1. Radiation from Accelerated Observers’ Warm Background
The flat space analog of black hole evaporation.
Title: The Unruh Effect: The crux of black hole evaporation.
Abstract:
An accelerating observer in Minkowski spacetime detects a thermal spectrum of particles in the vacuum state. This ‘Unruh effect’ provides an explanation of Hawking radiation via a flat spacetime route. I will talk about how the Unruh effect, which is occurs in flat spacetime can be used to understand Hawking’s effect, which occurs in extremely curved spacetime. Several derivations of the Unruh effect will be offered, particularly Unruh’s quantization method, Bisognano and Wichmann’s proof, and a heuristic semi-classical derivation. A derivation of Hawking’s radiation and proposed future experiments in support of the Unruh effect will be discussed.
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
How are Quantum Mechanics and Relativity brought together? What is black hole radiation?

3. What is the Unruh Effect?
Warm vacuum:
Same state, different descriptions.
Path dependent vacuum.
The very notion of a vacuum depends on the path of an observer through spacetime. Two different sets of observers will describe the same state in very different terms.
An accelerating observer will perceive an apparent event horizon forming
The effect that reveals the essentially thermal nature of the vacuum.
The prediction that an accelerating observer will observe black-body radiation where an inertial observer would observe none.
An observer moving with uniform acceleration through the Minkowski vacuum observes a thermal spectrum of particles.

4. The Result
Constant velocity
At Rest
Accelerating

5. History of the Unruh Effect
Schrodinger in 1939.
Stephen Fulling 1973.
Stephen Hawking 1974.
First discussion of particle production in curved spacetime was given by
Bisognano-Wichmann theorem is formulated in the general context of axiomatic quantum field theory, thus establishing that the Unruh effect is not limited to free field theory.
Schodinger’s paper was titled “The proper vibrations of an expanding universe”
Nonuniqueness of canonical field quantization in Riemannian space-time – Stephen Fulling under Wightman under Wheeler

6. History of the Unruh effect
Paul Davies 1974.
Bill Unruh 1975.
Bisognano and Wichmann 1975.
QFT in CST
Bill Unruh at University of British Columbia was a student of Wheeler , just like Wightman who advised Fulling!
Wheeler advised feynman, thorne, hu, misner, wightman, unruh!
Discovered in an attempt to understand the physics underlying the Hawking effect, using the laws of quantum fields in curved spacetime.

7. Dimensional Considerations
Newtonian Mechanics
Special Relativit y
Quantu m Mechani cs
Thermodynam ics

8. Origin of Unruh Effect Different notions of modes?
Where does the energy come from?
Consequence that observers with different notions of positive and negative frequency modes will disagree on the particle content of a given state.
Energy needed to excite the Rindler detector does not come from the background energy-momentum tensor, but from the energy we put into the detector to keep it accelerating.

9. Derivation of the Unruh Effect
Unruh’s quantization modes method
Field is expanded in modes
Number operator in Minkowski vacuum is calculated.
Normally, we calculate Bogolubov coefficients relating the Mnikowksi and Rindler modes and use them to determine the N in the Minkowski vacuum. Shortcut due to Unruh: find set of modes that share the same vacuum state (excited states different) but for which the overlap with Rindler modes is more direct. (start with R modes, analytically extend them to entire spacetime, express extension in terms of original R modes.)
A QFT that is massless scalar field in 2d, conformal coupling and minmal coupling coincide (flat spacetime anyways).

10. Review of QFT in Minkowski
Hbar , c, k are all 1

11. Review Cont.

12. Review of Acceleration Coordinates

13. Massless Klein-Gordon in Rindler
Modes need to be positive frequency wrt a future directed Killing vector, role is played by -\partial_\eta instead of \partial_\eta

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.
Moving mirror plays same role as a time-dependent background geometry.
Sudden distortion of modes instead of gradual.

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)
The essence of the Unruh effect is the fact that the density matrix describing the Minkowski vacuum, traced over the states in the region z<0, is precisely a Gibbs state for the boost Hamiltonian at temperature T = a/2pi.
Vacuum as Thermal Density Matrix
Sewell recognized the importance of their theorem to Unruh and Hawking effects.
A path integral argument given by many authors supports this interpretation, (Unruh and Weiss).

19. Unruh Event Horizon
Accelerated observer experiences a "heat bath" of photons around him
Due to the existence of an event horizonThe temperature of the heat bath follows the same Hawking temperature formula
Except that instead of being proportional to the gravitational force, it is proportional to the magnitude of the observer's acceleration.
Equivalence Principle
Accelerating reference frames, event horizons, radiation.
Event horizons, separated virtual particle pairs.

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:
Vacuum state near the horizon looks nonsingular to freely-falling observers.
Renormalized energy-momentum tensor is taken to be finite at the horizon.
The two-point function obeys the Hadamard condition.
The Static Observer Assumption

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.
using a generalized quantum Langevin equation to describe an oscillator moving under constant force and coupled to a 1D scalar field.
the rate of emission of radiation is exactly balanced by a corresponding absorption.
System is driven by zero-point oscillations of the vacuum field while simultaneously radiating energy into the vacuum.
Driving force and radiation reaction exactly balance leaving the system in equilibrium with no net radiation of energy.

25. Experimental Prospects
Acoustic black hole (Unruh)
Spin transitions due to vacuum (Bell)
Sound waves propagating in a supersonic fluid behave similarly to the quantum fields propagating in the vicinity of a black hole
Known polarization effect of high-energy electrons in circular accelerators is actually a manifestation of the Unruh effect

26. Experimental Prospects
Penning trap (Rogers)
Ionized gas (Yablonovitch)
Particles in crystal (Darbinyan)
A magnetically confined electron in a Penning trap would give the Unruh signal
Proposed by Joseph Rogers
Unruh radiation would be produced when a gas is suddenly ionized into a plasma
proposed by Eli Yablonovitch
Unruh radiation could be emitted by a beam of particles that channel through a crystal lattice
Suggested by Simon Darbinyan

27. Experimental Prospects
Lasers (Chen, 1999)
All the above experiments contain an inherent problem
Unruh signal would be buried under much stronger background signals
Electrons are to be accelerated and decelerated in every cycle by a standing wave formed by two counter-propagating, ultra-intense laser pulses

28. Detecting Unruh Radiation?
Unruh radiation would be detected from a minute change of the known classical Larmor radiation emitted when an electron is accelerated

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, 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
P. Davies, Scalar particle production, 1975.
Bisognano and Wichmann, On the duality condition for a hermitian scalar field,
Opposition to the radiation:
P. Grove, Inertial observer’s interpretation of the detection of radiation by linearly accelerated particle detectors
Ford and O’Connell, Is there Unruh radiation? 2006.
Experiments have the final word:
P. Chen, Testing Unruh radiation with ultra-intense lasers
H. Rosu, Unruh effect: Toward Experiments? 2001.

37. 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.