Uncertainty principle equation for virtual particles

[Ebi Rogha]

 

[PeroK]

What are $\Delta E$ and $\Delta t$ exactly?

 

[Ebi Rogha]

It seems there are different interpretations for them. A popular one is this:

ΔE is the uncertainty in the energy measurement and Δt is the uncertainty in the lifetime measurement.

 

[PeroK]

It seems there are different interpretations for them. A popular one is this:

ΔE is the uncertainty in the energy measurement and Δt is the uncertainty in the lifetime measurement.

How are you measuring the lifetime of a virtual particle?

Instead, the mathematics of QED or QCD (represented by the Feynman diagrams) includes a term in the amplitude for every energy-momentum for each virtual particle.

This includes energy-momenta that are off mass-shell. If you want to look that up.

I think that's the equivalent of the time-energy uncertainty relation.

 

[weirdoguy]

Virtual particles are not real, which in this context means that they do not have appropriate states (because there are no fields connected with virtual particles) that would let us measure anything connected with them. These insight articles are worth reading:

https://www.physicsforums.com/insights/what-are-virtual-particles-intro/
https://www.physicsforums.com/insights/misconceptions-virtual-particles/

 

[Haborix]

It seems there are different interpretations for them. A popular one is this:

ΔE is the uncertainty in the energy measurement and Δt is the uncertainty in the lifetime measurement.

This topic is subtle and requires extremely careful consideration, as you can see from the replies you have received so far. I will add one caution to the mix: do not confuse experimental precision (uncertainty) with the uncertainty relations. The real mystery of quantum mechanics is that even if we had perfect precision in our measurements, the accumulated data sets from measurements would show distributions whose uncertainties satisfy the uncertainty principle.

The energy-time uncertainty is particularly difficult to understand because there is not an operator associated with time in quantum mechanics.

 

[vanhees71]

Sigh. One should first start with discussing the energy-time uncertainty relation in the correct way. It's not as simple as with the uncertainty principle for two observables. Time is never an observable in quantum theory but a (real) parameter. A good discussion is given in Landau&Lifshitz vol. 2 and Messiah.

Then one should simply forget about "virtual particles" and remember that what's calculated in vacuum relativistic QFT are S-matrix elements, whose square are transition probability distribution rates from a given initial to a given final state. Particularly that takes into account that in a relativistic QFT you can interpret only asymptotic free states as "particles".

Feynman diagrams do NOT depict physical processes in a naive sense but are just an ingenious notational tool to express the formulae to be calculated in perturbation theory to get these S-matrix elements. There is no violation of energy, momentum, and angular momentum conservation anywhere in these diagrams, because for closed systems these quantities must be conserved because of the fundamental symmetries of special-relativistic spacetime, Minkowski space.

For a good explanation, why virtual particles taken in the naive sense of pop-sci books are utterly misleading, see the various Insights articles by Arnold Neumaier

https://www.physicsforums.com/insights/physics-virtual-particles/
https://www.physicsforums.com/insights/misconceptions-virtual-particles/
https://www.physicsforums.com/insights/vacuum-fluctuation-myth/
https://www.physicsforums.com/insights/vacuum-fluctuations-experimental-practice/