weirdness

The Weirdness of Quantum Mechanics : The Weirdness of Quantum Mechanics Neil Shenvi Whaley Group Department of Chemistry


Talk Outline : Talk Outline 1. Introduction to Quantum Mechanics a. The postulates of quantum mechanics b. The weirdness of the postulates 2. Quantum Weirdness in action a. The two slit experiment b. Quantum cryptography c. Quantum computation d. The EPR experiment 3. Interpretations of Quantum Mechanics a. The Copenhagen Interpretation b. The Neorealist Interpretation c. The Many Worlds Interpretation


Classical Mechanics: fact or fiction : Classical Mechanics: fact or fiction Sir Isaac Newton 1. An object in motion tends to stay in motion. 2. Force = mass times acceleration 3. For every action there is an equal and opposite reaction. Classical mechanics is “everyday” mechanics.


Quantum Mechanics: Why? : Quantum Mechanics: Why? Classical mechanics explains most of what we usually observe in nature, which is why it lasted for centuries. But it could not explain the results of certain experiments. Quantum mechanics was developed to explain these results. The Ultraviolet Catastrophe The Hydrogen Spectrum The Stern-Gerlach Experiment


Quantum Mechanics: When? : Quantum Mechanics: When? But small objects obey the laws of quantum mechanics. Large objects obey the laws of classical mechanics.


Quantum Mechanics: When? : Quantum Mechanics: When? How small is Small? 1 meter Classical mechanics 1 micrometer Classical mechanics 1 millimeter Classical mechanics 1 nanometer Quantum mechanics But quantum mechanics is very important!


Quantum Mechanics: When? : Quantum Mechanics: When? How important is Important? Without quantum mechanics: All atoms would be unstable. Chemical bonding would be impossible. Many biological reactions would not occur. Neil Shenvi’s dissertation title: Vanity of Vanities, All is Vanity Universe implodes Life does not exist Minimal consequences All molecules dissociate


Quantum Mechanics: What? : Quantum Mechanics: What? 1. The wavefunction postulate 3. The measurement postulate 2. The Schrödinger Equation The Fundamental Postulates of Quantum Mechanics


Postulate 1: The Wavefunction : Postulate 1: The Wavefunction Postulate 1: All information about a system is given by the system’s wavefunction. 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 evolves with time. 4. The existence of a wavefunction implies particle-wave duality.


The Weirdness of Postulate 1 : The Weirdness of Postulate 1 Variables versus Wavefunctions Classical particle: Quantum particle x x v


The Weirdness of Postulate 1 : The Weirdness of Postulate 1 Variables versus Wavefunctions “Classical Hydrogen”: Quantum Hydrogen Bohr model: the electron orbits the nucleus at a set radius Quantum model: an electron cloud surrounds the nucleus. Question for hecklers: How can it be a cloud if there is only one electron? (Warning: not real)


The Weirdness of Postulate 1 : The Weirdness of Postulate 1 Variables versus Wavefunctions Classical coin: Quantum coin Two values: H V Two values: Possible states of quantum coin: Possible states of quantum coin: … These states are called “superpositions”


The Weirdness of Postulate 1 : The Weirdness of Postulate 1 The Heisenberg Uncertainty Principle: It is impossible to know all properties of a particle simultaneously. Classical elephant: The elephant is definitely big and gray. Quantum elephant: The elephant is definitely big. The elephant is definitely gray. or


The Weirdness of Postulate 1 : The Weirdness of Postulate 1 The Heisenberg Uncertainty Principle: It is impossible to know all properties of a particle simultaneously. Classical particle: Quantum particle x x v


The Weirdness of Postulate 1 : The Weirdness of Postulate 1 The Heisenberg Uncertainty Principle: It is impossible to know all properties of a particle simultaneously. Classical particle: Quantum particle x x v


The Weirdness of Postulate 1 : The Weirdness of Postulate 1 The Heisenberg Uncertainty Principle: It is impossible to know all properties of a particle simultaneously. Classical particle: Quantum particle x x v


Postulate 2: The Schrödinger Equation : Postulate 2: The Schrödinger Equation Postulate 2: The wavefunction of a system obeys the Schrödinger Equation: Interesting facts about the Schrödinger Equation: 1. It is linear. 2. It implies that time evolution is unitary. 3. It is difficult to solve for large systems.


The Weirdness of Postulate 2 : The Weirdness of Postulate 2 Tunneling: A quantum mechanical particle can tunnel through barriers rather than going over them. Classical ball Quantum ball Classical ball does not have enough energy to climb hill. Quantum ball tunnels through hill despite lack of energy.


The Weirdness of Postulate 2 : The Weirdness of Postulate 2 Quantum trajectories: quantum particles take all paths. (See Feynman path integral formulation of QM.) Classical mouse Quantum mouse Takes one path. Takes all paths, even forbidden ones!


Postulate 3: Measurement : Postulate 3: Measurement Postulate 3: Measurement of a quantum mechanical system is associated with some linear, Hermitian operator Ô. Interesting facts about the measurement postulate: 1. It implies that measurement is inherently probabilistic. 2. It implies that measurement necessarily alters the observed system.


