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Heisenberg Time-Energy Uncertainty • The Heisenberg energy-time uncertainty principle is h DE Dt ³ 4p • The strong nuclear force has a very short range, around 10-15 m, which is about the distance light travels in 3.3x10-24 s. This force dies exponentially with distance. • Massive force carrying particles, pions, have masses around 140 MeV/c2, which is a mass energy = 140 MeV • The pions can wink into and out of existence for about 3.3x10-24 seconds by uncertainty, “embezzling 140 MeV at the energy bank”, so long as the debt is paid back quickly enough. Energy is conserved over longer times. Section 28.5 Heisenberg Time-Energy Uncertainty • Heisenberg energy-time uncertainty h DE Dt ³ 4p • The EM force has an “infinite” range (meaning 1/r2 form, this force is never quite “dead”.) This dependence is NOT exponential in r. • That’s because photons have zero rest mass, so it’s easy to create “soft” photons (low energy) by “embezzling” , which can last for longer times, therefore allowing longer range for these photons to reach out and carry the EM force to arbitrarily large distances. Section 28.5 Third Law of Thermodynamics • According to the Third Law of Thermodynamics, it is not possible to reach the absolute zero of temperature • In a classical kinetic theory picture, the speed of all particles would be zero at absolute zero • There is nothing in classical physics to prevent that • In quantum theory, the Heisenberg uncertainty principle indicates that the uncertainty in the speed of a particle cannot be zero • Quantum “zero point energy” -- can’t be tapped, used • The uncertainty principle provides a justification of the third law of thermodynamics Section 28.5 Quantum Tunneling • According to classical physics, an electron trapped in a box cannot escape • A quantum effect called tunneling allows an electron to escape under certain circumstances • Quantum theory allows the electron’s wave function to penetrate a short distance into the Section 28.6 wall Tunneling, cont. • The wave function extends a short distance into the classically forbidden region • According to Newton’s mechanics, the electron must stay completely inside the box and cannot go into the wall • If two boxes are very close together so that the walls between them are very thin, the wave function can extend from one box into the next box • The electron has some probability for passing through the wall • This probability dies exponentially fast with increase of the wall thickness Section 28.6 Scanning Tunneling Microscope • A scanning tunneling microscope (STM) operates by using tunneling • A very sharp tip is positioned near a conducting surface • If the separation is large, the space between the tip and the surface acts as a barrier for electron flow Scanning Tunneling Microscope, cont. • The barrier is similar to a wall since it prevents electrons from leaving the metal • If the tip is brought very close to the surface, an electron may tunnel between them • This produces a tunneling current • By measuring this current as the tip is scanned over the surface, it is possible to construct an image of how atoms are arranged on the surface • The tunneling current is highest when the tip is closest to an atom Section 28.6 STM Image Electric fields from the tip can also manipulate individual atoms! Section 28.6 STM, final • Tunneling plays a dual role in the operation of the STM • The detector current is produced by tunneling • Without tunneling there would be no image • Tunneling is needed to obtain high resolution • • • • The tip is very sharp, but still has some rounding The electrons can tunnel across many different paths • See fig. 28.17 C The majority of electrons that tunnel follow the shortest path – more distant paths are exponentially suppressed The STM can form images of individual atoms even though the tip is larger than the atoms Section 28.6 Wave-like Properties of Particles • The notion that the properties of both classical waves and classical particles are present at the same time is also called wave-particle duality • The possibility that all particles are capable of wavelike properties was first proposed by Louis de Broglie • De Broglie suggested that if a particle has a momentum p, its wavelength is h l= p • His doctoral thesis is said to have been only two pages long!! Probably an apocryphal story. Section 28.3 QUIZ • An electron with a KE of 100,000 eV has momentum p with pc = 0.33 MeV. What is its DeBroglie wavelength, λ = h/p, in meters? • helpful: hc = 2 x 10-25 J m = 1.25 x 10-12 MeV m • A) 9.0 nm • B) 5.5 μm • C) 3.3x10-24 m • D) 7.5x10-15 m • E) 3.8x10-12 m Color Vision • A complete understanding of human vision depends on the wave theory and the particle theory of light • Light is detected in the retina at the back of the eye • The retina contains rods and cones • Both are light-sensitive cells • When the cells absorb light, they generate an electrical signal that travels to the brain • Rods are more sensitive to low light intensities and are used predominately at night • Cones are responsible for color vision Section 28.7 Rods • About 10% of the light that enters your eye reaches the retina • The other 90% is reflected or absorbed by the cornea and other parts of the eye • The absorption of even a single