The Weirdness of Quantum Mechanics Dr. Neil Shenvi Department of Chemistry Yale University Talk Outline 1. The history of quantum mechanics 2. What is quantum mechanics? a. The postulates of quantum mechanics b. The weirdness of the postulates 3. Quantum weirdness in action a. The two slit experiment b. The EPR experiment 4. Interpretations of Quantum Mechanics a. The Copenhagen Interpretation b. The Neorealist Interpretation c. The Many Worlds Interpretation 5. Philosophical Implications Classical mechanics is the mechanics of everyday objects like tables and chairs 1. An object in motion tends to stay in motion. 2. Force equals mass times acceleration 3. For every action there is an equal and opposite reaction. Sir Isaac Newton Classical mechanics reigned as the dominant theory of mechanics for centuries 1687 – Newton’s Philosophiae Mathematica 1788 – Lagrange’s Mecanique Analytique 1834 – Hamiltonian mechanics 1864 – Maxwell’s equations 1900 – Boltzmann’s entropy equation However, several experiments at the beginning of the 20th-century defied explanation The Ultraviolet Catastrophe The Stern-Gerlach Experiment Newtonian explanations for these phenomena were wildly insufficient The Hydrogen Spectrum ? Quantum mechanics was developed to explain these results and developed into the most successful physical theory in history Increasing weirdness 1900 – Planck’s constant 1913 – Bohr’s model of the atom 1925 – Pauli exclusion principle 1926 – Schrodinger equation 1948 – Feynmann’s path integral formulation 1954 – Everett’s many-world theory Although quantum mechanics applies to all objects, the effects of quantum mechanics are most noticeable only for very small objects How small is very small? 1 meter Looks classical 1 millimeter Looks classical 1 micrometer Looks classical 1 nanometer Looks quantum! Nonetheless, quantum mechanics is still very important. How important is very important? Without quantum mechanics: Many biological reactions would not occur. Life does not exist Chemical bonding would be impossible. All molecules disintegrate All atoms would be unstable. Universe explodes Neil Shenvi’s dissertation title: Vanity of Vanities, All is Vanity Minimal consequences Talk Outline 1. The history of quantum mechanics 2. What is quantum mechanics? a. The postulates of quantum mechanics b. The weirdness of the postulates 3. Quantum Weirdness in action a. The two slit experiment b. The EPR experiment 4. Interpretations of Quantum Mechanics a. The Copenhagen Interpretation b. The Neorealist Interpretation c. The Many Worlds Interpretation 5. Philosophical Implications The laws of quantum mechanics are founded upon several fundamental postulates The Fundamental Postulates of Quantum Mechanics: Postulate 1: All information about a system is provided by the system’s wavefunction. Postulate 2: The motion of a nonrelativistic particle is governed by the Schrodinger equation Postulate 3: Measurement of a system is associated with a linear, Hermitian operator Postulate 1: All information about a system is provided by the system’s wavefunction. ( x) Pr( x ) x x Interesting facts about the wavefunction: 1. The wavefunction can be positive, negative, or complex-valued. 2. The squared amplitude of the wavefunction at position x is equal to the probability of observing the particle at position x. 3. The wave function can change with time. 4. The existence of a wavefunction implies particle-wave duality. The Weirdness of Postulate 1: Quantum particles are usually delocalized, meaning they do not have a well-specified position Classical particle Quantum particle Position = x Wavefunction = (x) The particle is here. With some high probability, the particle is probably somewhere around here The Weirdness of Postulate 1: At a given instant in time, the position and momentum of a particle cannot both be known with absolute certainty Classical particle Quantum particle Wavefunction = (x) Hello, my name is: Classical particle my position is 11.2392…Ang my momentum is -23.1322… m/s “I can tell you my exact position, but then I can’t tell you my momentum. I can tell you my exact momentum, but then I can’t tell you my position. I can give you a pretty good estimate of my position, but then I have to give you a bad estimate of my momentum. I can…” ? ?? ? This consequence is known as Heisenberg’s uncertainty principle The Weirdness of Postulate 1: a particle can be put into a superposition of multiple states at once Classical elephant: Valid states: Quantum elephant: Valid states: Gray Gray Multicolored Multicolored + Gray AND Multicolored Postulate 2: The motion of a nonrelativistic particle is governed by the Schrödinger equation i (t ) Hˆ (t ) t Time-dependent S.E.: Time-dependent S.E.: 2 2m dx 2 Molecular S.E.: d 2 Ĥ E ˆ V ( x ) ( x ) E ( x) Interesting facts about the Schrödinger Equation: 1. It is a wave equation whose solutions display interference effects. 