Agreed terms help sensible discussion: Singularity

Catastrophe

The devil is in the detail
Singularity is at the basis of Big Bang and is a controversial concept which should be understood in context.
N.B. You may find contradictions between different sources. These are not of my making.

Oxford Dictionary of Astronomy Ian Redpath Oxford University Press 2011.
A mathematical point at which certain physical quantities reach infinite values. For example, according to general relativity, the curvature of spacetime becomes infinite in a black hole. In the Big Bang theory the Universe was born from a singularity, in which the density and temperature of matter were infinite.

Note: Before going any further, I want to examine the concept of infinite or infinity, as it is going to occur all through the examination of singularity.

Merriam-Webster definition of infinite
1: extending indefinitely : ENDLESS infinite space
2: immeasurably or inconceivably great or extensive : INEXHAUSTIBLE infinite patience
3: subject to no limitation or external determination
4a: extending beyond, lying beyond, or being greater than any preassigned finite value however large infinite number of positive numbers
b: extending to infinity infinite plane surface
c: characterized by an infinite number of elements or terms an infinite set an infinite series
Merriam-Webster definition of infinity
1a: the quality of being infinite
b: unlimited extent of time, space, or quantity : BOUNDLESSNESS
2: an indefinitely great number or amount an infinity of stars
3a: the limit of the value of a function or variable when it tends to become numerically larger than any preassigned finite number
b: a part of a geometric magnitude that lies beyond any part whose distance from a given reference position is finite do parallel lines ever meet if they extend to infinity
c: a transfinite number (such as aleph-null)
4: a distance so great that the rays of light from a point source at that distance may be regarded as parallel

Just to make this point at the outset, a singularity is a mathematical point at which certain physical quantities reach infinite values, and we can see that infinite values are themselves not possible - they too are mathematical concepts. Any infinite object, if it existed in the real world, would itself be the whole world with no room for anything else. So infinity is itself a mathematical concept which may be characterised as 1/0, or any number divided by zero.

Encyclopaedia of Astronomy and Astrophysics Ed Robert A Meyers Academic Press 1989
"In the standard big bang model, one assumes that the universe began in an extremely dense, hot state and was expanding rapidly. In the absence of quantum effects, the density, temperature and pressure would have been infinite at time zero, a seemingly incomprehensible situation sometimes referred to as the singularity problem. Currently [1989] unknown effects of quantum gravity might somehow have rendered finite these otherwise infinite quantities at time zero. It would still be natural to wonder, however, why the universe came into being in a state of rapid expansion, and why it was intensely hot." . . . . . . . . . . . .
"Singularities and Quantum Gravity
. . . . . . . . . Violent fluctuations of space-time should generate particles in a manner analogous to that which occurs in the vicinity of a collapsing black hole, as first studied by Stephen Hawking in 1974. Such processes could conceivably be the source of all existing matter, and the possible removal of an infinite-density singularity at time zero would make it scientifically meaningful to ask what the universe was doing before the "big bang". . . . . . . . . .
"Another approach, called string field theory, involves replacing the pointlike particles of conventional quantum field theory with fundamental objects with extent in one spatial dimension. The full implications of such studies for particle physics and for cosmology are not yet clear. " [1989]

To the Ends of the Universe by Heather Couper and Nigel Henbest DK 1998
"From the last stable orbit to the singularity.
The last stable orbit marks the closest that anything can orbit the black hole. Once within this orbit, matter is sucked into the tangerine-shaped ergosphere, a region where everything is swept around by the black hole's rotation. The outer edge of the ergosphere is known as the static limit and the inner edge as the outer event horizon. The black hole itself begins at the outer event horizon; everything passing this disappears for good, unable to pull itself away from the immense gravity. Inside the inner event horizon, however, the spin of the black hole sets up an opposing force to create a region of relatively normal space. Most objects will continue spiralling toward the centre, but a rocket with powerful engines could manoeuvre around (but not out of) this region. At the centre is the infinitely dense singularity, where all the matter of the original star is concentrated."

Universe - The Definitive Visual Guide Ed Martin Rees DK 2012
A black hole is a region of space containing, at its centre, some matter squeezed into a point of infinite density, called a singularity. Within a spherical region around the singularity, the gravitational pull is so great that nothing, not even light, can escape.

The Natural History of the Universe Colin A Ronan BCA 1991
"Indeed, all structure is destroyed, so that matter inside the black hole loses all individuality - all "memory" of what it was before. It falls towards a centre known mathematically as a "singularity", where the density of matter becomes infinite and space-time is reduced to a mere point."

Dictionary of Geophysics, Astrophysics and Astronomy Ed Richard A Matzner CRC Press 2001
Singularities
: In general relativity and in other field theories, subsets of the spacetime on which some quantities (often curvature and matter-density) become infinite. . . . . . . . . . Genuine singularities signal the breakdown of the theory used to describe the process; a physical system emerging from a singularity has the initial values of some of its parameters undetermined, and some aspects of evolution of physical systems will be unpredictable. Consequently, for instance, the existence of the Big Bang implies that general relativity cannot completely predict the state of matter at very high densities. It is expected that the adequate theory to describe the universe in the vicinity of the Big Bang will be quantum gravity, a theory that combines classical relativity and quantum mechanics. In quantum gravity, the expectation goes, the state of infinitely large density would be replaced by a very high, but finite density, through which the evolution of the Universe can be calculated.

