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Quantum Mechanics and General Relativity Astronomy 315 Professor Lee Carkner Special Lecture Exercise #20 AGN Energy due to dropping Earth down black hole m = 5.97X1024 kg E = (0.1)(5.97X1024)(3X108)2 = Quasar luminosity of 1040 W (J/s) (1040 J/s)(60 s/min) = How many Earths per minute to power the quasar? (6X1041)/(5.37X1040) = Big and Small Quantum mechanics Atoms, electrons, photons, etc. General relativity Stars, galaxies, clusters, the universe, etc. Problems Each theory works well in its own realm Like with a black hole If you try to combine both theories, it doesn’t work Need a new “grand unified” theory that reconciles them Let us look at quantum mechanics and general relativity to see where we are right now Quantum Hypothesis The only way he could do it is if he thought of the emitted energy as being discrete instead of continuous Like rain instead of a river In 1905 Einstein (and others) realized that this is a fundamental rule What does “Quantum” Mean? Cannot have any value of the energy, only multiples of the smallest quantum Examples: You can play any note on a guitar, but only certain notes on a piano For example, electrons can only be in certain energy levels Photons The quantum of energy is called a photon Each photon has as energy = hf f is the frequency (in Hertz or 1/s) We can think of light as stream of particles, each with its own tiny amount of energy Wave-Particle Duality For example in diffraction experiments light passing through a narrow slit makes patterns like water waves passing through a narrow opening It just does! Light (and other sub-atomic particles) are their own thing de Broglie Wave What about electron (and other) particles? Every particle has a de Broglie wavelength that depends on its mass and speed but tiny particles (like electrons) have large enough de Broglie wavelengths to act wavelike Sub-atomic particles are not really particles (or waves) they just sometimes act like it The Jelly Bean Fallacy “When the revolutionary ideas of quantum physics were first coming out, people still tried to understand them in terms of oldfashioned ideas … But at a certain point the old-fashioned ideas would begin to fail, so a warning was developed that said, in effect, ‘Your old-fashioned ideas are no damn good …’ ” -- Richard Feynman The Bohr Model In the early 20th century atoms were understood by the planetary model The electrons should have been able to have any orbit and thus any energy, but in experiments it was found they had specific energies Electrons can only have specific states defined by a quantum number Explains line emission Interaction For example: but light is photons, which have energy, which will push on the particle Also, the precision of our seeing is based on the wavelength of light we use but shorter wavelengths of light have more energy and thus disturb the particle more Uncertainty We cannot know both the position of the particle and the momentum of the particle with the same accuracy Called the Heisenburg Uncertainty Principle We cannot have perfect information about the universe! Probability In the 19th century the universe was thought to be deterministic We now know that the universe is probabilistic For example, we can’t tell where exactly an electron is but we know the probability it might be in one place or another The Stochastic Man It doesn’t seem that way on our scale Einstein famously said, “God does not play dice with the universe.” but he was wrong! Quantum Tunneling We can’t say exactly where an electron is If we put the electron in a box, there is a high probability it is in the box and a very (very) low probability it is somewhere else The electron could, in effect, tunnel through solid material This has been observed experimentally The Quantum Universe Not as macroscopic objects For large particles and large numbers of particles the statistics are so good that everything seems deterministic Similar to how a casino can make money The Standard Model Quantum mechanics only is important for very small particles Quarks Six different types best known hadrons are the proton and neutron Leptons Six different types Gauge bosons Carry the forces Forces There are 4 fundamental forces in the universe From strongest to weakest: Strong nuclear force -Weak nuclear force -- Electromagnetism -Gravity -- Gravity Gravity is by far the weakest of the four forces Most important force over large distances However, our classical ideas about gravity need to be replaced with Einstein’s general relativity Newtonian Gravity We normally think of Newtonian gravity Put two masses together and they will feel a force that will make them move closer together Einsteinian Gravity Einstein proposed that mass causes spacetime to curve Like putting a bowling ball on a taut rubber sheet The Sun’s mass makes a “bowl” in the center of the solar system The Earth has tangential velocity and so rolls around and around in the “bowl” Light and Gravity Light is also affected by curved spacetime This implies that spacetime is a real thing Empty space is not really empty QM and GR General relativity is based on a smoothly curving spacetime continuum According to GR if we zoom in on a piece of space it should be smooth unless a mass distorts it We need a new theory to reconcile these two ideas Next Time Brian Greene talk tonight 7pm Olin Auditorium Also tomorrow at 10:30am in Sc 102 Sign in for extra credit Hand in list 3 Friday Quiz #3 Monday