I Describing the Big Bang

[.Scott]

TL;DR Summary

It started with a point-like singularity? Really?

I started reading a National Geographic article related to the Big Bang. It starts these statements:

Gazing up at the stars at night, it’s easy to imagine that space goes on forever. But cosmologists know that the universe actually has limits. First, their best models indicate that space and time had a beginning, a subatomic point called a singularity. This point of intense heat and density rapidly ballooned outward.

My first reaction was that this is a layman's approximation to the actual Physics view.
My second reaction was "What IS the actual Physics view?".

This singularity can't be a "point" because there is no such Physical thing. The amount of information you can store in an object of true zero diameter is zero. And if you make it 10-dimensional, it's still zero.

So, perhaps it was a fuzzy point.

And then it inflated (wiki article). That wiki article cites a standard college text book in describing it this way:

All of the mass-energy in all of the galaxies currently visible started in a sphere with a radius around 4 x 10-29 m then grew to a sphere with a radius around 0.9 m by the end of inflation

Per Wiki's "Shape of the Universe" (citing NASA sources):

Current observational evidence (WMAP, BOOMERanG, and Planck for example) imply that the observable universe is spatially flat to within a 0.4% margin of error of the curvature density parameter with an unknown global topology.

So we have "currently visible", "sphere", and not much curvature.
And the "sphere" we are talking about is the volume interior of a 3-D sphere. You can recast it as the surface of a 4-D sphere, but I don't believe Big Bang was suppose to posit a particular topology for our universe.

So, perhaps the problem is simply with "sphere". Perhaps when I hear "sphere", I should replace it with "some finite topology" - it could be a Klein bottle. So we have a fuzzy point, puffs up to some topology (perhaps a Klein bottle or Sphere) which includes our visible universe ... but probably some regions that are not visible. How could it exclude our geometric neighbors. So that "singularity" included, not just everything in the "visible universe", but everything in some finite topology. Sure, why not? Our fuzzy little point probably just got a bit bigger, but why not?

But presuming a finite topology when our best measurements say that it's flat to within an 0.4% margin is being pretty presumptuous. What happens if we try a flat 3D "plane" of infinite extent? Well that fuzzy point just turned into a flat 3D "plane" as well. After all, the Big Bang inflation was just a initial finite dimension multiplied by a constant. If the result is an infinite length, then the initial dimension must have been infinite as well.

Anyway, at this rate, I will never finish that National Geographics article.

 

[PeroK]

The NG article is not worth reading. According to Introduction to Modern Cosmology by Liddle:
The Big Bang model is reliable back to $10^{-10}s$. This is the hot dense state.

The best best model of the universe is that it is infinite. In the sense that there is no evidence of the curvature that would imply it were large and finite. That said, that's not proof that it is infinite.

The observable universe is the finite volume of the universe that we can detect so far. The observable universe increases in size as time passes and we can see further back.

Before the above time is "open to speculation" according to Liddle.

One idea for before the Big Bang is inflation. Liddle chapter 13. According to this (Alan Guth's theory) inflation ended at $10^{-34}s$.

In short, it's important to distinguish between the very early inflation model and the subsequent Big Bang model. And, important to distinguish between the observable universe and the entire universe.

The universe was never a single point in any valid mathematical model. Although, at the start of inflation, the observable universe must have been very small.

 

[jbriggs444]

The universe was never a single point in any valid mathematical model.

I think that this is the point that you (@.Scott) were trying to make. Any popularization that tries to describe the initial "singularity" as a "point" is technically incorrect. You were right about that.

The easiest analogy that I have for the idea of a "singularity" is to consider the graph of a function. For instance, consider $f(x) = \frac{-1}{x^2}$ for $x \ne 0$.

This function is well behaved everywhere within its range. But that range does not include $x = 0$. This is a "singularity".

