Origin of water on Earth

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Water covers about 71% of Earth's surface.

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The origin of water on Earth is the subject of a body of research in the fields of planetary science, astronomy, and astrobiology. Earth is unique among the rocky planets in the Solar System in having oceans of liquid water on its surface. Liquid water, which is necessary for all known forms of life, continues to exist on the surface of Earth because the planet is at a far enough distance (known as the habitable zone) from the Sun that it does not lose its water, but not so far that low temperatures cause all water on the planet to freeze.

It was long thought that Earth's water did not originate from the planet's region of the protoplanetary disk. Instead, it was hypothesized water and other volatiles must have been delivered to Earth from the outer Solar System later in its history. Recent research, however, indicates that hydrogen inside the Earth played a role in the formation of the ocean. The two ideas are not mutually exclusive, as there is also evidence that water was delivered to Earth by impacts from icy planetesimals similar in composition to asteroids in the outer edges of the asteroid belt.

History of water on Earth

One factor in estimating when water appeared on Earth is that water is continually being lost to space. H₂O molecules in the atmosphere are broken up by photolysis, and the resulting free hydrogen atoms can sometimes escape Earth's gravitational pull. When the Earth was younger and less massive, water would have been lost to space more easily. Lighter elements like hydrogen and helium are expected to leak from the atmosphere continually, but isotopic ratios of heavier noble gases in the modern atmosphere suggest that even the heavier elements in the early atmosphere were subject to significant losses. In particular, xenon is useful for calculations of water loss over time. Not only is it a noble gas (and therefore is not removed from the atmosphere through chemical reactions with other elements), but comparisons between the abundances of its nine stable isotopes in the modern atmosphere reveal that the Earth lost at least one ocean of water, a volume of water approximately equal to modern ocean volume, early in its history. This is likely to have occurred between the Hadean and Archean eons in cataclysmic events such as the moon forming impact.

Any water on Earth during the latter part of its accretion would have been disrupted by the Moon-forming impact (~4.5 billion years ago), which likely vaporized much of Earth's crust and upper mantle and created a rock-vapor atmosphere around the young planet. The rock vapor would have condensed within two thousand years, leaving behind hot volatiles which probably resulted in a majority carbon dioxide atmosphere with hydrogen and water vapor. Afterward, liquid water oceans may have existed despite the surface temperature of 230 °C (446 °F) due to the increased atmospheric pressure of the CO₂ atmosphere. As the cooling continued, most CO₂ was removed from the atmosphere by subduction and dissolution in ocean water, but levels oscillated wildly as new surface and mantle cycles appeared.

This pillow basalt on the seafloor near Hawaii was formed when magma extruded underwater. Other, much older pillow basalt formations provide evidence for large bodies of water long ago in Earth's history.

Geological evidence also helps constrain the time frame for liquid water existing on Earth. A sample of pillow basalt (a type of rock formed during an underwater eruption) was recovered from the Isua Greenstone Belt and provides evidence that water existed on Earth 3.8 billion years ago. In the Nuvvuagittuq Greenstone Belt, Quebec, Canada, rocks dated at 3.8 billion years old by one study and 4.28 billion years old by another show evidence of the presence of water at these ages. If oceans existed earlier than this, any geological evidence has yet to be discovered (which may be because such potential evidence has been destroyed by geological processes like crustal recycling). More recently, in August 2020, researchers reported that sufficient water to fill the oceans may have always been on the Earth since the beginning of the planet's formation.

Unlike rocks, minerals called zircons are highly resistant to weathering and geological processes and so are used to understand conditions on the very early Earth. Mineralogical evidence from zircons has shown that liquid water and an atmosphere must have existed 4.404 ± 0.008 billion years ago, very soon after the formation of Earth. This presents somewhat of a paradox, as the cool early Earth hypothesis suggests temperatures were cold enough to freeze water between about 4.4 billion and 4.0 billion years ago. Other studies of zircons found in Australian Hadean rock point to the existence of plate tectonics as early as 4 billion years ago. If true, that implies that rather than a hot, molten surface and an atmosphere full of carbon dioxide, early Earth's surface was much as it is today (in terms of thermal insulation). The action of plate tectonics traps vast amounts of CO₂, thereby reducing greenhouse effects, leading to a much cooler surface temperature and the formation of solid rock and liquid water.

Earth's water inventory

Where water is found on earth and in what proportions.

While the majority of Earth's surface is covered by oceans, those oceans make up just a small fraction of the mass of the planet. The mass of Earth's oceans is estimated to be 1.37 × 10²¹ kg, which is 0.023% of the total mass of Earth, 6.0 × 10²⁴ kg. An additional 5.0 × 10²⁰ kg of water is estimated to exist in ice, lakes, rivers, groundwater, and atmospheric water vapor. A significant amount of water is also stored in Earth's crust, mantle, and core. Unlike molecular H₂O that is found on the surface, water in the interior exists primarily in hydrated minerals or as trace amounts of hydrogen bonded to oxygen atoms in anhydrous minerals. Hydrated silicates on the surface transport water into the mantle at convergent plate boundaries, where oceanic crust is subducted underneath continental crust. While it is difficult to estimate the total water content of the mantle due to limited samples, approximately three times the mass of the Earth's oceans could be stored there. Similarly, the Earth's core could contain four to five oceans' worth of hydrogen.

