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The universe is ultimately governed by mathematics. So would it be surprising if its creator - if there is one - would be a mathematician? At this point, cutting-edge physics is no longer observable, just conceivable - but only through math. And what physicists are doing now is to figure out the most basic laws of physics that governs the fundamental forces in the universe, by showing how consistent their math models are to the limited evidence provided presently.
Wish them luck... |
“Some would ask, how could a perfect God create a universe filled with so much that is evil. They have missed a greater conundrum: why would a perfect God create a universe at all?” – Miriam Godwinson, Sid Meier’s Alpha Centauri
Thus far we have seen how the giant cosmic jigsaw puzzle known as the universe had been pieced together one by one: classical mechanics, thermodynamics, electromagnetism, radioactivity, quantum mechanics, and relativity.
As science marches on, it dawned upon physicists that all of these theories are interconnected, directly or indirectly, and many of them use measuring units that can be derived from each other. Speed for instance is a factor of distance and time, or how wattage is a factor of mass, area and time. It goes back as early as Kepler’s planetary laws, and with the founding of new branches, new links were discovered.
Now physicists are dreaming of explaining the mechanics of the universe using a silver bullet; aptly called the theory of everything, or TOE. But before that, we must understand how the standard rules and factors play out.
The Standard Model
The Standard Model (SM) of physics is a theory of the elementary particles, which are either fermions or bosons. It also explains three of the four basic forces of nature. The four fundamental forces are: gravity, electromagnetism, the weak force, and the strong force. Gravity is the one the model does not explain.
The model uses the parts of physics called quantum mechanics and special relativity, and the ideas of physical field and symmetry breaking. Some of the mathematics of the SM is group theory, and also as equations which have biggest and smallest points, called Lagrangians and Hamiltonians.
There are four basic known forces of nature. These forces affect fermions, and are carried by bosons traveling between those fermions. The standard model explains three of these four forces.
As science marches on, it dawned upon physicists that all of these theories are interconnected, directly or indirectly, and many of them use measuring units that can be derived from each other. Speed for instance is a factor of distance and time, or how wattage is a factor of mass, area and time. It goes back as early as Kepler’s planetary laws, and with the founding of new branches, new links were discovered.
Now physicists are dreaming of explaining the mechanics of the universe using a silver bullet; aptly called the theory of everything, or TOE. But before that, we must understand how the standard rules and factors play out.
The Standard Model
The Standard Model (SM) of physics is a theory of the elementary particles, which are either fermions or bosons. It also explains three of the four basic forces of nature. The four fundamental forces are: gravity, electromagnetism, the weak force, and the strong force. Gravity is the one the model does not explain.
The model uses the parts of physics called quantum mechanics and special relativity, and the ideas of physical field and symmetry breaking. Some of the mathematics of the SM is group theory, and also as equations which have biggest and smallest points, called Lagrangians and Hamiltonians.
There are four basic known forces of nature. These forces affect fermions, and are carried by bosons traveling between those fermions. The standard model explains three of these four forces.
Strong nuclear force: A force which can hold a nucleus together against the enormous forces of repulsion of the protons is strong indeed. However, it is not an inverse square force like the electromagnetic force and it has a very short range. Yukawa modeled the strong force as an exchange force in which the exchange particles are pions and other heavier particles. The range of a particle exchange force is limited by the uncertainty principle. It is the strongest of the four fundamental forces.
Weak nuclear force: This force can change the flavor of a fermion and causes beta decay. The weak force is carried by three gauge bosons: W+, W-, and the Z boson.
Electromagnetic force: This force explains electricity, magnetism, and other electromagnetic waves including light. This force is carried by the photon. The combined theory of the electron, photon, and electromagnetism is called quantum electrodynamics.
Gravity: This is the only fundamental force that is not explained by the SM. It may be carried by a particle called the graviton. Physicists are looking for the graviton, but they have not found it yet.
The strong and weak forces are only seen inside the nucleus of an atom. They only work over very tiny distances: distances that are about as far as a proton is wide. The electromagnetic force and gravity work over any distance, but the strength of these forces goes down as the affected objects get farther apart. The force goes down with the square of the distance between the affected objects: for example, if two objects become twice as far away from each other, the force of gravity between them becomes four times less strong (22=4).
