Quantum Fields - the Lego blocks of the Universe

The founding father, perhaps the grand-father of physics (theoretical physics per se), whose idea changed our world and post which our perception about the world changed forever was proposed by an ancient Greek pre-Socratic philosopher Democritus in 4 century BC. According to him, all the matter is made from small pieces called “atoms” (Greek: atomos), meaning “uncuttable”. Democritus believed that the atoms differed in size and shape and are in continuous motion and they collide and sometimes rebound or stick together. Therefore, changes in the matter were a result of this breakage or combination of atoms. His theory of atoms was elaborated later by the Greek philosopher Epicurus, and Roman Epicurean poet Lucretius.

Jump to 18^th century, Antonie Lavoisier gave the law of conservation of mass, while Joseph Louis Proust presented the law of definite proportions. English scientist John Dalton expanded on their work and gave the law of multiple proportions. He further found that this concept can be elegantly explained using the atomic theory, and used it to explain why chemical elements reacted in certain ways through a series of experiments involving gases. Thus, the first truly scientific theory of the atom was formed, since Dalton had reached his conclusions by experimentations and examinations. On the downside, Dalton did not take into account that in some elements atoms may exist in molecules. This for then corrected by Avogadro in 1811 using the Avogadro’s law. In 1879, Sir William Crookes developed Crookes tubes to investigate cathode rays. The particles emitted from the cathode (cathode rays) were believed to be negatively charged atoms or molecules. It was because atoms were believed to be the smallest fragment of matter. In 1896, Henri Becquerel and his students Marie and Pierre Curie had discovered rays from uranium salts could pass through opaque papers, thus radioactivity. Further experiments showed that the beam of radioactive ore consisted of three types of particles: positively charged, negatively charged and neutral. Thus, it was realized that the atoms are more complicated than what Dalton had proposed. Then in 1897, J.J. Thomson discovered the corpuscles (later named as electrons based on the theoretical particle predicted by George Johnstone Stoney in 1874) through his cathode ray experiments. He thus suggested that atoms were indeed divisible and corpuscles were the fundamental building blocks and proposed the plum pudding model of an atom. In 1911, a former student of Thomson, Ernest Rutherford interpreted the Geiger-Marsden experiments and rejected the plum pudding model, to propose a new Rutherford model with a newer fundamental particle, the proton. Rutherford, however, postulated the presence of the third particle but it no such experimental evidence was present. It was in 1932 that James Chadwick discovered the neutron.

So, by 1935, scientists had learnt that the nucleus consisted of a positively charged protons and a neutrally charged neutrons and the elements differed due to the difference in the number of protons. Also, the third fundamental particle, electron, circumambulates around the nucleus. Additionally, there existed three fundamental forces, the electromagnetic force (the electric and magnetic forces which were unified by Maxwell) which pulls the negatively charged electrons towards the positively charged protons, the nuclear forces which bounded protons and neutrons and, gravity, which pulled everything to every other thing in the universe.

Cut to - the 1980s, the atom was no longer fundamental or the smallest indivisible entity. The research revealed that that the protons and neutrons are further made up of three particles or two quarks (up and down quarks). Also, the nuclear force was split into two forces, the weak and the strong nuclear forces. The strong nuclear forces hold the quarks together, whereas the weak nuclear forces hold the protons and neutrons together. The weak nuclear forces also created the fourth fundamental particle, the neutrino. Thus the universe by 1980 consisted of four fundamental particles and four fundamental forces as opposed to the three-particle, three force universe in 1935s.

 “Ignorance is bliss”

“Little knowledge is a dangerous thing”

And so, as science continued its voyage, it was understood that even this model of four fundamental particles and four fundamental forces are incorrect. The best theories of physics today do not have a quark-electron system as the fundamental entities. In fact, they don’t rely on particles at all. These theories tell us that the fundamental building blocks of nature are fluid-like substances called fields, which are spread across the entire universe and ripples in interesting ways.

The concept of fields, however, is not new. In 1821 Faraday found that current-carrying wire generates circular lines of forces around it, which he termed as the magnetic field of current. In 1831, he discovered electromagnetic induction (changing magnetic fields induce electric current). So, originally it was faraday who introduced the concept of field and field lines and showed that electricity and magnetism are connected. However, Faraday’s lines of force were not accepted until James Maxwell mathematically unified the concept and published his field equations in 1861, and Heinrich Hertz demonstrated propagation of electromagnetic waves in laboratory’s using the first-ever receivers and transmitters in 1888.

The early 1900s, however, was again a revolutionary period for science. This period witnessed the birth of quantum mechanics, which describes the energy levels of nature at the smallest scales. Newtonian and Maxwellian electrodynamics together made up Classical physics. Its three defining characteristics: determinism, continuity and locality were all challenged by quantum mechanics. The underlying basis for quantum mechanics is that like energy is not continuous.

