = 1 |Dead> 1 Cat Unit circle represents all points in Hilbert space 2 2 b that satisfy a + b = 1 1 … Whatever the state of the cat is, it has to a |Alive> Cat be on this circle Superposition Y = a(|Alive>Cat ) + b(|Dead>Cat ) Unitary: a2 + b2 = 1 a2 = ½ |Dead>Cat b2 = ½ b a |Alive>Cat Amplitudes: a = cos 45o = 1/ 2 b = sin 45o = 1/ 2 Superposition Y = a(|Alive>Cat ) + b(|Dead>Cat ) Unitary: a2 + b2 = 1 a2 = ½ |Dead>Cat b2 = ½ This unit vector in Hilbert space points to the state of reality b 1 in the superposition (the state of the cat) 45o a |Alive>Cat Amplitudes: a = cos 45o = 1/ 2 b = sin 45o = 1/ 2 Superposition Y = a(|Alive>Cat ) + b(|Dead>Cat ) Unitary: a2 + b2 = 1 2 |Dead> |Dead> a = ½ Cat a2 = ¾ Cat 2 b = ½ b2 = ¼ b 1 b 1 45o 30o a a |Alive>Cat |Alive>Cat Amplitudes: Amplitudes: a = cos 45o = 1/ 2 a = cos 30o = 3 / 4 = 3 / 2 b = sin 45o = 1/ 2 b = sin 30o = 1/ 4 = 1/2 Superposition Y = a(|Alive>Cat ) + b(|Dead>Cat ) Unitary: a2 + b2 = 1 2 |Dead> |Dead> a = ½ Cat a2 = ¾ Cat 2 b = ½ b2 = ¼ What happens when an Observer b 1 b 1 looks45o in the box?????30o a a |Alive>Cat |Alive>Cat Amplitudes: Amplitudes: a = cos 45o = 1/ 2 a = cos 30o = 3 / 4 = 3 / 2 b = sin 45o = 1/ 2 b = sin 30o = 1/ 4 = 1/2 Copenhagen Interpretation of Superposition - Developed by Niels Bohr and Erwin Schrodinger in the 1920’s - Suppose we do the Schrodinger’s Cat experiment with result: … Y = a(|Alive>Cat ) + b(|Dead>Cat ) - The superposition “collapses” – the highest amplitude outcome is actually observed on average … A lower amplitude outcome might be observed (example: quantum tunneling) - What causes the superposition to “collapse”? … It’s a mystery! Electrons Tunneling through a Resistance Barrier Quantum Tunneling Disk Drive Read Head Spin Valve Data 1 1 0 1 1 0 1 Magnetic fields Media motion in disk media Quantum Tunneling Disk Drive Read Head Spin Valve Data 1 1 0 1 1 0 1 Magnetic fields Media motion in disk media Magnetic fields in head Insulator High resistance Low resistance state state - High amplitude: head doesn’t conduct current at all (high resistance state) Quantum Tunneling Disk Drive Read Head Spin Valve Data 1 1 0 1 1 0 1 Magnetic fields Media motion in disk media Magnetic fields 1101101 Direction of in head Insulator tunneling current in head High resistance Low resistance state state - High amplitude: head doesn’t conduct current “at all” (high resistance state) - Low amplitude: head conducts tiny current if magnetic field directions in head are aligned (low resistance state – tunneling current) Entanglement - When objects interact they share a single quantum state until a measurement is made … None of the individual objects can be fully described without considering all the others - Suppose the objects separate in space-time before the measurement happens … When one of them is measured, the properties of the others instantaneously adjust to be consistent with it - Entanglements only continue while the objects are isolated from contact with anything else … Any further interactions with other objects result in decoherence Entanglement - Example: 2 electrons interact … Each electron’s spin is either up ( ) or down ( ) … Spins must be opposite after the interaction A B or A B Entanglement - Example: 2 electrons interact … Each electron’s spin is either up ( ) or down ( ) … Spins must be opposite after the interaction A B or A B A B Entanglement - Example: 2 electrons interact … Each electron’s spin is either up ( ) or down ( ) … Spins must be opposite after the interaction A B or A B A B A Entangled B Entanglement - Example: 2 electrons interact … Each electron’s spin is either up ( ) or down ( ) … Spins must be opposite after the interaction A B or A B A B A Entangled B A B Entanglement - Example: 2 electrons interact … Each electron’s spin is either up ( ) or down ( ) … Spins must be opposite after the interaction A B or A B A B A Entangled B A B Entanglement and Decoherence - Example: 2 electrons interact … Each electron’s spin is either up ( ) or down ( ) … Spins must be opposite after the interaction A B or A B A B A Entangled B Spin of A instantaneously set regardless of distance between A & B A B 2 electrons are now decoherent At any rate, I am convinced that [God] does not play dice.