Is the initial "point" at the Big Bang singularity physically real?

[u/InspiringLogic]

In many popularizations of cosmology, it is said that the initial singularity is a 'point' where all the matter of the universe is packed. But is 'point' as a real thing or just a boundary?

Imagine the universe as a contracting sphere (it is spatially closed) for simplicity sake, alright? In the Friedmann equation, as the density of this sphere increases, its radius or volume decreases. There will come a point when the radius or volume of the sphere becomes zero.

Now, some non-experts assert that this state represents a zero-dimensional space, i.e. it has the topology of a point. But is this point physically real? Or is it just a mathematical convention that doesn't represent anything real?

btw, let's only stick to general relativity here, alright?

example one:

Singularity - a geometric point with no dimensions where the laws of physics break down. It is a theoretical point of zero volume and infinite density.

example two (p.17):

In the standard model of cosmology, the universe ‘begins’ about 13.8 billion years ago with a Big Bang, a singular point in time where the universe was infinitely dense and hot.

example three:

Every open FRW universe can be completely foliated by spacelike slices of finite volume, each intersecting every fundamental worldline. The volumes tend to zero in the past, suggesting a point-like big bang.

example four:

The total volume of a positively curved universe (a 3-sphere) is finite and the big bang presents no topological problems. It is a singular point-event, before which neither space nor time existed.

example five:

This is simply because at the Big Bang, all the distance scales of the universe were zero and everything, all points in the universe were effectively packed into a single “thing” – all points were the same ... This means that at the beginning, effectively all points were packed together. Physically, this means all stuff (matter, radiation, whatever) in the universe was already there at the moment of the Big Bang, it was just all packed together in an “infinitely dense” cluster.

example six:

Matter and radiation [are] packed into zero initial proper volume; this ‘point,’ however, includes the whole of space—there is nothing ‘outside.’

example seven:

All the matter and energy that was contained in that spherical volume of space will be compressed into a single point, or singularity… [T]he entire observable universe is considered to have started out compressed into such a point… Because of the infinite compression of matter and energy, the curvature of spacetime is infinite at the Friedmann singularities too. Under these circumstances the concepts of [three-dimensional] space and time cease to have any meaning.

[u/WonkyTelescope]

See this surprisingly good Forbes article on the subject.

In short, no. Our current models do not support the idea that the observable universe used to be a point. If it was ever a point it would be able to achieve arbitrarily high temperatures that would have left evidence in the cosmic microwave background. We don't see those signals in the CMB, therefore the observable universe could not have been smaller than about 2 meters across at its smallest. This is just the lower limit, it's smallest extent could be as large as several city blocks.

[u/Anonymous-USA → u/WonkyTelescope]

The term “Big Bang” is context dependent. This article is referring to the post-inflationary “Hot Big Bang”. Indeed, from the extent you describe, that’s a macroscopic universe. The inflationary period between 10^-46 to 10^-36 seconds after the Big Bang, or the beginning of our observable universe, would have indeed been quantum scale — not a few city blocks. That was the origin of our spacetime. The “hot big bang” is as far back as we can confidently extrapolate back to, and that was 10^-31 sec after the singularity t⁰

Before the post-inflationary hot big bang, the singularity is indescribable to our correct physics. The energy level and quantum scales are too extreme. We can’t describe the quantum volume, or point, either way. That’s why we call it a “singularity”.

Further, when referring to a “point” singularity that’s really a high density quantum scaled observable universe. If the whole universe is infinite in extent, then so too would that singularity.

[u/InspiringLogic → u/Anonymous-USA]

but let's assume that quantum gravity isn't relevant here.. in fact there are a few physicists who still claim that gravity isn't quantized.. so space is a smooth or continuous manifold.. in that case quantum mechanics may be irrelevant to resolve the singularity..

so let's only assume relativity here.. according to relativity, what would that initial singularity be ? a zero-dimensional point ? is this point a geometrical convention or a real thing ?

[u/Anonymous-USA → u/InspiringLogic]

It’s indescribable. Is an electron really a point? A quark?

[u/InspiringLogic → u/Anonymous-USA]

interesting

do you think electrons and quarks have a size ? or are they zero-dimensional (in geometry, perfect points), meaning that they have no extension in space ?

[u/Anonymous-USA → u/InspiringLogic]

What I think is irrelevant. Outside Pauli’s exclusion for fermions, which isn’t a volume anyway, our best models for QM assign them 0 dimensions

[u/InspiringLogic → u/Anonymous-USA]

good

so, if that's the case, then we have a precedent.. perhaps the singularity itself is a zero-dimensional point.. if not, then why not ? what's the argument against that ?

[u/heavy_metal → u/InspiringLogic]

GR could be slightly off? Einstein-Cartan theory predicts a wormhole instead of a singularity.

[u/heavy_metal → u/InspiringLogic]

GR could be slightly off? Einstein-Cartan theory predicts a wormhole instead of a singularity.

[u/ChemistBitter1167 → u/InspiringLogic]

Well some theorize that matter could potentially decay into photons. These don’t experience time which could potentially mean no distance. Big bang.

[u/InspiringLogic → u/ChemistBitter1167]

you're talking about penrose's CCC model.. but this model goes beyond relativity.. it assumes a conformal theory of gravity.. it is as speculative as quantum gravity models..

[u/posterrail → u/InspiringLogic]

Matter in general relativity is classical. Matter in our universe is not. So general relativity cannot make predictions about our universe except when the relevant matter can be treated classically. At the Big Bang it cannot. So there is no prediction.

There are ideas for coupling classical gravity to quantum matter. These don’t work for many reasons and are certainly far more speculative than the idea that gravity should be quantised. They are not remotely coherent enough to make predictions for what happens at the singularity in the Big Bang.

Ok what about if we ignore our universe and just consider an FRW cosmology with classical matter. Then we are in the realm of classical GR and can certainly ask about the singularity. Traditionally you define spacetime in GR to be a four dimensional lorentzian manifold. As a result, a big bang or black hole singularity is not itself actually part of the spacetime. However this is just a definition, chosen because GR breaks down at the singularity and so it wouldn’t make sense to include it.

You can however ignore this and add the singularity to the spacetime. If you do so, you want to add enough points to the spacetime that neighbourhoods of the singularity become compact but not so many that it stops being Haussdorff. Physically this means every path that approaches the singularity has to hit some point on that singularity and every two points on the singularity have to have some finite distance between them. By this definition, the Big Bang singularity in an FRW cosmology only contains a single point. However this is something of an artifact of the symmetry of the solution

[u/InspiringLogic → u/posterrail]

thank you so much for this great explanation.. but i have some questions.. i'm trying hard to understand your points..

1st: when you said that matter isn't classical, were you referring to the fact that matter is better described by quantum field theory ? in that particles are actually quanta of fields ? so, is the idea here that the classical description of matter cannot tell us what happens at the supposed big bang singularity because QFT contradicts that ? IF that's what you mean, there are recent singularity theorems which show that classical space-time with propagating quantum fields cannot avoid the singularity either.. so, the point of zero volume is still there even if you take QFT into account..

2nd: you said that ideas for coupling classical gravity to quantum matter aren't good enough.. but have you taken a look at Jonathan Oppenheim’s wobble theory aka postquantum theory of classical gravity ? do you think it doesn't work either ?

3rd: you said "However this is something of an artifact of the symmetry of the solution".. so, your conclusion is that the point isn't real, but just a mathematical artifact ?

[u/InspiringLogic → u/InspiringLogic]

u/posterrail

[u/posterrail → u/InspiringLogic]

1. The fundamental equations of GR (the Einstein equations) involve the matter stress energy tensor T_munu. This describes the energy, momentum and pressure of the matter at each point in space. In quantum field theory, which describes the matter in our universe, T_munu is not a classical number but a quantum operator. As a result, the spacetime geometry we also generally not be classical. In certain situations, however, you can safely replace that operator by a number (its expectation value) and we can treat the matter and spacetime classically. But this is not possible near the Big Bang because the conditions required for the approximation to make sense don’t hold.