In the case of the physical universe, we model it as a "manifold". Which means that near every point in the universe, we can map out all nearby points with cartesian coordinates. Here, "nearby" in physical terms is required to match "nearby" in coordinate terms. That preserves the topology.

If you model the universe as a manifold, the singularity cannot be part of the manifold. Because you cannot map all nearby points in cartesian coordinates that properly reflect the physical topology.

 

[.Scott]

I think that this is the point that you (@.Scott) were trying to make. Any popularization that tries to describe the initial "singularity" as a "point" is technically incorrect. You were right about that.

The easiest analogy that I have for the idea of a "singularity" is to consider the graph of a function. For instance, consider $f(x) = \frac{-1}{x^2}$ for $x \ne 0$.

This function is well behaved everywhere within its range. But that range does not include $x = 0$. This is a "singularity".

Or, if the universe really is topologically flat (or otherwise spatially infinite): $f(x,y,z,t) = \frac{-1}{t^2}$ for $t \ne 0$.

 

[Physics Detective]

The best best model of the universe is that it is infinite. In the sense that there is no evidence of the curvature that would imply it were large and finite. That said, that's not proof that it is infinite.

I remember when people used to say "the universe was once the size of a grapefruit". Then after the WMAP results in 2006 I think, this morphed into "the observable universe was once the size of a grapefruit". Then some other people started saying the universe must be infinite because it's flat, and it was even infinite at the time of the Big Bang. I'm happy with most aspects of Big Bang cosmology, but I'm not happy with that.

 

[phinds]

Then some other people started saying the universe must be infinite because it's flat, and it was even infinite at the time of the Big Bang.

If it is infinite now then it HAD to be infinite at the time of the singularity because you can't get from finite to infinite

I'm happy with most aspects of Big Bang cosmology, but I'm not happy with that.

The universe really doesn't give a rat's patootie what we humans are happy with. It is what it is.

As Feynman once said, "You don't like it? Go somewhere else, to another universe where the rules are simpler, philosophically more pleasing, more psychologically easy"

 

[Jaime Rudas]

The best best model of the universe is that it is infinite. In the sense that there is no evidence of the curvature that would imply it were large and finite. That said, that's not proof that it is infinite.

The best model of the universe we have (the ΛCDM model) is fully compatible with both a finite and infinite universe. Moreover, the most precise measurements we have (Planck 2018) have such a margin of error that it is impossible to determine whether the curvature is positive, negative, or zero.

 

[.Scott]

As Feynman once said, "You don't like it? Go somewhere else, to another universe where the rules are simpler, philosophically more pleasing, more psychologically easy"

Been there, done that.

 

[Physics Detective]

The universe really doesn't give a rat's patootie what we humans are happy with. It is what it is.

You will be aware of Newton's infinite universe. It's mentioned here and here. Gravity should have caused all the stars to "fall down in the middle" and there "compose one great spherical mass". However if the universe was infinite, each and every star would be pulled on all sides by other stars, so there would be no gravitational collapse. In short, the infinite universe cannot collapse.

Now flip it around, and think of the expanding universe. I rather liked Is Hubble’s Expansion due to Dark Energy? by Ramesh Gupta and Anirudh Pradhan dating from 2010. It says this: “Hence, it is concluded that: yes, indeed it is the dark-energy responsible for the Hubble’s expansion too, in-addition to the current on-going acceleration of the universe”. Bearing in mind what Adam Riess has been saying of late, think of whatever it is that is causing the universe to expand. The earliest version of this I could find was Schrödinger’s cosmic pressure. See the 2014 Cambridge companion to Einstein by Michel Janssen and ‎Christoph Lehner: “Schrödinger [1918] had pointed out another way of treating the cosmological constant: moving it from the left-hand side of Equation [7], where it represents a contribution to space-time curvature, to the right-hand side, where it represents a contribution to the energy-matter distribution. Then it would correspond physically to a kind of cosmic pressure”. If the universe is infinite, this cosmic pressure is counterbalanced at all locations. In short, the infinite universe cannot expand.

