Agreed terms help sensible discussion: Big Bang

[Catastrophe]

Agreed terms help sensible discussion: 2: Big Bang My few notes are in blue. Cat.

Cosmology A Very Short Introduction Peter Coles OUP 2001
. . . . . . . . . "For one thing, Einstein's theory itself breaks down at the very beginning of the Universe. The Big Bang is an example of what relativity theorists call a singularity, a point where the mathematics fall to pieces and measurable quantities become infinite. While we know how the Universe is expected to evolve from a given stage, the singularity makes it impossible to know from first principles what the Universe should look like in the beginning. . . . . . . . . . Most cosmologists interpret the Big Bang singularity in much the same way as the Black Hole singularity . . . i.e., as meaning that Einstein's equations break down at some point in the early Universe due to the extreme physical conditions present there. . . . . . . . . . This shortcoming is the reason why the word 'model' is probably more appropriate than 'theory' for the Big Bang."

I only begin with this reference because, for a very long time, I assumed that terms like Big Bang and singularity and Universe represented "absolute truth". They may well, depending on the subject, represent the best idea that science has come up with, and should be treated as such, but anything which cannot be observed, measured, and experimented with is not science, but philosophy. We all know, I believe, that science progresses and refines its terminology and ideas according to its gains in knowledge. This, in turn, keeps a check on Philosophy.

Oxford Dictionary of Astronomy Ian Ridpath OUP 2011.
"Big Bang Theory (BBT) The most widely accepted theory of the origin and evolution of the Universe. According to the Big Bang Theory, the Universe originated from an initial state of high temperature and density and has been expanding ever since. The best current measurements place the occurrence of the Big Bang at 13.73 billion years ago +/- 0.1 billion years. In other words, this is the age of the Universe."
"The theory of general relativity predicts the existence of a 'singularity' at the very beginning, where the temperature and density were infinite. Most cosmologists interpret this singularity as meaning that general relativity breaks down at the Planck era under the extreme physical conditions of the very early Universe, and that the very beginning must be addressed using a theory of quantum cosmology. With our present knowledge of high energy particle physics, we can run the clock back through the lepton era and hadron era to about a millionth of a second after the Big Bang, when the temperature was 10^13 K. Using more speculative theory, cosmologists have tried to push the model to within 10^-35 seconds of the singularity, when the temperature was 10^28 K."

Dictionary of Geophysics, Astrophysics and Astronomy Ed R A Matzner CRC Press 2001
Big Bang The initial explosion that gave birth to the Universe, and a standard model of the Universe in which all matter space and time expand from an initial state of enormous density and pressure. All models of the Universe constructed in the classical relativity theory (General Relativity) must take into account that at present the Universe is expanding. . . . . . . . . . This moment of infinite compression is called the Big Bang. It is a formal mathematical conclusion that only implies that every region of the Universe must have been much denser and hotter in the past than it is now. . . . . . . . . . The Robertson Walker models imply that the Big Bang occurred simultaneously for all matter in the Universe, but more general models exist in which there is a nonsimultaneous Big Bang.

The Icon Critical Dictionary of The New Cosmology Ed Peter Coles Icon Books 1998.
Big Bang Theory "The standard theoretical framework within which most cosmologists interpret observations and construct new theoretical ideas. . . . . . . The existence of the cosmic microwave background radiation is extremely strong evidence that the Universe must have been hot in the past. It is also not entirely correct to call it a theory and many prefer to use the word model. The difference between theory and model is subtle, but a useful definition is that a theory is usually expected to be completely self-contained (it can have no adjustable parameters, and all mathematical quantities are defined a priori), whereas a model is not complete in the same way. Owing to uncertain aspects of the Big Bang model, it is quite difficult to make cast-iron predictions from it, and it is consequently not easy to falsify (falsifiability being regarded in many quarters as an essential quality of a scientific theory)."
"In the Big Bang model, the Universe originated from an initial state of high temperature and density (the primordial fireball) and has been expanding ever since. The dynamics of the Big Bang are described by cosmological models, which are obtained by solving the Einstein Equations in the theory of General Relativity. The particular models that form the basis of the standard Big Bang Theory are the Friedmann models, which describe a universe which is both homogeneous and isotropic. These models all predict the existence of a singularity at the very beginning, at which the temperature and density are infinite. . . . . . . . . . Most cosmologists interpret the singularity as meaning that the Einstein Equations break down at the Planck time under the extreme physical conditions of the very early Universe and that the very beginning must be addressed using a theory of quantum cosmology. This incompleteness is the reason why the word model is probably more appropriate."
. . . . . . . . . . . . . . .
"There is another important gap in the Big Bang theory, apart from the problem of initial conditions and the breakdown of known laws of physics at the initial singularity. The Big Bang model describes the properties of the Universe only in an average sense, because it is built into the theory that the Universe is the same in every place and looks the same in every direction.

