In today's article, we will be attempting to understand the Quantum Field Theory. As an overview, Quantum Physics or Quantum Mechanics is a fundamental theory that provides descriptions of the physical properties of nature at the scale of atomic and subatomic particles. Meaning, Quantum physics is the study of extremely small particles like atoms, protons, electrons, etc, and even subatomic or elementary particles like gluons, Higgs boson, photons, quarks, etc. Initially, I thought quantum mechanics and quantum field theory meant the same thing, but quantum field theory is a part of quantum mechanics that combines the elements of special and general relativity to explain the behavior and interactions at a subatomic level. Quantum Mechanics begins with several scientists like Einstein, Planck, etc observing the particle-wave duality of light, which states that light exhibits properties of both waves and particles, but it is with the help of Bohr and Heisenberg, they further extended their understandings that even matter - specifically subatomic particles - also attains this kind of particle-wave duality. From this emerges Erwin Schrodinger's The Schrodinger Equation, which is a wave function that describes how matter waves change over time and also helps us predict analytically and precisely the probability of the evolution of quantum systems. However, the marco physics didn't cooperate with microphysics. It's been long known that Erwin Schrodinger's quantum mechanics model never worked out with Einstein's general and special relativity because relatively wants events to be continuous and deterministic, meaning that every cause matches up with a specific local effect, whereas quantum mechanics produces events that are discontinuous and probabilistic rather than definite outcomes. Take for example quantum jump or leap, it is the quantum phenomenon where an electron or an atom can abruptly transition from one discrete energy state to another when it interacts with photons of light. The abrupt transition states that the electron moves to a different energy state without having to move through space or in other words has a discontinuous trajectory. Overall, in the microscopic realm, there is uncertainty, chaos, fluctuations, entanglements all of which go against Einstien's gentle, smooth and deterministic model of the curved spacetime continuum.
The contradiction between Relativity and Quantum Mechanics left an English theoretical physicist, Paul Dirac, curious if he could find a way to combine these two equations. Dirac started with Einstein's relativity equation and attempted to unify it with the spin - an intrinsic property of all elementary particles - of a quantum object. He was stuck in a tangent of messy mathematics until he stumbled upon a new idea of including anti-spin into his equations. This lead all that messy mathematics to simplify into a single beautiful equation known as the Dirac equation, which successfully predicted the motion of electrons at any speed, even whilst present in other fields like an electromagnetic field, compared to Schrodinger's equation that was confined to only describing the possible positions of electrons with no internal properties. But, what was this anti-spin? To better understand, Dirac was basically solving a quadratic equation where he got two solutions, one being positive and another being negative; the positive solution, as Dirac knew, represented matter, but the negative solution allowed the existence of antimatter. Initially, Dirac was rather confused, leading him to ignore the negative solution, but later on, he realized that anti-matter is real except they don't seem to be present in numerous quantities. Dirac attempts to explain his negative solution through a thought experiment called the Dirac Sea. Let's assume that there are imaginary electrons everywhere in the universe covering all the negative energy states from negative infinity to zero; introducing another electron to that sea results in an electron sitting on top or in the positive energy state, which is what we interact regularly. Similarly, we can also remove an electron from that sea that leaves a hole in the surface; the hole acts as a particle itself because it takes up the space of the electron, meaning it has the same mass but has the opposite properties. Although the Dirac sea doesn't exist, these holes act as a visualization of what is now called the antimatter; in this case, they represent the antimatter particle of electron aka the positron. It is said that the universe during the big bang released an equal amount of matter and anti-matter, but why is one more abundant than the other is because when matter and antimatter interact with each other they release energy, so essentially all the energy that we now have - maintaining energy conservation - are the interactions of matter and antimatter during the big bang. We can better understand why the interacts between matter and anti-matter release energy by further expanding on Dirac's Sea analogy. As anti-matter represents holes in the Dirac sea, if you bring in an electron from a positive energy state near that hole, it essentially falls into the hole or in reality interacts with the Positron to release the positive energy stored in it due to it being in a positive energy state, again maintaining energy conversation. As a whole, it is quite intriguing to me to comprehend how powerful mathematics can be as Dirac just proved the existence of anti-matter almost as a mere accident. Dirac's success in relating relativity with quantum mechanics gave rise to the idea that all elementary particles have their own fields. Why fields? because in this equation, elementary particles are represented as Einstien's model of spacetime fabric, which solely talks about fields (Einstein's spacetime is very similar to fields).
Coming back to the big question, What is the Quantum Field theory or QFT, it is a theory that describes all elementary particles and their anti-particle counterparts as excitations or vibrations in their respective fundamental fields that exists throughout the universe. Meaning that every elementary particle has a field like the electromagnetic field of a proton, but in this case, it is of every elementary particle, where the particle itself is an oscillation or spike or peaks in the field. By representing particles as fields, Dirac's equation worked better in predicting the evolution and interactions of the quantum system than the Schrodinger equation that was confined to only the physical properties of individual elementary particles, whereas the Dirac equation described the interactions as an overall change in the entire quantum system. This theory came to be known as the Second Quantization with Schrodinger's equation being the First Quantization. Secondly, the Schrodinger equation never accounts for the creation and the destruction of elementary particles, whereas in Dirac's equation, it heavily contributes to the creation and destruction of particles and anti-particles counterparts via the concept the excitations or vibrations in its respective field. Its a weird analogy to think about all particles and subatomic particles as fields vibrations because essentially, the theory states that when you zoom in to a chair to their atoms and elementary particles, suppose, then all you would find are particles acting as oscillations in their fields that have the possibility of being and evolving in and at any locations of the universe. After all, the main purpose of the field theory or quantum physics, in general, is to understand different possibilities of when phenomena showing quantum behavior occur. However, there are infinite ways on what can happen to a quantum system before and after the measurement is taken, so to solve this problem came the American genius, Richard Feynman. This is the man who figures out a methodology called the Path Integral Formulation to show that a quantum system can and will take all of the possible paths before and after a measurement where they are in a superposition with different possibilities at different locations. However, the most extreme path-like ones that seem to break the speed of the light barrier seem to cancel out with other similar possibilities, resulting in only a few interactions and evolutions that we experience daily. But coming back to the main idea is that Quantum field theory is the most successful theory ever to proposed mainly due to the sheer predict power about quantum systems and its ability to encompass relativity with quantum mechanics, two of the most famous but contradicting theories, elevates its profoundness and foreshadows its possibility to achieve even more remarkable discoveries in the near future.