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The uncertainty principle allows for the creation of virtual particles (with non-zero mass) that exist for very short durations. This allows empty space to have particle pairs that pop into existence for very short periods and then get destroyed when recombine. This appears to me as a violation of the energy conservation law over very short time durations.

I am wondering if the uncertainty principle, $\Delta p \Delta x \geq \frac{h}{4\pi}$, allows the existence of virtual (or real) massive particles that travel faster than the speed of light for very short distances.

What is known about this possible implication of the uncertainty principle?

I am aware of the discovery that some particles found to break the speed of light.

Qmechanic
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Mohammad Al-Turkistany
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2 Answers2

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  1. The link about superluminal neutrions you cite is missing the fact that later on an error was discovered, and neutrinos do not, in fact, travel faster than light (see e.g. the Wikipedia article). To date, nothing that travels faster than light is known.

  2. The uncertainty principle does not "allow for the creation of virtual particles". The idea of such pairs coming into existence and annihilating again relies on a misinterpretation of a particular kind of Feynman diagram, called the "vacuum bubbles", which are just the diagrams without external legs which contribute to the vacuum energy. QFT does not assign actual particle states to lines which are not external, so there is no rigorous basis for talking about the "creation" of virtual particles.

  3. The uncertainty principle does also not allow faster than light speeds. That the standard deviation $\Delta p$ of momentum means only that - if you do many momentum measurements on identically prepared states, your data set will have this as its standard deviation. But, in general, the "speed" of a quantum object is not well-defined - it is typically not localized at a point, so it does not have a speed in the classical sense, and so it is not clear how its momentum would relate to its speed, or how a large standard deviation in momentum would lead to faster than light speeds.

  4. You also cannot use the uncertainty principle for $p$ and $x$ in relativistic settings because there is no straightforward relativistic position operator (the closest you get to one are the so-called Newton-Wigner operators).

ACuriousMind
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In Peskin's introduction to quantum field theory, he talks about this in chapter 2, section 4 in a subsection titled causality, which is on page 27 in my book.

He explains that yes, there is some non-zero probability that a particle will move faster than the speed of light. However, he shows any two local operators that are separated by a spacelike interval commute. This follows from lorentz invariance.

Then he argues that since these operators commute, two measurements separated by a space-like interval cannot affect each other, and so causality is preserved.

This last step seems vague to me, and this isn't really my area of expertise, but I hope I have given you a better idea of what is going on or pointed you in the right direction at least.

Brian Moths
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