The Natural History of the Universe Colin A Ronan Marshall Edition 1991
"Mathematics and reality. The theory of the Big Bang has much observational evidence to support it. Yet there is another side to the study of the Universe. Mathematics often enables cosmologists, like other scientists, to work out in theory what Nature should be like before experimentalists and observers have confirmed that such is the case."
"Mathematical reasoning is the only way to grasp the fundamentals that lie behind what we observe. This is so because mathematics is a language in which ideas can be formulated in a precise way and which allows the mind to work out logical sequences at profound depths, where mere words would present quite unsurmountable obstacles. Time and again, mathematical reasoning has provided insights available in no other way."

Cosmic Dispatches - Reports on Astronomy and Cosmology Ed John N Wilford Norton 2002
"Astronomers detect explosion second only to Big Bang. Astronomers have detected a titanic explosion in the outer reaches of the cosmos - one so violent and bright that for about 40 seconds it apparently outshone all the rest of the Universe. Except for the Big Bang that is generally believed to have created the Universe, no other cosmic explosion of such magnitude has ever been discovered."
Dr Stephen Hawking and Dr James Hartle "pictured a finite, closed Universe in the shape of a sphere, only in four dimensions. It starts with a Big Bang, expands to a maximum point like the spherical Earth's equator, and then contracts toward an eventual collapse in what is sometimes called the Big Crunch. Like Earth's surface, this has no edges and would seem to require a closed universe."

Universe The Definitive Visual Guide. Gen Ed Martin Rees DK 2012.
"The Big Bang and Particle Physics:
For some decades, physicists have directed their search towards a better understanding of matter and the four fundamental forces. Part of the purpose has been to clarify what happened in the early Universe, shortly after the Big Bang.
Evidence for the Big Bang: [Note: from a 2012 perspective, but see later].
The strongest evidence for the Big Bang is the radiation it left, called the cosmic microwave background radiation (CMBR). George Gamow predicted its existence in 1948. It's detection in the 1960s was confirmation, for most cosmologists, of the Big Bang Theory. Other observations help support this theory.
Background radiation: The spectrum of the CMBR, discovered by Arno Penzias and Robert Wilson indicates a uniformly hot early Universe.
Expansion: If the Universe is expanding and cooling, it must once have been smaller and hotter.
Balance of elements: Big Bang theory exactly predicts the proportion of light elements, hydrogen, helium and lithium, seen in the Universe today.
General Relativity: Einstein's theory predicts that the Universe must either be expanding or contracting - it cannot stay the same size,"

The Grand Design. Stephen Hawking and Leonard Mlodinow, Bantam Press 2010.
"It is not yet clear whether a model in which time continued back beyond the big bang would be better at explaining present observations because it seems the laws of the evolution of the universe may break down at the big bang. If they do, it would make no sense to create a model which encompasses time before the big bang, because what existed then would have no observable consequences for the present, and so we might as well stick with the idea that the big bang was the creation of the world."





