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Warped Passages - Lisa Randall [111]

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with the grayscale dots, when you go from an effective theory with short-distance resolution to another with less precise resolution, in essence you change the “pixel size” with which you choose to analyze your theory. The renormalization group tells you how to calculate the influence that such short-distance interactions could have on the particles in your long-distance theory. You extrapolate physical processes from one length or energy scale to another.


Virtual Particles

Renormalization group calculations make these extrapolations by taking into account the effect of quantum mechanical processes and virtual particles. Virtual particles, a consequence of quantum mechanics, are strange, ghostly twins of actual particles. They pop in and out of existence, lasting only the barest moment. Virtual particles have the same interactions and the same charges as physical particles, but they have energies that look wrong. For example, a particle moving very fast clearly carries a lot of energy. A virtual particle, on the other hand, can have enormous speed but no energy. In fact, virtual particles can have any energy that is different from the energy carried by the corresponding true physical particle. If it had the same energy, it would be a real particle, not a virtual one. Virtual particles are a strange feature of quantum field theory that you have to include to make the right predictions.

So how can these apparently impossible particles exist? A virtual particle with its borrowed energy could not exist were it not for the uncertainty principle, which allows particles to have the wrong energy so long as they do so for such a short time that it would never be measured.

The uncertainty principle tells us that it would take infinitely long to measure energy (or mass) with infinite precision, and that the longer a particle lasts, the more accurate our measurement of its energy can be. But if the particle is short-lived and its energy cannot possibly be determined with infinite precision, the energy can temporarily deviate from that of a true long-lived particle. In fact, because of the uncertainty principle, particles will do whatever they can get away with for as long as they can. Virtual particles have no scruples and misbehave whenever no one is watching. (A physicist from Amsterdam even suggested that they are Dutch.)

You can think of the vacuum as a reservoir of energy—virtual particles are particles that emerge from the vacuum, temporarily borrowing some of its energy. They exist only fleetingly and then disappear back into the vacuum, taking with them the energy they borrowed. That energy might return to its place of origin, or it might be transferred to particles in some other location.

The quantum mechanical vacuum is a busy place. Even though the vacuum is by definition empty, quantum effects give rise to a teeming sea of virtual particles and antiparticles that appear and disappear—even though no stable, long-lasting particles are present. All particle-antiparticle pairs can in principle be produced, albeit only for very short visits, too short to be seen directly. But however brief their existence, we care about virtual particles because they nonetheless leave their imprint on the interactions of long-lived particles.

Virtual particles have measurable consequences because they influence the interactions of the real physical particles that enter and leave an interaction region. During its brief span of its existence, a virtual particle can travel between real particles before disappearing and repaying its energy debt to the vacuum. Virtual particles thereby act as intermediaries that influence the interactions of long-lived stable particles.

For example, the photon in Figure 47 (Chapter 7), which was exchanged to generate the classical electromagnetic force, was in fact a virtual photon. It didn’t have the energy of a true photon, but it didn’t have to. It only needed to last long enough to communicate the electromagnetic force and make the real charged particles interact.

Another example of virtual particles

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