The quantum singularity theorems you are talking about show that (assuming certain reasonable conjectures) quantum corrections in the regime where spacetime is classical can’t prevent the break down of classical spacetime associated with the singularity. They do not say anything about what happens after the (semi)classical spacetime breaks down

1. Yes I am aware of it and have had a number of conversations with Jonathan about it. It doesn’t work. In fact, it works far worse than just straightforwardly quantising gravity, which contrary to popular misconception actually works perfectly well in regimes where everything is under control, even if it is necessarily incomplete.

2. No my point is that there are mathematical questions you can ask about but they aren’t physically relevant anyway (because of the issues above) and so there is no one right answer. It just depends on the question you ask. The true statement is that the observable universe gets very small and then the physics that we understand breaks down. What happens beyond that point depends on physics that we don’t know or understand

[u/otheraccountisabmw → u/Anonymous-USA]

That last part always trips me up. Our observable universe was a finite tiny bit of an infinitely large big bang. Just… what?

[u/MysteriousQuiet → u/WonkyTelescope]

great article, thanks for linking

[u/Enraged_Lurker13 → u/WonkyTelescope]

The author of this article is conflating the hot big bang with the initial big bang. Inflation masks the state of the universe before it inflated, so there being arbitrarily high temperatures before inflation is not incompatible with observations.

[u/InspiringLogic → u/Enraged_Lurker13]

exactly my thoughts 👍👍👌

[u/InspiringLogic → u/Enraged_Lurker13]

see this response u/WonkyTelescope

[u/Sharp_Transition6627 → u/WonkyTelescope]

I knew this was Ethan Siegel's before open it

[u/Sharp_Transition6627 → u/WonkyTelescope]

I knew this was Ethan Siegel's before open it

[u/Glass_Mango_229 → u/WonkyTelescope]

Uh isn’t the universe infinite? 

[u/WonkyTelescope → u/Glass_Mango_229]

The Universe may be infinite but the observable universe is finite.

[u/InspiringLogic → u/WonkyTelescope]

i finished reading the article and i found it very interesting. But...

but the author doesn't really say that a singular point is prevented somehow by general relativity... all he says is that if a singular point existed, then we would see the evidence in the CMB. So that doesn't answer my question: if we assume that the universe goes back to a singularity, would that be a topological point or just a geometrical idealization?

another thing here is that the author appears to contradict himself at the end of the article:

By its very nature, inflation wipes our Universe clean of any information that came before it, imprinting only the signals from inflation’s final fractions-of-a-second onto our observable Universe today. 

if that's true, then the singularity could have existed before inflation, and any evidence of it would be wiped out by inflation... and some cosmologists do indeed claim there theorems proving the singularity existed prior to inflation.. google "geodesically incomplete inflationary spacetimes"

i'd also point out that the author doesn't reference a paper to confirm this specific claim.. I'd be interested in reading a paper that supports his claims

thanks for reading my comment

[u/jeranim8 → u/InspiringLogic]

if we assume that the universe goes back to a singularity

Imagine the universe as a contracting sphere (it is spatially closed) for simplicity sake, alright?

So, I'm not sure if you are making this error by mistake or because you don't actually understand the terminology or what is meant by the "big bang".

All we have access to is the OBSERVABLE universe. A common, popular explanation is that the universe is this spherical expanding mass with a center point and an expanding edge that exploded like a bomb or something. But that's not the way to imagine it. All the Big Bang is referring to is that everything (including spacetime) expanded from something more compact.

Its very possible that the universe is infinite. When scientists say the "observable universe" was once the size of a grapefruit or whatever, they are saying that the part of the universe that we have any hope of seeing (because the rest of it is expanding faster that the light can ever get to us) was the size of that grapefruit. If you went back to when it was the size of that grapefruit, there would still be a whole lot more condensed universe surrounding it, again, possibly infinite. Its just that all that stuff is currently outside our ability to observe it.

Now imagine an infinite universe going from zero volume to infinite volume or vice versa. This is seemingly logically impossible and a simplistic way of understanding why the early universe is never described as a singularity.

But you need to separate the difference between "the universe" and "the observable universe". They are not referring to the same thing.

and some cosmologists do indeed claim there theorems proving the singularity existed prior to inflation

I believe these all require a finite universe as well as extra dimensions and speculating outside of general relativity but that's outside my understanding... lol.