The Weirdness of Postulate 3 : The Weirdness of Postulate 3 Measurement: Deterministic versus probabilistic Classical Elephant: Quantum Elephant: Before measurement After measurement For a known state, outcome is probabilistic. For a known state, outcome is deterministic. or


The Weirdness of Postulate 3 : The Weirdness of Postulate 3 Measurement: Objective versus destructive Classical Elephant: Quantum Elephant: Before measurement After measurement Measurement alters state. State is unchanged by measurement.


Quantum Weirdness in Action : Quantum Weirdness in Action 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


The Two Slit Experiment : The Two Slit Experiment What happens if we use two slits instead of only one? The One Slit Experiment


The Two Slit Experiment : The Two Slit Experiment The Two Slit Experiment


The Two Slit Experiment : The Two Slit Experiment Actual result: interference pattern. Is this a quantum phenomenon? The Results


The Two Slit Experiment : The Two Slit Experiment Explanation: This is just a “crowd wave” phenomenon like waves in water. The Classical “Explanation”


The Two Slit Experiment : The Two Slit Experiment Emit particles one at a time. The Test


The Two Slit Experiment : The Two Slit Experiment Particle is really described by a wavefunction which acts like a probability wave. This wave interferes with itself. The Quantum Explanation


The Two Slit Experiment : The Two Slit Experiment Result: Interference pattern disappears! Why? Curioser and Curioser


The Two Slit Experiment : The Two Slit Experiment Result: Interference pattern disappears! Why? Curioser and Curioser


Quantum Consequences : Quantum Consequences 0 1 1 0 1 0 1 1 0 1  Alice Bob Eve the eavesdropper  Eavesdropping on classical information goes undetected Because measurement alters quantum states, eavesdropping on quantum information can be detected. Quantum Cryptography


Quantum Cryptography : Quantum Cryptography The no cloning theorem Classical information can be copied, but quantum information cannot.


Quantum Cryptography : Quantum Cryptography Quantum key distribution Problem: Alice and Bob want to share a secret “key”, (i.e. a string of bits), but Eve the eavesdropped is listening. 0 1 1 0 1 0 1 1 0 1 Alice Bob Eve 0 1 1 0 1 Solution: use quantum information to encode the bits.


Quantum Cryptography : Quantum Cryptography Quantum key encoding


Quantum Cryptography : Quantum Cryptography Eve’s dilemma H R L H V L H L Which basis should Eve use to measure the qubits? Eve must choose either Basis A: |H, |V or Basis B: |R, |L


Quantum Cryptography : Quantum Cryptography Detecting eavesdropping Alice and Bob compare bases over open channel B B A A A B A A A B B A A B A B When their bases don’t match, they discard that bit. At no point does Alice reveal her key, or Bob his result.


Quantum Cryptography : Quantum Cryptography Detecting eavesdropping Now they pick a few of the remaining bits and compare their results.


Quantum Cryptography : Quantum Cryptography Detecting eavesdropping   It can be shown that no strategy Eve employs can prevent Alice and Bob from detecting her eavesdropping. So quantum key distribution protocols can provide a guarantee for secure key distribution. C.H. Bennett and G. Brassard "Quantum Cryptography: Public Key Distribution and Coin Tossing", Proceedings of IEEE International Conference on Computers Systems and Signal Processing, Bangalore India, December 1984, pp 175-179.


Quantum Consequences : Quantum Consequences Because quantum particles can be in many states at once, we can build quantum computers which are much faster than normal computers. Smith, A 555-1032 Smith, A B 555-4023 Smith, A S 555-9192 Smith, Amos 555-1126 Smith, B A 555-7287 Smith, Bob 555-1102 Smith, Bob L 555-1443 Smith, Cynthia 555-3739 Smith, David 555-4487 Smith, Ernest 555-1271 Smith, A 555-1032 Smith, A B 555-4023 Smith, A S 555-9192 Smith, Amos 555-1126 Smith, B A 555-7287 Smith, Bob 555-1102 Smith, Bob L 555-1443 Smith, Cynthia 555-3739 Smith, David 555-4487 Smith, Ernest 555-1271 Example: Find the number 555-1422 in the phone book Classical computers must search sequentially Quantum computers can search all the entries at the same time. Quantum Computation


Quantum Computation : Quantum Computation Quantum Search Imagine we are looking for the solution to a problem with N possible solutions. We have a black box that can check whether a given answer is correct. 78 Question: What number between 1 and 100 am I thinking of? Black box No 3 Black box Yes


Quantum Computation : Quantum Computation Quantum Search The best a classical computer can do on average is N/2 queries. ... Black box 1+2+3+... no+no+yes+no+... Classical computer Quantum computer Using Grover’s algorithm, a quantum computer can find the answer in N queries. Superposition over all N possible inputs.