Weak nuclear force: This force can change the flavor of a fermion and causes beta decay. The weak force is carried by three gauge bosons: W+, W-, and the Z boson.
Electromagnetic force: This force explains electricity, magnetism, and other electromagnetic waves including light. This force is carried by the photon. The combined theory of the electron, photon, and electromagnetism is called quantum electrodynamics.
Gravity: This is the only fundamental force that is not explained by the SM. It may be carried by a particle called the graviton. Physicists are looking for the graviton, but they have not found it yet.
The strong and weak forces are only seen inside the nucleus of an atom. They only work over very tiny distances: distances that are about as far as a proton is wide. The electromagnetic force and gravity work over any distance, but the strength of these forces goes down as the affected objects get farther apart. The force goes down with the square of the distance between the affected objects: for example, if two objects become twice as far away from each other, the force of gravity between them becomes four times less strong (22=4).
Beyond the Standard Model
The standard model falls short of being a theory of everything. It does not include the full theory of gravitation as described by general relativity, or account for the accelerating expansion of the universe (as possibly described by dark energy). The model does not contain any dark matter particle that has all the properties got from observational cosmology. The SM is believed to be theoretically self-consistent. It has demonstrated huge and continued successes in experimental predictions, but it does leave some things unexplained.
The standard model falls short of being a theory of everything. It does not include the full theory of gravitation as described by general relativity, or account for the accelerating expansion of the universe (as possibly described by dark energy). The model does not contain any dark matter particle that has all the properties got from observational cosmology. The SM is believed to be theoretically self-consistent. It has demonstrated huge and continued successes in experimental predictions, but it does leave some things unexplained.
Electroweak Theory
The discovery of the W and Z particles, the intermediate vector bosons, in 1983 brought experimental verification of particles whose prediction had already contributed to the Nobel prize awarded to Weinberg, Salam, and Glashow in 1979. The photon , the particle involved in the electromagnetic interaction, along with the W and Z provide the necessary pieces to unify the weak and electromagnetic interactions. With masses around 80 and 90 Gev, respectively, the W and Z were the most massive particles seen at the time of discovery while the photon is massless. The difference in masses is attributed to spontaneous symmetry breaking as the hot universe cooled. The theory suggests that at very high temperatures where the equilibrium kT energies are in excess of 100 GeV, these particles are essentially identical and the weak and electromagnetic interactions were manifestations of a single force. The question of how the W and Z got so much mass in the spontaneous symmetry breaking is still a perplexing one. The symmetry-breaking mechanism is called a Higgs field, and requires a new boson, the Higgs boson to mediate it.
The discovery of the W and Z particles, the intermediate vector bosons, in 1983 brought experimental verification of particles whose prediction had already contributed to the Nobel prize awarded to Weinberg, Salam, and Glashow in 1979. The photon , the particle involved in the electromagnetic interaction, along with the W and Z provide the necessary pieces to unify the weak and electromagnetic interactions. With masses around 80 and 90 Gev, respectively, the W and Z were the most massive particles seen at the time of discovery while the photon is massless. The difference in masses is attributed to spontaneous symmetry breaking as the hot universe cooled. The theory suggests that at very high temperatures where the equilibrium kT energies are in excess of 100 GeV, these particles are essentially identical and the weak and electromagnetic interactions were manifestations of a single force. The question of how the W and Z got so much mass in the spontaneous symmetry breaking is still a perplexing one. The symmetry-breaking mechanism is called a Higgs field, and requires a new boson, the Higgs boson to mediate it.
Grand Unified Theory
In the mid-1970's physicists were excited with the recent success of Steven Weinberg, Abdus Salam and Sheldon Glashow in creating a unification theory for the electromagnetic and weak forces. By applying what is called 'group theory' , physicists such as Glashow, Georgi and others proposed that you could use the symmetries of 'SU(5)' to unite the weak and electromagnetic forces with the strong nuclear force which is mediated by gluons. This became known as 'Grand Unification Theory' or 'GUT', and quickly evolved into many variants including 'super-symmetric GUTs (SUSY- GUTs)', 'super gravity theory' and 'dimensionally-extended SUSY GUTs', before being replaced by string theory in the early 1980's.
