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Radiation from Accelerated Observers’ Warm Background

Radiation from Accelerated Observers’ Warm Background. The flat space analog of black hole evaporation. Michael R.R. Good University of North Carolina, 2006. Road Map. Introduction/History Construction of the Unruh effect: How can the Unruh effect explain Hawking radiation?

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Radiation from Accelerated Observers’ Warm Background

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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.

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