All About Space 2016 At that time there was no Issue Number or date. 2016 came from Copyright at back.
What happened before the Big Bang?
"Some cosmologists are wondering if the Big Bang was merely an intermediate phase and not the true start of the Universe at all. Theories such as the ekpyrotic universe, 'big bounce' models, and cyclic cosmology have all been round for a while, but new data from sensitive space-probes could put some of these on a firmer footing." Quote from article.
by Kulvinder Singh Chadha

The Theory of (nearly) Everything Ed Daniel Bennett BBC ScienceFocus.com 2016
A lengthy section entitled The Story of the Universe.by Stuart Clark and Elizabeth Pearson.
Chapter headings are:
1. The Big Bang
2. Inflation 19-35 seconds post-Big Bang
3. Particle Creation 1 minute post-Big Bang
4. The Decoupling of Matter and Energy 380,000 years post-Big Bang
5. The Cosmic Dark Ages 1 million years post-Big Bang
6. The Formation of the Solar System 8.8 billion years post-Big Bang.
As such reference is made to the Big Bang, that Section of Agreed Terms is suggested.

Astronomy Special Issue The Beginning and End of the Universe January 2021
Relevant contents:
THE BEGINNINGS
It began with a Bang by Dan Hooper

From Wiki Big Bang
Quote
Before observations of dark energy, cosmologists considered two scenarios for the future of the universe. If the mass density of the universe were greater than the critical density, then the universe would reach a maximum size and then begin to collapse. It would become denser and hotter again, ending with a state similar to that in which it started—a Big Crunch.[18]

. . . . . . . . . . . . . . .
Modern observations of accelerating expansion imply that more and more of the currently visible universe will pass beyond our event horizon and out of contact with us. The eventual result is not known. The ΛCDM model of the universe contains dark energy in the form of a cosmological constant. This theory suggests that only gravitationally bound systems, such as galaxies, will remain together, and they too will be subject to heat death as the universe expands and cools. Other explanations of dark energy, called phantom energy theories, suggest that ultimately galaxy clusters, stars, planets, atoms, nuclei, and matter itself will be torn apart by the ever-increasing expansion in a so-called Big Rip.[128]
Quote

Models not involving the Big Bang really constitute their own thread, but these are included for those interested.

Non-standard cosmology - Wikipedia
https://en.wikipedia.org › wiki › Non-standard_cosmol...
A non-standard cosmology is any physical cosmological model of the universe that was, or still ... Nevertheless, there remained vocal detractors of the Big Bang theory ... Alternativetheories do not have a means to explain these abundances.
‎History · ‎Alternatives to Big Bang... · ‎Alternatives and... · ‎Alternatives to General...

Cyclic model - Wikipedia
https://en.wikipedia.org › wiki › Cyclic_model
It was proposed in 2001 by Paul Steinhardt of Princeton University and Neil Turok of Cambridge University. The theory describes a universe exploding into ...
‎Overview · ‎The Steinhardt–Turok model · ‎The Baum–Frampton model




Please note: this is work in progress. Additions may be made in the middle

 

[Helio]

Great topic!

I take BBT to be a result of Lemaitre's original theory where he took the discovery of today's expansion (Slipher's work originally), along with Hubble/Humason's work on distances, and recognized that GR is a robust theory that incorporates this expansion view, solving the dilemma both Einstein, deSitter and others had with their static models due to their bias for a static universe.

Thus, only when we rewind the clock to we approach a singularity point. But that does not require the actual theory to go there. A scientific theory almost always has limits so that going beyond those limits should require the metaphysics or pseudoscience labels. Calling untestable and problematic extrapolations "science" or even part of a model is detrimental to the importance behind the label "science". We open the door to more scientism, science by consensus, etc. that may seem helpful to get science passed its self-imposed boundaries, but it also pollutes both its meaning and efficacy.

That being said....

Cole. . . . . . . . . "For one thing, Einstein's theory itself breaks down at the very beginning of the Universe. The Big Bang is an example of what relativity theorists call a singularity, a point where the mathematics fall to pieces and measurable quantities become infinite.

So which is it? A theory or something that includes regions that "fall to pieces". A theory must be discarded or modified when there are pieces all over the floor. BBT, once again, isn't required, nor was ever intended by Lemaitre, to go there. This is similar to Darwin's "Origin of the Species", where his work never once suggested abiogenesis, but how one species (already in existence) could continually advance, or digress, new varieties over extreme amounts of time to a point where a new species would be found.