Cosmic Dispatches: Reports on Astronomy and Cosmology Ed John Noble Wilford Norton 2002
Chapter 8 Cosmology comes of Age If the galaxies are racing apart now, in the past they must have been closer together. Indeed, in the beginning, all cosmic material must have been compressed to a point of infinite density, known as a singularity, when it began the postulated expansion known as the Big Bang. Note: I find this conclusion rather hasty.
Chapter 12 From the Big Bang to a Theory of Everything Working with Dr Roger Penrose, now at Oxford University, Dr Hawking considered the problem of what happens when enormous amounts of stellar matter collapse into a black hole, as predicted by relativity. They concluded that the collapse must continue into an increasingly smaller and denser point called a singularity. At such a point, where the density must be infinite, all the basic laws of physics would have broken down. . . . . . . . . . if Einstein's math is correct, the primeval atom out of which the Universe supposedly emerged must have been the mother of all singularities. The idea, hailed as a critical underpinning for the Big Bang, is now generally accepted.

Magic Universe: A Grand Tour of Modern Science Nigel Calder Oxford University Press 2005
According to general relativity, when all of the energy of the Universe was concentrated together at the initiation of a Big Bang, its diameter should have been zero - a geometric point called a singularity. Quantum theory, on the other hand, requires that it should be not quite zero. The same discrepancy occurs in the concentration of matter at the centre of a black hole.

Cosmology - a Very Short Introduction by Peter Coles Oxford University Press 2001.
"The presence of a singularity at the very beginning of the Universe is very bad news for the Big Bang model. Like the black hole singularity, it is a real singularity where the temperature and density become truly infinite. In this respect the Big Bang can be thought of as a kind of time reverse of the gravitational collapse that forms a black hole. As was the case with the Schwarzschild solution, many physicists thought that the initial cosmological singularity could be a consequence of the special form of the solutions of Einstein's equations used to model the Big Bang, but this is now known not to be the case. Hawking and Penrose generalised Penrose's original black hole theorems to show that a singularity invariably exists in the past of an expanding Universe in which certain very general conditions apply. Physical theory completely fails us at the instant of the Big Bang where the nasty infinities appear."
"So is it possible to avoid this singularity? And, if so, how? It is most likely that the initial cosmological singularity might well just be a consequence of extrapolating deductions based on the classical theory of general relativity into a situation where the theory is no longer valid."

Note: I am going to repeat that. " It is most likely that the initial cosmological singularity might well just be a consequence of extrapolating deductions based on the classical theory of general relativity into a situation where the theory is no longer valid."

Cosmology - a Very Short Introduction - continued:
"What is needed is quantum gravity . . . . . . . . . There are, however, ways of avoiding the initial singularity in classical general relativity without appealing to quantum effects. Firstly, one could try to avoid the singularity by proposing an equation of state for matter in the very early Universe that does not obey the conditions laid down by Hawking and Penrose. The most important of these conditions is a restriction on the behaviour of matter at high energies, called the strong energy condition. . . . . . . . . . Models in which this condition is violated right at the very beginning can have a bounce rather than a singularity. Running the clock back, the Universe reaches a minimum size and then expands again."
Note: I am going to repeat that. "Models in which this condition is violated right at the very beginning can have a bounce rather than a singularity. Running the clock back, the Universe reaches a minimum size and then expands again."

Black Holes and Time Warps by Kip S Thorne. Papermac 1994.
Note. There is an enormous amount of relevant material in this book. I have tried to select some material from this. Those wishing to follow further should consult the book itself.
To recapitulate, at the center of a black hole, in the spacetime region where the oscillating BKL (Belinsky-Khalatnikov-Lifshitz) tidal forces reach their peak, there resides a singularity: a region in which time no longer exists, and space has given way to quantum foam."
"One task of the laws of quantum gravity is to govern the probabilities for the various curvatures and topologies within a black hole's singularity. Another, presumably, is to determine the probabilities for the singularity to give birth to "new universes", that is, to give birth to new, classical (non-quantum) regions of spacetime, in the same sense as the big bang singularity gave birth to our Universe . . . ".

The New Cosmology Ed Peter Coles Icon Books 1998
A 'pathological' mathematical behaviour in which the value of a particular variable becomes infinite. To give a very simplified example, consider the calculation of the Newtonian force due to gravity exerted by a massive body on a test particle at a distance r. This force is proportional to 1/r^2, so if we tried to calculate the force for objects at zero separation, the result would be infinite. Singularities are not always signs of serious mathematical problems; sometimes they are simply caused by an inappropriate choice of coordinates. For example, something strange and akin to a singularity happens on some of the maps of the world in a standard atlas. These maps look quite sensible until we look at regions very near to the poles. In the standard Mercator projection, the north and south poles appear not as points, as they should, but as spread out into a straight line along the top and bottom of the map. If you were to travel to one of the poles you would not find anything catastrophic happening. The singularity that causes these lines to appear is an example of coordinate singularity, and it can be transformed away simply by using a different kind of projection."
"Singularities occur with depressing regularity in solutions of the equations of general relativity. Some of these are coordinate singularities like the one discussed above, and are not particularly serious. However, Einstein's theory does predict the existence of real singularities where real physical quantities (such as the matter density) becomes infinite. The curvature of spacetime can also become infinite in certain situations."
"Probably the most famous example of a singularity is that which lies at the centre of a black hole. This appears in the original Schwarzschild solution corresponding to a hole with perfect spherical symmetry. For many years physicists thought that the existence of a singularity of this kind was merely a consequence of the rather artificial nature of this spherical solution. However, a series of mathematical investigations, culminating in the singularity theorems devised by Roger Penrose, showed that no special symmetry is required, and also that singularities can arise as a result of gravitational collapse."
"As if to apologise for predicting these singularities in the first place, general relativity does its best to hide them from us. A Schwarzschild black hole is surrounded by an event horizon that effectively protects outside observers from the singularity itself. It seems likely that all singularities in general relativity are protected in this way, and so-called naked singularities are not thought to be physically realistic.

