Monday 6 May 2024

The Theory of Everything - how far is reality?

In the animal kingdom, the most dissatisfied species is humans. They are never content with their present situation and always seek to change their circumstances. Self-contentment brings an end to creativity, exploration, and innovation. If humans were content with their situation collectively, they might still be in the Stone Age, attempting to ignite fire with stones. Just like the wild animals of that era still live their lives the same way. Human evolution in terms of lifestyle, methodology, and practicality always surpasses their past generations due to their overall dissatisfaction. And this constant advancement fuels new discoveries and innovations.

Engrossed scientists in discoveries and innovations all pursue the ultimate goal of science - simplifying complex mysteries. Scientists from different branches embrace different approaches to find simple solutions to the complex mysteries of science. For instance, psychologists attempt to determine the correlation between the intricate workings of the body and brain with other related elements, believing that understanding these relationships simplifies complex problems. Biologists strive to understand how all these processes occur more straightforwardly by understanding the structure and functioning of cells. Chemists delve deeper into understanding the chemical structure of molecules and the process of chemical reactions. If they can unveil the nature of chemical reactions, their work becomes easier. Understanding the workings of atoms and subatomic particles further simplifies their tasks. But physicists refuse to halt anywhere. They delve into the interiors of atoms, even into the nucleus.

In the world of science, physics is a kind of imperialism. They believe that all substances and energies in the universe and all their interactions are encompassed within physics. Everything that has happened in the universe since its birth and everything that will happen in the future is included within the realm of physics. Therefore, the scope of physics extends from the internal structure of atoms to galaxies. The farther we go in time, the wider the scope of theoretical physics expands. Satisfaction is nowhere to be found in the visible universe. Even more countless theories of the invisible hypothetical universe are being discovered. Amongst all these theories, the ultimate goal of physicists is to explain everything in the universe correctly - a theory called the Theory of Everything[1].

Theoretical physicists believe that the Theory of Everything (TOE) will be such an eternal theory of physics that it will provide the correct answers to all questions - how the universe originated, why it originated, how everything in the universe - from quarks to cosmos - functions. Here, 'everything' means understanding everything comprehensively or just the fundamental aspects is a matter of debate.

Having differences is natural because many claims of physicists seem to be either wrong or time-consuming to prove in an empirical sense. For example, explaining how clouds form in the sky can be accurately described by the principles of physics. However, it may not be possible to create a mathematical model of a small cloud using the equations of physics that will accurately predict its formation at a specific time in the sky and match its shape and volume from all directions - this is not feasible for physics because it requires the use of highly changeable indices, which cannot be accurately applied even by many supercomputers.

Examples like this abound. For instance, if a glass is dropped from the hand, it will surely fall because of gravity. But whether it will shatter upon hitting the ground or not requires knowing many more things beforehand - such as what the glass is made of, how heavy it is, at what distance and with what speed it was dropped, whether any force was applied during the fall, and countless parameters starting from the structural elements of the glass. Considering all these parameters, it can be said that the glass will break. But is it possible to accurately predict how many pieces the glass will break into after it shatters? Is it possible to determine the shape and volume of those pieces?

So, no one expects to provide all details from the theory of everything. However, it is hoped that this theory can explain the origin of all natural forces in the universe, calculate energy, how the universe was created, and how it will end.

When we talk about the theory of everything, what exactly are we trying to understand? What will happen if this theory is discovered? And what if it's not discovered, or what are the consequences? Before answering these questions, we need to understand how physicists conceive such a theory.

In the 5th century BC, the Greek philosophers Leucippus and Democritus proposed atomism, or the theory of atoms, as the first theory of everything. With this theory, they sought to explain that everything in the universe is made up of atoms. For thousands of years, it was believed that atoms were indivisible.

What was the reason for calling atomism the theory of everything? The reason was that at that time, whenever the question of what everything is made of arose, the answer was - atoms. And the internal workings of matter were also explained through the interactions of atoms with each other. Despite the presence of different types of atoms in different substances, all substances were considered to be composed of atoms. Therefore, at that time, the fundamental elements of matter were atoms.[2]

Within the next few centuries, there was significant advancement in physics. Natural forces were discovered.

