- #1

- 201

- 4

## Main Question or Discussion Point

I have seen that the more a particle has a high energy, i.e ##E##, the more its lifetime is short, respecting so the uncertainty principle.

But by the definition of this uncertainty principle :

##E\,\Delta t \geq \dfrac{\hbar}{2}##, I can write :

##\Delta t \geq \dfrac{\hbar}{2E}##, then ##\Delta t## has a lower limit and not an upper limit.

If this was a upper limit, this would mean that ##\Delta t##, i.e. the apparition time, should be observed in a time interval lower than ##\dfrac{\hbar}{2E}## : for example, if a detector had a time resolution greater than ##\dfrac{\hbar}{2E}##, the particle could not be detected, could it ?

So in which case can we write : ##\Delta t \leq \dfrac{\hbar}{2E}## ??

It seems that I have confusions with this principle.

Any clarification is welcome

But by the definition of this uncertainty principle :

##E\,\Delta t \geq \dfrac{\hbar}{2}##, I can write :

##\Delta t \geq \dfrac{\hbar}{2E}##, then ##\Delta t## has a lower limit and not an upper limit.

If this was a upper limit, this would mean that ##\Delta t##, i.e. the apparition time, should be observed in a time interval lower than ##\dfrac{\hbar}{2E}## : for example, if a detector had a time resolution greater than ##\dfrac{\hbar}{2E}##, the particle could not be detected, could it ?

So in which case can we write : ##\Delta t \leq \dfrac{\hbar}{2E}## ??

It seems that I have confusions with this principle.

Any clarification is welcome