IMO, it is important to take extrapolations of a theory into untestable regions and try to glue it to the theory.

"While we know how the Universe is expected to evolve from a given stage,".... Yes, here Cole is where he should be; we can rewind the clock to as far as the theory can take us which is close to the Planck time, apparently, so this is the correct stage to conduct acts, but....

". . . . . Most cosmologists interpret the Big Bang singularity..." Oops, suddenly we are including BBS (might as well give it initials at this point, even if the concept is bogus). Suddenly we quickly find that we are now "off stage".

"... that Einstein's equations break down at some point in the early Universe due to the extreme physical conditions present there. . . . . . . . . . This shortcoming is the reason why the word 'model' is probably more appropriate than 'theory' for the Big Bang." So, we have bounced back from the metaphysics of the singularity (t=0) moment. But a scientific model, like a theory, should also not imply that it incorporates regions that cannot fit the SM method.
I believe Kuhn, and I agree, argued that a theory or model should be understood for its utility - that it allows physicists to use it as a tool. GPS is just one of many benefits from the tool of GR. But perhaps semantics may help and I have used it as well.

I only begin with this reference because, for a very long time, I assumed that terms like Big Bang and singularity and Universe represented "absolute truth".

Language is important and there should never be suggestion that science represents "absolute truths", else we should still hold the Earth is the center of the universe. All science is a work in progress, building upon itself , like a building is remodeled on that island I mentioned in earlier threads.

They may well, depending on the subject, represent the best idea that science has come up with, and should be treated as such, but anything which cannot be observed, measured, and experimented with is not science, but philosophy. We all know, I believe, that science progresses and refines its terminology and ideas according to its gains in knowledge. This, in turn, keeps a check on Philosophy.

Nice!

"Oxford Dictionary of Astronomy Ian Ridpath OUP 2011.:
Big Bang Theory (BBT) The most widely accepted theory of the origin and evolution of the Universe."

But most people incorrectly infer that "origin" means from t=0, but the "stage" viewpoint (above) is the correct approach.

According to the Big Bang Theory, the Universe originated from an initial state of high temperature and density and has been expanding ever since.

I hope you will forgive my pedantic take on many of these points, but if we are to be true to the topic...

BBT is, again, not about origins, yet it, admittedly, is easy to infer that the beginnings of the universe are intrinsic to the model. Perhaps there is a word that better expresses this idea, if not we should invent one.

Oxford Dictionary of Astronomy Ian Ridpath OUP 2011.:
"The theory of general relativity predicts the existence of a 'singularity' at the very beginning, where the temperature and density were infinite."

It does not. It must be inferred, placing the events a t=0 outside the purview of science and into the realm of metaphysics.

Here is a paper that starts-off suggesting singularities are "well behaved" in the FLRW framework, yet states, "the singularity might have been avoided". It mixes the idea of the BBS as science, and suggests we may not even have a BBS. The key is whether or not the SM can be made to operate in this extrapolated instant. It does not, btw.

..."With our present knowledge of high energy particle physics, we can run the clock back through the lepton era and hadron era to about a millionth of a second after the Big Bang, when the temperature was 10^13 K. Using more speculative theory, cosmologists have tried to push the model to within 10^-35 seconds of the singularity, when the temperature was 10^28 K."
So we see the extrapolation becomes problematic close to t=0, pushing us past the current boundary of the BBT.

Dictionary of Geophysics, Astrophysics and Astronomy Ed R A Matzner CRC Press 2001:
Big Bang The initial explosion that gave birth to the Universe,

When one reads "explosion" as a description of BBT, be cautious. Explosions are events that thrust stuff into existing space. BBT is an expansion of spacetime. Expressions of an explosion of spacetime would be okay, no doubt.

'and a standard model of the Universe in which all matter space and time expand from an initial state of enormous density and pressure. All models of the Universe constructed in the classical relativity theory (General Relativity) must take into account that at present the Universe is expanding. . . . . . . . . .
Right, it is the expansion of today, once again, that gave us the BBT.

...This moment of infinite compression is called the Big Bang.
That's not how it should be seen.