A short digression on the birth of quantum mechanics: The problem of electricity and magnetism was quite resolved after Maxwell’s equations came into the picture. However, in 1824, a French engineer, Sadi Carnot, published his works on efficiencies of heat engines and gave birth to classical thermodynamics. He also postulated the first law of thermodynamics. The mysterious concept of entropy was introduced by German Rudolph Clausius. He showed that entropy for irreversible processes always increases and postulated the Second law of thermodynamics as well. He also showed that it is entropy which distinguishes reversible from irreversible cycles. In Newtonian mechanics, all the processes are reversible. But in nature one can easily find irreversible processes, to which Newtonian mechanics defends using probabilistic arguments, that is, the irreversible looking process is indeed reversible, only the reversibility is highly improbable. This suggests that the increase in entropy has something to do with probability. In the classical thermodynamics of Clausius, entropy and other quantities are state functions, that is, they are treated mathematically continuous, and therefore despite years of efforts to understand the entropy, even by Max Plank, all proved futile. It was an Austrian physicist Ludwig Boltzmann, who around 1870s, showed that there is an entirely different way to think about entropy. Boltzman rewrote all of the classical thermodynamics as a theory of the large scale statistics of atoms and molecules, thereby creating statistical mechanics. Statistical mechanics differentiates macroscopic and microscopic matter. But his theories were strongly criticized by Wilhelm Ostwald, who believed that matter consists of continuous fields of energy and Ernst Mach who did not believe in the existence of atoms or molecules since they were not experimentally observed until then. The major barrier for acceptance of statistical interpretation was the fact that thermodynamic properties such as pressure, temperature etc. were studied as properties of matter, which at macroscopic scale appeared smooth. Thus, these properties were also believed to be continuous, in fact, up until the mid-1800s, the heat was thought of as a sort of fluid, called caloric. Boltzman suffered severe depression due to harsh criticisms for his theories, and in 1906 committed suicide. Coming back to Plank, in the mid-1890s he got interested to understand the Kirchoff's black body spectrum. Lord Rayleigh, probably the most senior British physicist of his generation used the equipartition theorem from classical physics, which although was roughly accurate at lower frequencies, at higher ones resulted in Ultraviolet Catastrophe. Wien used the Maxwell-Boltzmann distribution of atoms which could then describe the high-frequency emissions, but breaks down for low-frequency emissions. Plank had long resisted using Boltzmann’s methods, but at the end surrendered. Inspired by the calculation of Boltzmann, which he had carried out in gas theory, in which Boltzmann had taken energy to be broken into small discrete chunks. He merely used this quantization for calculative purposes, and Plank adopted the same idea only to apply to the spectral problem. He found that by allowing quanta of energy, he could derive the formulae for the distribution of energy among frequencies as a function of temperature. Thus on December 14, 1900, quantum mechanics was born.

Quantum field theory emerges when we try to combine the quantum mechanics, the discrete natured quanta, with the continuous fields like the ones Faraday had talked about. Faraday and Maxwell had shown that light is nothing but waves of electromagnetic fields, which happen to fall into the visible region. But when quantum mechanics is applied to this, it is found that light is not as smooth as it looks. Instead, as proposed by Einstein through the photoelectric effect experiment, light consists of particles called photons, which are discrete packets of waves. This idea actually applies to all the particles in the universe.

So, there exists a field (or fluid) that fill the entire universe and the ripples in these fields (or fluid) that gets tied up into little bundles of energy using the rules of quantum mechanics, and it is these we call as particles. For example, the ripples in the electromagnetic field get bundled up into quanta which are observed as photons or what we call a photon of light. In the same way, all the electrons lying in our body are not fundamental, instead, the electron field is fundamental. All the electrons are merely the result of the ripples created in these electron fields. Thus, in a way we all are connected to each other. A good analogy is to think about ripples created at different parts of the ocean, no matter what they all would be the part of the same underlying ocean. Therefore, the basic underlying building blocks are not particles, but fields.

Using the standard model of physics, if one performs simulation for the empty space or vacuum, it doesn’t appear calm, at all. 

This is because irrespective of particles present, the field is omnipresent and additionally is governed by the rules of quantum mechanics. Therefore, it is the  Heisenberg’s uncertainty principle which doesn’t allow this field to sit still. Thus, the field keeps on fluctuating and bubbling and it is these what is called quantum vacuum fluctuations. These are not as abstract as it sounds. It is indeed measurable and the forces which these quantum fluctuations exert is called Casimir force. These have been observed to behave in quite a similar way as the theories had predicted. After doing some more experiments and calculations, for the systems our resources could solve, for example calculating the magnetic moment of the electron, the experimental data matches with the theoretical calculations when derived with the first principles up to 11-12 significant digits. It is therefore believed that Quantum Field Theories are the best theories ever developed in science.

