Georges Lemaître primeval atom

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• Helios
The etymonline dictionary gives 1893 as the first use in the mathematical sense, albeit without providing any concrete references.This seems to be an accurate summary of the content.

Helios

TL;DR Summary
what did Georges Lemaître do? What did he suppose? What did he solve?
[ Wikipedia quote ] Georges Lemaître first noted in 1927 that an expanding universe could be traced back in time to an originating single point, which he called the "primeval atom".

Exactly what did Georges Lemaître do? What did he suppose? What did he solve?

Did Lemaître think the universe was finite or infinite?
Did Lemaître think his primeval atom had a size? Points don't have size. Originating single points don't have size. Did he think his atom was a point?

[ Wikipedia quote ] According to the Big Bang theory, the universe at the beginning was very hot and very small, and since then it has been expanding and cooling down.

Once the infinite sized universe was very small? What is small infinity?

Lemaitre - and Friedmann, and Robertson, and Walker - were all studying Einstein Field Equations. The solution to which, arrived at under some assumptions best resembling the observed universe, has a singularity in the past. That's Lemaitre's primeval atom.
As the universe gets closer to the singularity (i.e. as we extrapolate to the past), the scale factor goes to zero - that's the meaning of very small.

I.e. he didn't suppose much about the result, just saw what the equations told him and dressed it in words - perhaps inflected by his priestly circumstances.

I don't know what was thought of the (in)finiteness of the universe at the time, but the solution accommodates both finite and infinite cases.

pinball1970, Ibix and Helios
Helios said:
[ Wikipedia quote ] According to the Big Bang theory, the universe at the beginning was very hot and very small, and since then it has been expanding and cooling down.
You should include a link to the article you are quoting. Context can be more important than you personally realize and you may have missed something with what you quote.
Helios said:
Once the infinite sized universe was very small? What is small infinity?
People are often sloppy about the distinction between the observable universe, which is and always has been finite in size, and various models of the entire universe, which can be finite or infinite in size. Without seeing the context of the quote we can't tell if they are talking about a closed finite universe or if they are leaving out the word "observable" for some reason.

Helios
Bandersnatch said:
as a singularity in the past. That's Lemaitre's primeval atom.
Singularity is a point or not a point? The so-called "atom" can only be finite. How can this be for the infinite case?

The singularity is not a point. It's a time at which the distance between all points in the (finite or infinite) universe becomes zero, if you take the maths literally. If the idea of distinct points that are separated by zero distance seems slightly self-contradictory, that's the point. That's what a singularity is, where the maths doesn't really work anymore.

Remember that "atom" is from the Greek meaning "indivisible". I don't think it should be taken to mean some kind of atom in the modern physics sense.

Ibix said:
I don't think it should be taken to mean some kind of atom in the modern physics sense.
Well no but Lemaître had "some kind of atom" in mind so he must have had universal finitude in mind to call it an atom. The infinite case would not have been called an atom, no?

I do not know what Lemaitre thought.

I do know that the singularity that comes from the maths arises in both the finite and infinite cases and is not more of a problem for one model than the other.

I also know that the word "atom" comes from Greek and means "uncuttable" and that this does not, to me, have any connotation of finiteness. I do not see where you are getting that from. But I do not speak Greek or Lemaitre's native French, so would not regard myself as an expert.

Ibix said:
the singularity that comes from the maths
As an aside perhaps,
When did the term "singularity" become the widespread mathematical term it is now.
Wiki, the usual go to, did not have any reference to its history of usage.

256bits said:
As an aside perhaps,
When did the term "singularity" become the widespread mathematical term it is now.
Wiki, the usual go to, did not have any reference to its history of usage.
The etymonline dictionary gives 1893 as the first use in the mathematical sense, albeit without providing any concrete references.
Reading up on the history of mathematical analysis on Wikipedia, this time stamp seems plausible, as the nineteenth century is when the branch of mathematics was formed (although naively one would be inclined to think it should be some 50 years earlier, since that's when the bulk of the work was done by the greats like Cauchy, Poisson, Riemann, or Fourier).
The same dictionary gives 1965 for the beginning of use in the astronomical sense, i.e. during the golden age of general relativity. Again, no specific reference is given, but it could be referring to Penrose's work on black holes from that year.

DrClaude and 256bits
Maybe you can find more clues here:

"Georges Lemaitre and the Foundations of Big Bang Cosmology"
- - - - https://arxiv.org/abs/2007.09459

It's been a while since I read it but I remember his primeval atom was at least mentioned.