In 1687, Newton's law of gravitation was published. The discovery of this force was the first indication of natural forces among the natural forces. Newton's discovery revealed the principle of gravitation or gravitational force. Gravity is an extremely weak force. But this weak force has held all the objects in the universe invisibly together. Gravitational force is an attractive force. Its influence is everywhere in the universe. According to the theory of gravity - the force of attraction between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between the two objects. The larger and more massive the objects are, the greater the amount of gravitational force between them. Again, the closer they are, the greater the amount of force. If the distance doubles, the amount of force decreases by four times. According to the theory of gravitational force, no object attracts any other object. Newton's theory of gravity explains how the force of attraction works between objects, but it does not explain why it attracts. However, it is the attraction of the gravitational force that roughly explains why the satellites-planets-stars-galaxies of the universe revolve around each other.

Between 1750 and 1850, scientists from many countries in Europe conducted numerous experiments in various ways on electricity and magnetism. Among them, the most important discovery was that - due to the movement of electric charges, magnetism is created, and moving magnetic charges can generate electricity. Danish physicist Hans Christian Ørsted was certain in 1820 that there is a mutual relationship between electricity and magnetism. He named this relationship electromagnetism.

In 1831, British physicist Michael Faraday proved in the laboratory that magnetism is produced from an electric current, and electricity can be generated from a magnetic field. Fourteen years later, Faraday discovered that there is also a close relationship between electricity and light.

Then, in 1861, Scottish physicist James Clerk Maxwell accurately conceptualized - if there is a change in the electric field, then a magnetic field is created, and if there is a change in the magnetic field, then an electric field is created. Furthermore, it can be said more precisely - electricity can be found from magnetism, and magnetism can be found from electricity. Electric fields and magnetic fields are always perpendicular to each other. Maxwell mathematically demonstrated that the speed of light in a vacuum is three hundred thousand kilometres per second. Later, we have seen that light is a visible part of the electromagnetic spectrum. But in the vast invisible part, there are less energetic radio waves, infrared rays, microwaves, and more energetic ultraviolet rays or non-ionizing radiation, X-rays, gamma rays, etc. In the 20th and 21st centuries, we have seen the extensive use of electromagnetic waves in technology from Earth to space, from mobile phones to medical science - everywhere.

Maxwell's theory led to the discovery of the second fundamental force of nature - electromagnetic force. Electromagnetic force is much more powerful than gravitational force. Mathematically, electromagnetic force is very similar to gravitational force. The amount of electromagnetic force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them, just like gravitational force. Similarly to gravitational force, the intensity of this force increases if the amount of charge increases. If the distance between the charge doubles, the force decreases by a factor of four.

However, the key difference between gravitational force and electromagnetic force is that - this force can be either attractive or repulsive. If the charges are of the same type (both positive or both negative), the electromagnetic force will be repulsive. But if the charges are of opposite types (one positive and one negative), then the force will be attractive. As a result, in the case of large objects, gravitational force and electromagnetic force neutralize each other. Therefore, electromagnetic force is not effective in large objects. However, this force is very active between atoms and molecules. All kinds of chemical reactions and biological processes occur due to the electromagnetic force.

In 1895, X-rays were discovered, followed by radioactivity in 1896, and the discovery of electrons in 1897. After these discoveries, many physicists came to the idea that everything in physics has been discovered, and everything can be explained by the theories of gravitation and electromagnetism. In 1900, in a lecture at the British Association for the Advancement of Science, Lord Kelvin famously stated, "There is nothing new to be discovered in physics now. All that remains is more and more precise measurement."[3]

But it didn't take long for Lord Kelvin's words to be proven wrong. From the beginning of the 20th century, there has been a whirlwind of new discoveries in physics. On one hand, under the guidance of Max Planck, the journey of quantum mechanics began. On the other hand, Albert Einstein, in 1905 alone, published four groundbreaking papers that revolutionized our understanding of the entire universe. The theory of special relativity was formulated, establishing the relationship between mass, energy, and the speed of light.[4]

The discovery of the principle of relativity led to challenges in the theory of gravitation. According to Newton's theory, there is no change in the mass with the motion of an object, but according to Einstein's theory, there is a change in mass with a change in motion. Furthermore, in Newton's theory of gravitation, the distance between objects that are subject to gravitational force is not defined with respect to any frame of reference. But according to Einstein's theory of relativity, this distance depends on the reference frame. In the case of slowly moving objects, this difference in distance is not significant, but to calculate the gravitational force between extremely fast-moving celestial bodies, the principle of relativity must be applied to measure distances.

Einstein realized the need to revise Newton's theory of gravitational force. After a decade of research, in 1915, Einstein published the general theory of relativity, which essentially replaced Newton's theory of gravitation. According to this theory, gravitational force creates curvature in space-time, which depends on the distribution of mass in space and time. Essentially, the general theory of relativity transformed physics into geometry. The practical evidence of the general theory of relativity is regularly found in astrophysics. Its practical applications include all modern satellites, GPS navigation, and more.