The Theory of (nearly) Everything Ed Daniel Bennett BBC ScienceFocus.com 2016
"Singularity
In the case of Astrophysics, a singularity is a mathematically predicted condition where space-time becomes so locally distorted by gravitation that the force of gravity tends to infinity and current theories of physics break down." . . . . . . . . .
"In principle, the material in the black hole would continue to collapse all the way to a dimensionless point - a singularity with infinite density and a force of gravity that headed off to infinity as it was approached. In reality, we don't know what would actually happen, because the singularity is an admission that our physics has broken down."

Astronomy Special Issue Cosmos Relativity Right or Wrong? Jesse Emspak October 2020
"The (massive) star can no longer support its own weight with radiation pressure from fusion, so it collapses. The implosion triggers a shock wave that tears the star apart in a violent supernova explosion. For stars that begin life with more than 20 solar masses, the core left behind collapses to infinite density and becomes a singularity. An event horizon forms around the singularity, and you have a black hole.

The State of the Universe: A Primer in Modern Cosmology Pedro G Ferreira Phoenix 2006
"The concept of a beginning is clearly different from how we normally think of it. . . . . . . But in the present context, we are talking about the origin of space-time - of space and time. This means that we cannot dissociate the beginning from time itself. The beginning will be the moment from which it makes sense to talk about time. . . . . . . In taking what we see today and extrapolating back in time, we have come to this unusual conclusion - that time began. Could it be that we are overreaching ourselves and pushing our theory of the Universe beyond its range of validity? . . . . . . Stephen Hawking and Roger Penrose (were able to prove that) if the evolution of the Universe was completely described by Einstein's general theory of relativity and the energy content was of the type we are familiar with today, then the Universe must have had a beginning. There is no way, according to their argument, of circumventing that initial time by rearranging matter and radiation in strange configurations, or by folding and warping space-time in such a way that it does not have to start at a single point, or what is known as a singularity. . . . . . . . . . In other words, if we go back in time and find that the dominant source of energy has a sufficiently negative pressure, it will show that the Universe does not inevitably have to start off from a singularity. There is a possibility that the Universe has been expanding eternally."
"Furthermore, because gravity is the geometry of space-time, it is conceivable that time itself may be quantized, leading to a host of weird possibilities. Does time increase in chunks, or quanta? Is there a probability that time can jump backwards? If a quantum theory of gravity has such exotic properties, then the laws of physics that we are used to . . . will be very different at or near the initial singularity."
"So at some point it must have undergone a transition between a contracting phase and the expanding phase we see today. This transition will not have happened when the Universe had contracted to a point - at the singularity. It will have happened when the Universe had reached a minimum but finite size, set by the strength of gravity, the tension of the fundamental strings, and the scale at which quantum effects became important. If we move further back in time, we find that the Universe gets bigger and cooler ad infinitum. In other words, there was no beginning and no singularity; the Universe may have started off very much how it will end - in a cold and placid state."
"We may be led to conclude that the existence of quantum mechanics entails that there was no beginning - that the Universe may have passed a very hot and dense state but that it was merely a transition from some other state in which it was contracting. But this conclusion is based on very speculative proposals for a quantum theory of gravity."

All About Space Issue 95 2019 Big Bang Was it really the beginning? Andrew May

“There’s agreement on many points, though such as the notion that the entire visible universe was originally compressed into a superdense primeval atom. . . . . . . . . . The simplest approach is to extrapolate the expansion back to a state of infinite density called a singularity. The whole space-time continuum would be compressed down to a dimensionless point and everything science normally deals with – matter and energy, space and time, the laws of physics – would have no meaning. These things – including time – would only come into existence with the Big Bang. . . . . . . . . . . it’s an unavoidable consequence of that initial singularity which tends to crop up in any model based purely on general relativity. . . . . . .“

“It provides an excellent description of gravity and the large scale structure of space-time, but we need a different type of physics – quantum theory – to explain the behaviour of matter on a subatomic scale. . . . . . . (Hawking wrote) ‘The quantum theory of gravity has opened up a new possibility in which there would be no boundary to space time’.

Other theories developed. “the expansion would gradually slow down . . . . . . (and) the Universe would start to contract, and continue contracting all the way back to a super-dense state . . . . . . it would be like replaying the Big Bang in reverse” or, maybe “‘a Big Crunch’ or ‘a Big Bounce’ ” – with the whole cycle repeating over and over again.” Then came dark energy, “ but a cyclic Universe may still be possible.” The ekpyrotic model aka ‘Big Splat’ was “formulated in terms of a controversial variant of quantum gravity called M-theory.”

