From Particles to Fields: The Most Beautiful Theory in Physics! QFT

Quantum field theory or QFT is the basis of the best theory we have in physics today to explain nearly everything, called the Standard Model of particle physics. What is Quantum Field theory? Why is it necessary? How is it different than quantum mechanics?

Classical mechanics indicates that an orbiting electron creates electromagnetic radiation which means that it would constantly lose energy, and fall to the nucleus. This does not happen. Quantum Mechanics solved this problem by showing that electrons travel in quantized orbits at their lowest energy state, and that they do not orbit but exist as a clould around the nucleus.

In quantum mechanics, objects are wavefunctions described by the Schrodinger equation. The location of a particle is unknown until the moment of measurement. We cannot know where it is beforehand, only the probability of finding it at any specific location.

This is a great model but it also has some problems. First of all, quantum mechanics is not relativistic. It will give you the wrong result if the quantum object is moving close the speed of light. The practical result of this is that as it doesn’t incorporate a speed limit, the speed of light, needed to make causality work. It allows for two measurements to influence each other faster than light. This would mean that there would be some reference frame in which the future could influence the past, breaking causality.

A second problem with quantum mechanics is that it only tells you how a particle evolves over time. It does not tell you how it is created or annihilated. So it can’t account for things like beta decay, due to the weak nuclear force, where a neutron transforms into a proton, an electron and an antineutrino.

This is where quantum field theory explains things that quantum mechanics cannot explain on its own. So what is quantum field theory? QFT a mathematical framework that combines classical field theory, special relativity, and quantum mechanics There is a field for every particle of the standard model.

All of these fields extend out in all of spacetime. The fields are always there and exist everywhere including inside your body. Although they exist everywhere and you can’t see them, they are not nothing. They are teeming with virtual particles. These are particle-antiparticle pairs that get created and destroyed constantly.

We can visualize these fields as a kind of ocean. Just like the ocean always has some turbulence, the fields always have a kind of turbulence even in their ground state of minimal energy. This turbulence is due to virtual particle creation and annihilation. In these turbulent seas, if there is enough energy, a larger wave can be created which CAN be measured. These are the real particles.

Energy can be transferred between two fields via a mediating boson field. This is considered an interaction or a force. Matter particles can’t interact on their own without a mediating boson.

So while in quantum mechanics there is no way for the neutron to split its energy into 3 different particles – a proton, electron and antineutrino, in quantum field theory this can be done via energy exchange between the fields. Although the number of particles may change, the total energy is always conserved. In other words, the energy of the fields is the same before and after the energy exchange. So by having quantum fields we can mathematically account for and model creation and annihilation of particles, as well as the mechanism of force exchange.

The icing on the cake is that the theory is fully relativistic, and free of causality violations. But even this modification of quantum mechanics is not perfect. For example, QFT is still missing gravity. We do not have a quantum field theory for gravity. So even QFT which is extremely accurate for the forces and particles we know of in the standard model, remains as yet incomplete.