2. It implies that time evolution is unitary and therefore reversible. 3. It is very, very difficult to solve for large systems (i.e. more than three particles). The Weirdness of Postulate 2: A quantum mechanical particle can tunnel through barriers rather than going over them. Classical ball Classical ball does not have enough energy to climb hill. Quantum ball Quantum ball tunnels through hill despite insufficient energy. This effect is the basis for the scanning tunneling electron microscope (STEM) The Weirdness of Postulate 2: Quantum particles take all paths. Classical mouse Quantum mouse Classical particles take a single path specified by Newton’s equations. The Schrodinger equation indicates that there is a nonzero probability for a particle to take any path This consequence is stated rigorously in Feymnann’s path integral formulation of quantum mechanics Postulate 3: Measurement of a quantum mechanical system is associated with some linear, Hermitian operator Ô. Oˆ Oˆ Oˆ dx * ( x) Oˆ ( x)( x) Interesting facts about the measurement postulate: 1. It implies that certain properties can only achieve a discrete set of measured values 2. It implies that measurement is inherently probabilistic. 3. It implies that measurement necessarily alters the observed system. The Weirdness of Postulate 3: Even if the exact wavefunction is known, the outcome of measurement is inherently probabilistic Classical Elephant: Quantum Elephant: Before measurement or After measurement For a known state, outcome is deterministic. For a known state, outcome is probabilistic. The Weirdness of Postulate 3: Measurement necessarily alters the observed system Classical Elephant: Quantum Elephant: Before measurement After measurement State of the system is unchanged by measurement. Measurement changes the state of the system. The Weirdness of Postulate 3: Properties are actions to be performed, not labels to be read Classical Elephant: Quantum Elephant: Position = here Color = grey Size = large Position: The ‘position’ of an object exists independently of measurement and is simply ‘read’ by the observer ‘Position’ is an action performed on an object which produces some particular result In other words, properties like position or momentum do not exist independent of measurement! (*unless you’re a neorealist…) Talk Outline 1. The history of quantum mechanics 2. What is quantum mechanics? a. The postulates of quantum mechanics b. The weirdness of the postulates 3. Quantum Weirdness in action a. The two slit experiment b. The EPR experiment 4. Interpretations of Quantum Mechanics a. The Copenhagen Interpretation b. The Neorealist Interpretation c. The Many Worlds Interpretation 5. Philosophical Implications The two-slit experiment is one of the classic validations of the predictions of quantum theory The Two Slit Experiment - the one slit experiment - the two slit experiment - the results - the classical “explanation” - the test - the quantum explanation - curioser and curioser Experiments on interference made with particle rays have given brilliant proof that the wave character of the phenomena of motion as assumed by the theory does, really, correspond to the facts. -A. Einstein In the one-slit experiment, particles that pass through the single slit produce an image on the detector The One Slit Experiment Gaussian distribution of detected particles Detector Particle emitter Particles What happens if we use two slits instead of only one? If we use two slits, we might expect to obtain the sum of two single-slit distributions… The Two Slit Experiment Expected result: sum of two Gaussians Detector Particle emitter Particles Warning: the “expected result” presented by this slide is patently false …but in reality, we obtain an interference pattern. The Two Slit Experiment Actual result: interference pattern. Detector Particle emitter Particles Question: Is this a quantum phenomenon? A clever physicist might attempt to explain this result as the consequence of “crowd waves”… The Classical “Explanation” - Interference phenomena are caused by disturbances propagating through huge numbers of water particles