“ . . . what came before the Big Bang fall(s) into two categories: either the question is meaningless or an endless cycle of previous universes.” But there is the third option “that our universe is just one tiny bubble in a vast multiverse alongside countless other bubble universes stretching infinitely far into the past and future.” “Loop quantum gravity, with its potential for a ‘not—quite—a—singularity bounce” might be an answer.

Current Wikipedia Gravitational singularity gives the following (extracted 22 May 2021:
Quote
Interpretation
Many theories in physics have mathematical singularities of one kind or another. Equations for these physical theories predict that the ball of mass of some quantity becomes infinite or increases without limit. This is generally a sign for a missing piece in the theory, as in the ultraviolet catastrophe, re-normalization, and instability of a hydrogen atom predicted by the Larmor formula.

Some theories, such as the theory of loop quantum gravity, suggest that singularities may not exist.[8] This is also true for such classical unified field theories as the Einstein–Maxwell–Dirac equations. The idea can be stated in the form that due to quantum gravity effects, there is a minimum distance beyond which the force of gravity no longer continues to increase as the distance between the masses becomes shorter, or alternatively that interpenetrating particle waves mask gravitational effects that would be felt at a distance.
Quote
This may be selected as being of particular interest:
"Some theories, such as the theory of loop quantum gravity, suggest that singularities may not exist."
This in turn might prompt the question: since it seems that the unknowns seems to stack up the closer one gets to t = 0, can all (or most) of the advantages of the Big Bang Model be retained whilst allowing wider consideration of alternatives as one approaches t = 0? Would this, in turn, lend slightly more emphasis on cyclic models? Alternatively, do quantum gravity effects come out on top?
See note to Cosmology - A Very Short Introduction:
Note: I am going to repeat that. "Models in which this condition is violated right at the very beginning can have a bounce rather than a singularity. Running the clock back, the Universe reaches a minimum size and then expands again."
But see also: "Neither general relativity nor quantum mechanics can currently describe the earliest moments of the Big Bang, but in general, quantum mechanics does not permit particles to inhabit a space smaller than their wavelengths."

WORK IN PROGRESS There is much more in preparation.

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Catastrophe

The devil is in the detail
New topic- Singularity

WORK IN PROGRESS

Cat

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Catastrophe

The devil is in the detail
Singularity is at the basis of Big Bang and is a controversial concept which should be understood in context.
N.B. You may find contradictions between different sources. These are not of my making.

Oxford Dictionary of Astronomy Ian Redpath Oxford University Press 2011.
A mathematical point at which certain physical quantities reach infinite values. For example, according to general relativity, the curvature of spacetime becomes infinite in a black hole. In the Big Bang theory the Universe was born from a singularity, in which the density and temperature of matter were infinite.

Note: Before going any further, I want to examine the concept of infinite or infinity, as it is going to occur all through the examination of singularity.

Merriam-Webster definition of infinite
1: extending indefinitely : ENDLESS infinite space
2: immeasurably or inconceivably great or extensive : INEXHAUSTIBLE infinite patience
3: subject to no limitation or external determination
4a: extending beyond, lying beyond, or being greater than any preassigned finite value however large infinite number of positive numbers
b: extending to infinity infinite plane surface
c: characterized by an infinite number of elements or terms an infinite set an infinite series
Merriam-Webster definition of infinity
1a: the quality of being infinite
b: unlimited extent of time, space, or quantity : BOUNDLESSNESS
2: an indefinitely great number or amount an infinity of stars
3a: the limit of the value of a function or variable when it tends to become numerically larger than any preassigned finite number
b: a part of a geometric magnitude that lies beyond any part whose distance from a given reference position is finite do parallel lines ever meet if they extend to infinity
c: a transfinite number (such as aleph-null)
4: a distance so great that the rays of light from a point source at that distance may be regarded as parallel

Just to make this point at the outset, a singularity is a mathematical point at which certain physical quantities reach infinite values, and we can see that infinite values are themselves not possible - they too are mathematical concepts. Any infinite object, if it existed in the real world, would itself be the whole world with no room for anything else. So infinity is itself a mathematical concept which may be characterised as 1/0, or any number divided by zero.

Encyclopaedia of Astronomy and Astrophysics Ed Robert A Meyers Academic Press 1989
"In the standard big bang model, one assumes that the universe began in an extremely dense, hot state and was expanding rapidly. In the absence of quantum effects, the density, temperature and pressure would have been infinite at time zero, a seemingly incomprehensible situation sometimes referred to as the singularity problem. Currently [1989] unknown effects of quantum gravity might somehow have rendered finite these otherwise infinite quantities at time zero. It would still be natural to wonder, however, why the universe came into being in a state of rapid expansion, and why it was intensely hot." . . . . . . . . . . . .
"Singularities and Quantum Gravity
. . . . . . . . . Violent fluctuations of space-time should generate particles in a manner analogous to that which occurs in the vicinity of a collapsing black hole, as first studied by Stephen Hawking in 1974. Such processes could conceivably be the source of all existing matter, and the possible removal of an infinite-density singularity at time zero would make it scientifically meaningful to ask what the universe was doing before the "big bang". . . . . . . . . .
"Another approach, called string field theory, involves replacing the pointlike particles of conventional quantum field theory with fundamental objects with extent in one spatial dimension. The full implications of such studies for particle physics and for cosmology are not yet clear. " [1989]