It produced a lot of excitement in the late-70s and early-80's because it seemed as though it could provide an explanation for the strong, weak and electromagnetic forces, and do so in a common mathematical language. It's major prediction was that at the enormous energy of 1000 billion billion volts (10^15 GeV) the strong nuclear force would become similar (or unified) with the electromagnetic and weak forces. Applying these ideas to cosmology also led to the creation of Inflationary Cosmology.
Today, the so-called Standard Model of nuclear physics unifies physics (except for gravity) and uses some of the basic ideas of GUT to do so. Physicists are still trying to confirm several basic ideas in GUT theory such as 'spontaneous symmetry breaking' by looking for the Higgs Boson. GUT also uncovered a new 'Supersymmetry' in nature, which has continued to be searched for. The unpleasant thing about the current Standard Model is that it has several dozen adjustable constants that have to be experimentally fine-tuned to reproduce our physical world including such numbers as the constant of gravity, speed of light, fine structure constant, and the constants that determine how strongly the leptons and quarks interact. Physicists think that this is way too much, and so the search is on for a better theory that has far fewer ad hoc constants. There is also the problem that the Standard Model doesn't include gravity.
In the mid-1970's physicists were excited with the recent success of Steven Weinberg, Abdus Salam and Sheldon Glashow in creating a unification theory for the electromagnetic and weak forces. By applying what is called 'group theory' , physicists such as Glashow, Georgi and others proposed that you could use the symmetries of 'SU(5)' to unite the weak and electromagnetic forces with the strong nuclear force which is mediated by gluons. This became known as 'Grand Unification Theory' or 'GUT', and quickly evolved into many variants including 'super-symmetric GUTs (SUSY- GUTs)', 'super gravity theory' and 'dimensionally-extended SUSY GUTs', before being replaced by string theory in the early 1980's.
It produced a lot of excitement in the late-70s and early-80's because it seemed as though it could provide an explanation for the strong, weak and electromagnetic forces, and do so in a common mathematical language. It's major prediction was that at the enormous energy of 1000 billion billion volts (10^15 GeV) the strong nuclear force would become similar (or unified) with the electromagnetic and weak forces. Applying these ideas to cosmology also led to the creation of Inflationary Cosmology.
Today, the so-called Standard Model of nuclear physics unifies physics (except for gravity) and uses some of the basic ideas of GUT to do so. Physicists are still trying to confirm several basic ideas in GUT theory such as 'spontaneous symmetry breaking' by looking for the Higgs Boson. GUT also uncovered a new 'Supersymmetry' in nature, which has continued to be searched for. The unpleasant thing about the current Standard Model is that it has several dozen adjustable constants that have to be experimentally fine-tuned to reproduce our physical world including such numbers as the constant of gravity, speed of light, fine structure constant, and the constants that determine how strongly the leptons and quarks interact. Physicists think that this is way too much, and so the search is on for a better theory that has far fewer ad hoc constants. There is also the problem that the Standard Model doesn't include gravity.
String Theory
String theory is a set of attempts to model the four known fundamental interactions—gravitation, electromagnetism, strong nuclear force, weak nuclear force—together in one theory. This tries to resolve the alleged conflict between classical physics and quantum physics by elementary units—the one classical force: gravity, and a new quantum field theory of the other three fundamental forces.
Einstein had sought a unified field theory to explain the fundamental interactions within one model revealing the mechanics of the universe. Yet today's search for a unified field theory that is quantized and that explains matter's structure, too, is called the search for a theory of everything. The most prominent contender as a TOE is string theory converted into superstring theory with its 6 higher dimensions in addition to the 4 common dimensions (3D + time).
Multiple superstring theories appear to converge upon a shared range of geometry that, according to string theorists, is apparently the geometry of space. The mathematical framework that unifies the multiple superstring theories upon that shared geometrical range is M-theory. Many string theorists are optimistic that M-theory explains our universe's very structure and perhaps explains how other universes, if they exist, are structured as well. M-theory/supergravity theory has 7 higher dimensions + 4D.
String theory is a set of attempts to model the four known fundamental interactions—gravitation, electromagnetism, strong nuclear force, weak nuclear force—together in one theory. This tries to resolve the alleged conflict between classical physics and quantum physics by elementary units—the one classical force: gravity, and a new quantum field theory of the other three fundamental forces.