The universe might not give a rat's patootie about that, but I do.

 

[fresh_42]

The best model of the universe we have (the ΛCDM model) is fully compatible with both a finite and infinite universe. Moreover, the most precise measurements we have (Planck 2018) have such a margin of error that it is impossible to determine whether the curvature is positive, negative, or zero.

Zero is by nature always below the margin of error. Not offensive, just curiosity: as we can only observe a (tiny?!) fraction of it, isn't this question mute?

 

[Ibix]

So, perhaps the problem is simply with "sphere". Perhaps when I hear "sphere", I should replace it with "some finite topology"

I find dropping a dimension easier to explain, although this causes different problems.

There are three classes of FLRW universe - closed, flat and open. Dropping a dimension, a closed universe is a sphere (the surface of a ball), a flat universe is an infinite flat sheet, and an open universe is an infinite sheet, everywhere shaped like a saddle (curving upwards in the x direction and downwards in the y direction). In all three cases, the observable universe is a circle drawn on it with the Earth at the center. In all three cases this 2d sheet is the universe now, and time is perpendicular to the sheet. So the past is one side of the sheet and the future is the other and spacetime is a (2+1)d volume, not just the 2d surface.

Roughly speaking the singularity, when time started, is at the center of the closed model, but is just another plane somewhere below "now" in the other two models. But here's where the problems with this visualisation start. The singularity isn't actually part of spacetime - it's a boundary and it's a mistake to think of it as a plane or a point (although that's how it appears in the model I described). It's literally where our notions of geometric entities like volume and distance fail to work. It's literally indescribable - most probably meaning that our physical theories are incomplete and we need a better theory to describe what's actually going on.

Other problems with the 2d model I described include that you can't have an open model embedded in a Euclidean three space - you can't embed a constant curvature surface that doesn't intersect itself. And closed universes can eventually collapse - so although it's convenient to visualise an expanding closee universe as a set of nested spheres you eventually reach a point where the universe starts contracting and the next sphere needs to be smaller, and the Big Crunch singularity is the outermost sphere, but is identical to the Big Bang singularity that "looks like" a point at the center.

That, of course, is why we use maths to describe the actual thing - visualisations have their limits. But the important thing it lets you do is keep track of tge difference between a spherical closed universe and the one-dimension-less spherical region we call the observable universe.

 

[Ibix]

Zero is by nature always below the margin of error. Not offensive, just curiosity: as we can only observe a (tiny?!) fraction of it, isn't this question mute?

It might turn out to have a non-zero curvature. But if it truly has a zero curvature we will never be able to confirm that it is not just really, really large, yes. Unless we come up with some other future theory that lets us prove that it must be flat/non-flat by some other measure.

 

[Jaime Rudas]

Zero is by nature always below the margin of error.

Not in this case. The curvature parameter $\Omega_{\kappa}=0.0007 ± 0.0019$, meaning its zero value is WITHIN the margin of error.

Not offensive, just curiosity: as we can only observe a (tiny?!) fraction of it, isn't this question mute?

According to the model, the universe is homogeneous, so knowing the characteristics of a small portion is enough to infer those of the whole.

 

[.Scott]

Other problems with the 2d model I described include that you can't have an open model embedded in a Euclidean three space - you can't embed a constant curvature surface that doesn't intersect itself

I think you are referring to 3D "surfaces" that have no 2D equivalents - especially when they are allowed to fold into a four and fifth dimension.

You can have a 3D topology that "overlap" themselves without there being "special places" - 1D "poles" that cannot be orbited because in a single orbit you would fail to return to the place where you started.
The Klein bottle is one (or, for 3D, the surface of a Klein bottle cylinder). There would be no local clues that our 3-D surface is twisted so badly (such as those poles). And I see no reason why such a surface would interfere with itself.

 

[Ibix]

I think you are referring to 3D "surfaces" that have no 2D equivalents - especially when they are allowed to fold into a four and fifth dimension.

