Radiation from Accelerated Observers

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Radiation from Accelerated Observers Warm
Background

• The flat space analog of black hole evaporation.

Michael R.R. Good University of North Carolina,
2006
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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

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What is the Unruh Effect?

• Warm vacuum
• Same state, different descriptions.
• Path dependent vacuum.

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The Result
Constant velocity
Accelerating
At Rest
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History of the Unruh Effect

• Schrodinger in 1939.
• Stephen Fulling 1973.
• Stephen Hawking 1974.

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History of the Unruh effect

• Paul Davies 1974.
• Bill Unruh 1975.
• Bisognano and Wichmann 1975.
• QFT in CST

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Dimensional Considerations
Newtonian Mechanics
Special Relativity
Quantum Mechanics
Thermodynamics
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Origin of Unruh Effect

• Different notions of modes?
• Where does the energy come from?

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Derivation of the Unruh Effect

• Unruhs quantization modes method
• Field is expanded in modes
• Number operator in Minkowski vacuum is
  calculated.

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Review of QFT in Minkowski
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Review Cont.
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Review of Acceleration Coordinates
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Massless Klein-Gordon in Rindler
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Analytically Extended Modes
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Bogolubov Transformation
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Thermal Spectrum of Particles
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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.

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Bisognano and Wichmanns proof

• Theorem about the action of complex Lorentz
  transformations on the vacuum.
• Minkowski vacuum is a thermal state for the boost
  Hamiltonian (axiomatic QFT)

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Unruh Event Horizon
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Hawking Radiation

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

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Hawking and Unruh

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

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Derivation of Hawking Radiation

• Static observer near black hole detects
• Static observer at infinity detects

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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.

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Opposition to Unruh Radiation

• Exact calculation in scalar electrodynamics.
  (Ford and OConnell, 2006)
• System in equilibrium.
• Driven while radiating.
• Balance with no net flux.
• Thermalization without radiation.

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Experimental Prospects

• Acoustic black hole (Unruh)
• Spin transitions due to vacuum (Bell)

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Experimental Prospects

• Penning trap (Rogers)
• Ionized gas (Yablonovitch)
• Particles in crystal (Darbinyan)

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Experimental Prospects

• Lasers (Chen, 1999)

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Detecting Unruh Radiation?
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Interesting Research Directions

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

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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 observers interpretation of
  the detection of radiation by linearly
  accelerated particle detectors. 1985.
• Ford and OConnell, 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.

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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.