The Singularities of Infinity Stones
"Before creation itself, there were six singularities. Then the universe exploded into existence, and the remnants of these systems were forged into concentrated ingots... Infinity Stones."
The Infinity Stones, originally referred to as Infinity Gems or Soul Gems, are six immensely powerful fictional gems appearing in Marvel comic books and their screen adaptation, the Marvel Cinematic Universe. They were described as six different singularities existing before the beginning of the universe. They were scattered all over the universe once it was created.
The infinity stones itself may be pure fiction, but Marvel Comics might have done their research before constructing a background story of preexisting singularities upon the creation of the universe. In reality, the initial state of the universe we live in, at the beginning of the Big Bang, was once argued by physicists to have been a singularity.
In mathematics, a singularity of a function is a limit at which the function is ill-defined ā typically because of a discontinuity or infinity enters the equation. For example, the function f=1/x is singular at x = 0. The problem was raised from the fact that we could have singularities in mathematical equations of one of the fundamental forces that govern our universe.Ā
General relativity, Einstein's theory of space, time, and gravity, allows the existence of singularities. The theory of Ā general relativity characterizes gravity by the curvature of spacetime, as expressed by the metric tensor. The values of this tensor are given by the Einstein field equations, and solutions to these equations can be singular.Ā They are known as gravitational singularities or spacetime singularities.Ā
In the context of spacetime theory, gravitational singularities or spacetime singularities are limits (or, loosely speaking, "regions") in which the Einstein field equations break down. This happens when mathematical value of a property (eg. the density) of a region in space reaches an infinite number. Because these equations are taken to be a fundamental description of spacetime itself, this is often taken to imply that these limits indicate an end, or "edge," of space and time.Ā
The reactions to the discovery of singular solutions to Einstein field equations was quite striking. In the period 1938-39, Oppenheimer and his students Snyder and Volkoff investigated what would happen in general relativity to a massive star that collapsed, and discovered what we now would call a āblack holeā solution to the mathematical equations.Ā Under certain conditions, Einstein field equation gives us two characterizations of a spacetime singularity:
(1) Curvature singularity, for which spacetime curvatureĀ grows beyond all bounds ("blows up"); which only happens in curvature singularity, and
(2) Non-curvature singularity, a singularity that cannot be removed by any choice of coordinates (e.g. conical singularity).
While these criteria work for black holes, however, they are not sufficient to capture all spacetime singularities. The standard characterization of a spacetime singularity had to be more general, and rely on the notion of the geodesics of a spacetime.
Geodesics are the "straightest-possible" lines of a space-time. They are the paths that an object in free-fall (i.e., not subjected to any non-gravitational forces, like the thrust of a rocket engine, or a pull of a rope) will follow. For any geodesic, we can ask whether it is possible to extend it without limit. If this is not possible, then the geodesic path comes to an end in some finite distance.Ā
Spacetime singularity was therefore defined as "geodesic incompleteness". In other words, a spacetime is singular if it contains geodesics that cannot be extended to infinity. In such cases, it seems that there is an "edge" or and "end" to spacetime, which lies some at some finite distance.
curved singularity in the center of a black hole
Nevertheless, Einstein himself rejected the idea that singularities exist in nature. He thought of it as an abomination, and adopted the attitude that nature would never allow such a thing. Einstein felt that it has to be assumed that general relativity itself, as a theory, would either:
(i) break down in the region of a singularity, and that some more advanced theory would rule out such singularities; orĀ
(ii)Ā that some as yet undetermined principle in GR would forbid such singularities.Ā
The authority of Einstein meant that few people spent any time investigating singular solutions to GR for some 20 years thereafter. However the situation changed dramatically in the 1960ās. Substantial progress was made when Hawking, Penrose, and Geroch proved several singularity theorems (The PenroseāHawking singularity theorems).
Hawking and Penroseās theorem implies that not only were the singular solutions legitimate solutions of the GR equations, they were almost inevitable if certain reasonable premises were satisfied. A singularity in solutions of the Einstein field equations is one of two things:
(1) space-like singularity: a situation where matter is forced to be compressed to a point
(2) time-like singularity: a situation where certain light rays come from a region with infinite curvature
Space-like singularities are a feature of non-rotating uncharged black-holes, while time-like singularities are those that occur in charged or rotating black hole. Both of them have the property of geodesic incompleteness, in which either some light-path or some particle-path cannot be extended beyond a certain proper-time or affine-parameter (affine-parameter being the null analog of proper-time).
