Virtual Particles #

Previously, we saw how the transfer of photons between electrons explains why they repel one another when close together.

But we still haven’t resolved the issue that conservation of energy seems to have been violated. How do we account for this?

Heisenberg Uncertainty Principle (HUP) #

The Heisenberg Uncertainty Principle states that the more precisely the time of a particle is determined, the less precisely the energy can be determined. Mathematically, the product of uncertainties regarding those two values cannot be smaller than some constant. We express this as $$ \Delta E \cdot \Delta t \geq \frac{h}{4 \pi} $$ These uncertainty values mean that we can “create” small amounts of energy out of nowhere for a very tiny period of time. Hence, particles (being a manifestation of energy) can “appear” seemingly out of nowhere as long as they disappear fast enough. We call such particles virtual particles.

In our earlier examples, the photon that is transferred between electrons is a virtual particle. In fact, any interactions in Quantum Electrodynamics can be explained by the interactions of virtual particles. They don’t really exist in our usual sense, so our law of conservation of energy is pretty safe for now.

Interestingly, virtual particles also explains why electrons repel more at closer distances. At closer distances, the virtual photon requires less time to travel from one electron to the next. The time period where we are uncertain about what is going on is shorter, so the amount of energy that can be “created out of nowhere” is greater. This implies that more momentum can be transferred from one electron to the other.

Infinite Possibilities #

While the idea of a virtual particle is simple, it isn’t without issues. Since the particles don’t exist in the usual sense, we don’t have a way to observe them.

Let’s examine the repulsion of electron again. The transfer of one virtual photon is the simplest case of their interaction. However, we can’t say for sure that’s what is truly happening! Why can’t two photons be transfered instead of one?

In fact, there’s countless other possibilities that can explain this interaction. None of them is sufficient to describe what actually happens. The truth lies in the “average” of all the infinite possibilities.

How do we deal with these infinites then? The answer lies in Feynman Diagrams.

A remark about HUP #

This is only an elementary description of the Heisenberg Uncertainty Principle to explain how virtual particles works. In fact, what we have stated may be an uncommon statement of the principle, which may have been a source of confusion if you have read about it earlier. The more common form of the Heisenberg Uncertainty Principle relates momentum and displacement instead. You can watch more about it here: