- #1
jcap
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The Unruh temperature is given by
$$T=\frac{\hbar\ a}{2\pi c k_B}.$$
As I understand it one can think of pairs of electrons and positrons popping out of the vacuum and then annihilating. Imagine that we apply an electric field ##\vec{E}## to a region of space. Each electron and positron would be accelerated in opposite directions parallel to the field so that they will take slightly longer to annihilate. Thus I could imagine the properties of the vacuum changing in such a circumstance. We could naively use Newton's 2nd law to find the equation of motion of an electron/positron:
$$\vec{E}\ e=m_e\ \vec{a}.$$
Substituting the magnitude of the acceleration ##a## into the Unruh formula we get
$$T=\frac{\hbar}{2\pi c k_B}\frac{E\ e}{m_e}.$$
If we take the applied electric field strength ##E=1\ \hbox{MV/m}## then the Unruh temperature is
$$T\approx 10^{-2}\ \hbox{K}.$$
Perhaps this temperature could be measured?
$$T=\frac{\hbar\ a}{2\pi c k_B}.$$
As I understand it one can think of pairs of electrons and positrons popping out of the vacuum and then annihilating. Imagine that we apply an electric field ##\vec{E}## to a region of space. Each electron and positron would be accelerated in opposite directions parallel to the field so that they will take slightly longer to annihilate. Thus I could imagine the properties of the vacuum changing in such a circumstance. We could naively use Newton's 2nd law to find the equation of motion of an electron/positron:
$$\vec{E}\ e=m_e\ \vec{a}.$$
Substituting the magnitude of the acceleration ##a## into the Unruh formula we get
$$T=\frac{\hbar}{2\pi c k_B}\frac{E\ e}{m_e}.$$
If we take the applied electric field strength ##E=1\ \hbox{MV/m}## then the Unruh temperature is
$$T\approx 10^{-2}\ \hbox{K}.$$
Perhaps this temperature could be measured?
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