Quantum Computation : Quantum Computation Quantum Factoring Find the factors of: 57 3 x 19 Find the factors of: 1623847601650176238761076269172261217123987210397462187618712073623846129873982634897121861102379691863198276319276121 whimper All known algorithms for factoring an n-bit number on a classical computer take time proportional to O(n!). But Shor’s algorithm for factoring on a quantum computer takes time proportional to O(n2 log n).


Slide44 : # bits 1024 2048 4096 factoring in 2006 105 years 5x1015 years 3x1029 years factoring in 2024 38 years 1012 years 7x1025 years factoring in 2042 3 days 3x108 years 2x1022 years Significance of Quantum Factorization: with a classical computer # bits 1024 2048 4096 # qubits 5124 10244 20484 # gates 3x109 2X1011 X1012 factoring time 4.5 min 36 min 4.8 hours with potential quantum computer (e.g., clock speed 100 MHz) R. J. Hughes, LA-UR-97-4986


The Scandalous Claims of QM : The Scandalous Claims of QM Are the claims of quantum mechanics really so revolutionary?


Objections to Quantum Mechanics : Quantum mechanics is: 1. Incomplete 2. Incorrect 3. Or both Quantum Mechanics: Real Black Magic Calculus. - A. Einstein Einstein was shocked. Objections to Quantum Mechanics 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 Weirdness in Action : Quantum Weirdness in Action The EPR Experiment - elements of reality - the thought experiment - the thought results - the Bell Inequality - the real experiment - the real results - the quantum conclusion 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 Earth Mars


The EPR Experiment : The EPR Experiment Elements of Reality 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.” 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.”


The EPR Experiment : The EPR Experiment The Thought Experiment 1. Create a valid two particle quantum state like: | = |HV - |VH Particle 1 Particle 2


The EPR Experiment : The EPR Experiment The Thought Experiment 2. Separate the particles by a spacelike distance. Since the particles are very far apart (light years, say), relativity tells us that manipulating one particle cannot instantaneously affect the other particle. | = |H V - |V H Particle 1 Particle 2


The EPR Experiment : The EPR Experiment The Thought Experiment 3. Measure Particle 1. QM tells us that there is a 50-50 chance of Particle 1 being in state |H or |V. But as soon as we measure Particle 1, we immediately know the state of Particle 2! | = |H V - |V H Particle 1 Particle 2


The EPR Experiment : The EPR Experiment The Thought Experiment 4. Think about the definition of an element of reality. | = |H V - |V 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 Experiment : The EPR Experiment The Thought Results | = |H V - |V H Particle 1 Particle 2 But quantum mechanics cannot predict a priori the state of Particle 2 with certainty. It only gives us probabilities!


The EPR Experiment : The EPR Experiment 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.”


The EPR Experiment : The EPR Experiment The Bell Inequality In 1964, John Bell showed that Einstein’s claim of realism and the predictions of QM yield testable results.


The EPR Experiment : The EPR Experiment The Real Experiment Earth Mars Photon 1 Photon 2 | = |HV - |VH On Earth and on Mars, we measure each photon in a randomly chosen basis and collect a large amount of data.


The EPR Experiment : The EPR Experiment The Real Results +1 -1 +1 +1 -1 -1 ... +1 +1 +1 +1 -1 -1 … ... …


The EPR Experiment : The EPR Experiment The Quantum Conclusion Local realism is false. Choose one (and only one): Warning: 4 out of 5 physicists recommend keeping locality.


The Interpretations of QM : The Interpretations of QM Or “What happens to the wavefunction?” 1. The Copenhagen Interpretation 2. Neorealism 3. Many Worlds The fundamental question:


The Interpretations of QM : The Interpretations of QM The Copenhagen (“orthodox”) Interpretation - N. Bohr Measurement collapses the wavefunction. “Observations not only disturb what is to be measured, they produce it. …” - P. Jordan Particles properties cannot be assigned values independent of measurement.


The Interpretations of QM : The Interpretations of QM The Copenhagen (“orthodox”) Interpretation - N. Bohr Pros: Favored by the vast majority of physicists (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? What determines the outcome of a measurement if hidden variables are not allowed?


The Interpretations of QM : The Interpretations of QM The neorealist interpretation - A. Einstein Particle properties do have values independent of measurement, so 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


The Interpretations of QM : The Interpretations of QM 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 Interpretations of QM : The Interpretations of QM The Many Worlds Interpretation - H. Everett The wavefunction never collapses. The universe is really a multi-verse.


The Interpretations of QM : The Interpretations of QM 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.


Some Classical Scientific Axioms : Some Classical Scientific Axioms 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


Some Classical Scientific Axioms : Some Classical Scientific Axioms 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


Concluding Quotes : Concluding Quotes I think it is safe to say that no one understands quantum mechanics. - R. Feynman [QM] has accounted in a quantitative way for atomic phenomena with numerical precision never before achieved in any field of science. N. Mermin I do not like it, and I am sorry I ever had anything to do with it. -E. Schrödinger


Acknowledgements : Acknowledgements Christina Shenvi Prof. K. Birgitta Whaley Prof. Bob Harris Veritas Fellowship and the Wednesday Night Men’s Bible Study Cartoons provided by: prescolaire.grandmonde.com