The theorem applies if the following four physical assumptions are made:
(i) Einstein's equations hold (with zero or negative cosmological constant).
(ii) The energy density is nowhere less than minus each principal pressure nor less than minus the sum of the three principal pressures (the 'energy condition').
(iii)There are no closed timelike curves.
(iv) Every timelike or null geodesic enters a region where the curvature is not specially alined with the geodesic. (This last condition would hold in any sufficiently general physically realistic model).
In common with earlier results, timelike or null geodesic incompleteness is used here as the indication of the presence of space-time singularities.Ā
The Penrose theorem guarantees that some sort of geodesic incompleteness occurs inside any black hole whenever matter satisfies reasonable energy conditions (It does not hold for matter described by a super-field, i.e., the Dirac field). The energy condition required for the black-hole singularity theorem is weak: it says that light rays are always focused together by gravity, never drawn apart, and this holds whenever the energy of matter is non-negative.
Hawking's singularity theorem is for the whole universe, and works backwards in time: in Hawking's original formulation, it guaranteed that the Big Bang has infinite density (Hawking later revised his position in 1988).
These theorems indicate that our universe began with an initial singularity, the "Big Bang." They also indicate that in certain circumstances, collapsing matter will form a black hole with a central singularity. This purely theoretical work coincided roughly with several other developments, all in the 1960ās, including the discovery of the microwave background, quasar (quasi-stellar objects), and pulsar.
It is now established that supermassive black holes, which contain what is predicted to be singularities at the center of these black holes, are at the centers of almost all galaxies, and that scattered throughout these galaxies are much smaller black holes left over from massive supernova explosions. Far from being a mathematical pathology, as Einstein thought, singularities may be a crucial part of our universe, probably ever since the very beginning of time and space.Ā
The Origin of The Universe - Before Creation ItselfĀ Ā
Big Bang Theory and Cosmic Inflation
We live in a finite expanding universe which has not existed forever, and that all the matter, energy and space in the universe was once squeezed into an infinitesimally small volume, which erupted in a cataclysmic "explosion" which has become known as the Big Bang. Current best estimates are that this occurred some 13.7 billion years ago.
The Big Bang theory describes the origin of the Universe, starting from a big initial explosion, from which Space and Time came to existence, followed by the first particles, first atoms, and in the end, planets, stars and galaxies. The theory was proposed the first time in 1927 by the Belgian priest and astronomer Georges LemaĆ®tre. He proposed that at the beginning of all things, there was an Initial Singularity, a point of infinite density and temperature thought to have contained all of the mass and space-time of the universe before it exploded and rapidly expand in the Big Bang and subsequent inflation, creating the present-day Universe. The initial singularity is part of the Planck epoch, the earliest period of time in the history of the universe. Observations seem to confirm this theory and its theoretical features.Ā
An absolute relevant evidence about the expansion of the Universe from an initial singularity is the famous Hubble's Law: even though it is related to the astronomer Edwin Hubble (because he confirmed the law itself), this mathematical relation was discovered by LemaƮtre himself, from the equations of General Relativity; it consists in the proportionality between the distance d and the recessional velocity v of distant galaxies:
where H0 is the so called Hubble constant". Because we talk about recessional velocity, it means that in a distant past (13.7 billion years ago, according to current measurement), all galaxies were closer from each others and, therefore, going back in time, all the matter of the Universe had to be contained in a single point of space.
In the late 1960s, substantial progress was made when some remarkable mathematical work by R Penrose, later extended by Penrose and Hawking, established that not only were the singular solutions legitimate solutions of the GR equations, but they were almost inevitable. To put this another way - no matter what kind of universe one had, there had to be singularities in it somewhere.Ā
These results indicated that singularities might be actual features of our universe, and this meant that their investigation was more than a theoretical exercise.Ā It is worth noting that at the time, LemaĆ®tre, Prenrose, and Hawking, as well as all the other physicists, used only General relativity to arrive at the conclusion that at the beginning of the Universe, a body containing all mass, energy, and spacetime in the Universe was compressed to an infinitely dense point, an initial singularity.Ā
An evolutionary scenario, developed in the 1980s, called Inflation (or Cosmic Inflation), that implies an extremely exponential expansion in first instants of the Universe, due to an unknown particle or force: according to this theory, inflation started 10^-36 s after the Big Bang, and it lasted 10^-34 s, an infinitesimally short time in which the Universe expanded from a subatomic scale (10^-28 m), to a macroscopic scale (10^16 m ~ 1 light-year).
