Aidyan
- 182
- 14
As I understand it, the energy-time uncertainty relation \triangle E \triangle t \geq \hbar /2 expresses a trade-off between the precision with which energy and time can be simultaneously measured. I understand that, unlike position and momentum, time is not an operator, so the relation is not a formal uncertainty between two observables. Instead, it reflects the idea that the shorter the duration \triangle t over which a quantum state exists, the more uncertain is its energy \triangle E. For example, it underlies the phenomenon of the broadening of spectral lines.
I'm wondering whether it can be applied to a volume of space, where the time interval is related to a length L divided to the speed of light c as: \triangle t=\frac{L}{c}. Then \triangle E \geq \frac{\hbar}{2 \triangle t}=\frac{\hbar c}{2 L}=\frac{\hbar c}{2 V^{1/3}}. If so, can this be applied to macroscopic objects occupying a volume V? Does this make sense? If not, why not?
I'm wondering whether it can be applied to a volume of space, where the time interval is related to a length L divided to the speed of light c as: \triangle t=\frac{L}{c}. Then \triangle E \geq \frac{\hbar}{2 \triangle t}=\frac{\hbar c}{2 L}=\frac{\hbar c}{2 V^{1/3}}. If so, can this be applied to macroscopic objects occupying a volume V? Does this make sense? If not, why not?