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1.  Physics lecture series at UC Merced Lecture by Raymond Y. Chiao May 2, 2007 -- INTERFACE OF QM AND GR -- NOT AT HIGH ENERGIES, BUT AT LOW TEMPERATURES, WHERE COHERENT QUANTUM FLUIDS (e.g. superfluids) FORM.-- INTERFACE OF QM AND GR -- NOT AT HIGH ENERGIES, BUT AT LOW TEMPERATURES, WHERE COHERENT QUANTUM FLUIDS (e.g. superfluids) FORM.

2. Goal: the Quantum Transducer (Not an “anti-gravity” effect, but a reflection of radiative gravito-magnetic fields by quantum mass currents) -- A TRANDUCER IS A DEVICE THAT CONVERTS ONE TYPE OF WAVE INTO ANOTHER TYPE OF WAVE -- RECIPROCAL DEVICE – CAN REVERSE ARROWS RECIPROCAL PROCESS GENERATES GR WAVES SOURCE OF GR WAVES-- A TRANDUCER IS A DEVICE THAT CONVERTS ONE TYPE OF WAVE INTO ANOTHER TYPE OF WAVE -- RECIPROCAL DEVICE – CAN REVERSE ARROWS RECIPROCAL PROCESS GENERATES GR WAVES SOURCE OF GR WAVES

3. What is a gravitational wave? It is a time-varying tidal gravitational field (think of jello with grapes embedded inside it)

4. Gravitational field of the Earth Cf. Millikan oil drop experiment

5. Equivalence Principle Galileo’s “Leaning Tower of Pisa” Experiment - DEMONSTRATION: DROP KEYS AND A RED PENCIL ONTO TABLE - PENCIL MADE OF CARBON - KEYS MADE OF METAL, MAINLY ALUMINUM - INDEPENDENT OF STRONG FORCE- DEMONSTRATION: DROP KEYS AND A RED PENCIL ONTO TABLE - PENCIL MADE OF CARBON - KEYS MADE OF METAL, MAINLY ALUMINUM - INDEPENDENT OF STRONG FORCE

6. Statements of Equivalence Principle All objects fall with precisely the same acceleration due to gravity, independent of their masses, their internal composition, their internal thermodynamic state, etc. Inertial mass = Gravitational mass (Newton) Gravity = Geometry (Einstein) -- EOTVOS, DICKE, BRAGINSKY’S EXPERIMENTS SHOW THAT E.P. HOLDS TO A PART IN A TRILLION.-- EOTVOS, DICKE, BRAGINSKY’S EXPERIMENTS SHOW THAT E.P. HOLDS TO A PART IN A TRILLION.

7. Newton’s Equivalence Principle Experiment

8. EOTVOS, DICKE, BRAGINSKY, ETC., EXPERIMENTS SHOW THAT THE EQUIVALENCE PRINCIPLE HOLDS TO A PART IN A TRILLION.

9. Geodesic: The shortest path between two points on a curved surface -- THE SHORTEST GEOMETRICAL PATH IS THE SAME SHORTEST PATH FOR ALL MATERIAL OBJECTS, INDEPENDENT OF THEIR COMPOSITION, e.g., ant or airplane. -- EINSTEIN’S VIEWPOINT: GRAVITATIONAL FORCE IS ACTUALLY DUE TO THE GEODESIC MOTION OF A PARTICLE IN A CURVED SPACE-TIME MANIFOLD, LIKE THAT ON THE SPHERE-- THE SHORTEST GEOMETRICAL PATH IS THE SAME SHORTEST PATH FOR ALL MATERIAL OBJECTS, INDEPENDENT OF THEIR COMPOSITION, e.g., ant or airplane. -- EINSTEIN’S VIEWPOINT: GRAVITATIONAL FORCE IS ACTUALLY DUE TO THE GEODESIC MOTION OF A PARTICLE IN A CURVED SPACE-TIME MANIFOLD, LIKE THAT ON THE SPHERE

10. Einstein’s statement of E.P. All freely falling particles, independent of their masses, composition, etc., follow GEODESICS in space-time.

11. Equivalence principle revisited:Does a dropped charge radiate?

12. Orbiting charged and neutral objects

13. Two charged objects in orbit

14. “Millikan oil drops”

15. Coupling between gravitational and electromagnetic fields When the mass of “Millikan oil drops” is sufficiently large, then the coupling of the drops to gravitational fields can become large. When the charge of “Millikan oil drops” is sufficiently large, then the coupling of the drops to electromagnetic fields can become large.

16. Coupling between gravity and electromagnetic waves Gravitational radiation fields can be coupled to electromagnetic radiation fields by “Millikan oil drops” If their mass is sufficiently large If their charge is sufficiently large If they are sufficiently rigid If they are sufficiently dissipationless

17. How big a mass is needed?The Planck mass

18. Interaction of two “Millikan oil drops” via electricity and via gravity

19. A quantum transducer converts gravity waves into electromagnetic waves

20. Time-reversed quantum transducer

21. Why quantum mechanics? Efficiency of quantum transducers depends on “quantum rigidity” Efficiency of quantum gravity wave antennas depends on “quantum dissipationlessness” Both arise from the ENERGY GAP of the quantum system and the quantum adiabatic theorem.

22. Energy gapof a two-level quantum system

23. Electron on surface of superfluid helium drop in strong B field

24. Classical Cyclotron Motion

25. How come “quantum rigidity”? Quantization of cyclotron motion leads to simple-harmonic oscillator energy levels. Energy gap causes “quantum rigidity” Boltzmann factor is extremely small at milli-Kelvin temperatures.

26. Gravito-Hall effect:An electron moving on the surface of superfluid helium On a sphere, the electrons are confined to the surface, and thus the WHOLE sphere moves

27. Quantum rigidity and Mossbauer effect The gravito-Hall effect, when quantized, leads to the quantum rigidity of “Millikan oil drop.” The energy gap leads to a rigid motion of the entire drop as a whole. This is like the Mossbauer effect.

28. What is the Mossbauer effect?

29. Rigid, hard-sphere scattering cross-section (think of steel balls embedded inside jello)

30. Scattering from “Millikan oil drops” Scattered electromagnetic wave power becomes comparable scattered gravity wave power from a pair of drops, when the ratio of coupling constants is given by

31. Hertz-like experiment: The “quantum transceiver”

32. Microwave Hertz-like experiment with normal Faraday cages

33. An important application: “Gravity Radio” Intercontinental communication by microwave-frequency gravity waves directly through the interior of the Earth

34. CONCLUSION: A pair of Planck-mass-scale “Millikan oil drops” should become an efficient transducer between EM and GR waves in a strong B field due to quantum rigidity and quantum dissipationlessness. A “quantum transceiver” should therefore be possible to construct in the laboratory.

35. A common misconception corrected Why aren’t the drops too heavy to move when they are irradiated by an EM wave?

36. Answer: Equivalence principle Drops don’t move at all according to local inertial observers

37. Time-reversal symmetry Again, drops don’t move at all according to local inertial observers

39. Feynman diagram

40. Gravity waves from the Big Bang

41. Vacuum Maxwell’s equations for weak gravitational fields

42. Maxwell’s equations for weak gravitational fields