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Quantum Mechanics: what is it and why is it interesting? Dr. Neil Shenvi Department of Chemistry Yale University

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Talk Outline 1. The history of quantum mechanics 2. The explanatory power of quantum mechanics 3. What is quantum mechanics? a.The postulates of quantum mechanics b.The weirdness of the postulates 4. The usefulness of quantum mechanics 5. The philosophy of quantum mechanics

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Classical mechanics is the mechanics of everyday objects like tables and chairs Sir Isaac Newton 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.

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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

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However, several experiments at the beginning of the 20 th -century defied explanation The Ultraviolet Catastrophe The Hydrogen Spectrum The Stern-Gerlach Experiment Newtonian explanations for these phenomena were wildly insufficient ?

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The Stern-Gerlach experiment involved passing atomic “magnets” through a magnetic field + - ? ? ? ? ? Ag atoms Question 1. How many beams do we expect to emerge from the magnet? A. 1 B.2 C.3 D. A diffuse cloud Exactly two well-defined beams emerge from the magnet!

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Quantum mechanics was developed to explain these results and developed into the most successful physical theory in history 1900 – Planck’s constant 1913 – Bohr’s model of the atom 1925 – Pauli exclusion principle 1926 – Schrodinger equation 1948 – Feynmann’s path integral formulation Increasing weirdness 1954 – Everett’s many-world theory

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Quantum mechanics applies to all objects, no matter how big or small Quantum mechanics (atoms and molecules) Classical mechanics (large molecules) Thermodynamics (collections of molecules) Mechanical Engineering (macroscopic objects) Penmanship (letters) Spelling (words) Grammar (sentences) Creative writing (books)

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However, the effects of quantum mechanics are most noticeable only for very small objects How small is very small? 1 meterLooks classical 1 micrometerLooks classical 1 millimeterLooks classical 1 nanometerLooks quantum!

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Nonetheless, quantum mechanics is still very important. How important is very important? Without quantum mechanics: All atoms would be unstable. Universe explodes Chemical bonding would be impossible. All molecules disintegrate Many biological reactions would not occur. Life does not exist Neil Shenvi’s dissertation title: Vanity of Vanities, All is Vanity Minimal consequences

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Talk Outline 1. The history of quantum mechanics 2. The explanatory power of quantum mechanics 3. What is quantum mechanics? a.The postulates of quantum mechanics b.The weirdness of the postulates 4. The usefulness of quantum mechanics 5. The philosophy of quantum mechanics

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Quantum mechanics is essential for understanding fundamental concepts in physics, chemistry, and biology Decay of nuclear isotopes Stability of the atom The periodic table Chemical bonding Photoabsorption spectra

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Classical puzzle #1: How can nuclear decay ever occur at room temperature? E R R Barrier Height = ? Question 2. What is the approximate activation energy for nuclear decay? A. 10 kcal / mol B.100 kcal / mol C.100,000 kcal / mol D.10,000,000 kcal / mol Pu U + He 2+ 238 94 234 92 4 2 Most chemical reactions have an activation energy of < 20 kcal/mol !

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Quantum mechanical tunneling is responsible for spontaneous fission E R R U Th + He 2+ 238 92 234 90 4 2 Quantum tunneling Spontaneous fission through quantum tunneling is the basis for nuclear power, nuclear weapons (unfortunately), smoke detectors, and artificial heart generators.

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Classical puzzle #2: why are atoms stable? Bohr (i.e. “planetary”) model of the atom Problem 1: why don’t electrons fall into the nucleus? Problem 2: why don’t atoms disintegrate on collision?

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Quantum mechanics shows that electrons can only populate discrete orbitals around the nucleus Quantum atom Atom collapse is prohibited Atoms are stable to collision

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Classical puzzle #3: Where does the structure of the periodic table come from? Quantum solutions to electrons confined to a sphere Periodic table of elements * * Classical mechanics offers no explanation for the general structure of the periodic table Quantum mechanics yields the general structure of the periodic table from a very simple model of atoms …

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Classical puzzle #4: Why do atoms form chemical bonds? “Classical” H 2 moleculeQuantum H 2 molecule There are no stable solutions to the four-body problem in Newtonian mechanics Overlap of the hydrogen 1s orbitals stabilizes the H 2 molecule Question 3. Hydrogen molecule (H 2 ) is held together by: A.Attraction between the two H nuclei B.The decreased kinetic energy of the electrons C.Repulsive forces between the electrons D.Glue

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Classical puzzle #5: Why do molecules absorb light only at particular frequencies? Chlorophyll A

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Quantum mechanics predicts that molecules have discrete energy levels, leading to discrete absorption frequencies Chlorophyll A E Photon absorption

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In theory, quantum mechanics allows us to predict the properties of atoms and molecules from scratch, without ever appealing to experiment Quantum mechanics allows the prediction of: Atomic properties: ionization energy, UV absorption spectra Molecular structure: bond lengths, bond angles, dissociation energies Spectral features: infrared absorption, microwave absorption Chemical features: rate constants, enthalpy of reaction Biochemical features (often only in theory): crystal structure binding affinity The caveat: the larger the system, the more difficult the calculations become.

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Talk Outline 1. The history of quantum mechanics 2. The explanatory power of quantum mechanics 3. What is quantum mechanics? a.The postulates of quantum mechanics b.The weirdness of the postulates 4. The usefulness of quantum mechanics 5. The philosophy of quantum mechanics

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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

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Postulate 1: All information about a system is provided 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 can change with time. 4. The existence of a wavefunction implies particle-wave duality.