While not considered to be one of the major sources of water on the planet, it should also be noted that biological processes such as photosynthesis and respiration are key factors in the hydrologic cycling of water on earth. These processes may have also had a more vital role on the early earth, and as such, they could impact the amount of available water present in a given location at a given time. This is due to one of these aforementioned processes consuming water, and the other generating water, and the balance between them is therefore what truly determines their impact. If photosynthesis occurs in higher degrees than respiration, earth's water inventory would decrease, while if respiration occurs in higher degrees than photosynthesis, earth's water inventory would increase.

Hypotheses for the origins of Earth's water

Extraplanetary sources

Water has a much lower condensation temperature than other materials that compose the terrestrial planets in the Solar System, such as iron and silicates. The region of the protoplanetary disk closest to the Sun was very hot early in the history of the Solar System, with temperatures ranging from 500-1500 Kelvin or 227-1227 Celsius, and therefore, it is not feasible that oceans of water condensed with the Earth as it formed. Further from the young Sun where temperatures were lower, water could condense and form icy planetesimals, which accumulated to form the Oort cloud. The boundary of the region where ice could form in the early Solar System is known as the frost line (or snow line), and is located in the modern asteroid belt, between about 2.7 and 3.1 astronomical units (AU) from the Sun. It is therefore necessary that objects forming beyond the frost line–such as comets, trans-Neptunian objects, and water-rich meteoroids (protoplanets)–delivered water to Earth. However, the timing of this delivery is still in question.

One hypothesis claims that Earth accreted (gradually grew by accumulation of) icy planetesimals about 4.5 billion years ago, when it was 60 to 90% of its current size. In this scenario, Earth was able to retain water in some form throughout accretion and major impact events. This hypothesis is supported by similarities in the abundance and the isotope ratios of water between the oldest known carbonaceous chondrite meteorites and meteorites from Vesta, both of which originate from the Solar System's asteroid belt. It is also supported by studies of osmium isotope ratios, which suggest that a sizeable quantity of water was contained in the material that Earth accreted early on. Measurements of the chemical composition of lunar samples collected by the Apollo 15 and 17 missions further support this, and indicate that water was already present on Earth before the Moon was formed.

The solar system's layout; which can help explain why incoming icy planetesimals from the outer solar system can be filtered out by the gaseous planets before they can reach the terrestrial planets.

One problem with this hypothesis is that the noble gas isotope ratios of Earth's atmosphere are different from those of its mantle, which suggests they were formed from different sources. To explain this observation, a so-called "late veneer" theory has been proposed in which water was delivered much later in Earth's history, after the Moon-forming impact. However, the current understanding of Earth's formation allows for less than 1% of Earth's material accreting after the Moon formed, implying that the material accreted later must have been very water-rich. Models of early Solar System dynamics have shown that icy asteroids could have been delivered to the inner Solar System (including Earth) during this period if Jupiter migrated closer to the Sun. Jupiter's relatively quick development however, made it difficult for the inner solar system to receive matter from the outer solar system, limiting the accumulation of water on the terrestrial planets. This is in addition to other factors, such as the conditions for the goldilocks zone, where liquid water, and by extension life as we know it, can exist, as opposed to solid ice forming snowball planets or gaseous water vapor forming gas giants.

Yet a third hypothesis, supported by evidence from molybdenum isotope ratios from a 2019 study, suggests that the Earth gained most of its water from the same interplanetary collision that caused the formation of the Moon. Albeit, as mentioned above, the majority of this water would have remained in a gaseous phase until significant planetary cooling occurred.

The evidence from 2019 shows that the molybdenum isotopic composition of the Earth's mantle originates from the outer Solar System, likely having brought water to Earth. The explanation is that Theia, the planet said in the giant-impact hypothesis to have collided with Earth 4.5 billion years ago forming the Moon, may have originated in the outer Solar System rather than in the inner Solar System, bringing water and carbon-based materials with it.

Geochemical analysis of water in the Solar System

Carbonaceous chondrites such as the Allende Meteorite (above) likely delivered much of the Earth's water, as evidenced by their isotopic similarities to ocean water.

Isotopic ratios provide a unique "chemical fingerprint" that is used to compare Earth's water with reservoirs elsewhere in the Solar System. One such isotopic ratio, that of deuterium to hydrogen (D/H), is particularly useful in the search for the origin of water on Earth. Hydrogen is the most abundant element in the universe, and its heavier isotope deuterium can sometimes take the place of a hydrogen atom in molecules like H₂O. Most deuterium was created in the Big Bang or in supernovae, so its uneven distribution throughout the protosolar nebula was effectively "locked in" early in the formation of the Solar System. By studying the different isotopic ratios of Earth and of other icy bodies in the Solar System, the likely origins of Earth's water can be researched.

