Virtual Particle's Violate Causality?

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OK - let me try and answer this once and for all. The question "do virtual particles travel faster than light" is a somewhat ill defined question unless you define what you mean by a virtual particle and what you mean by its velocity (or momentum).

Some people hold to the interpretation that:

"In perturbation theory, systems can go through intermediate "virtual states" that normally have energies different from that of the initial and final states. This is because of another uncertainty principle, which relates time and energy."

This is a quote from the page you link to. In that interpretation they define the energy of the virtual particle via $E^2 = p^2 c^2+m^2c^4$ and then say that since $p^2 c^2+m^2c^4$ is not equal to the square of the sum of the energies before (or after) the virtual particle was formed (or decayed), they say that energy was not conserved. This view is embodied in the Heisenberg uncertainty principle.

In this view, the virtual particles can travel faster than light. This is not a violation of causality though since you can't measure them going faster than light.

However, this is not the modern way of interpreting this. Energy conservation is probably one of the most fundamental laws we have, so modern physicists would rather hang on to it. So they say that energy is conserved, but $E^2 = p^2 c^2+m^2c^4$ is violated. Since this equation draws a 4d circle in Minkowski space, a particle obeying it is said to be on-mass-shell, while one disobeying it is said to be off-mass-shell, or just off-shell. The more off-shell a particle is, the shorter its lifetime, which is the modern embodiment of the HUP.

In this interpretation, the virtual particle never goes faster than light.

So which interpretation is correct? Both are, and neither are at the same time! Since you cannot experimentally tell them apart - there is no measurement you can make that distinguishes them - then they are equally valid viewpoints. This is why they are called interpretations.

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If they don't last forever I take it they don't loose energy over time.

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OK - let me try and answer this once and for all. The question "do virtual particles travel faster than light" is a somewhat ill defined question unless you define what you mean by a virtual particle and what you mean by its velocity (or momentum).

Some people hold to the interpretation that:

"In perturbation theory, systems can go through intermediate "virtual states" that normally have energies different from that of the initial and final states. This is because of another uncertainty principle, which relates time and energy."

This is a quote from the page you link to. In that interpretation they define the energy of the virtual particle via $E^2 = p^2 c^2+m^2c^4$ and then say that since $p^2 c^2+m^2c^4$ is not equal to the square of the sum of the energies before (or after) the virtual particle was formed (or decayed), they say that energy was not conserved. This view is embodied in the Heisenberg uncertainty principle.

In this view, the virtual particles can travel faster than light. This is not a violation of causality though since you can't measure them going faster than light.

However, this is not the modern way of interpreting this. Energy conservation is probably one of the most fundamental laws we have, so modern physicists would rather hang on to it. So they say that energy is conserved, but $E^2 = p^2 c^2+m^2c^4$ is violated. Since this equation draws a 4d circle in Minkowski space, a particle obeying it is said to be on-mass-shell, while one disobeying it is said to be off-mass-shell, or just off-shell. The more off-shell a particle is, the shorter its lifetime, which is the modern embodiment of the HUP.

In this interpretation, the virtual particle never goes faster than light.

So which interpretation is correct? Both are, and neither are at the same time! Since you cannot experimentally tell them apart - there is no measurement you can make that distinguishes them - then they are equally valid viewpoints. This is why they are called interpretations.

so causality is violated unobservable becuase we cant measure virtual particles? my friend said "While virtual particles can break causality, we can never observe virtual particles, and so we never can observe causality violations. What is a virtual particle? Virtual particles are how we understand that quantum interactions occur. For example, suppose two electrons come along and bump off of each other. One electron experiences the electric field of the other electron. The force between the two electrons is due to exchange of photons. These photons are virtual.

Given this, the influence of one electron on another is the result of a sum over all of the virtual photons exchanged---this is the Feynman path integral. While some virtual photons travel faster than the speed of light, some (in fact, many more) photons also travel slower than the speed of light. This means that the net effect is mediated at a speed that respects causality.

Summary: While one photon in the interaction may travel faster than the speed of light, the net effect of the interaction requires that one sum over all photons exchanged. Because the probability of a virtual photon traveling slower than the speed of light is MUCH greater than the probability of a virtual photon traveling faster than the speed of light, the net effect means that the information between the two electrons is exchanged in a manner which respects causality''

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• 2 weeks later...

so virtual particle's don't do any of that sci-fi stuff like a time loop or going back in time sort of thing?

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• 1 month later...

the author of the article said "virtual particles can travel slower or faster than light,forwards and bavkwards in time,however they are virtual.

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