To the Ends of the Universe by Heather Couper and Nigel Henbest DK 1998
"From the last stable orbit to the singularity.
The last stable orbit marks the closest that anything can orbit the black hole. Once within this orbit, matter is sucked into the tangerine-shaped ergosphere, a region where everything is swept around by the black hole's rotation. The outer edge of the ergosphere is known as the static limit and the inner edge as the outer event horizon. The black hole itself begins at the outer event horizon; everything passing this disappears for good, unable to pull itself away from the immense gravity. Inside the inner event horizon, however, the spin of the black hole sets up an opposing force to create a region of relatively normal space. Most objects will continue spiralling toward the centre, but a rocket with powerful engines could manoeuvre around (but not out of) this region. At the centre is the infinitely dense singularity, where all the matter of the original star is concentrated."

Universe - The Definitive Visual Guide Ed Martin Rees DK 2012
A black hole is a region of space containing, at its centre, some matter squeezed into a point of infinite density, called a singularity. Within a spherical region around the singularity, the gravitational pull is so great that nothing, not even light, can escape.

The Natural History of the Universe Colin A Ronan BCA 1991
"Indeed, all structure is destroyed, so that matter inside the black hole loses all individuality - all "memory" of what it was before. It falls towards a centre known mathematically as a "singularity", where the density of matter becomes infinite and space-time is reduced to a mere point."

Dictionary of Geophysics, Astrophysics and Astronomy Ed Richard A Matzner CRC Press 2001
Singularities
: In general relativity and in other field theories, subsets of the spacetime on which some quantities (often curvature and matter-density) become infinite. . . . . . . . . . Genuine singularities signal the breakdown of the theory used to describe the process; a physical system emerging from a singularity has the initial values of some of its parameters undetermined, and some aspects of evolution of physical systems will be unpredictable. Consequently, for instance, the existence of the Big Bang implies that general relativity cannot completely predict the state of matter at very high densities. It is expected that the adequate theory to describe the universe in the vicinity of the Big Bang will be quantum gravity, a theory that combines classical relativity and quantum mechanics. In quantum gravity, the expectation goes, the state of infinitely large density would be replaced by a very high, but finite density, through which the evolution of the Universe can be calculated.

Cosmic Dispatches: Reports on Astronomy and Cosmology Ed John Noble Wilford Norton 2002
Chapter 8 Cosmology comes of Age If the galaxies are racing apart now, in the past they must have been closer together. Indeed, in the beginning, all cosmic material must have been compressed to a point of infinite density, known as a singularity, when it began the postulated expansion known as the Big Bang. Note: I find this conclusion rather hasty.
Chapter 12 From the Big Bang to a Theory of Everything Working with Dr Roger Penrose, now at Oxford University, Dr Hawking considered the problem of what happens when enormous amounts of stellar matter collapse into a black hole, as predicted by relativity. They concluded that the collapse must continue into an increasingly smaller and denser point called a singularity. At such a point, where the density must be infinite, all the basic laws of physics would have broken down. . . . . . . . . . if Einstein's math is correct, the primeval atom out of which the Universe supposedly emerged must have been the mother of all singularities. The idea, hailed as a critical underpinning for the Big Bang, is now generally accepted.

Magic Universe: A Grand Tour of Modern Science Nigel Calder Oxford University Press 2005
According to general relativity, when all of the energy of the Universe was concentrated together at the initiation of a Big Bang, its diameter should have been zero - a geometric point called a singularity. Quantum theory, on the other hand, requires that it should be not quite zero. The same discrepancy occurs in the concentration of matter at the centre of a black hole.

Cosmology - a Very Short Introduction by Peter Coles Oxford University Press 2001.
"The presence of a singularity at the very beginning of the Universe is very bad news for the Big Bang model. Like the black hole singularity, it is a real singularity where the temperature and density become truly infinite. In this respect the Big Bang can be thought of as a kind of time reverse of the gravitational collapse that forms a black hole. As was the case with the Schwarzschild solution, many physicists thought that the initial cosmological singularity could be a consequence of the special form of the solutions of Einstein's equations used to model the Big Bang, but this is now known not to be the case. Hawking and Penrose generalised Penrose's original black hole theorems to show that a singularity invariably exists in the past of an expanding Universe in which certain very general conditions apply. Physical theory completely fails us at the instant of the Big Bang where the nasty infinities appear."
"So is it possible to avoid this singularity? And, if so, how? It is most likely that the initial cosmological singularity might well just be a consequence of extrapolating deductions based on the classical theory of general relativity into a situation where the theory is no longer valid."

Note: I am going to repeat that. " It is most likely that the initial cosmological singularity might well just be a consequence of extrapolating deductions based on the classical theory of general relativity into a situation where the theory is no longer valid."