photon by a rod cell causes the cell to generate a small electrical signal • The signal from an individual cell is not sent directly to the brain • The eye combines the signals from many rod cells before passing the combination signal along the optic nerve • About 50 photons within about 0.1 s must be received for the brain to know light as actually arrived Section 28.7 Cones • The retina contains three types of cone cells • They respond to light of different colors • The brain deduces the color of light by combining the signals from all three types of cones • Each type of cone cell is most sensitive to a particular frequency. Section 28.7 Cones, cont. • The explanation of color vision depends on two aspects of quantum theory • Light arrives at the eye as photons whose energy depends on the frequency of the light • When an individual photon is absorbed by a cone, the energy of the photon is taken up by a pigment molecule within the cell • The energy of the pigment molecule is quantized • Photon absorption is possible because the difference in energy levels in the various pigments match the energy of the photon Cones, final Ditto for the other two colors • In the simplified energy level diagram (A), a pigment molecule can absorb a photon only if the photon energy precisely matches the pigment energy level • More realistically (C), a range of energies is absorbed • Quantum mechanics and the existence of quantized energies for both photons and pigment molecules are necessary for color vision Section 28.7 The Nature of Quanta • The principles of conservation of energy, momentum, and charge are believed to hold true under all circumstances, including in the quantum regime. • Forces are carried by particles (photons (EM force), weak force bosons W and Z, and strong force bosons (gluons) or, at a composite level, by “pions” • The uncertainty theory of force carrying particles requires very brief, temporary, fluctuations in Energy that appear to violate energy conservation -- but rather quickly the fluctuations return to a state of conserved energy. Section 28.8 Puzzles About Quanta • The relation between gravity and quantum theory is a major unsolved problem • No one knows how Planck’s constant enters the theory of gravitation or what a quantum theory of gravity looks like • If there were very heavy particles, weighing 1016 times as much as protons and with one unit of electric charge, the EM and Gravity forces would be equal. That would be a kind of unification, but still not a quantum theory of gravity. Section 28.8 Puzzles About Quanta • String Theory in 10 dimensions (six extra spatial dimensions, each curled up in tiny tiny loops) does deal with gravity as well as the other forces of nature. String theory even “unifies” the four forces of nature, in a certain sense.[Grav., E&M, Strong and Weak Nuclear Forces] • But the gravity of String Theory is still not quantized like the other three forces. Section 28.8 Puzzles About Quanta • Why are there two kinds of charge? • Why do the positive and negative charges come in the exact same-size quantized units? • Qe=-Qp is measured to be the same to closer than one part in 1020 H2 molecules are exactly neutral, to better than 1.6x10-39 Coulombs. • Experiment: flow of H2 gas from large insulated bottle. Bottle does not charge up, no electric current has flowed (within errors of measurement; there always is measurement error, at some level) Puzzles About Quanta • Also, a net charge on the H atom would cause matter in the universe to repel itself, to expand even faster than observed. Given that the EM force is 1038 times bigger than the Gravity force, in H atoms, this again implies a charge imbalance < 10-20 Puzzles About Quantum Mechanics (QM) • What new things happen in the regime where the micro- and macroworlds meet? • Actually, small silicon “beams” vibrating, with the position of the beam sensed in silicon, in the right experimental setup are observed to be in “quantum states” • Also, quantum computing research is beginning to observe quantum coherence in small but “macroscopic” systems of many kinds • Puzzle: How do QM and the Uncertainty Principle apply to living things? Puzzles About Quantum Mechanics (QM) • Schrodinger’s cat (from the early days of quantum theory): a cat, a flask of poison, and a radioactive source are placed in a sealed box. If an internal monitor detects radioactivity (i.e. a single atom decaying), the flask is shattered, releasing the poison that kills the cat. The Copenhagen interpretation of quantum mechanics implies that after a while, the cat is simultaneously alive and dead. Yet, when one looks in the box, one sees the cat either alive or dead, not both alive and dead. This poses the question of when exactly quantum superposition ends and reality collapses into one possibility or the other. Puzzles About Quantum Mechanics (QM) • More on QM, the Uncertainty Principle, and living things? • Does the Uncertainty Principle have anything to do with “free will” in humans? (Is free will just an illusion?) • The probabilistic nature of quantum mechanics makes the future essentially unpredictable, which would seem to be a necessary condition for free will • But is it a sufficient condition for free will? • Yogi Berra: “Making predictions is difficult, especially about the future.”