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The Weirdness of Postulate 1: Quantum particles are usually delocalized, meaning they do not have a well-specified position Classical particleQuantum particle The particle is here. With some high probability, the particle is probably somewhere around here Position = x Wavefunction = (x)

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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 particleQuantum 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…” ? ? ? ? Question 4. What is the name of the law that limits our knowledge of the simultaneous position and momentum of particles? A.Pauli’s exclusion principle B.Planck’s law C.The Heisenberg uncertainty principle D.The Dirac equation

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The Weirdness of Postulate 1: a particle can be put into a superposition of multiple states at once Classical elephant: Valid states: Quantum elephant: Gray Multicolored GrayMulticolored Valid states: + Gray AND Multicolored

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Postulate 2: The motion of a nonrelativistic particle is governed by the Schrödinger equation 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). Time-dependent S.E.: Molecular S.E.:

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

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The Weirdness of Postulate 2: Quantum particles take all paths. This consequence is stated rigorously in Feymnann’s path integral formulation of quantum mechanics Classical mouseQuantum 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

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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 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.

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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 After measurement For a known state, outcome is probabilistic. For a known state, outcome is deterministic. or

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The Weirdness of Postulate 3: Measurement necessarily alters the observed system Classical Elephant:Quantum Elephant: Before measurement After measurement Measurement changes the state of the system. State of the system is unchanged by measurement.

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The Weirdness of Postulate 3: Properties are actions to be performed, not labels to be read Classical Elephant:Quantum Elephant: The ‘position’ of an object exists independently of measurement and is simply ‘read’ by the observer Position = here Color = grey Size = large ‘Position’ is an action performed on an object which produces some particular result Position: In other words, properties like position or momentum do not exist independent of measurement! (*unless you’re a neorealist…)

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Talk Outline 1. The history of quantum mechanics 2. The explanatory power of quantum mechanics 3. What is quantum mechanics? a.The postulates of quantum mechanics b.The weirdness of the postulates 4. The usefulness of quantum mechanics 5. The philosophy of quantum mechanics

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Many technologies depend crucially on quantum mechanical effects NMR spectroscopy Scanning tunneling microscope Quantum cryptography Quantum computation

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The quantized character of nuclear spin is the basis of NMR and MRI technology O H H H H B 2.09.3ppm H H H H The energy difference between the spin up and spin down states of protons is what enables NMR spectrometers to differentiate between different types of hydrogen

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Electron tunneling between tip and sample is the basis for the scanning tunneling electron microscope Images originally created by IBM. tip sample tunneling e-e- tip z E

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The measurement theorem enables secure quantum cryptography by guaranteeing that eavesdropping is detectable 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. AliceBobEavesdropper To steal the data, Eve must measure the quantum particles. But since measurement alters the state of the particle, her presence can always be detected.

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A quantum computer can perform certain operations much faster than any classical computer Smith, A555-1032 Smith, A B555-4023 Smith, A S555-9192 Smith, Amos555-1126 Smith, B A555-7287 Smith, Bob555-1102 Smith, Bob L555-1443 Smith, Cynthia555-3739 Smith, David 555-4487 Smith, A555-1032 Smith, A B555-4023 Smith, A S555-9192 Smith, Amos555-1126 Smith, B A555-7287 Smith, Bob555-1102 Smith, Bob L555-1443 Smith, Cynthia555-3739 Smith, David 555-4487 Searching an unordered database: Factoring large numbers 16238476016501762387610762691722612171239872103974621876187 12073623846129873982634897121861102379691863198276319276121 = ? x ? whimper 16238476016501762387610762691722612171239872103974621876187 12073623846129873982634897121861102379691863198276319276121 = ? x ? 162384760165011238798712 X 87230987183740987123761

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Talk Outline 1. The history of quantum mechanics 2. The explanatory power of quantum mechanics 3. What is quantum mechanics? a.The postulates of quantum mechanics b.The weirdness of the postulates 4. The usefulness of quantum mechanics 5. The philosophy of quantum mechanics

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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

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First, quantum mechanics implies that almost no event is strictly impossible Classical physicsQuantum physics 99.99..% 100% 10 -10 1000000 “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

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Second, quantum mechanics abrogates notions of causality and (human?) determinism Classical physicsQuantum physics cause effect ? + Physics no longer rigorously provides an answer to the question “what caused this event?” (MacBeth) ? HHT

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Third, within the Copenhagen interpretation, human consciousness appears to have a distinct role When does the wave function collapse during measurement? | time Wavefunction….wavefunction…wavefunction…………particle! “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

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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 too 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

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Finally, quantum mechanics challenges our assumption that ultimate reality will accord with our natural intuition about what is reasonable and normal Classical physicsQuantum 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

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What effect does QM have on the fundamental assumptions of the 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

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It makes things complicated… 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 Weirdness of Quantum mechanics ? ? ? ? Copenhagen interpretation EPR Experiment: Pick one (only) Neo-realism Many worlds interpretation ? ? ? Probabilistic nature of QM

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Concluding Quotes The more success the quantum theory has the sillier it looks. - A. Einstein [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

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Acknowledgements Dr. Christina Shenvi Prof. John Tully Prof. K. Birgitta Whaley Prof. Bob Harris Cartoons provided by: prescolaire.grandmonde.com and www.clker.com

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