Cosmology - a Very Short Introduction - continued:
"What is needed is quantum gravity . . . . . . . . . There are, however, ways of avoiding the initial singularity in classical general relativity without appealing to quantum effects. Firstly, one could try to avoid the singularity by proposing an equation of state for matter in the very early Universe that does not obey the conditions laid down by Hawking and Penrose. The most important of these conditions is a restriction on the behaviour of matter at high energies, called the strong energy condition. . . . . . . . . . Models in which this condition is violated right at the very beginning can have a bounce rather than a singularity. Running the clock back, the Universe reaches a minimum size and then expands again."
Note: I am going to repeat that. "Models in which this condition is violated right at the very beginning can have a bounce rather than a singularity. Running the clock back, the Universe reaches a minimum size and then expands again."

Black Holes and Time Warps by Kip S Thorne. Papermac 1994.
Note. There is an enormous amount of relevant material in this book. I have tried to select some material from this. Those wishing to follow further should consult the book itself.
To recapitulate, at the center of a black hole, in the spacetime region where the oscillating BKL (Belinsky-Khalatnikov-Lifshitz) tidal forces reach their peak, there resides a singularity: a region in which time no longer exists, and space has given way to quantum foam."
"One task of the laws of quantum gravity is to govern the probabilities for the various curvatures and topologies within a black hole's singularity. Another, presumably, is to determine the probabilities for the singularity to give birth to "new universes", that is, to give birth to new, classical (non-quantum) regions of spacetime, in the same sense as the big bang singularity gave birth to our Universe . . . ".

The New Cosmology Ed Peter Coles Icon Books 1998
A 'pathological' mathematical behaviour in which the value of a particular variable becomes infinite. To give a very simplified example, consider the calculation of the Newtonian force due to gravity exerted by a massive body on a test particle at a distance r. This force is proportional to 1/r^2, so if we tried to calculate the force for objects at zero separation, the result would be infinite. Singularities are not always signs of serious mathematical problems; sometimes they are simply caused by an inappropriate choice of coordinates. For example, something strange and akin to a singularity happens on some of the maps of the world in a standard atlas. These maps look quite sensible until we look at regions very near to the poles. In the standard Mercator projection, the north and south poles appear not as points, as they should, but as spread out into a straight line along the top and bottom of the map. If you were to travel to one of the poles you would not find anything catastrophic happening. The singularity that causes these lines to appear is an example of coordinate singularity, and it can be transformed away simply by using a different kind of projection."
"Singularities occur with depressing regularity in solutions of the equations of general relativity. Some of these are coordinate singularities like the one discussed above, and are not particularly serious. However, Einstein's theory does predict the existence of real singularities where real physical quantities (such as the matter density) becomes infinite. The curvature of spacetime can also become infinite in certain situations."
"Probably the most famous example of a singularity is that which lies at the centre of a black hole. This appears in the original Schwarzschild solution corresponding to a hole with perfect spherical symmetry. For many years physicists thought that the existence of a singularity of this kind was merely a consequence of the rather artificial nature of this spherical solution. However, a series of mathematical investigations, culminating in the singularity theorems devised by Roger Penrose, showed that no special symmetry is required, and also that singularities can arise as a result of gravitational collapse."
"As if to apologise for predicting these singularities in the first place, general relativity does its best to hide them from us. A Schwarzschild black hole is surrounded by an event horizon that effectively protects outside observers from the singularity itself. It seems likely that all singularities in general relativity are protected in this way, and so-called naked singularities are not thought to be physically realistic.

The Theory of (nearly) Everything Ed Daniel Bennett BBC ScienceFocus.com 2016
"Singularity
In the case of Astrophysics, a singularity is a mathematically predicted condition where space-time becomes so locally distorted by gravitation that the force of gravity tends to infinity and current theories of physics break down." . . . . . . . . .
"In principle, the material in the black hole would continue to collapse all the way to a dimensionless point - a singularity with infinite density and a force of gravity that headed off to infinity as it was approached. In reality, we don't know what would actually happen, because the singularity is an admission that our physics has broken down."

Astronomy Special Issue Cosmos Relativity Right or Wrong? Jesse Emspak October 2020
"The (massive) star can no longer support its own weight with radiation pressure from fusion, so it collapses. The implosion triggers a shock wave that tears the star apart in a violent supernova explosion. For stars that begin life with more than 20 solar masses, the core left behind collapses to infinite density and becomes a singularity. An event horizon forms around the singularity, and you have a black hole.

The State of the Universe: A Primer in Modern Cosmology Pedro G Ferreira Phoenix 2006
"The concept of a beginning is clearly different from how we normally think of it. . . . . . . But in the present context, we are talking about the origin of space-time - of space and time. This means that we cannot dissociate the beginning from time itself. The beginning will be the moment from which it makes sense to talk about time. . . . . . . In taking what we see today and extrapolating back in time, we have come to this unusual conclusion - that time began. Could it be that we are overreaching ourselves and pushing our theory of the Universe beyond its range of validity? . . . . . . Stephen Hawking and Roger Penrose (were able to prove that) if the evolution of the Universe was completely described by Einstein's general theory of relativity and the energy content was of the type we are familiar with today, then the Universe must have had a beginning. There is no way, according to their argument, of circumventing that initial time by rearranging matter and radiation in strange configurations, or by folding and warping space-time in such a way that it does not have to start at a single point, or what is known as a singularity. . . . . . . . . . In other words, if we go back in time and find that the dominant source of energy has a sufficiently negative pressure, it will show that the Universe does not inevitably have to start off from a singularity. There is a possibility that the Universe has been expanding eternally."
"Furthermore, because gravity is the geometry of space-time, it is conceivable that time itself may be quantized, leading to a host of weird possibilities. Does time increase in chunks, or quanta? Is there a probability that time can jump backwards? If a quantum theory of gravity has such exotic properties, then the laws of physics that we are used to . . . will be very different at or near the initial singularity."
"So at some point it must have undergone a transition between a contracting phase and the expanding phase we see today. This transition will not have happened when the Universe had contracted to a point - at the singularity. It will have happened when the Universe had reached a minimum but finite size, set by the strength of gravity, the tension of the fundamental strings, and the scale at which quantum effects became important. If we move further back in time, we find that the Universe gets bigger and cooler ad infinitum. In other words, there was no beginning and no singularity; the Universe may have started off very much how it will end - in a cold and placid state."
"We may be led to conclude that the existence of quantum mechanics entails that there was no beginning - that the Universe may have passed a very hot and dense state but that it was merely a transition from some other state in which it was contracting. But this conclusion is based on very speculative proposals for a quantum theory of gravity."