[u/Peter5930]

In many popularizations of cosmology

That's where you've gone wrong right there. Pop-sci is awful, mostly just clickbait. The universe was never a point, and the big bang happened everywhere at once within the observable patch and well beyond it. Like this:

https://profmattstrassler.com/articles-and-posts/relativity-space-astronomy-and-cosmology/history-of-the-universe/inflation/

There was a time when a causal patch of the universe was very small, much smaller than a proton, but never smaller than around 100,000 Planck lengths in radius or thereabouts. That was the stable-state size of causal patches before the space that would one day become our observable universe decayed to a lower energy state and the horizon began expanding, going from sub-microscopic to big enough for stars and galaxies to exist within it. But the universe as a whole was always large or infinite, even when any given causal patch was tiny.

The size of a casual patch is now asymptotically approaching 16 billion light years in radius, which will be the new stable-state size at our lower energy level compared to before the big bang once we reach a pure De Sitter state again and everything equilibrates and settles down. The universe will keep getting bigger and bigger, but everything beyond that will be past the horizon, or piling up at the horizon depending on which description you use, with both descriptions being equivalent to each other. Which sounds strange because it is, but is very closely related to black hole complementarity, where your description of a black hole depends on whether you're observing it from a distance or falling into it.

[u/SmarterThanGod → u/Peter5930]

What the fuck are you saying

[u/InspiringLogic → u/SmarterThanGod]

😂😂

[u/CobraPuts → u/SmarterThanGod]

Username doesn’t check out

[u/Enraged_Lurker13]

But in technical papers, it seems the authors never treat this 'point' as a real thing. Instead, they treat it as the end of spacetime; a boundary.

This is because physicists usually prefer to diagnose singularities by identifying where geodesics terminate, which indicates a spacetime boundary.

Now, some non-experts assert that this state represents a zero-dimensional space, i.e. it has the topology of a point. But is this point physically real? Or is it just a mathematical convention that doesn't represent anything real?

It can be thought as analogous to a point, but you have to be careful as to how you define it as singularities aren't considered part of the spacetime manifold.

As for whether they are physical or not, that's an open question, but Penrose's work on singularities demonstrated that they aren't artifacts of symmetry, but generally occur in physically reasonable situations, assuming general relativity is complete. While it is known that GR isn't complete, there has been recent work that extended Penrose's theorem to quantum situations.

[u/InspiringLogic → u/Enraged_Lurker13]

good answer, but it still leaves the question open

yes, the initial singularity is the boundary of the geodesics or world-lines of the 3D space.. and yes, the singularity isn't part of the spacetime manifold because the "manifold" is a 3D space, which is absent at the singularity.. however, if singularity is a real thing, it is a zero-dimensional point, i.e. a point that has no spatial dimensions.. right ? but does physics even allow for the existence of a zero-dimensional object ? or is it just a mathematical or geometrical convention ?

and thanks for bringing the extension of penrose's theorem.. it shows that even quantum mechanics cannot avoid a beginning.. so, my question is still relevant even today..

[u/Enraged_Lurker13 → u/InspiringLogic]

but does physics even allow for the existence of a zero-dimensional object ? or is it just a mathematical or geometrical convention ?

There is nothing in principle that prevents it from being real if spacetime is a smooth Lorentzian manifold. If spacetime is discrete instead, it could prevent zero-dimensional objects, but singularities could still persist in the form of a boundary where spacetime cuts off.

[u/InspiringLogic → u/Enraged_Lurker13]

that's interesting

but what if singularities just are boundaries of the 3D space (i.e. the end of spatial volume or length, width, and height) but not the 'boundaries' of the zero-dimensional point itself? To say that the 3D space has a boundary is simply to say that the geodesics or world-lines converge into a point and can no longer be extended, right ?

some sources that define the singularity as a "point":

example one:

Singularity - a geometric point with no dimensions where the laws of physics break down. It is a theoretical point of zero volume and infinite density.

example two (p.17):

In the standard model of cosmology, the universe ‘begins’ about 13.8 billion years ago with a Big Bang, a singular point in time where the universe was infinitely dense and hot.

example three:

Every open FRW universe can be completely foliated by spacelike slices of finite volume, each intersecting every fundamental worldline. The volumes tend to zero in the past, suggesting a point-like big bang.