The Icon Critical Dictionary of The New Cosmology Ed Peter Coles Icon Books 1998.
Big Bang Theory ...The difference between theory and model is subtle, but a useful definition is that a theory is usually expected to be completely self-contained (it can have no adjustable parameters, and all mathematical quantities are defined a priori), whereas a model is not complete in the same way. Owing to uncertain aspects of the Big Bang model, it is quite difficult to make cast-iron predictions from it, and it is consequently not easy to falsify (falsifiability being regarded in many quarters as an essential quality of a scientific theory)."
Wrong. Any theory or model of the universe is easy to falsify. Shall I post the "Bullet BB List"? What observations can astronomers make that will excuse BBT in getting it wrong or contradictory to well-tested and trusted observations?

"In the Big Bang model, the Universe originated from an initial state of high temperature and density (the primordial fireball) and has been expanding ever since..."
Yes, singularities aren't required for this theory.

"These models all predict the existence of a singularity at the very beginning, at which the temperature and density are infinite"
Bunk. Singularities are extrapolations outside the BBT. It's just that it is so easy to go another Planck units of time to get there that it's tempting to imply the theory goes there, but it doesn't.

' Most cosmologists interpret the singularity as meaning that the Einstein Equations break down at the Planck time under the extreme physical conditions of the very early Universe and that the very beginning must be addressed using a theory of quantum cosmology. This incompleteness is the reason why the word model is probably more appropriate."
Once again we see contradiction from one paragraph to another. If, as earlier stated , all the models predict a singularity -- predictions are very important in science and are required -- but we have no physics that works, then we don't have a viable model.

The Natural History of the Universe Colin A Ronan Marshall Edition 1991
"Mathematics and reality. The theory of the Big Bang has much observational evidence to support it. Yet there is another side to the study of the Universe. Mathematics often enables cosmologists, like other scientists, to work out in theory what Nature should be like before experimentalists and observers have confirmed that such is the case."
Yes, one example that comes to mind is.... the BBT! Lemaitre first recognized the possibility of expansion, or contraction, from GR before learning of evidence for it. Friedman's pure math work did the same except, without evidence, he did not suggest a physics model, but a math-only model.

"Mathematical reasoning is the only way to grasp the fundamentals that lie behind what we observe. This is so because mathematics is a language in which ideas can be formulated in a precise way and which allows the mind to work out logical sequences at profound depths, where mere words would present quite unsurmountable obstacles. Time and again, mathematical reasoning has provided insights available in no other way."
Yep, Galileo called math the language of science.

 

[Catastrophe]

Great topic!

I take BBT to be a result of Lemaitre's original theory where he took the discovery of today's expansion (Slipher's work originally), along with Hubble/Humason's work on distances, and recognized that GR is a robust theory that incorporates this expansion view, solving the dilemma both Einstein, deSitter and others had with their static models due to their bias for a static universe.

Thus, only when we rewind the clock to we approach a singularity point. But that does not require the actual theory to go there. A scientific theory almost always has limits so that going beyond those limits should require the metaphysics or pseudoscience labels. Calling untestable and problematic extrapolations "science" or even part of a model is detrimental to the importance behind the label "science". We open the door to more scientism, science by consensus, etc. that may seem helpful to get science passed its self-imposed boundaries, but it also pollutes both its meaning and efficacy.

That being said....

Cole. . . . . . . . . "For one thing, Einstein's theory itself breaks down at the very beginning of the Universe. The Big Bang is an example of what relativity theorists call a singularity, a point where the mathematics fall to pieces and measurable quantities become infinite.

So which is it? A theory or something that includes regions that "fall to pieces". A theory must be discarded or modified when there are pieces all over the floor. BBT, once again, isn't required, nor was ever intended by Lemaitre, to go there. This is similar to Darwin's "Origin of the Species", where his work never once suggested abiogenesis, but how one species (already in existence) could continually advance, or digress, new varieties over extreme amounts of time to a point where a new species would be found.

IMO, it is important to take extrapolations of a theory into untestable regions and try to glue it to the theory.