EDIT: And yeah, I know it's history/philosophy. The author seems to have an uncanny (and uncited) ability to (almost) read Lemaitre's mind though. Which is quite a feat as the man passed away in the 60s... :)

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DrClaude
Bandersnatch said:
The etymonline dictionary gives 1893 as the first use in the mathematical sense, albeit without providing any concrete references.
Reading up on the history of mathematical analysis on Wikipedia, this time stamp seems plausible, as the nineteenth century is when the branch of mathematics was formed (although naively one would be inclined to think it should be some 50 years earlier, since that's when the bulk of the work was done by the greats like Cauchy, Poisson, Riemann, or Fourier).
The same dictionary gives 1965 for the beginning of use in the astronomical sense, i.e. during the golden age of general relativity. Again, no specific reference is given, but it could be referring to Penrose's work on black holes from that year.

From the OED:
1893 A. R. Forsyth Theory Functions Complex Variable xxi. 606 All the essential singularities of a discontinuous group lie on the axis of a when the group is real.
1965 Physical Rev. Lett. 14 58/1 An exterior observer will always see matter outside r = 2m, the collapse through r = 2m to the singularity at r = 0 being invisible to him.
That latter article is Penrose's Gravitational Collapse and Space-Time Singularities. Bravo @Bandersnatch!

Bandersnatch
sbrothy said:
Maybe you can find more clues here:

"Georges Lemaitre and the Foundations of Big Bang Cosmology"
- - - - https://arxiv.org/abs/2007.09459

It's been a while since I read it but I remember his primeval atom was at least mentioned.

EDIT: And yeah, I know it's history/philosophy. The author seems to have an uncanny (and uncited) ability to (almost) read Lemaitre's mind though. Which is quite a feat as the man passed away in the 60s... :)
I know this is an old thread but it popped into my head when I stumbled over this one:

"Resurfaced 1964 VRT video interview of Georges Lemaître"
-- https://arxiv.org/abs/2301.07198

pinball1970, DrClaude and Bandersnatch
sbrothy said:
I know this is an old thread but it popped into my head when I stumbled over this one:

"Resurfaced 1964 VRT video interview of Georges Lemaître"
-- https://arxiv.org/abs/2301.07198

I must admit I'd have expected his book "The Primeval Atom" to have entered the public domain by now. I haven't had much success finding it though. For those willing to bend a few rules (or miss a few pages) I'm sure it's out there somewhere, but I'm not gonna post any links as I'm sure that goes against the letter of the rules, or at the very least the spirit of the rules.

As possible source could perhaps be found here:

"Lemaître chose to publish a full version of his fiery primeval-atom model in French in Revue des Questiones Scientifiques. 82 This semi-popular journal had been set up in 1877 by the Scientific Society of Brussels, a Catholic organization that sought a rapprochement between the Church and modern science at a period of unrelenting anti-clericalism in France and Belgium."

"Georges Lemaitre and the Foundations of Big Bang Cosmology"
- - - - https://arxiv.org/abs/2007.09459

It's kinda funny seeing the man squirm a little to keep his religious beliefs out of his science (or perhaps more honestly) fighting the interviwer's attempts to get him to mix them up). All in all he does a better job at it than most. He was, after all, a priest.

The interviewer asks a kinda silly question though:

"JV: You are one of the creators of a theory that is a part, if you will, of what Hoyle calls the ”Big Bang” theories, the theories of the big explosion. What is your theory, and if possible at all Monsignor† , could you explain it in just a few words?"

Heh, Good luck with that! :P

Regards.

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Klystron
sbrothy said:
I know this is an old thread but it popped into my head when I stumbled over this one:

"Resurfaced 1964 VRT video interview of Georges Lemaître"
-- https://arxiv.org/abs/2301.07198
I have just come across this on YT

Lemaitre also was possibly the first to demonstrate that there is no singularity or misbehavior at the horizon of a Schwarzschild (vacuum) solution, by producing the so called Lemaitre coordinates for this solutions (which are simply the Gaussian Normal coordinates).

I would've sneaked this in by editing one of my own posts but seeing that the thread hasn't aged more I thought I might as well post it. Also, it being more philosophy/history than actual physics makes it a nice fit. It's not that I think people are unable to search Arxiv on their own but here goes:

"Eddington, Lemaitre and the hypothesis of cosmic expansion"
-- https://arxiv.org/abs/1907.12297

Regards.

vanhees71