All About Space What happened before the Big Bang? by Kulvinder Singh Chadha 2016
Dr Cai and Professor Brandenberger McGill's High-Energy Theory Group
What he means is that in the multidimensional scenario, although ekpyrosis can 'smooth' out some problems like cosmic inflation, the singularity is still present and the physics surrounding that are as vague and problematic as ever. But Dr Cai's work, . . . . . . . . . does away with singularities entirely."
"In their model, a previous universe collapsed until it could go no further, and then bounced out as a new universe. 'In our scenario, the whole of cosmic evolution then becomes smooth. The physics around the bounce, including the background [CMB] and perturbation, are well controlled and calculable," he says. By removing the singularity, a lot of associated problems (such as infinite densities and zero dimensions - which have little support in physics) are also removed."

All About Space Issue 95 2019 Big Bang Was it really the beginning? Andrew May

“There’s agreement on many points, though such as the notion that the entire visible universe was originally compressed into a superdense primeval atom. . . . . . . . . . The simplest approach is to extrapolate the expansion back to a state of infinite density called a singularity. The whole space-time continuum would be compressed down to a dimensionless point and everything science normally deals with – matter and energy, space and time, the laws of physics – would have no meaning. These things – including time – would only come into existence with the Big Bang. . . . . . . . . . . it’s an unavoidable consequence of that initial singularity which tends to crop up in any model based purely on general relativity. . . . . . .“

“It provides an excellent description of gravity and the large scale structure of space-time, but we need a different type of physics – quantum theory – to explain the behaviour of matter on a subatomic scale. . . . . . . (Hawking wrote) ‘The quantum theory of gravity has opened up a new possibility in which there would be no boundary to space time’.

Other theories developed. “the expansion would gradually slow down . . . . . . (and) the Universe would start to contract, and continue contracting all the way back to a super-dense state . . . . . . it would be like replaying the Big Bang in reverse” or, maybe “‘a Big Crunch’ or ‘a Big Bounce’ ” – with the whole cycle repeating over and over again.” Then came dark energy, “ but a cyclic Universe may still be possible.” The ekpyrotic model aka ‘Big Splat’ was “formulated in terms of a controversial variant of quantum gravity called M-theory.”

“ . . . what came before the Big Bang fall(s) into two categories: either the question is meaningless or an endless cycle of previous universes.” But there is the third option “that our universe is just one tiny bubble in a vast multiverse alongside countless other bubble universes stretching infinitely far into the past and future.” “Loop quantum gravity, with its potential for a ‘not—quite—a—singularity bounce” might be an answer.

Current Wikipedia Gravitational singularity gives the following (extracted 22 May 2021:
Quote
Interpretation
Many theories in physics have mathematical singularities of one kind or another. Equations for these physical theories predict that the ball of mass of some quantity becomes infinite or increases without limit. This is generally a sign for a missing piece in the theory, as in the ultraviolet catastrophe, re-normalization, and instability of a hydrogen atom predicted by the Larmor formula.

Some theories, such as the theory of loop quantum gravity, suggest that singularities may not exist.[8] This is also true for such classical unified field theories as the Einstein–Maxwell–Dirac equations. The idea can be stated in the form that due to quantum gravity effects, there is a minimum distance beyond which the force of gravity no longer continues to increase as the distance between the masses becomes shorter, or alternatively that interpenetrating particle waves mask gravitational effects that would be felt at a distance.
Quote
This may be selected as being of particular interest:
"Some theories, such as the theory of loop quantum gravity, suggest that singularities may not exist."
This in turn might prompt the question: since it seems that the unknowns seems to stack up the closer one gets to t = 0, can all (or most) of the advantages of the Big Bang Model be retained whilst allowing wider consideration of alternatives as one approaches t = 0? Would this, in turn, lend slightly more emphasis on cyclic models? Alternatively, do quantum gravity effects come out on top?
See note to Cosmology - A Very Short Introduction:
Note: I am going to repeat that. "Models in which this condition is violated right at the very beginning can have a bounce rather than a singularity. Running the clock back, the Universe reaches a minimum size and then expands again."
But see also: "Neither general relativity nor quantum mechanics can currently describe the earliest moments of the Big Bang, but in general, quantum mechanics does not permit particles to inhabit a space smaller than their wavelengths."