Earth

The deuterium to hydrogen ratio for ocean water on Earth is known very precisely to be (1.5576 ± 0.0005) × 10⁻⁴. This value represents a mixture of all of the sources that contributed to Earth's reservoirs, and is used to identify the source or sources of Earth's water. The ratio of deuterium to hydrogen has increased over the Earth's lifetime between 2 and 9 times the ratio at the Earth's origin, because the lighter isotope is more likely to leak into space in atmospheric loss processes. Hydrogen beneath the Earth's crust is thought to have a D/H ratio more representative of the original D/H ratio upon formation of the Earth, because it is less affected by those processes. Analysis of subsurface hydrogen contained in recently released lava has been estimated to show that there was a 218‰ higher D/H ratio in the primordial Earth compared to the current ratio. No process is known that can decrease Earth's D/H ratio over time. This loss of the lighter isotope is one explanation for why Venus has such a high D/H ratio, as that planet's water was vaporized during the runaway greenhouse effect and subsequently lost much of its hydrogen to space.

Asteroids

Comet Halley as imaged by the European Space Agency's Giotto probe in 1986. Giotto flew by Halley's Comet and analyzed the isotopic levels of ice sublimating from the comet's surface using a mass spectrometer.

Multiple geochemical studies have concluded that asteroids are most likely the primary source of Earth's water. Carbonaceous chondrites—which are a subclass of the oldest meteorites in the Solar System—have isotopic levels most similar to ocean water. The CI and CM subclasses of carbonaceous chondrites specifically have hydrogen and nitrogen isotope levels that closely match Earth's seawater, which suggests water in these meteorites could be the source of Earth's oceans. Two 4.5 billion-year-old meteorites found on Earth that contained liquid water alongside a wide diversity of deuterium-poor organic compounds further support this. Earth's current deuterium to hydrogen ratio also matches ancient eucrite chondrites, which originate from the asteroid Vesta in the outer asteroid belt. CI, CM, and eucrite chondrites are believed to have the same water content and isotope ratios as ancient icy protoplanets from the outer asteroid belt that later delivered water to Earth.

A further asteroid particle study supported the theory that a large source of earth's water has come from hydrogen atoms carried on particles in the solar wind which combine with oxygen on asteroids and then arrive on earth in space dust. Using atom probe tomography the study found hydroxide and water molecules on the surface of a single grain from particles retrieved from the asteroid 25143 Itokawa by the Japanese space probe Hayabusa.

Comets

Comets are kilometer-sized bodies made of dust and ice that originate from the Kuiper belt (20-50 AU) and the Oort cloud (>5,000 AU), but have highly elliptical orbits which bring them into the inner solar system. Their icy composition and trajectories which bring them into the inner solar system make them a target for remote and in situ measurements of D/H ratios.

It is implausible that Earth's water originated only from comets, since isotope measurements of the deuterium to hydrogen (D/H) ratio in comets Halley, Hyakutake, Hale–Bopp, 2002T7, and Tuttle, yield values approximately twice that of oceanic water. This is also supported by analysis using the comparison of isotopic ratios for both carbon and nitrogen isotopes, which attribute only a few percent of the water present on earth to comet sources, indicating a much higher reliance on incoming asteroid matter. Using the cometary D/H ratio, models predict that less than 10% of Earth's water was supplied from comets.

Other, shorter period comets (<20 years) called Jupiter family comets likely originate from the Kuiper belt, but have had their orbital paths influenced by gravitational interactions with Jupiter or Neptune. 67P/Churyumov–Gerasimenko is one such comet that was the subject of isotopic measurements by the Rosetta spacecraft, which found the comet has a D/H ratio three times that of Earth's seawater. Another Jupiter family comet, 103P/Hartley 2, has a D/H ratio which is consistent with Earth's seawater, but its nitrogen isotope levels do not match Earth's.

Why is there anything at all?

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Why_is_there_anything_at_all

This question has been written about by philosophers since at least the ancient Parmenides (c. 515 BC).

"Why is there anything at all?" or "Why is there something rather than nothing?" is a question about the reason for basic existence which has been raised or commented on by a range of philosophers and physicists, including Gottfried Wilhelm Leibniz, Ludwig Wittgenstein, and Martin Heidegger, who called it "the fundamental question of metaphysics".

Introductory points

There is something

No experiment could support the hypothesis "There is nothing" because any observation obviously implies the existence of an observer.

Defining the question

The question is usually taken as concerning practical causality (rather than a moral reason for), and posed totally and comprehensively, rather than concerning the existence of anything specific, such as the universe or multiverse, the Big Bang, God, mathematical and physical laws, time or consciousness. It can be seen as an open metaphysical question, rather than a search for an exact answer.

The circled dot was used by the Pythagoreans and later Greeks to represent the first metaphysical being and the metaphysical life, the Monad or the Absolute.

On timescales

The question does not include the timing of when anything came to exist.

Some have suggested the possibility of an infinite regress, where, if an entity cannot come from nothing and this concept is mutually exclusive from something, there must have always been something that caused the previous effect, with this causal chain (either deterministic or probabilistic) extending infinitely back in time.

