Quantum Mechanics and General Relativity

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