"While we know how the Universe is expected to evolve from a given stage,".... Yes, here Cole is where he should be; we can rewind the clock to as far as the theory can take us which is close to the Planck time, apparently, so this is the correct stage to conduct acts, but....

". . . . . Most cosmologists interpret the Big Bang singularity..." Oops, suddenly we are including BBS (might as well give it initials at this point, even if the concept is bogus). Suddenly we quickly find that we are now "off stage".

"... that Einstein's equations break down at some point in the early Universe due to the extreme physical conditions present there. . . . . . . . . . This shortcoming is the reason why the word 'model' is probably more appropriate than 'theory' for the Big Bang." So, we have bounced back from the metaphysics of the singularity (t=0) moment. But a scientific model, like a theory, should also not imply that it incorporates regions that cannot fit the SM method.
I believe Kuhn, and I agree, argued that a theory or model should be understood for its utility - that it allows physicists to use it as a tool. GPS is just one of many benefits from the tool of GR. But perhaps semantics may help and I have used it as well.

Language is important and there should never be suggestion that science represents "absolute truths", else we should still hold the Earth is the center of the universe. All science is a work in progress, building upon itself , like a building is remodeled on that island I mentioned in earlier threads.

Nice!

"Oxford Dictionary of Astronomy Ian Ridpath OUP 2011.:
Big Bang Theory (BBT) The most widely accepted theory of the origin and evolution of the Universe."

But most people incorrectly infer that "origin" means from t=0, but the "stage" viewpoint (above) is the correct approach.

I hope you will forgive my pedantic take on many of these points, but if we are to be true to the topic...

BBT is, again, not about origins, yet it, admittedly, is easy to infer that the beginnings of the universe are intrinsic to the model. Perhaps there is a word that better expresses this idea, if not we should invent one.

Oxford Dictionary of Astronomy Ian Ridpath OUP 2011.:
"The theory of general relativity predicts the existence of a 'singularity' at the very beginning, where the temperature and density were infinite."

It does not. It must be inferred, placing the events a t=0 outside the purview of science and into the realm of metaphysics.

Here is a paper that starts-off suggesting singularities are "well behaved" in the FLRW framework, yet states, "the singularity might have been avoided". It mixes the idea of the BBS as science, and suggests we may not even have a BBS. The key is whether or not the SM can be made to operate in this extrapolated instant. It does not, btw.

..."With our present knowledge of high energy particle physics, we can run the clock back through the lepton era and hadron era to about a millionth of a second after the Big Bang, when the temperature was 10^13 K. Using more speculative theory, cosmologists have tried to push the model to within 10^-35 seconds of the singularity, when the temperature was 10^28 K."
So we see the extrapolation becomes problematic close to t=0, pushing us past the current boundary of the BBT.

Dictionary of Geophysics, Astrophysics and Astronomy Ed R A Matzner CRC Press 2001:
Big Bang The initial explosion that gave birth to the Universe,

When one reads "explosion" as a description of BBT, be cautious. Explosions are events that thrust stuff into existing space. BBT is an expansion of spacetime. Expressions of an explosion of spacetime would be okay, no doubt.

'and a standard model of the Universe in which all matter space and time expand from an initial state of enormous density and pressure. All models of the Universe constructed in the classical relativity theory (General Relativity) must take into account that at present the Universe is expanding. . . . . . . . . .
Right, it is the expansion of today, once again, that gave us the BBT.

...This moment of infinite compression is called the Big Bang.
That's not how it should be seen.

The Icon Critical Dictionary of The New Cosmology Ed Peter Coles Icon Books 1998.
Big Bang Theory ...The difference between theory and model is subtle, but a useful definition is that a theory is usually expected to be completely self-contained (it can have no adjustable parameters, and all mathematical quantities are defined a priori), whereas a model is not complete in the same way. Owing to uncertain aspects of the Big Bang model, it is quite difficult to make cast-iron predictions from it, and it is consequently not easy to falsify (falsifiability being regarded in many quarters as an essential quality of a scientific theory)."
Wrong. Any theory or model of the universe is easy to falsify. Shall I post the "Bullet BB List"? What observations can astronomers make that will excuse BBT in getting it wrong or contradictory to well-tested and trusted observations?