Arguments against attempting to answer the question

The question is outside our experience

Philosopher Stephen Law has said the question may not need answering, as it is attempting to answer a question that is outside a spacetime setting while being within a spacetime setting. He compares the question to asking "what is north of the North Pole?"

Causation may not apply

The ancient Greek philosopher Aristotle argued that everything in the universe must have a cause, culminating in an ultimate uncaused cause. (See Four causes.)

However, David Hume argued that a cause may not be necessary in the case of the formation of the universe. Whilst we expect that everything has a cause because of our experience of the necessity of causes, the formation of the universe is outside our experience and may be subject to different rules. Kant supports and extends this argument.

We may only say the question because of the nature of our minds

Kant argues that the nature of our mind may lead us to ask some questions (rather than asking because of the validity of those questions).

The brute fact approach

In philosophy, the brute fact approach proposes that some facts cannot be explained in terms of a deeper, more "fundamental" fact. It is in opposition to the principle of sufficient reason approach.

On this question, Bertrand Russell took a brute fact position when he said, "I should say that the universe is just there, and that's all." Sean Carroll similarly concluded that "any attempt to account for the existence of something rather than nothing must ultimately bottom out in a set of brute facts; the universe simply is, without ultimate cause or explanation."

The question may be impossible to answer

Roy Sorensen has discussed that the question may have an impossible explanatory demand, if there are no existential premises.

Explanations

Something may exist necessarily

Philosopher Brian Leftow has argued that the question cannot have a causal explanation (as any cause must itself have a cause) or a contingent explanation (as the factors giving the contingency must pre-exist), and that if there is an answer, it must be something that exists necessarily (i.e., something that just exists, rather than is caused).

Natural laws may necessarily exist, and may enable the emergence of matter

Philosopher of physics Dean Rickles has argued that numbers and mathematics (or their underlying laws) may necessarily exist. If we accept that mathematics is an extension of logic, as philosophers such as Bertrand Russell and Alfred North Whitehead did, then mathematical structures like numbers and shapes must be necessarily true propositions in all possible worlds.

Physicists, including popular physicists such as Stephen Hawking and Lawrence Krauss, have offered explanations (of at least the first particle coming into existence aspect of cosmogony) that rely on quantum mechanics, saying that in a quantum vacuum state, virtual particles and spacetime bubbles will spontaneously come into existence. The actual mathematical demonstration of quantum fluctuations of the hypothetical false vacuum state spontaneously causing an expanding bubble of true vacuum was done by quantum cosmologists in 2014 at the Chinese Academy of Sciences.

A necessary being bearing the reason for its existence within itself

Gottfried Wilhelm Leibniz attributed to God as being the necessary sufficient reason for everything that exists (see: Cosmological argument). He wrote:

"Why is there something rather than nothing? The sufficient reason... is found in a substance which... is a necessary being bearing the reason for its existence within itself."

A state of nothing may be impossible

The pre-Socratic philosopher Parmenides was one of the first Western thinkers to question the possibility of nothing, and commentary on this has continued.

A state of nothing may be unstable

Nobel Laureate Frank Wilczek is credited with the aphorism that "nothing is unstable." Physicist Sean Carroll argues that this accounts merely for the existence of matter, but not the existence of quantum states, space-time, or the universe as a whole.

It is possible for something to come from nothing

See also: A Universe from Nothing

Some cosmologists believe it to be possible that something (e.g., the universe) may come to exist spontaneously from nothing. Some mathematical models support this idea, and it is growing to become a more prevalent explanation among the scientific community for why the Big Bang occurred.

Other explanations

Robert Nozick proposed some possible explanations.

1. Self-Subsumption: "a law that applies to itself, and hence explains its own truth."
2. The Nothingness Force: "the nothingness force acts on itself, it sucks nothingness into nothingness and produces something..."

Mariusz Stanowski explained: "There must be both something and nothing, because separately neither can be distinguished".

Humour

Philosophical wit Sidney Morgenbesser answered the question with an apothegm: "If there were nothing, you'd still be complaining!", or "Even if there was nothing, you still wouldn't be satisfied!"

Grand Unified Theory

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Grand_Unified_Theory

 

Beyond the Standard Model
Simulated Large Hadron Collider CMS particle detector data depicting a Higgs boson produced by colliding protons decaying into hadron jets and electrons

A Grand Unified Theory (GUT) is any model in particle physics that merges the electromagnetic, weak, and strong forces (the three gauge interactions of the Standard Model) into a single force at high energies. Although this unified force has not been directly observed, many GUT models theorize its existence. If the unification of these three interactions is possible, it raises the possibility that there was a grand unification epoch in the very early universe in which these three fundamental interactions were not yet distinct.

