Particles and Quantum Fields

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After all, moving electrons around can generate excitations in the photon field—the basis of radio, light bulbs, and lasers. How do these conversations happen? But the strings are nailed to the wood, which can transfer the vibrations from one to the other strings. You can increase or decrease the mechanical connection between the two strings, making the transfer of energy easier or harder. In addition, the frequency of waves that can be sustained on each string are different, so a wave that will last a long time on one string may die out quickly on another.

Plucking a string to produce an A will not work well on a string tuned to produce a B. This is how you can picture the interaction of particles.


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Different strings on a guitar are like different types of fields—though fields all coexist at every point in space and time, which makes them harder to picture than the nicely separated guitar strings. The fact that the fields are quantized means that an excitation in one field must be of just the right size to produce a sustained excitation in another field.

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For example, an electron moving around on the electron field deforms the coupled photon field. But if you accelerate the electron, you start to shake the photon field, and the deformation can turn into excitations we call photons. The result is what we call light. We have talked about how fields can excite other fields, but it is also possible for fields to excite themselves. As a consequence of this latter fact, as I sit here looking at the light coming from the window, the waves of the photons coming toward my eye from the sun are not affected by the photon waves coming down from the lights in the ceiling.

This is how water waves act: if you watch the waves coming from the wake of a boat pass through the waves on a lake, where the waves overlap the water will be choppy and confused, but after the waves pass through each other, they continue on as if nothing had happened. Fields that are weakly coupled to each other and to themselves are a great boon for particle physicists. For example, we can calculate how the electron field affects the photon field without worrying too much about how the photon field, in turn, affects the electron field—and then how the photon field then responds to that response, ad infinitum.

If we carry out these calculations, we know we can safely ignore this feedback loop at some point, because at each iteration the ability of one wave to affect another is very small. Indeed, the most accurate physical theory yet devised is quantum electrodynamics, the quantum field theory account of electricity, magnetism, and light, and it owes its great success to weak coupling. Experimental physicists can measure one particular quantity, the magnetic moment of the electron, to twelve decimal places. Theoretical physicists can calculate the same quantity to the same precision using four iterations of the idea that the electron field talks to the photon field, which talks back to the electron field, and so on.

The remarkable thing is that the theoretical value agrees with the experimental value.

Waves, Particles and Fields: Introducing Quantum Field Theory - CRC Press Book

However, other fields are tightly coupled to each other: unlike waves on a lake or photons, their waves do not pass through each other freely. Instead, when they interact, the waves throw each field into a chaotic mess; the motion of one field depends powerfully on the motion of the other field, and vice versa. Quarks, for example, are strongly coupled to a field called the gluon field. Unlike the weak coupling between photons and electrons or between photons and quarks , any perturbation in the quark field causes the gluon field to move in lockstep; but as soon as the gluon field moves, the quark field in turn reacts to this motion, and so on, back and forth.

At first glance, this strong coupling makes it hard to see that there are two fields present. This is why we speak of protons and neutrons even though they are really bags of quarks and gluons.

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When you wiggle the quark or the gluon field, you force all the other fields to move with it. This still causes excitations and waves, which still look like particles. Only by looking at very short distances and over very short times can we pry apart this motion of all the fields and manage to see only one quark or one gluon acting independently. Creating the Higgs Boson We have seen that the most fundamental things in the universe are quantum fields. They are quantized, and they oscillate, and they sometimes transfer their oscillations to other fields. Let us put this all together and try to visualize a Higgs boson being created at the LHC.

Particles, Fields and Forces

When I picture what is going on at the LHC when a Higgs boson is born, I picture the waves of two protons, moving toward each other from opposite directions. The protons are a bundle of oscillating fields—quark and gluon fields—all moving together to form the thing we see as a single particle. They are guided along the ring of the LHC by deformations of the photon field that is, by magnetic fields generated by powerful magnets , which act like barriers, pushing these waves along a curved path. Eventually, these two proton waves are guided toward a crossing point and move past each other with incredible energies and at incredible speeds At this moment, occasionally one of the oscillating gluons in one of the bundles that make up a proton will combine with an oscillating gluon in the other proton to create a wave in the previously calm Higgs field.

The Higgs field itself always exists, everywhere in spacetime, but an excitation of the field was only created when oscillations in coupled fields were transferred over. Since the gluon fields are only tenuously and indirectly connected to the Higgs field, this is a very rare event. As the excitation we call the Higgs boson moves off, the remnants of the combined quark and gluon fields which made up the colliding protons find themselves momentarily out of balance; after losing energy to the Higgs field, the waves no longer have the right properties to move as one in the form we call protons. For example, their energy and momentum will no longer add up to the correct mass for a sustained excitation of the proton field.

Eventually, after a jumble of confusing rearrangement of energy among all the quark and gluon fields, the fields sort themselves out, forming new stable waves corresponding to new particles. But that takes a bit of time, and by then the oscillations that once were protons will have moved far away from the newly created Higgs particle.

As this oscillation in the Higgs fields evolves in time, its vibration might leak over to one of the other fields that the Higgs field is coupled to: the photon field, or the quark fields, for example. It is impossible to predict exactly when this will happen, or into which field the transfer will take place, but eventually, the energy carried in the Higgs field will transfer over, starting up oscillations in one of those other fields.

When this happens, we say that the Higgs boson decayed: the Higgs field is quiet again, and in its place are new excitations in other fields a pair of photons, a quark and an antiquark, or something else. Those particles will then themselves travel off, scattering against other excitations of other fields, pulling and pushing other fields, a wave in their own quantum sea. The analogies I have used are only analogies. You can certainly bend them in the wrong direction, and the picture I have painted is only a poor reflection of the mathematics of quantum field theory.

To make predictions and analyze experiments, we of course turn this picture into something much more precise—something we can use to do calculations.

For example, you cannot say exactly where the energy in the Higgs field will end up, but you can say very precise things about the probability of its ending up in different fields; there is a 0. Armed with this picture of the quantum world, we will turn in the next article to all the fields we know about, as described by the Standard Model of particle physics. After introducing the zoo of particles around us, I will explain what is going on with the Higgs field and the Higgs boson, in particular—and why they reveal how deeply strange our Universe is.

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