The period table of physics now looks something like this,

What it shows us is that all the matter is made up of just four particles, the up quark, the down quark, electron and an electron neutrino. However, remember that the fields underlying these particles are fundamental not the particles. Strangely, however, which scientists do not fully understand, there exists six other particles and their underlying fields which exist in the universe. The only difference between I with II and III is that the particles in III are heavier than II  which is further heavier than I. So, all of us are made of the four fields (I), and only in more exotic locations are the other fields required (II and III). Now, these 12 fields interact with each other, and they do so using four different forces – electromagnetic, gravity, weak nuclear and strong nuclear. As discussed, the strong nuclear force holds quarks inside the nucleus, whereas the weak nuclear force is responsible for radioactive decay and in combining protons and neutrons. Again each of these forces is associated with a field. Faraday revealed the electromagnetic fields. Then there is W and Z bosons field which carries the weak interaction and gluon field which carries the strong interaction. Lastly, the field of gravity in space and time itself, which was given by Einstein through the general theory of relativity. So, there are 12 matter fields and 4 force fields and the world we live in consists of these 16 fields interacting with each other. This is what the greatest theory of physics is, called the standard model.

In recent years another field has come into the light, which was predicted in the 1960s by physicist Peter Higgs and was finally discovered by the Large Hadron Collider (LHC) in 2013, that is, the Higgs field. It is this field which gives mass to everything in the universe. So the properties of particles like their charge and mass is simply the way of telling how their fields interact with the other fields. For example, the electric charge is the way the electron field interacts with the electromagnetic field. The mass of an electron is the way the electron field interacts with the Higgs field.

The equation presented below is the one for the standard model of physics. This is the holy grail. It is this equation which has correctly predicted the result of every single experiment ever done in science. All the experiments performed by all the scientists over centuries, from Faraday to Maxwell, to Colomb, everything gets concise into this equation and this is the best thing physicists have until now. 

Having said that, there’s still, scope for improvement because there exists dark matter, dark energy, the fields of which are still to be incorporated into the equation.

Another challenge to the equation is our lack of understanding of the big bang. Physicists still do not know what kicked it off and what happened during the first fraction of seconds during the inflation, however, they understand relatively well what had happened afterwards the first fraction of seconds and until today. One can say all this with substantial confidence because the physicists have even photographed the early staged universe which is called as the Cosmic Microwave Background.

Right after the Big Bang, the universe was extremely hot, so much that everything was in the plasma state. This enormous explosion was throwing everything away and stretching the space to create our now known universe. The extremely hot plasma materials during this time, as per the Wein’s displacement law (which quantitatively says that any object above 0 Kelvin emits radiation of a certain wavelength), emitted highly energetic radiations (high energy=high frequency=low wavelength) which fell in the range of gamma wavelength. Thus the early universe was filled with gamma rays. However, the dense and hot environment did not allow these radiations to permeate through them. With passing time, the universe cooled down and the hot plasma cooled enough to form atoms, and 13.7 billion years after, us! The gamma radiation emitted by these plasma materials,  a fraction of second before they were forged into atoms, thereby was let loose into the universe. The passage of time witnessed the expansion of the universe. As the universe expanded, space stretched, and so the gamma waves that were in the space stretched too. Thus they transformed into X-rays and then to UV rays and later sometimes even to the visible spectrum. Yes! During this time of the universe, the entire space was colourful and not the dull black as now. But space kept on stretching until now when these wavelengths fell into microwave wavelength. Since the waves have stretched with the entire space they occupy (which was the entire universe at that time), and so they still fill the entire universe even now. Astronomers collected all these stretched waves and it is called the “cosmic background radiation” or CBR.

This flickering tells the physicists about the phenomenon which was unfolding in the early stage universe when it was a baby. As we know that fields are fundamental and not the particles and so the radiation must be the result of some field interactions. Scientists believe that this flickering is actually caused by the quantum fluctuations happening in the first fraction of seconds after the universe was born, which then expanded with the universe. In fact, the measurements match what would be expected if small thermal variations, generated by the quantum fluctuations in a very tiny space, had expanded to the size of the observable universe we see today. But which field is the one which flickered and has been observed in the CMB is still questionable.

The equation for the standard model of the universe still looks quite long, isn’t it? Can physicists have just one term from which all others, the Higgs field, gravity field, nuclear fields, particles and everything? Surprisingly, physicists do have a possible answer to that as well, which is the String Theory.

References

Fermilab. 2013. Particles, fields and the future of physics. July 11.

The Royal Institution. 2017. Quantum fields: the real building blocks of the universe. February 15.

Universe Today. 2016. Atomic theory. July 28. Accessed July 23, 2019. https://www.universetoday.com/tag/atomic-theory/.

Wikipedia. 2019. Atomic theory. July 22. Accessed July 23, 2019. https://en.wikipedia.org/wiki/Atomic_theory.