Experiments have confirmed that at high energy, the electromagnetic interaction and weak interaction unify into a single combined electroweak interaction. GUT models predict that at even higher energy, the strong and electroweak interactions will unify into one electronuclear interaction. This interaction is characterized by one larger gauge symmetry and thus several force carriers, but one unified coupling constant. Unifying gravity with the electronuclear interaction would provide a more comprehensive theory of everything (TOE) rather than a Grand Unified Theory. Thus, GUTs are often seen as an intermediate step towards a TOE.

The novel particles predicted by GUT models are expected to have extremely high masses—around the GUT scale of 10¹⁶ GeV/c² (only three orders of magnitude below the Planck scale of 10¹⁹ GeV/c²)—and so are well beyond the reach of any foreseen particle hadron collider experiments. Therefore, the particles predicted by GUT models will be unable to be observed directly, and instead the effects of grand unification might be detected through indirect observations of the following:

• proton decay,
• electric dipole moments of elementary particles,
• or the properties of neutrinos.

Some GUTs, such as the Pati–Salam model, predict the existence of magnetic monopoles.

While GUTs might be expected to offer simplicity over the complications present in the Standard Model, realistic models remain complicated because they need to introduce additional fields and interactions, or even additional dimensions of space, in order to reproduce observed fermion masses and mixing angles. This difficulty, in turn, may be related to the existence of family symmetries beyond the conventional GUT models. Due to this and the lack of any observed effect of grand unification so far, there is no generally accepted GUT model.

Models that do not unify the three interactions using one simple group as the gauge symmetry but do so using semisimple groups can exhibit similar properties and are sometimes referred to as Grand Unified Theories as well.

Unsolved problem in physics

Are the three forces of the Standard Model unified at high energies? By which symmetry is this unification governed? Can the Grand Unification Theory explain the number of fermion generations and their masses?

History

Historically, the first true GUT, which was based on the simple Lie group SU(5), was proposed by Howard Georgi and Sheldon Glashow in 1974. The Georgi–Glashow model was preceded by the semisimple Lie algebra Pati–Salam model by Abdus Salam and Jogesh Pati also in 1974, who pioneered the idea to unify gauge interactions.

The acronym GUT was first coined in 1978 by CERN researchers John Ellis, Andrzej Buras, Mary K. Gaillard, and Dimitri Nanopoulos, however in the final version of their paper they opted for the less anatomical GUM (Grand Unification Mass). Nanopoulos later that year was the first to use the acronym in a paper.

Motivation

The fact that the electric charges of electrons and protons seem to cancel each other exactly to extreme precision is essential for the existence of the macroscopic world as we know it, but this important property of elementary particles is not explained in the Standard Model of particle physics. While the description of strong and weak interactions within the Standard Model is based on gauge symmetries governed by the simple symmetry groups SU(3) and SU(2) which allow only discrete charges, the remaining component, the weak hypercharge interaction is described by an abelian symmetry U(1) which in principle allows for arbitrary charge assignments. The observed charge quantization, namely the postulation that all known elementary particles carry electric charges which are exact multiples of one-third of the "elementary" charge, has led to the idea that hypercharge interactions and possibly the strong and weak interactions might be embedded in one Grand Unified interaction described by a single, larger simple symmetry group containing the Standard Model. This would automatically predict the quantized nature and values of all elementary particle charges. Since this also results in a prediction for the relative strengths of the fundamental interactions which we observe, in particular, the weak mixing angle, grand unification ideally reduces the number of independent input parameters but is also constrained by observations.

Grand unification is reminiscent of the unification of electric and magnetic forces by Maxwell's field theory of electromagnetism in the 19th century, but its physical implications and mathematical structure are qualitatively different.

Unification of matter particles

For an elementary introduction to how Lie algebras are related to particle physics, see Particle physics and representation theory.

Schematic representation of fermions and bosons in SU(5) GUT showing 5 + 10 split in the multiplets. Neutral bosons (photon, Z-boson, and neutral gluons) are not shown but occupy the diagonal entries of the matrix in complex superpositions.

SU(5)

Main article: Georgi–Glashow model

The pattern of weak isospins, weak hypercharges, and strong charges for particles in the SU(5) model, rotated by the predicted weak mixing angle, showing electric charge roughly along the vertical. In addition to Standard Model particles, the theory includes twelve colored X bosons, responsible for proton decay.

SU(5) is the simplest GUT. The smallest simple Lie group which contains the Standard Model, and upon which the first Grand Unified Theory was based, is

${\displaystyle \mathrm{S}\mathrm{U}(5)\supset \mathrm{S}\mathrm{U}(3)\times \mathrm{S}\mathrm{U}(2)\times \mathrm{U}(1).}$

Such group symmetries allow the reinterpretation of several known particles, including the photon, W and Z bosons, and gluon, as different states of a single particle field. However, it is not obvious that the simplest possible choices for the extended "Grand Unified" symmetry should yield the correct inventory of elementary particles. The fact that all currently known matter particles fit perfectly into three copies of the smallest group representations of SU(5) and immediately carry the correct observed charges, is one of the first and most important reasons why people believe that a Grand Unified Theory might actually be realized in nature.

