- #1

- 206

- 40

## Summary:

- Does vacuum excitation violate the conservation of energy?

Hi, there. I am reading the article

Here he calculate the transition probability of a vacuum excitation for a detector.

Suppose there is a lab where the electricmagnetic field is quantizedthe, and a detector atom is travelling relative to the lab. Assume that the initial state of the detector atom and the field is the ground state ##\left | g,0 \right >##. Then the transition probability of the vacuum excitation is given by

##p\left ( \Omega \right)=\sum_{out} \left | \left < {e}, {out} \right | U \left | {g}, 0 \right > \right | ^2##

where the sum over states ##\left | {out} \right >## represent a sum over an orthonormal basis of possible final states of the field.

At last, he derived a expression for ##P\left ( \Omega \right )## which is not zero.

But if the detector atom was at the ground state and the field was at the vacuum state initially, and then the atom was excited and the field could be some state other than the vaccum state, the law of conservation of energy seems to be violated.

How could that be possible?

*Relativistic quantum optics: The relativistic invariance of the light-matter interaction models*by Eduardo Martin-Martinez el al (2018).Here he calculate the transition probability of a vacuum excitation for a detector.

Suppose there is a lab where the electricmagnetic field is quantizedthe, and a detector atom is travelling relative to the lab. Assume that the initial state of the detector atom and the field is the ground state ##\left | g,0 \right >##. Then the transition probability of the vacuum excitation is given by

##p\left ( \Omega \right)=\sum_{out} \left | \left < {e}, {out} \right | U \left | {g}, 0 \right > \right | ^2##

where the sum over states ##\left | {out} \right >## represent a sum over an orthonormal basis of possible final states of the field.

At last, he derived a expression for ##P\left ( \Omega \right )## which is not zero.

But if the detector atom was at the ground state and the field was at the vacuum state initially, and then the atom was excited and the field could be some state other than the vaccum state, the law of conservation of energy seems to be violated.

How could that be possible?