Einstein had sought a unified field theory to explain the fundamental interactions within one model revealing the mechanics of the universe. Yet today's search for a unified field theory that is quantized and that explains matter's structure, too, is called the search for a theory of everything. The most prominent contender as a TOE is string theory converted into superstring theory with its 6 higher dimensions in addition to the 4 common dimensions (3D + time).
Multiple superstring theories appear to converge upon a shared range of geometry that, according to string theorists, is apparently the geometry of space. The mathematical framework that unifies the multiple superstring theories upon that shared geometrical range is M-theory. Many string theorists are optimistic that M-theory explains our universe's very structure and perhaps explains how other universes, if they exist, are structured as well. M-theory/supergravity theory has 7 higher dimensions + 4D.
A Cosmic Wild Goose?
A single theory that explains every inner working of the most fundamental forces in the universe may be elegant. But then again, there are those who think it is a folly.
Thus far, we’ve found out that the more answers we have, the more questions came out of them. That’s one thing, another would be to descend into hubris; and as we had shown in a previous article, would lead to some embarrassing humility.
Godel's incompleteness theorem (refer below) seems to preclude a theory of everything that is complete and correct. However, there is nothing obvious that precludes us from having a theory of everything that fudges certain issues in ways that aren't totally consistent. In other words, if the theoretician is allowed to introduce errors (thus preventing correctness), nothing stops those errors making the theory complete.
A complete theory of everything never has to be used to be useful, though – at least not yet. If it's genuinely complete and of everything, it defines absolutely the number of forces, the number of fundamental particles, the topology of the universe (as distinct from its geometry), the number of dimensions that can be said to exist, the nature of time and the identities of those constants that are genuinely universal.
Which is why, as some would say, we’re intruding into the realm of gods. Let’s just hope the gods are willing to share their powers.
A single theory that explains every inner working of the most fundamental forces in the universe may be elegant. But then again, there are those who think it is a folly.
Thus far, we’ve found out that the more answers we have, the more questions came out of them. That’s one thing, another would be to descend into hubris; and as we had shown in a previous article, would lead to some embarrassing humility.
Godel's incompleteness theorem (refer below) seems to preclude a theory of everything that is complete and correct. However, there is nothing obvious that precludes us from having a theory of everything that fudges certain issues in ways that aren't totally consistent. In other words, if the theoretician is allowed to introduce errors (thus preventing correctness), nothing stops those errors making the theory complete.
A complete theory of everything never has to be used to be useful, though – at least not yet. If it's genuinely complete and of everything, it defines absolutely the number of forces, the number of fundamental particles, the topology of the universe (as distinct from its geometry), the number of dimensions that can be said to exist, the nature of time and the identities of those constants that are genuinely universal.
Which is why, as some would say, we’re intruding into the realm of gods. Let’s just hope the gods are willing to share their powers.
Ponder this
Why are the steps towards the theory of everything seems convoluted? Electromagnetism was first combined with weak nuclear force, and later strong nuclear force, before finally adding gravitation into the mix?
What would explain the drive towards this goal? Discovery itself is just too convenient. As we have mentioned before science should serve the here and now. What are the possible outcomes, the endgame, so to speak?
Discuss
What are the social and philosophical implications if a theory of everything were to be formulated and confirmed? How would it affect human civilisation, say, in the next century? How would it affect the conflict between science and religion?
And how would future humans see themselves, and where they fit in nature? You can use historical references for this, for example Copernicus' and Galileo's cosmological discoveries, or the effects of Darwin's theory of evolution.
Further readings
Theory of everything, an overview of TOE.
Fundamental interactions, outlines the four fundamental forces in nature.
Gravity, discovered in the 17th century, though its significance at the time was unforeseen.
Electromagnetism, discovered in the 18th and 19th century, later discovered to be linked to light spectrum.
Strong and weak nuclear forces, discovered in the 20th century, when nuclear physics became a norm.
Electroweak theory, the combination between electromagnetism and weak nuclear force.
Grand unified theory, the combination between Electroweak Theory and strong nuclear force.
String theory, more formally known as M-theory.