The two smallest irreducible representations of SU(5) are 5 (the defining representation) and 10. (These bold numbers indicate the dimension of the representation.) In the standard assignment, the 5 contains the charge conjugates of the right-handed down-type quark color triplet and a left-handed lepton isospin doublet, while the 10 contains the six up-type quark components, the left-handed down-type quark color triplet, and the right-handed electron. This scheme has to be replicated for each of the three known generations of matter. It is notable that the theory is anomaly free with this matter content.

The hypothetical right-handed neutrinos are a singlet of SU(5), which means its mass is not forbidden by any symmetry; it doesn't need a spontaneous electroweak symmetry breaking which explains why its mass would be heavy (see seesaw mechanism).

SO(10)

Main article: SO(10)

The pattern of weak isospin, W, weaker isospin, W′, strong g3 and g8, and baryon minus lepton, B, charges for particles in the SO(10) Grand Unified Theory, rotated to show the embedding in E₆.

The next simple Lie group which contains the Standard Model is

${\displaystyle \mathrm{S}\mathrm{O}(10)\supset \mathrm{S}\mathrm{U}(5)\supset \mathrm{S}\mathrm{U}(3)\times \mathrm{S}\mathrm{U}(2)\times \mathrm{U}(1).}$

Here, the unification of matter is even more complete, since the irreducible spinor representation 16 contains both the 5 and 10 of SU(5) and a right-handed neutrino, and thus the complete particle content of one generation of the extended Standard Model with neutrino masses. This is already the largest simple group that achieves the unification of matter in a scheme involving only the already known matter particles (apart from the Higgs sector).

Since different Standard Model fermions are grouped together in larger representations, GUTs specifically predict relations among the fermion masses, such as between the electron and the down quark, the muon and the strange quark, and the tau lepton and the bottom quark for SU(5) and SO(10). Some of these mass relations hold approximately, but most don't (see Georgi-Jarlskog mass relation).

The boson matrix for SO(10) is found by taking the 15 × 15 matrix from the 10 + 5 representation of SU(5) and adding an extra row and column for the right-handed neutrino. The bosons are found by adding a partner to each of the 20 charged bosons (2 right-handed W bosons, 6 massive charged gluons and 12 X/Y type bosons) and adding an extra heavy neutral Z-boson to make 5 neutral bosons in total. The boson matrix will have a boson or its new partner in each row and column. These pairs combine to create the familiar 16D Dirac spinor matrices of SO(10).

E₆

Main article: E6 (mathematics)

In some forms of string theory, including E₈ × E₈ heterotic string theory, the resultant four-dimensional theory after spontaneous compactification on a six-dimensional Calabi–Yau manifold resembles a GUT based on the group E₆. Notably E₆ is the only exceptional simple Lie group to have any complex representations, a requirement for a theory to contain chiral fermions (namely all weakly-interacting fermions). Hence the other four (G₂, F₄, E₇, and E₈) can't be the gauge group of a GUT.

Extended Grand Unified Theories

Non-chiral extensions of the Standard Model with vectorlike split-multiplet particle spectra which naturally appear in the higher SU(N) GUTs considerably modify the desert physics and lead to the realistic (string-scale) grand unification for conventional three quark-lepton families even without using supersymmetry (see below). On the other hand, due to a new missing VEV mechanism emerging in the supersymmetric SU(8) GUT the simultaneous solution to the gauge hierarchy (doublet-triplet splitting) problem and problem of unification of flavor can be argued.

GUTs with four families / generations, SU(8): Assuming 4 generations of fermions instead of 3 makes a total of 64 types of particles. These can be put into 64 = 8 + 56 representations of SU(8). This can be divided into SU(5) × SU(3)_F × U(1) which is the SU(5) theory together with some heavy bosons which act on the generation number.

GUTs with four families / generations, O(16): Again assuming 4 generations of fermions, the 128 particles and anti-particles can be put into a single spinor representation of O(16).

Symplectic groups and quaternion representations

Symplectic gauge groups could also be considered. For example, Sp(8) (which is called Sp(4) in the article symplectic group) has a representation in terms of 4 × 4 quaternion unitary matrices which has a 16 dimensional real representation and so might be considered as a candidate for a gauge group. Sp(8) has 32 charged bosons and 4 neutral bosons. Its subgroups include SU(4) so can at least contain the gluons and photon of SU(3) × U(1). Although it's probably not possible to have weak bosons acting on chiral fermions in this representation. A quaternion representation of the fermions might be:

${\displaystyle {\left[\begin{array}{c}e+i\overline{e}+jv+k\overline{v}\\ u_r+i{\overline{u}}_{\overline{\mathrm{r}}}+j{d}_{\mathrm{r}}+k{\overline{d}}_{\overline{\mathrm{r}}}\\ u_g+i{\overline{u}}_{\overline{\mathrm{g}}}+j{d}_{\mathrm{g}}+k{\overline{d}}_{\overline{\mathrm{g}}}\\ u_b+i{\overline{u}}_{\overline{\mathrm{b}}}+j{d}_{\mathrm{b}}+k{\overline{d}}_{\overline{\mathrm{b}}}\end{array}\right]}_{\mathrm{L}}}$