After the discovery of special and general relativity theories, Einstein spent the rest of his life attempting to unify the principles of natural forces. However, he did not see success. Scientists today believe Einstein failed because he was not enthusiastic about using quantum mechanics. Furthermore, applying quantum mechanics to the theory of gravitation remains challenging.

Following the discovery of the nucleus of the atom, protons, and neutrons, two more natural forces were discovered from the theory of radioactivity – weak nuclear force and strong nuclear force. The weak nuclear force is responsible for radioactivity, which led to the formation of various elements in the universe. We usually do not experience this force in our daily lives.

The fourth natural force in nature is the strong nuclear force. This force holds protons and neutrons tightly within the nucleus. Among the four natural forces, the strong nuclear force is the most powerful. It is not felt outside the nucleus. The strong nuclear force is an extremely strong attractive force.

Einstein and other theoretical physicists attempted to unify these four natural forces into a grand unified theory or unified theory. Apart from gravitational force, the other three forces are applicable on the subatomic scale of particles (quarks, protons, electrons, and neutrinos). To understand the workings of subatomic particles correctly, quantum mechanics must be applied. Therefore, to properly understand the workings of the atomic nucleus, whether it's the electromagnetic force, weak nuclear force, or strong nuclear force, all must be transformed into quantum mechanics.

Furthermore, when applying the force of gravity to large celestial bodies like planets, stars, and galaxies, there is no need to transform it into quantum mechanics. However, if we want to understand the early universe, we must start from singularities. At that time, everything was microscopic. So, gravitational theory also needs to be transformed into quantum mechanics.

Whether it's Newton's theory of gravitation or Einstein's general theory of relativity, both are classical theories. None of them can be transformed into quantum mechanics because quantum mechanics operates under Heisenberg's uncertainty principle. Applying the uncertainty principle to general relativity will not yield realistic results. For example, then a black hole will not be entirely black, and a singularity will not be entirely empty.

To grasp the principles of everything, all of nature's forces must be unified. To do this, the quantum transformation of all four forces is necessary. These principles' quantum forms are called quantum field theory. In quantum field theory, particles or matter exchange particles are fermions (electrons and quarks), and force exchange particles among fermions are bosons (photons).

The quantum transformation of the electromagnetic force has been made possible through Richard Feynman's discovery of quantum electrodynamics.

Using quantum field theory, Professor Abdus Salam, Steven Weinberg, and Sheldon Glashow unified electromagnetism and weak nuclear force.

The weak nuclear force and the electromagnetic force are fundamentally the same. However, they appear different because the exchange particles of the weak nuclear force have mass, whereas the exchange particles of the electromagnetic force do not have mass. But in both fields, the exchange particles are bosons. In the field of the electromagnetic force, the exchange particle is the photon, which has zero rest mass and travels at the speed of light. In the field of the weak nuclear force, the exchange particle has mass. As a result, the speeds of these bosons change with distance.

In weak nuclear interactions, charge changes occur. This means that charge-neutral neutrons transform into positively charged protons or negatively charged electrons. Consequently, the current obtained is called a charged current. On the other hand, in the electromagnetic force field, there is no change in charge. Therefore, in this case, the current obtained is called neutral current.

Weinberg and Salam suggested that the only difference between the weak nuclear force and the electromagnetic force is the mass of the exchange boson. In the field of the weak nuclear force, the exchange particle, the W boson, is nearly 100 times heavier than the mass of a proton. Because of this, heavy photons are also referred to as bosons of the weak nuclear force.

Abdus Salam and Steven Weinberg proposed that in the weak nuclear force field, both neutral and charged currents could occur. Both types of exchange particles in the weak nuclear force are collectively called the W+, W-, and Z0 bosons. +, -, and 0 denote positive, negative, and neutral charged bosons, respectively. These three are collectively referred to as intermediate vector bosons. These vector bosons are very heavy inside the nucleus. It is there that weak interactions occur. Outside the nucleus, electromagnetic interactions occur.

In 1973, at CERN's examination, it was possible to demonstrate weak nuclear interactions without any exchange of charge. The existence of neutral currents was proven. Similar results were obtained at Fermilab. In 1978, at the Stanford University Linear Accelerator (SLAC), weak nuclear force and electromagnetic force were found to be reconcilable by observing the interactions of electrons and positrons. For this discovery, the 1979 Nobel Prize in Physics was awarded to scientists Abdus Salam, Steven Weinberg, and Sheldon Glashow.

