- #1
Ebi Rogha
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Uncertainty principle equation for virtual particles
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In summary: 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.
- #2
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What are ##\Delta E## and ##\Delta t## exactly?
- #3
Ebi Rogha
- 24
- 6
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.
ΔE is the uncertainty in the energy measurement and Δt is the uncertainty in the lifetime measurement.
- #4
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How are you measuring the lifetime of a virtual particle?Ebi Rogha said:
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.
- #5
weirdoguy
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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/
https://www.physicsforums.com/insights/what-are-virtual-particles-intro/
https://www.physicsforums.com/insights/misconceptions-virtual-particles/
- #6
Haborix
- 339
- 374
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.Ebi Rogha said:
The energy-time uncertainty is particularly difficult to understand because there is not an operator associated with time in quantum mechanics.
- #7
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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/
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/
1. What is the uncertainty principle equation for virtual particles?
The uncertainty principle equation for virtual particles is a mathematical expression that relates the uncertainty in the position and momentum of a particle. It is represented by the equation ΔxΔp ≥ h/4π, where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and h is Planck's constant.
2. How does the uncertainty principle apply to virtual particles?
The uncertainty principle applies to virtual particles because they are constantly fluctuating and do not have a definite position or momentum. This means that their position and momentum cannot be simultaneously known with certainty, and the uncertainty principle equation can be used to calculate the limits of this uncertainty.
3. What is the significance of the uncertainty principle for virtual particles in quantum mechanics?
The uncertainty principle is a fundamental principle in quantum mechanics that states that there is a limit to how precisely certain physical properties of a particle can be known. For virtual particles, this means that their position and momentum cannot be simultaneously known with certainty, and this has implications for the behavior and interactions of these particles at the quantum level.
4. How does the uncertainty principle for virtual particles relate to the Heisenberg uncertainty principle?
The uncertainty principle for virtual particles is a specific application of the Heisenberg uncertainty principle, which states that there is a fundamental limit to how precisely certain physical properties of a particle can be known. The uncertainty principle for virtual particles applies this principle specifically to the position and momentum of these particles.
5. Can the uncertainty principle for virtual particles be violated?
No, the uncertainty principle for virtual particles is a fundamental principle in quantum mechanics and cannot be violated. It is a consequence of the wave-particle duality of quantum particles and is supported by experimental evidence. Attempts to violate this principle have been unsuccessful, and it is considered a fundamental aspect of the behavior of particles at the quantum level.
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