A further complication with quaternion representations of fermions is that there are two types of multiplication: left multiplication and right multiplication which must be taken into account. It turns out that including left and right-handed 4 × 4 quaternion matrices is equivalent to including a single right-multiplication by a unit quaternion which adds an extra SU(2) and so has an extra neutral boson and two more charged bosons. Thus the group of left- and right-handed 4 × 4 quaternion matrices is Sp(8) × SU(2) which does include the Standard Model bosons:

${\displaystyle \mathrm{S}\mathrm{U}(4,\mathbb{H}{)}_{\mathrm{L}}\times {\mathbb{H}}_{\mathrm{R}}=\mathrm{S}\mathrm{p}(8)\times \mathrm{S}\mathrm{U}(2)\supset \mathrm{S}\mathrm{U}(4)\times \mathrm{S}\mathrm{U}(2)\supset \mathrm{S}\mathrm{U}(3)\times \mathrm{S}\mathrm{U}(2)\times \mathrm{U}(1)}$

If ${\displaystyle \psi }$ is a quaternion valued spinor, ${\displaystyle A_{\mu }^{ab}}$ is quaternion hermitian 4 × 4 matrix coming from Sp(8) and ${\displaystyle B_{\mu }}$ is a pure vector quaternion (both of which are 4-vector bosons) then the interaction term is:

${\displaystyle \overline{{\psi }^a}{\gamma }_{\mu }\left(A_{\mu }^{ab}{\psi }^b+{\psi }^a{B}_{\mu }\right)}$

Octonion representations

It can be noted that a generation of 16 fermions can be put into the form of an octonion with each element of the octonion being an 8-vector. If the 3 generations are then put in a 3x3 hermitian matrix with certain additions for the diagonal elements then these matrices form an exceptional (Grassmann) Jordan algebra, which has the symmetry group of one of the exceptional Lie groups (F₄, E₆, E₇, or E₈) depending on the details.

${\displaystyle \psi =\left[\begin{array}{ccc}a& e& \mu \\ \overline{e}& b& \tau \\ \overline{\mu }& \overline{\tau }& c\end{array}\right]}$

${\displaystyle [{\psi }_A,{\psi }_B]\subset {\mathrm{J}}_3(\mathbb{O})}$

Because they are fermions the anti-commutators of the Jordan algebra become commutators. It is known that E₆ has subgroup O(10) and so is big enough to include the Standard Model. An E₈ gauge group, for example, would have 8 neutral bosons, 120 charged bosons and 120 charged anti-bosons. To account for the 248 fermions in the lowest multiplet of E₈, these would either have to include anti-particles (and so have baryogenesis), have new undiscovered particles, or have gravity-like (spin connection) bosons affecting elements of the particles spin direction. Each of these possesses theoretical problems.

Beyond Lie groups

Other structures have been suggested including Lie 3-algebras and Lie superalgebras. Neither of these fit with Yang–Mills theory. In particular Lie superalgebras would introduce bosons with incorrect^{[clarification needed]} statistics. Supersymmetry, however, does fit with Yang–Mills.

Unification of forces and the role of supersymmetry

The unification of forces is possible due to the energy scale dependence of force coupling parameters in quantum field theory called renormalization group "running", which allows parameters with vastly different values at usual energies to converge to a single value at a much higher energy scale.

The renormalization group running of the three gauge couplings in the Standard Model has been found to nearly, but not quite, meet at the same point if the hypercharge is normalized so that it is consistent with SU(5) or SO(10) GUTs, which are precisely the GUT groups which lead to a simple fermion unification. This is a significant result, as other Lie groups lead to different normalizations. However, if the supersymmetric extension MSSM is used instead of the Standard Model, the match becomes much more accurate. In this case, the coupling constants of the strong and electroweak interactions meet at the grand unification energy, also known as the GUT scale:

${\displaystyle {\mathrm{\Lambda }}_{\text{GUT}}\approx {10}^{16}\text{GeV}.}$

It is commonly believed that this matching is unlikely to be a coincidence, and is often quoted as one of the main motivations to further investigate supersymmetric theories despite the fact that no supersymmetric partner particles have been experimentally observed. Also, most model builders simply assume supersymmetry because it solves the hierarchy problem—i.e., it stabilizes the electroweak Higgs mass against radiative corrections.

Neutrino masses

Since Majorana masses of the right-handed neutrino are forbidden by SO(10) symmetry, SO(10) GUTs predict the Majorana masses of right-handed neutrinos to be close to the GUT scale where the symmetry is spontaneously broken in those models. In supersymmetric GUTs, this scale tends to be larger than would be desirable to obtain realistic masses of the light, mostly left-handed neutrinos (see neutrino oscillation) via the seesaw mechanism. These predictions are independent of the Georgi–Jarlskog mass relations, wherein some GUTs predict other fermion mass ratios.