"In the Big Bang model, the Universe originated from an initial state of high temperature and density (the primordial fireball) and has been expanding ever since..."
Yes, singularities aren't required for this theory.

"These models all predict the existence of a singularity at the very beginning, at which the temperature and density are infinite"
Bunk. Singularities are extrapolations outside the BBT. It's just that it is so easy to go another Planck units of time to get there that it's tempting to imply the theory goes there, but it doesn't.

' Most cosmologists interpret the singularity as meaning that the Einstein Equations break down at the Planck time under the extreme physical conditions of the very early Universe and that the very beginning must be addressed using a theory of quantum cosmology. This incompleteness is the reason why the word model is probably more appropriate."
Once again we see contradiction from one paragraph to another. If, as earlier stated , all the models predict a singularity -- predictions are very important in science and are required -- but we have no physics that works, then we don't have a viable model.

The Natural History of the Universe Colin A Ronan Marshall Edition 1991
"Mathematics and reality. The theory of the Big Bang has much observational evidence to support it. Yet there is another side to the study of the Universe. Mathematics often enables cosmologists, like other scientists, to work out in theory what Nature should be like before experimentalists and observers have confirmed that such is the case."
Yes, one example that comes to mind is.... the BBT! Lemaitre first recognized the possibility of expansion, or contraction, from GR before learning of evidence for it. Friedman's pure math work did the same except, without evidence, he did not suggest a physics model, but a math-only model.

"Mathematical reasoning is the only way to grasp the fundamentals that lie behind what we observe. This is so because mathematics is a language in which ideas can be formulated in a precise way and which allows the mind to work out logical sequences at profound depths, where mere words would present quite unsurmountable obstacles. Time and again, mathematical reasoning has provided insights available in no other way."
Yep, Galileo called math the language of science.

Helio, all are quotes for background, except my few notes in pale blue Cat
Updating continues since your reply and will do further.

 

[Helio]

Helio, all are quotes for background, except my few notes in pale blue .

I didn’t see them blue, but now I do.

I put your words in the quote box.

 

[Catastrophe]

I didn’t see them blue, but now I do.

I put your words in the quote box.

No, I have since put book/periodical titles in bold and my few notes in blue. I can understand that many of the quotations need comment, but I left them 'as is' since they were quotes. Thank you for your excellent commentary.

Cat

P.S, I take it that you have seen the first exercise on "Universe, simply labelled 'Agreed Terms help sensible discussion'? The Big Bang section was repeated in Part 2, to a point. I cannot go back and label my few comments in blue there, as time to edit has expired, but I think they are clear.

 

[Atlan0001]

The "Planck era" is forever, since it is also the Planck level of things where we can't reach any further down and in. It is the place of an eternally constant "spinning wheels in the mud of physics". Not that there isn't anything past it down and in, there is just no possibility of any relative instrumentality ever reaching to that level below the Planck level. At that point, that level, that distance in and away from us and all our instrumentality, we will reach the point of just "spinning our wheels" (quite a hot spinning of wheels) and nothing more. So, its a horizon, a wall, we won't reach beyond (it does not mean, nor say, that there isn't anything there in it / beyond it, including before it as a matter of time, just whatever is beyond, is beyond our reach, from where we are, where we exist, into whatever is there). Since the Planck level and the Big Bang are one and the same, the same physics of horizon and unreachability apply. The only difference being some horizons can be traveled toward, infinitely and forever, only never to be gotten closer to than when the traveler started. That is the meaning of the Planck constant regarding its constant of distance down and in from us (down and in from anywhere), and the meaning of the Big Bang up and out from us (up and out from anywhere), the micro-verse PLanck level horizon's macro-verse self. We will never get any closer to, nor any farther away from, that nakedly singular constant of horizon than we, as finite local, relative, observers, are now (than any were a trillion, trillion, and more years ago (could we tell any difference between then and now?)) (than any will be a trillion, trillion, and more years from now (could they tell any difference between now and then?)).