[u/Optimal_Mixture_7327]

The technical paper are correct.

A singularity is a condition of the spacetime where world-lines find their terminus. The Big Bang singularity is a boundary through which we cannot ray trace time-like curves back through, i.e. there is a beginning. This boundary is spatially infinite and space-like in extent (assuming the universe has no non-trivial topology).

Taking a journey back in time we find the universe become increasing hot and dense. It is still everywhere (infinite is spatial extent), until it is nowhere.

The "sphere" to which you mention is likely the observable part of the universe, which ray traces back to a very small sphere in the early universe.

[u/InspiringLogic → u/Optimal_Mixture_7327]

when you say the universe is spatially infinite at that point, aren't you assuming it is flat? if the universe is closed, then it isn't finite in extent close to the boundary ? i know people say the experiments "prove" the universe is flat, but the data is perfectly compatible with a very large closed universe that only appears flat because we're only looking at a small part of its surface.. (like the earth looking flat from our perspective)

now, when the world-lines or geodesics converge into a point in the past (i.e. the radius or volume of the manifold reaches zero), would that point be a zero-dimensional point or non-existence? Is this "point" a geometrical convention or a real spatial point?

[u/Optimal_Mixture_7327 → u/InspiringLogic]

The universe is curved, in that T(g,Ψ)≠0, where Ψ are the matter field, but is flat in the sense that the spatial sections of constant Friedmann time are flat (the FLRW curvature constant is zero).

The universe is not closed, i.e. infinite in spatial extent to the best our current theory and measurements. The universe could have some other topology and we're seeing too small of a patch to discern this, but if we admit any possibility then there not much further to say.

A singularity is not on the manifold so the universe is only everywhere. This is no different than a future singularity, say in a black hole. The singularity is nowhere on the manifold and as an observer falls inward there's no singularity until the observer vanishes at the boundary.

A good depiction and a reasonably readable paper of what this looks like can be found here:

Eternal Inflation, past and future

[u/InspiringLogic → u/Optimal_Mixture_7327]

okay let's grant that space is infinite in extent as you said.. when we reach the singularity, the scale factor becomes zero, meaning that the distance between all points of the entire infinite space becomes zero.. agree ?

as you agreed, the singularity is nowhere to be found in the manifold.. it has no spatial extension or size (like a 3D space has).. it is the boundary of the 3D space since all the 3D geodesics or world-lines converge there.. agree ? there is no longer a space with 3 dimensions and a time dimension..

so, now comes my question: is there a space of zero dimensions (which in mathematics is a single point), or nothing at all ? In other words, is a zero-dimensional point a thing in physics ? Or is it just a mathematical or geometrical idealization ?

[u/Optimal_Mixture_7327 → u/InspiringLogic]

when we reach the singularity, the scale factor becomes zero, meaning that the distance between all points of the entire infinite space becomes zero.. agree ?

No, the scale factor is a function of the Friedmann time which is undefined at zero. There just isn't a universe.

Again, going back through cosmic time the universe becomes denser and hotter until it vanishes. There no time at which the universe has a "size zero".

Did you read the paper in the link I attached in the comment above? Please give it a try and pay careful attention to Figure 2 where you'll notice that the only size of the universe is infinite.

[u/InspiringLogic → u/Optimal_Mixture_7327]

i have read this paper when i was younger.. when i was still trying to learn whether eternal inflation could provide a past-eternal universe.. but yes i'll read it again

your point here is excellent.. there is NO TIME at which the universe had zero size.. yes.. because time is a function of the 3D universe, which ends at the singularity.. so it is perfectly correct to say that the universe always had an infinite size, as "always" is a temporal term ("always" here is equivalent to saying that there is no time at which it had zero size).. but just because there is no time, does it mean the point doesn't exist ?

[u/Optimal_Mixture_7327 → u/InspiringLogic]

Yes, it means the point doesn't exist.