Proposed theories

Several theories have been proposed, but none is currently universally accepted. An even more ambitious theory that includes all fundamental forces, including gravitation, is termed a theory of everything. Some common mainstream GUT models are:

• Pati–Salam model – SU(4) × SU(2) × SU(2)
• Georgi–Glashow model – SU(5); and Flipped SU(5) – SU(5) × U(1)
• SO(10) model; and Flipped SO(10) – SO(10) × U(1)
• E₆ model; and Trinification – SU(3) × SU(3) × SU(3)
• minimal left-right model – SU(3)_C × SU(2)_L × SU(2)_R × U(1)_B−L
• 331 model – SU(3)_C × SU(3)_L × U(1)_X
• chiral color

Note: These models refer to Lie algebras not to Lie groups. The Lie group could be ${\displaystyle [\mathrm{S}\mathrm{U}(4)\times \mathrm{S}\mathrm{U}(2)\times \mathrm{S}\mathrm{U}(2)]/{\mathbb{Z}}_2,}$ just to take a random example.

The most promising candidate is SO(10). (Minimal) SO(10) does not contain any exotic fermions (i.e. additional fermions besides the Standard Model fermions and the right-handed neutrino), and it unifies each generation into a single irreducible representation. A number of other GUT models are based upon subgroups of SO(10). They are the minimal left-right model, SU(5), flipped SU(5) and the Pati–Salam model. The GUT group E₆ contains SO(10), but models based upon it are significantly more complicated. The primary reason for studying E₆ models comes from E₈ × E₈ heterotic string theory.

GUT models generically predict the existence of topological defects such as monopoles, cosmic strings, domain walls, and others. But none have been observed. Their absence is known as the monopole problem in cosmology. Many GUT models also predict proton decay, although not the Pati–Salam model. As of now, proton decay has never been experimentally observed. The minimal experimental limit on the proton's lifetime pretty much rules out minimal SU(5) and heavily constrains the other models. The lack of detected supersymmetry to date also constrains many models.

Proton Decay. These graphics refer to the X boson and Higgs boson families.

• 
  Dimension 6 proton decay mediated by the X boson ${\displaystyle (3,2{)}_{-\frac{5}{6}}}$ in SU(5) GUT
   
• 
  Dimension 6 proton decay mediated by the X boson ${\displaystyle (3,2{)}_{\frac{1}{6}}}$ in flipped SU(5) GUT
• 
  Dimension 6 proton decay mediated by the triplet Higgs ${\displaystyle T(3,1{)}_{-\frac{1}{3}}}$ and the anti-triplet Higgs ${\displaystyle \overline{T}(\overline{3},1{)}_{\frac{1}{3}}}$ in SU(5) GUT

Some GUT theories like SU(5) and SO(10) suffer from what is called the doublet-triplet problem. These theories predict that for each electroweak Higgs doublet, there is a corresponding colored Higgs triplet field with a very small mass (many orders of magnitude smaller than the GUT scale here). In theory, unifying quarks with leptons, the Higgs doublet would also be unified with a Higgs triplet. Such triplets have not been observed. They would also cause extremely rapid proton decay (far below current experimental limits) and prevent the gauge coupling strengths from running together in the renormalization group.

Most GUT models require a threefold replication of the matter fields. As such, they do not explain why there are three generations of fermions. Most GUT models also fail to explain the little hierarchy between the fermion masses for different generations.

Ingredients

A GUT model consists of a gauge group which is a compact Lie group, a connection form for that Lie group, a Yang–Mills action for that connection given by an invariant symmetric bilinear form over its Lie algebra (which is specified by a coupling constant for each factor), a Higgs sector consisting of a number of scalar fields taking on values within real/complex representations of the Lie group and chiral Weyl fermions taking on values within a complex rep of the Lie group. The Lie group contains the Standard Model group and the Higgs fields acquire VEVs leading to a spontaneous symmetry breaking to the Standard Model. The Weyl fermions represent matter.

Current evidence

The discovery of neutrino oscillations indicates that the Standard Model is incomplete, but there is currently no clear evidence that nature is described by any Grand Unified Theory. Neutrino oscillations have led to renewed interest toward certain GUT such as SO(10).

One of the few possible experimental tests of certain GUT is proton decay and also fermion masses. There are a few more special tests for supersymmetric GUT. However, minimum proton lifetimes from research (at or exceeding the 10³⁴~10³⁵ year range) have ruled out simpler GUTs and most non-SUSY models.  The maximum upper limit on proton lifetime (if unstable), is calculated at 6×10³⁹ years for SUSY models and 1.4×10³⁶ years for minimal non-SUSY GUTs.

The gauge coupling strengths of QCD, the weak interaction and hypercharge seem to meet at a common length scale called the GUT scale and equal approximately to 10¹⁶ GeV (slightly less than the Planck energy of 10¹⁹ GeV), which is somewhat suggestive. This interesting numerical observation is called the gauge coupling unification, and it works particularly well if one assumes the existence of superpartners of the Standard Model particles. Still, it is possible to achieve the same by postulating, for instance, that ordinary (non supersymmetric) SO(10) models break with an intermediate gauge scale, such as the one of Pati–Salam group.