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  1. Radiation from Accelerated Observers’ Warm Background The flat space analog of black hole evaporation. Michael R.R. Good University of North Carolina, 2006

  2. Road Map • Introduction/History • Construction of the Unruh effect: • How can the Unruh effect explain Hawking radiation? • Unruh Radiation versus Unruh Effect: • How does an accelerated observer radiate energy to an inertial detector? • Experimental Prospects: • How can the Unruh effect be experimentally verified? • Outlook/Research directions

  3. What is the Unruh Effect? • Warm vacuum: • Same state, different descriptions. • Path dependent vacuum.

  4. The Result Constant velocity At Rest Accelerating

  5. History of the Unruh Effect • Schrodinger in 1939. • Stephen Fulling 1973. • Stephen Hawking 1974.

  6. History of the Unruh effect • Paul Davies 1974. • Bill Unruh 1975. • Bisognano and Wichmann 1975. • QFT in CST

  7. Dimensional Considerations Newtonian Mechanics Special Relativity Quantum Mechanics Thermodynamics

  8. Origin of Unruh Effect • Different notions of modes? • Where does the energy come from?

  9. Derivation of the Unruh Effect • Unruh’s quantization modes method • Field is expanded in modes • Number operator in Minkowski vacuum is calculated.

  10. Review of QFT in Minkowski

  11. Review Cont.

  12. Review of Acceleration Coordinates

  13. Massless Klein-Gordon in Rindler

  14. Analytically Extended Modes

  15. Bogolubov Transformation

  16. Thermal Spectrum of Particles

  17. Davies Moving Mirror • Motion of a single reflecting boundary can create particles. • Excited field modes causes particles to appear. • The detector responds to a flux of particles from the mirror that is constant in time and has the spectrum of thermal radiation.

  18. Bisognano and Wichmann’s proof • Theorem about the action of complex Lorentz transformations on the vacuum. • Minkowski vacuum is a thermal state for the boost Hamiltonian (axiomatic QFT)

  19. Unruh Event Horizon

  20. Hawking Radiation • Occurs on the event horizon of a black hole • A virtual particle pair is created on the event horizon

  21. Hawking and Unruh • Hawking and Unruh analogy, where is the surface gravity of the black hole:

  22. Derivation of Hawking Radiation • Static observer near black hole detects: • Static observer at infinity detects:

  23. Hawking Radiation from Unruh • At infinity V2 1 so the temperature observed is: • Assume the quantum state of some scalar field  looks like Minkowski vacuum as seen by freely falling observers near black hole.

  24. Opposition to Unruh Radiation • Exact calculation in scalar electrodynamics. (Ford and O’Connell, 2006) • System in equilibrium. • Driven while radiating. • Balance with no net flux. • Thermalization without radiation.

  25. Experimental Prospects • Acoustic black hole (Unruh) • Spin transitions due to vacuum (Bell)

  26. Experimental Prospects • Penning trap (Rogers) • Ionized gas (Yablonovitch) • Particles in crystal (Darbinyan)

  27. Experimental Prospects • Lasers (Chen, 1999)

  28. Detecting Unruh Radiation?

  29. Interesting Research Directions • Lasers in the vacuum • Geometric algebra interpretation of Unruh • Unruh effect and causality • GEMS maps • Classical correspondence • Spectral deformation theory

  30. Important References Pedagogical: • K. Thorne, Black Holes and Time Warps, 1994. - Chapter 12 "Black holes evaporate", especially p. 444 (box 12.5) "Acceleration Radiation". • A. Kanwal, Zero-Point Energy Presentation, Rutgers University. • Birrell and Davies, Quantum fields in curved space, 1982. • Wald, Black hole thermodynamics, 1994. The pioneering papers: • W. Unruh, Notes on black hole evaporation. 1976. • P. Davies, Scalar particle production,1975. • Bisognano and Wichmann, On the duality condition for a hermitian scalar field, 1975. Opposition to the radiation: • P. Grove, Inertial observer’s interpretation of the detection of radiation by linearly accelerated particle detectors.1985. • Ford and O’Connell, Is there Unruh radiation?2006. Experiments have the final word: • P. Chen, Testing Unruh radiation with ultra-intense lasers. 1999. • H. Rosu, Unruh effect: Toward Experiments?2001.

  31. Outlook Research plan for the next 12 months • Detailed investigation of Unruh radiation experiments. • Help with designing experimental tests of Unruh radiation using ultra-intense lasers to accelerate electrons. • Further investigation of the Unruh effect and its relationship with Hawking radiation • Explore Unruh radiation with geometric algebra. Long term objectives • Understanding quantum field theory in curved spacetime, black hole thermodynamics • Understanding the nature of the quantum event.