Over the last few decades, the use of only general relativity to predict what happened in the beginnings of the Universe has been heavily criticized. It is known that Einstein's equations are only a partial description of reality. The notion of a singularity, infinite density in an infinitely small volume, is anathema to physicists; physicists detest infinities. Infinities in an equation are always a sign that something is wrong.Ā
While singularities might be unavoidable in classical context, there are some reasons to suspect that quantum processes might prevent true singularities from developing. For example, the above-mentioned positive energy condition (one of the premises that have to be satisfied in Hawkingās singularity theorems proposed in 1973) can be violated by quantum fields, which means that the premises of the singularity theorems are not secure.Ā Quantum mechanics becomes a significant factor in the high-energy environment of the earliest universe, and general relativity on its own fails to make accurate predictions.Ā
In 1988, Hawking revised his position in his book āA Brief History of Time,ā where he stated that "there was in fact no singularity at the beginning of the universe" (p. 50). This revision followed from quantum mechanics, in which general relativity must break down at times less than the Planck time. Hence general relativity cannot be used to show a singularity.
In his more recent book, "The Grand Design," published in 2010, Hawking wrote the following about the Big Bang, where there are also calculations resulting in "singularities":
"Measurements of helium abundance and the CMBR [Cosmic Microwave Background Radiation] provided convincing evidence in favor of the big bang picture of the very early universe, but although one can think of the big bang picture as a valid description of early times, it is wrong to take the big bang literally, that is, to think of Einsteinās theory as providing a true picture of the origin of the universe. That is because general relativity predicts there to be a point in time at which the temperature, density, and curvature of the universe are all infinite, a situation mathematicians call a singularity. To a physicist this means that Einsteinās theory breaks down at that point and therefore cannot be used to predict how the universe began, only how it evolved afterward. So although we can employ the equations of general relativity and our observations of the heavens to learn about the universe at a very young age, it is not correct to carry the big bang picture all the way back to the beginning.
In other words, the fact that singularities are mathematically illogical cannot be used to claim that black holes (or the Big Bang) are existentially illogical. Black holes (and the Big Bang) are confirmed by massive amounts of information which does not include singularities. Singularities are simply mathematical results that show that something is missing or unknown in the mathematical equations.Ā
In response to the inaccuracy of considering only general relativity, a way to avoid infinities is to adopt a different theory of space and time. What is lacking to the picture of the origin of the universe is a theory that integrates gravity with quantum mechanics. On this matter, alternative theoretical formulations for the beginning of the Universe have been proposed.
One such theory is loop quantum gravity which says that there is a minimum unit of space and a minimum unit of time. Once a minimum unit of space is filled, nothing more can be crammed into it. If anything more is to be added, it has to fit into the next minimum unit of space. Hence, no infinities and no singularities.
Another theory proposed to reconcile gravity with quantum mechanics to explain the beginning of the universe is a string theory-based model in which two branes, enormous membranes much larger than the Universe, collided, creating mass and energy.
To return to the topics of the infinity stones by Marvel Comics, the story of their origin added a thin layer of science into an elaborate fiction. Released in 1972, Marvel Premiere Vol. 1 #1 introduced the green Soul Gem, the first of six such Gems identified in Avengers Annual #7. At the time, LemaĆ®treās theory of the big bang with preexisting initial singularity was the accepted theory to explain the beginning of the universe, not to mention Penroseās and Hawkingās breakthrough that supported it then. Describing the origin of the infinity stones as singularities was a brilliant way to present their significance to the readers by employing scientific theories.
Source :Ā Boston UniversityĀ | Max Planck Institute
Hawking, S., & Penrose, R. (1970). The Singularities of Gravitational Collapse and Cosmology. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 314(1519), 529-548. Retrieved from http://www.jstor.org/stable/2416467
Penrose, Roger (2014).Ā Spacetime Singularities: The Story of Black Holes. University of Oxford. Retrieved fromĀ http://pitp.physics.ubc.ca/quant_lect/2014/GR100/Spacetime+Gravity_B-BHoles.pdf
gifs : Infinity StonesĀ @avengers-of-the-galaxy |Ā Cosmos: A SpaceTime OdysseyĀ
