Unruh effect

The Unruh effect, discovered in 1976 by Bill Unruh of the University of British Columbia, is the prediction that an accelerating observer will observe black-body radiation where an inertial observer would observe none. In other words, the background appears to be warm from an accelerating reference frame. The quantum state which is seen as ground state for observers in inertial systems is seen as a thermodynamic equilibrium for the uniformly accelerated observer.

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Explanation

Unruh demonstrated that the notion of vacuum depends on the path of the observer through spacetime. From the viewpoint of the accelerating observer, the vacuum of the inertial observer will look like a state containing many particles in thermal equilibrium — a warm gas.

Although the Unruh effect is initially counter intuitive, it makes intuitive sense if the word vacuum is interpreted appropriately, as below.

Vacuum interpretation

In modern terms, the concept of "vacuum" is not the same as "empty space", as all of space is filled with the quantized fields that make up a universe. Vacuum is simply the lowest possible energy state of these fields, a very different concept from "empty".

The energy states of any quantized field are defined by the Hamiltonian, based on local conditions, including the time coordinate. According to special relativity, two observers moving relative to each other must use different time coordinates. If those observers are accelerating, there may be no shared coordinate system. Hence, the observers will see different quantum states and thus different vacua.

In some cases, the vacuum of one observer is not even in the space of quantum states of the other. In technical terms, this comes about because the two vacua lead to unitarily inequivalent representations of the quantum field canonical commutation relations. This is because two mutually accelerating observers may not be able to find a globally defined coordinate transformation relating their coordinate choices.

An accelerating observer will perceive an apparent event horizon forming (see Rindler spacetime). The existence of Unruh radiation can be linked to this apparent event horizon, putting it in the same conceptual framework as Hawking radiation. On the other hand, the Unruh effect shows that the definition of what constitutes a "particle" depends on the state of motion of the observer.

The (free) field needs to be decomposed into positive and negative frequency components before defining the creation and annihilation operators. This can only be done in spacetimes with a timelike Killing vector field. This decomposition happens to be different in Cartesian and Rindler coordinates (although the two are related by a Bogoliubov transformation). This explains why the "particle numbers", which are defined in terms of the creation and annihilation operators, are different in both coordinates.

Just as the Rindler spacetime can be seen as a toy model for black holes and cosmological horizons, the Unruh effect provides a toy model to explain Hawking radiation.

Calculations

The temperature observed by a uniformly accelerating particle is:

So the temperature of the vacuum, seen by an observer accelerated by the Earth's gravitational acceleration of g = 9.81 m/s², is only 4×10⁻²⁰ K. For an experimental test of the Unruh effect it is planned to use accelerations up to 10²⁶ m/s², which would give a temperature of about 400,000 K. ^[1]

Other implications

The Unruh effect also causes the decay rate of accelerated particles to differ from inertial particles. Stable particles like the electron could have nonzero transition rates to higher mass states when accelerated fast enough.^{[2] [3] [4]}

See also

• Rindler coordinates
• Pair production
• Virtual particle
• Hawking radiation
• Superradiance

References

1. ^ M. Visser, Experimental Unruh radiation?, in Newsletter of the Topical Group on Gravitation of the APS (Ed. J. Pullin) arXiv:gr-qc/0102044. H. Rosu, Gravitation and Cosmology 7, 1 (2001).
2. ^ R. Mueller, Decay of accelerated particles, Phys. Rev. D 56, 953-960 (1997) arXiv:hep-th/9706016.
3. ^ D. A. T. Vanzella and G. E. A. Matsas, Decay of accelerated protons and the existence of the Fulling-Davies-Unruh effect, Phys. Rev. Lett. 87, 151301 (2001)arXiv:gr-qc/0104030.
4. ^ H. Suzuki and K. Yamada, Analytic Evaluation of the Decay Rate for Accelerated Proton, Phys. Rev. D 67, 065002 (2003) arXiv:gr-qc/0211056.

• Thorne, Kip, Black Holes and Time Warps: Einstein's Outrageous Legacy, W. W. Norton & Company; Reprint edition, January 1, 1995, ISBN 0-393-31276-3. (1994) - Chapter 12 "Black holes evaporate", especially pp. 444 (box 12.5) "Acceleration Radiation".
• Unruh, W.G., "Notes on black hole evaporation", Phys. Rev. D 14, 870 (1976) (Original Paper)