Detector Large rock Large pond Warning: the “classical ‘explanation’” presented on this slide is patently false …but an even cleverer physicist can test this hypothesis by configuring the emitter to emit the particles one at a time The Two Slit Experiment Detector Particle emitter Result: Interference pattern remains! The quantum mechanical explanation is that each particle passes through both slits and interferes with itself The Quantum Explanation Superposition state + + Detector The wavefunction of each particle is a probability wave which produces a probability interference pattern when it passes through the two slits. If a measurement device is placed on one of the slits, then the interference pattern disappears Curioser and Curioser Measurement device + Detector The measurement device has collapsed the wavefunction, leading to a loss of interference Curioser and Curioser Wavefunction collapse! Measuring device + or Detector Quantum mechanics makes several revolutionary claims about the fundamental behavior of particles The claims of quantum mechanics: 1. Particles act like waves. Particles can interfere with themselves. 2. Particles do whatever they want. There is a non-zero probability of finding a particle essentially anywhere in the universe. 3. Measurement is inherently probabilistic. No supplemental knowledge will make measurement deterministic. Anyone who is not shocked by quantum mechanics has not understood it. -Niels Bohr Einstein was so shocked by these claims that he was convinced that quantum mechanics must be wrong Quantum mechanics is: 1. Incomplete 2. Incorrect 3. Or both Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. Quantum theory says a lot, but does not really bring us any closer to the secret of the Old One. I, at any rate, am convinced that He does not throw dice. - A. Einstein Quantum Mechanics: Real Black Magic Calculus. - A. Einstein To call attention to the problems with quantum mechanics, Einstein devised a brilliant thought experiment The EPR Experiment - elements of reality - the thought experiment - the thought results - the Bell Inequality - the real experiment - the real results - the quantum conclusion Earth Mars I still do not believe that the statistical method of the Quantum Theory is the last word, but for the time being I am alone in my opinion. - A. Einstein The EPR paper asked the question “what does it mean for a theory to be complete”? Elements of Reality A. Einstein, B. Podolsky, N. Rosen. Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Phys. Rev. 47, 1935, 777-780. 1. A theory is complete if “every element of the physical reality must have a counterpart in the physical theory.” 2. “If, without in any way disturbing the system, we can predict with certainty … the value of a physical quantity, then there exists an element of reality (emphasis added) corresponding to this physical quantity.” In the hypothetical experiment, two particles are first placed in an entangled state The Thought Experiment 1. Create a valid two particle quantum state like: | = |HT + |TH Particle 1 Particle 2 The particles are then separated by an extremely large distance The Thought Experiment 2. Separate the particles by a spacelike distance. | = |H |T T + H Particle 1 Particle 2 Since the particles are very far apart (light years, say), relativity tells us that manipulating one particle cannot instantaneously affect the other particle. The state of particle 1 is measured, immediately yielding the state of the particle 2 The Thought Experiment 3. Measure Particle 1. | = |H |T T + H Particle 1 Particle 2 QM tells us that there is a 50-50 chance of Particle 1 being in state |H or |T. But as soon as we measure Particle 1, we immediately know the state of Particle 2! According to Einstein’s definition, the state of particle 2 was therefore an element of reality The Thought Experiment 4. Think about the definition of an element of reality. | = |H |T T + H Particle 1 Particle 2 In other words, we can determine the state of Particle 2, without disturbing Particle 2 in any way (by measuring Particle 1). Thus, the state of Particle 2 must correspond to an element of reality. The EPR paper concluded that QM does not predict all elements of reality and must be incomplete The Thought Results Conclusion of the EPR paper: Since it has been shown that quantum mechanics cannot predict all elements of reality with certainty, “we are forced to conclude that the quantum-mechanical description of reality given by wave functions is not complete.” HT