I think you can describe 2d surfaces of constant negative curvature. You just can't embed them in 3d Euclidean space, which is where the visualisation comes unstuck.

 

[phinds]

isn't this question mute?

Just FYI, you mean "moot", not "mute".

 

[fresh_42]

Just FYI, you mean "moot", not "mute".

Google translated it correctly, and I haven't cross-checked. But now, as you mention it. Ever since I started writing so much in English, I tend to make all the mistakes due to writing what I "hear" in my mind. It's sometimes quite embarrassing.

 

[.Scott]

"Constant Negative Curvature"?
Saddle shapes surfaces have negative curvature at all points - and are commonly described as having "constant negative curvature".

But I think you may be referring to something more difficult. I believe you mean a surface where, for example, the circumference of a 1-meter circle is a constant that is greater than 2 pi meters. For example, one where it is exactly 6.5 meters at every point.

There is a wiki article on this.

 

[Jaime Rudas]

"Constant Negative Curvature"?
Saddle shapes surfaces have negative curvature at all points - and are commonly described as having "constant negative curvature".
.

No, two-dimensional saddle-shaped surfaces have negative curvature but this is not constant.

 

[phinds]

Google translated it correctly, and I haven't cross-checked. But now, as you mention it. Ever since I started writing so much in English, I tend to make all the mistakes due to writing what I "hear" in my mind. It's sometimes quite embarrassing.

But completely understandable. Your English is excellent.

 

[Ibix]

"Constant Negative Curvature"?
Saddle shapes surfaces have negative curvature at all points - and are commonly described as having "constant negative curvature".

As Jaime has noted, their radius of curvature is not constant. Take a section along the length of the horse - constant curvature in Euclidean space can only be achieved by making a circle in this direction. So immediately you can see that you can't have an infinite surface with constant negative curvature. In fact I think you can't have a finite one either - I think you'll find that negative curvature cannot be made constant in a 2d space embedded in Euclidean 3-space.

Diagrams of saddles are often used to illustrate negative curved space, and they are indeed negatively curved. Just not with constant curvature.

 

[Ibix]

Just FYI, you mean "moot", not "mute".

I noticed this too, but decided to remain mute.

 

[phinds]

I noticed this too, but decided to remain mute.

I just can't help myself. I need to honor my badge:

 

[.Scott]

I think you can describe 2d surfaces of constant negative curvature. You just can't embed them in 3d Euclidean space, which is where the visualisation comes unstuck.

This quote (above) is where I got the "constant negative curvature". I can't say that you misused the term, because it is what it is most often called. But I would call it "continuous negative curvature" - just to avoid the other potential interpretation.

That gets us back to this:

Other problems with the 2d model I described include that you can't have an open model embedded in a Euclidean three space - you can't embed a constant curvature surface that doesn't intersect itself. ...

So, now that I know that you are referring to a saddle surface (as an example), why could you not have one in a Euclidean 3-space? There are still two ways of interpreting that statement, but neither one looks like a problem.

 

[Ibix]

why could you not have one in a Euclidean 3-space?

Because the saddle's radius of curvature isn't constant, and and FLRW negative curvature space is.

That's why I keep going on about constant curvature.

 

[.Scott]

Because the saddle's radius of curvature isn't constant, and and FLRW negative curvature space is.

That's why I keep going on about constant curvature.

OK. So, it's NOT a saddle surface that you were talking about.
That's what I originally suspected when I said this:

But I think you may be referring to something more difficult. I believe you mean a surface where, for example, the circumference of a 1-meter circle is a constant that is greater than 2 pi meters. For example, one where it is exactly 6.5 meters at every point.

There is a wiki article on this.

 

[DaveC426913]

As long as we're wondering about typos...

Take a section along the length of the horse

Does that horse have a saddle?

(Serious question though. Whether correct or incorrect, I still don't know what it means in the thread context)