The possibility of unifying electromagnetic force and weak nuclear force, observed through the exchange of W and Z bosons, inspired scientists to further consolidate other forces. Quantum chromodynamics was developed to incorporate the strong nuclear force. Within nuclei, protons and neutrons were found to be composed of smaller particles called quarks. Quarks are categorized into six types: up, down, top, bottom, charm, and strange. Protons are made up of two up quarks and one down quark, while neutrons consist of two down quarks and one up quark. The force between quarks increases as they move farther apart, preventing individual quarks from being isolated in nature.

In the Standard Model of particle physics, the inclusion of the Higgs boson completes the theory. According to the Standard Model, all matter in the universe is composed of six types of quarks and six types of leptons (electron, electron neutrino, muon, muon neutrino, tau, and tau neutrino). Among these, only four particles (up quark, down quark, electron, and electron neutrino) are considered fundamental constituents of all matter. Forces on the subatomic scale are mediated by force-carrying bosons (Z, W, photon, gluon, and Higgs).

While the theory of fundamental particles in the Standard Model can explain phenomena on both atomic and nuclear scales, it fails to unify interactions on a larger scale due to the inability to quantize the meaningful gravitational force.

In 1976, scientists envisioned a possibility: the concept of supergravity emerged as a potential theory for incorporating gravity into the framework of Einstein's General Relativity by introducing some theoretical quantum particles. The idea of supergravity originated mainly from the concept of supersymmetry. Symmetry or symmetry breaking is widely used in particle physics for the mathematical needs of quantum mechanics. A system is called symmetric if it remains the same under transformations of space-time or quantum states. For example, a perfect circle. The concept of supersymmetry is somewhat more complex. According to the principles of supersymmetry, every particle will have a bosonic component and a fermionic component. That is, if a quark carries a certain mass, there will be another particle with the same mass that carries force. On the other hand, a photon carries force naturally. In supersymmetry, there will be another partner photon that carries mass. After the mathematical processes of the entire system, if one of these hypothetical particles becomes positive, the other becomes negative and cancels out.[5]

Supergravity theory assumes that the carrier of the gravitational force will be the "graviton," which has a spin number of 2. It is a supersymmetric particle. Particles with spins of 3/2, 1, 1/2, and 0 can also be added to the graviton, where their spins are 5 (2s + 1 = 2 x 2 + 1 = 5), 3/2, 1/2, and 0, respectively. The energy of particles with spins of 0, 1, and 2 will be positive, while particles with spins of 3/2 and 1/2 will be negative. Thus, the sum of energies of these hypothetical particles will be the sum of positive and negative energies. However, calculating this infinite series of hypothetical particles can be time-consuming even for powerful computers, taking years after years. And if there's an error in the calculation, there's no going back—everything must start from scratch. So, while supergravity or supersymmetry (SUSY) may be successful mathematically, it's not very realistic. Super symmetry has not yet been proven in the Large Hadron Collider.

General relativity is a classical theory. When scientists attempted to quantize it, they pursued another method. We know gravity exists everywhere in the universe, and it is continuous. However, quantum systems are discrete. Scientists thought of quantum gravity as loops, where space-time would be quantized – meaning divided into small loops or spin networks. Just as in quantum mechanics, where energy levels are calculated in discrete steps, gravity would also be calculated in loop quantum gravity. This would allow for quantization of both two-dimensional area and three-dimensional volume. However, loop quantum gravity does not support singularities. This means that loop quantum gravity cannot provide answers to how the universe began. If it cannot answer this question, it cannot lay claim to the entire theory.

At this time, scientists introduced another theory of different concept – called string theory. More probable than supergravity theory, string theory posits that everything in the universe is made up of extremely small strings or filaments. According to the standard model of particle physics, where fundamental particles like electrons and quarks are assumed to be the end point, string theory suggests that these are not the ultimate particles; they are also made up of even smaller string-shaped waves. String theory is more complex than any other theory because it operates in a ten-dimensional world instead of the conventional four-dimensional space-time.[6]

Imagining ourselves living in a ten-dimensional space rather than the familiar three-dimensional space is not easy. But even on a smaller scale than electrons and quarks, space-time can be divided in such a way that there are ten dimensions. The concept of a ten-dimensional space is necessary in string theory for mathematical purposes. String theorists have attempted to mathematically prove that this theory is extremely successful and effective as a unified theory of everything. However, various research groups have discovered several more forms of string theory using different mathematical approaches. It has been observed that in the realm of multiple-dimensional space, one can split the five primary forms of string theory, each representing the conventional four-dimensional space-time, in various ways. All these forms were united into the extended version of string theory called M-theory. Stephen Hawking wrote in his book "The Grand Design", "Perhaps M stands for 'Master', 'Miracle', 'Mystery' - or all of them."[7] However, John Gribbin explained that the M in M-theory stands for "Membrane" instead of "String" or "Superstring."[8] It is believed that M-theory can explain everything in the universe. To work with M-theory, one needs eleven-dimensional space. It is said that in the ten-dimensional string theory, one dimension was dropped.