TH TH HT In 1964, John Bell showed that Einstein’s claim of realism and the predictions of QM yield testable results. The Bell Inequality: Sx1Sv1 Sz1Sv1 Sz1Sv 2 S x1Sv 2 2 All local hidden variable theories S x1Sv1 S z1Sv1 S z1Sv 2 S x1Sv 2 2 2 Quantum mechanics | = |HT |TH Particle 1 Particle 2 By performing the Bell experiment, we can let nature tell us which is correct: Einstein’s hidden variable theory or quantum mechanics In the last few decades, the Bell experiment has been carried out numerous times using entangled photons… The Real Experiment | = |HT - |TH Photon 1 Paris Photon 2 London In Paris and in London, we measure each photon in a randomly chosen basis and collect a large amount of data. …and vindicates the predictions of quantum mechanics The Real Results Paris Measurement Result +1 -1 London Measurement Result +1 +1 +1 +1 … -1 -1 ... … +1 +1 -1 -1 ... Result: Too much correlation to be explained classically! Quantum mechanics wins! The Bell experiment demonstrates that local realism is false; either locality or realism must be jettisoned. The Bell experiment demands that we choose one (and only one) of the following principles can be valid: Locality - the principle that effects cannot propagate faster than the speed of light. c Realism - the principle that objects have properties independent of measurement. Warning: 4 out of 5 physicists recommend keeping locality. Talk Outline 1. The history of quantum mechanics 2. What is quantum mechanics? a. The postulates of quantum mechanics b. The weirdness of the postulates 3. Quantum Weirdness in action a. The two slit experiment b. The EPR experiment 4. Interpretations of Quantum Mechanics a. The Copenhagen Interpretation b. The Neorealist Interpretation c. The Many Worlds Interpretation 5. Philosophical Implications Given the weirdness of quantum mechanics, the obvious question is: why does reality appear so normal? QM tells me that this is reality: |HT - |TH x But all I ever see is: v There are three major interpretations of quantum mechanics: Copenhagen, neorealist, and many-worlds The Copenhagen interpretation: measurement induces wavefunction collapse Neorealist: hidden variables or pilot waves produce nonlocal phenomena Many-worlds: measurement leads to bifurcation of multiverse | The Copenhagen interpretation views the measurement device as distinct from a “normal” quantum system The Copenhagen (“orthodox”) Interpretation - N. Bohr Particles properties cannot be assigned values independent of measurement. Measurement collapses the wavefunction. “Observations not only disturb what is to be measured, they produce it. …” - P. Jordan | The major downside of the Copenhagen interpretation is that it fails to define what a “measurement device” is The Copenhagen (“orthodox”) Interpretation - N. Bohr Pros: The traditional textbook explanation (perhaps this is a con?). Cons: If universe is quantum mechanical, then so is the measurement device. Why does it behave differently? What is a “measurement device”? How do you define it? How is it related to human consciousness? What determines the outcome of a measurement if hidden variables are not allowed? The neorealist interpretation posits the existence of hidden variables or pilot waves that preserve realism The neorealist interpretation - A. Einstein Particle properties do have values independent of measurement, so the wavefunction never collapses. I recall that during one walk Einstein suddenly stopped, turned to me and asked whether I really believed that the moon exists only when I look at it. The rest of this walk was devoted to a discussion of what a physicist should mean by the term "to exist." - A. Pais But these hidden variables and pilot waves have never been detected and have suspicious properties The neorealist interpretation - A. Einstein Pros: Retains metaphysical realism. Particles really do exist. Cons: Retains metaphysical realism… at the cost of postulating undetectable, superluminescent pilot waves responsible for all of our quantum effects. Fiddles with causality: effects propagate backwards in time. The many-worlds interpretation asserts that whenever measurement occurs, the universe splits The Many Worlds Interpretation - H. Everett The wavefunction never collapses. The universe is really a multi-verse. |H |H + |T |H + |T |T Many-worlds is the most beautiful of the interpretations, but is also the most bizarre The Many Worlds Interpretation - H. Everett Pros: Uniform. No wavefunction collapse. No measurement problems. Cons: Postulates a infinite number of undetectable “alternate universes” with which we are currently in coherence. Removes possibility of actually knowing anything about the “real” universe. What determines which universe “we” are in? Quantum Russian Roulette. Talk Outline 1. The history of quantum mechanics 2. What is quantum mechanics? a. The postulates of quantum mechanics b. The weirdness of the postulates 3. Quantum Weirdness in action a. The two slit experiment b. The EPR experiment 4. Interpretations of Quantum Mechanics a. The Copenhagen Interpretation b. The Neorealist Interpretation c. The Many Worlds Interpretation 5. Philosophical Implications Quantum mechanics has many important implications for epistemology and metaphyics • • • • • The possibility of almost anything The absence of causality/determinism The role of human consciousness The limits of human knowledge The cognitive dissonance of reality First, quantum mechanics implies that almost no event is strictly impossible Classical physics 100% Quantum physics 99.99..% 1000000 -10 10 “the random nature of quantum physics means that there is always a minuscule, but nonzero, chance of anything occurring, including that the new collider could spit out man-eating dragons [emph. added]” - physicist Alvaro de Rujula of CERN regarding the Large Hadron Collider, quoted by Dennis Overbye, NYTimes 4/15/08 Second, quantum mechanics abrogates notions of causality and (human?) determinism Classical physics cause Quantum physics effect effect H + T H ? (MacBeth) (MacBeth) Physics no longer rigorously provides an answer to the question “what caused this event?” ? Third, within the Copenhagen interpretation, human consciousness appears to have a distinct role When does the wave function collapse during measurement? | Wavefunction….wavefunction…wavefunction…………particle! time “The very study of the physical world leads to the conclusion that the concept of consciousness is an ultimate reality” “it follows that the being with a consciousness must have a different role in quantum mechanics than the inanimate object” – physicist Eugene Wigner, Nobel laureate and founder of quantum mechanics Fourth, the fact that the wavefunction is the ultimate reality implies that there is a severe limit to human knowledge | KEEP OUT “…classical mechanics took to superficial a view of the world: it dealt with appearances. However, quantum mechanics accepts that appearances are the manifestation of a deeper structure (the wavefunction, the amplitude of the state, not the state itself)” – Peter Atkins Finally, quantum mechanics challenges our assumption that ultimate reality will accord with our natural intuition about what is reasonable and normal Classical physics Quantum physics I think it is safe to say that no one understands quantum mechanics. Do not keep saying to yourself, if you can possibly avoid it, 'But how can it possibly be like that?' … Nobody knows how it can be like that. – Richard Feynman What effect does QM have on the fundamental assumptions of science? 1. Rationality of the world 2. Efficacy of human reason 3. Metaphysical realism 4. Regularity of universe 5. Spatial uniformity of universe 6. Temporal uniformity of universe 7. Causality 8. Contingency of universe 9. Desacralization of universe 10. Methodological reductionism (Occam’s razor) 11. Value of scientific enterprise 12. Validity of inductive reasoning 13. Truthfulness of other scientists It makes things complicated… ? ? ? ? ? ? ? 1. Rationality of the world Weirdness of Quantum mechanics 2. Efficacy of human reason 3. Metaphysical realism Copenhagen interpretation 4. Regularity of universe 5. Spatial uniformity of universe EPR Experiment: Pick one (only) 6. Temporal uniformity of universe 7. Causality 8. Contingency of universe Many worlds interpretation 9. Desacralization of universe 10. Methodological reductionism (Occam’s razor) Neo-realism 11. Value of scientific enterprise 12. Validity of inductive reasoning 13. Truthfulness of other scientists Probabilistic nature of QM Concluding Quotes [QM] has accounted in a quantitative way for atomic phenomena with numerical precision never before achieved in any field of science. N. Mermin The more success the quantum theory has the sillier it looks. - A. Einstein I do not like it, and I am sorry I ever had anything to do with it. -E. Schrödinger Acknowledgements • • • • Dr. Christina Shenvi Prof. John Tully Prof. K. Birgitta Whaley Prof. Bob Harris Cartoons provided by: prescolaire.grandmonde.com and www.clker.com