What is the energy-time uncertainty relationship in quantum mechanics?

[g.lemaitre]

This is from Hogdson's book the Mind Matters

These virtual photons may be absorbed by other particles; if so, there is a transmission of electromagnetic force; but, if not, the virtual photons are considered as reabsorbed by the electron (as they must be, to avoid violating laws requiring conservation of energy and momentum). The energy of such virtual photons can be considered as ‘borrowed’, the justification for that being the energy-time uncertainty relationship: the more energetic such virtual photons are. the less will be the time of their existence, so as to ensure that the product of time and ‘borrowed’ energy stays under the Planck constant h.

Does anyone know what the actual equation he is talking about and I was wondering if anyone could give me a few more details regarding the energy-time uncertainly relationship.

 

[jinawee]

I haven't done a QM course yet, but I think this is one of the cases where the Heisenberg's uncertainty principle is misunderstood.

The equation would be: $$\Delta E\Delta t \geq \frac{\hbar}{2}$$

What it really means is that $\Delta t$ is the time it takes the system to evolve in time. If the energy uncertainty is very small, the evolution of the system will be very slow (for a thorough analysis consult Griffiths).

In particle physics it can be also thought as the characteristic time for an interaction (or semething like this, someone should explain it better).

But it doesn't mean that you can violate energy conservation. I think in this case it's related to summing up Feynman diagrams, so the total sum does verify energy conservation.