The powerful claim of M-theory is that it can explain everything in terms of its principles. Although no concrete evidence for it has been found yet, mathematically, M-theory can explain the workings of everything from one-dimensional strings, two-dimensional membranes, to three-dimensional objects. Mathematically, M-theory is so potent that it supports the idea of countless new universes. Scientists are exploring the theory of everything to express everything in a single universe. However, if M-theory is indeed that theory, then it gives rise to a new problem - the birth of even more countless universes. So, there is doubt about how successful it will be as a theory of everything.

Now the question arises, why do we need the theory of everything? There is no other branch of science, apart from physics, that is so concerned with this. But why do we need this theory in physics?

Einstein spent more than half of his life searching for the theory of everything - the Grand Unified Theory. He hoped to find a mathematical formula within which everything in the universe could be encapsulated. He was not successful, but physics did not suffer any loss from it.[9]

Later, theoretical physicists set their sights on a theory even more ambitious than Grand Unification, one that could provide answers to all the fundamental questions of the universe. Behind popularizing this theory, the contributions of scientists like Stephen Hawking were among the most significant. In 1981, in his first lecture as the Lucasian Professor, Stephen Hawking expressed hope that in the next twenty years, the Theory of Everything (TOE) would be discovered. Then, once the theoretical physicists had it in their hands, there would be no more work left to do. Stephen Hawking concluded his Brief History of Time in this manner: if we can discover a complete theory, it will not only be understandable to scientists, but to everyone. Then we will all be able to discuss why and how we and our universe came into existence.

Stephen Hawking's life partner, Jane Hawking, in her remarkable memoir "Music to Move the Stars: A Life with Stephen," recounts an anecdote where James Marsh, when making a film, contemplated naming it after one of Stephen Hawking's popular books, "The Theory of Everything."[10] Released in 2014, this film gained widespread popularity - for it was a reflection of Stephen Hawking's life. The book "The Theory of Everything" is a collection of seven popular science lectures by Stephen Hawking, initially published in 1996 as "The Cambridge Lectures." Later, in 2005, the book was published under the title "The Theory of Everything." The seventh and final chapter of the book is titled "The Theory of Everything." Five years later, in 2010, Stephen Hawking collaborated with Leonard Mlodinow to publish another popular book, "The Grand Design." In this book as well, there is a chapter titled "The Theory of Everything." Stephen Hawking considered the Theory of Everything to be the Grand Design of the universe.

But Stephen Hawking had sufficient doubt that the entire mystery of the universe could be solved by the sole theory of physics. In his 2002 lecture titled "Gödel and the End of Physics," Stephen Hawking said, "Many will be disappointed if we do not find one ultimate theory that can explain everything. I used to be one of them, but I have changed my mind. I am now glad that our search for understanding will never come to an end and that we will always have new discoveries to look forward to."

[1] P.C.W. Davies and J. Brown (Eds.), "Superstrings: A Theory of Everything?" Cambridge University Press, Cantor Edition, Victoria, 1992.

[2] James R. Johnson, "Does a Theory of Everything Exist?" Philosophy and Cosmology, Issue 26, 2021.

[3] "A Theory of Everything?" Nature, Issue 433, January 2005.

[4] Don Lincoln, "Einstein's Unfinished Dream: Practical Progress Towards a Theory of Everything," Oxford University Press, 2023.

[5] Moataz H. Imam (Ed.), "Are We There Yet? The Search for a Theory of Everything," Bentham Science Publishers, 2011.

[6] Brian Greene, "The Elegant Universe," Vintage Books, New York, 2003.

[7] Stephen Hawking and Leonard Mlodinow, "The Grand Design," Bantam Books, London, 2010.

[8] John Gribbin, "In Search of Superstrings," Second Edition, Icon Books, London, 2007.

[9] Michio Kaku, "The God Equation: The Quest for a Theory of Everything," Doubleday, New York, 2021.

[10] Stephen Hawking, "The Theory of Everything," Phoenix Books, California, 2005.

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