WORK IN PROGRESS There is much more in preparation.
Singularity continued 27 May 2021.

Terra Australis

Terra Australis

Cat: I have mostly read what you have compiled here and I find it fascinating. I need to go back and re-read. A singularity describes an event for which there is no rule and no repeat of the observations. Correct?
If black holes do indeed condense down to a singularity which then creates another universe we will never know about it. It is beyond finding out. If it could be measured it would not exist.
It's very deep I'm not sure I have a grasp on it.
One thought I have which may not be anything is that the laws of physics say that for every action there must be a reaction. So did a parallel universe come into existence at the same time as our known universe!
Love to hear more

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Terra Australis

For every quantum particle that has been discovered, an anti-particle has been discovered as well. Is this correct? This duality of existence may suggest that there is another universe.

If two particles display entanglement, this entanglement may exist between equal and opposite particles in the undiscovered parallel universe, not in our known universe. Entanglement denies the presence of random occurrences does it not?

Could entanglements exist between the parallel universe rather than within our own universe? This would keep both in balance.
Very deep!
.... and if this thought sounds completely crazy I don't mind being told so.

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David-J-Franks

For every quantum particle that has been discovered, an anti-particle has been discovered as well. Is this correct? This duality of existence may suggest that there is another universe.

If two particles display entanglement, this entanglement may exist between equal and opposite particles in the undiscovered parallel universe, not in our known universe. Entanglement denies the presence of random occurrences does it not?

Could entanglements exist between the parallel universe rather than within our own universe? This would keep both in balance.
Very deep!
.... and if this thought sounds completely crazy I don't mind being told so.
Entanglement denies the presence of random occurrences does it not?
What do you mean by random?

Catastrophe

Terra Australis

What do you mean by random?
Random: an event with no precursor, no predictor no cause of effect.
It exists as a lone entity.

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David-J-Franks

Random: an event with no precursor, no predictor no cause of effect.
It exists as a lone entity.
Do you know of any such events with no precursor, no predictor no cause of effect and that exists as a lone entity?

Catastrophe

Terra Australis

The short answer to this is no as I don't see random and uncertain as the same.
It's a good discussion question because it is more difficult to answer when looking at the behaviour of quantum particles and whether their trajectories are random or controlled by some as yet undiscovered variable.
Quantum entanglement random or not?
The primordial singularity could be viewed by some as a candidate for randomness.
If we can imagine something then it is not a random event, and what we might see as being random is only that because we don't know everything about it.

I'm interested to know all your thoughts.

David-J-Franks

The short answer to this is no as I don't see random and uncertain as the same.
It's a good discussion question because it is more difficult to answer when looking at the behaviour of quantum particles and whether their trajectories are random or controlled by some as yet undiscovered variable.
Quantum entanglement random or not?
The primordial singularity could be viewed by some as a candidate for randomness.
If we can imagine something then it is not a random event, and what we might see as being random is only that because we don't know everything about it.

I'm interested to know all your thoughts.
whether their trajectories are random or controlled by some as yet undiscovered variable.
I don't think their trajectories are either random or controlled. I think it's down to cause-and-effect. Their current trajectory was determined by what last hit it or what force last acted on it.

The point of me asking you in post 8 to give me an example of something random was just my roundabout way to say I don't believe there's such a thing as random. If there's an undiscovered variable I don't think it would be random.

I find 'random' to be nonsense because it would mean something could happen without a reason. Unpredictable is a better word. for example a dice through is not random but it's unpredictable.

Catastrophe

The devil is in the detail
" I don't believe there's such a thing as random. If there's an undiscovered variable I don't think it would be random. "

I agree. Random is something which does not fit into a known pattern.

Cat

Catastrophe

The devil is in the detail
Checked and found this:

"
What is the real meaning of random?

adjective. proceeding, made, or occurring without definite aim, reason, or pattern: the random selection of numbers. Statistics. of or characterizing a process of selection in which each item of a set has an equal probability of being chosen.

"

Cat

Terra Australis

Think we are all on the same page
I treat every question/er respectfully

Catastrophe

The devil is in the detail
Cat: I have mostly read what you have compiled here and I find it fascinating. I need to go back and re-read. A singularity describes an event for which there is no rule and no repeat of the observations. Correct?
If black holes do indeed condense down to a singularity which then creates another universe we will never know about it. It is beyond finding out. If it could be measured it would not exist.
It's very deep I'm not sure I have a grasp on it.
One thought I have which may not be anything is that the laws of physics say that for every action there must be a reaction. So did a parallel universe come into existence at the same time as our known universe!
Love to hear more
I am no expert, but my opinion, for what it is worth, is that a singularity is a mathematical fiction. Meaning, sorry, it is a mathematical invention (division by zero), but non-existent in reality. If I understand correctly, physics breaks down at "t = 0" so in that gap, nothing is known, rather like the black hole question. I see here a possibility (no worse and possibly better than division by zero) for a cyclic opportunity. Likewise with black holes (as well as big bangs). Of course, there are problems such as entropy in a cyclic system. I am not convinced that entropy would not decrease in a contracting phase of the Universe. So far, I am not a fan of "multiverses" unless there are new solid definitions agreed. Hope that helps.

Cat

Terra Australis

Cat:Thank you. It's interesting to know your thoughts re this.
Much appreciated.

Catastrophe