1 / 25

Quantum Mechanics and General Relativity

Quantum Mechanics and General Relativity. Astronomy 315 Professor Lee Carkner Special Lecture. Exercise #20 AGN. Energy due to dropping Earth down black hole m = 5.97X10 24 kg E = (0.1)(5.97X10 24 )(3X10 8 ) 2 = Quasar luminosity of 10 40 W (J/s) (10 40 J/s)(60 s/min) =

vclifford
Download Presentation

Quantum Mechanics and General Relativity

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Quantum Mechanics and General Relativity Astronomy 315 Professor Lee Carkner Special Lecture

  2. 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) =

  3. Big and Small • Quantum mechanics • Atoms, electrons, photons, etc. • General relativity • Stars, galaxies, clusters, the universe, etc.

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. The Jelly Bean Fallacy • “When the revolutionary ideas of quantum physics were first coming out, people still tried to understand them in terms of old-fashioned 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

  11. 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

  12. 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

  13. 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!

  14. 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

  15. 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!

  16. 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

  17. 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

  18. 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

  19. Forces • There are 4 fundamental forces in the universe • From strongest to weakest: • Strong nuclear force -- • Weak nuclear force -- • Electromagnetism -- • Gravity --

  20. 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

  21. 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

  22. 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”

  23. Light and Gravity • Light is also affected by curved spacetime • This implies that spacetime is a real thing • Empty space is not really empty

  24. 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

  25. 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

More Related