Experimental Unruh Radiation?

Matt Visser, Washington University St. Louis visser@kiwi.wustl.edu

Experimental detection of Hawking radiation from real general-relativistic black holes seems a close to hopeless proposition. Even the detection of the Hawking radiation that is expected to arise from condensed matter analog models for general relativity, while much more accessible than that from true gravitational black holes, is also currently far from laboratory realization. Given this, perhaps the next best thing to do is to attempt an experimental verification of the existence of Unruh radiation. This is the hope of Pisin Chen (Stanford) and Toshi Tajima (Austin) who have analyzed the possibility of using intense lasers to accelerate electrons extremely rapidly [1].

Recall that the Unruh effect implies that a uniformly accelerating particle will find itself surrounded by a thermal heat bath of temperature

\begin{displaymath}
k T = {\hbar a \over 2\pi c}.
\hfill\qquad\qquad\qquad (1)
\end{displaymath}

More precisely, uniform acceleration through the usual quantum vacuum (Minkowski vacuum) of the electromagnetic field will distort the two-point function of the zero-point fluctuations (ZPF) in such a way that

\begin{displaymath}
\langle E_{i}(-\tau/2) E_{j}(+\tau/2) \rangle =
{4\hbar\ove...
...\;
{(a/c)^4 \over \sinh^4(a \tau/2c)}.
\hfill\qquad\qquad (2)
\end{displaymath}

Here $\tau$ is the proper time as measured at some fixed position in the accelerated frame, while $a$ is the acceleration. As $a \to 0$

\begin{displaymath}
\langle E_{i}(-\tau/2) E_{j}(+\tau/2) \rangle =
{64\hbar c\over\pi \tau^4},
\end{displaymath}

which recovers the usual unaccelerated Minkowski space result.

In the setup considered by Chen and Tajima [1], they use a laser-driven classical EM field to accelerate a single electron. Because they are not accelerating the entire detector, just a single electron, searching for an Unruh temperature as in equation (1) is meaningless. Instead, they suggest looking for the effects due to equation (2): The acceleration of the electron through the Minkowski vacuum state modifies the correlations in the zero-point fluctuations of the vacuum, which causes an additional jitter in the electron's motion, which then modifies the radiation emitted by the electron -- over and above the classical Larmor radiation. This additional acceleration-related radiation has a characteristic acceleration dependence (a distorted thermal spectrum) and a characteristic angular dependence, which should in principle be measurable in the not too distant future. In particular there is a "blind spot" in the angular dependence of the classical Larmor radiation [1,2], and if you sit in this blind spot any radiation you see should be traceable to this distortion of the zero-point fluctuations.

There are two tricky points to keep in mind, one of physics and one of sociology/linguistics:

(1) There is a maximum electric field beyond which the QED vacuum falls apart due to copious production of electron-positron pairs (Schwinger effect). This vacuum breakdown occurs for

\begin{displaymath}
{e} E_{max} \approx {m_e c^2\over\lambda_e} =
{m_e c^2\over\hbar/ (m_e c)} = m_e^2 c^3/\hbar,
\end{displaymath}

and corresponds to a maximum acceleration

\begin{displaymath}
{a}_{max} \approx m_e c^3/\hbar \approx 10^{29} \; m/s^2
\approx 10^{28} \; g_{earth}.
\end{displaymath}

The accelerations posited by Chen and Tajima are up to $10^{25}$ $g_{earth}$, so they are approaching but not quite over this vacuum breakdown limit. Thus if you succeed in building the experiment suggested by Chen and Tajima you are close to ultimate limits on this type of experiment -- there's not much extra maneuvering room.

(2) The linguistic problem is this: If you ultimately succeed in seeing this ZPF-induced modification to Larmor radiation, should you really call it the Unruh effect? [2,3] Or should you just call it basic quantum field theory? After all you are not directly measuring the Unruh temperature itself. [To add to the confusion there is a subspecies of physicist that still does not believe in quantum field theory (QFT), and instead goes through quite contorted gymnastics to try to interpret all of quantum physics in terms of a classical stochastic background of zero-point fluctuations. I do not expect this subspecies to be convinced by the experiment, regardless of the outcome.]

I think it fair to say that most of the relativity and quantum communities would view a successful experiment along these lines as a beautiful verification of the basic ideas of flat-space QFT. The connection with curved-space QFT is tenuous at best, but this does not reduce the interest in performing this type of experiment.

References

[1] Testing Unruh Radiation with Ultra-intense Lasers. Pisin Chen and Toshi Tajima. Physical Review Letters 83, 256-259 (1999).

[2] Blind spot may reveal vacuum radiation. Haret Rosu, Physics World, October 1999, 21-22.

[3] On the estimates to Measure Hawking Effect and Unruh Effect in the Laboratory. Haret Rosu, International Journal of Modern Physics D3, 545 (1994); gr-qc/9605032.



Jorge Pullin
2001-02-11