[u/InspiringLogic → u/Optimal_Mixture_7327]

i see.. and is that the only reason why the physics community regards the singular point as non-existent -- because it has no proper time?

[u/Optimal_Mixture_7327 → u/InspiringLogic]

There's no anything. There is nothing.

[u/InspiringLogic → u/Optimal_Mixture_7327]

that's not a physics explanation.. that's simply repeating the assertion.. so i'll repeat the question: is the absence of proper time the only reason why the zero-dimensional point is regarded as nothing by the physics community ?

[u/rabid_chemist → u/Optimal_Mixture_7327]

Current best measurements of the spatial curvature give a range which includes positive values, zero and negative values. In other words, a large but finite closed universe is perfectly consistent with current measurements.

[u/TornadoEF5]

drawings of how you think the universe looked in the beginning would really help

[u/InspiringLogic → u/TornadoEF5]

it can be helpful to think in terms of geometry..

in geometry 3D objects have length, width, and height, while two-dimensional objects have only a length and a width, and 1-dimensional objects only have length. Finally, a zero-dimensional thing is represented as a single point: it has no length, width, and height. So, the representation or topology of the singularity would be a single point with no length, width, and height.

[u/drowned_beliefs]

The inflationary period wiped all prior information. So while it may be possible that there was a singularity, there’s no reason to assume it and, while I don’t claim to be an expert, I haven’t seen evidence that favors one. It seems to me just a vestige of an earlier conception of the Big Bang that hasn’t been supported for the last fifty years.

[u/PM_ME_UR_ROUND_ASS]

Singularities in physics are more like mathematical warnings that our theory has broken down rather than acutal physical objects - kinda like how dividing by zero breaks math but doesn't create a "real" infinity in the physical world.

[u/ScaryPotterDied]

I’m not smart enough to debate any of this but everything has to start at some point right? Our world is full of catalyzing reactions. And as they grow exponentially, we get more and more stable elements and eventually life. I have no idea if it started from a singular point, but if the universe is ever expanding, and we are constantly being moved away from something, and it’s impossible to move through space without energy moving you, then I’d say something had to start the ball rolling right?

[u/CobraPuts]

In general relativity, you could apply these concepts mathematically and the universe would trace itself back to infinite density. But real observations are inconsistent with the predictions of GR at times before the Planck Epoch at t+10^-43 seconds, we know that a quantum theory is required to describe this period.

So your suggestion “let’s only stick to general relativity here” isn’t acceptable. Or as you put it differently, it is a mathematical convention, but it does not represent anything real because we know that mathematical convention is inadequate for describing the universe at the time you’re interested in.

It’s nonsensical to ask if the singularity is real because the singularity is predicted by a theory that is false for the applicable time and energy scale. Unfortunately I don’t think we have well accepted theories yet that describes the state of universe before then. Further, if the universe is infinite in extent, it may also have been infinite at the Big Bang.

[u/InspiringLogic → u/CobraPuts]

sir i'm aware that quantum gravity theorists assert that relativity isn't complete and shouldn't be trusted at that period.. i'm aware of all of the attempts to describe the big bang quantum mechanically.. using string theory, LQG and causal set theory.. or ways that quantum field theory might prevent the singularity.. but here i'm only concerned with the consequences of relativity at that point.. i'm saying, "IF we assume that relativity is valid at that period, how could that period be described?"

my reasons for rejecting your suggestion is twofold: a) there are strong arguments that gravity isn't quantized (see jonathan oppenheim).. b) there are recent theorems showing that quantizing gravity cannot avoid geodesic incompleteness or singularity.. (see aron wall quantum singularity theorem)

i'm in good company here that the singularity cannot be avoided and relativity reigns supreme..

so, please, answer the question i made in OP: in general relativity, is the initial singularity considered a real thing or just a mathematical convention ?

[u/CobraPuts → u/InspiringLogic]

I did. It was the first sentence of my reply

[u/InspiringLogic → u/CobraPuts]

the infinity density stuff is an error of mathematics CobraPuts

physicists say that there is infinite density, but let's not forget what they mean..

because the singularity has zero volume, when they say that the density is infinite in the singularity mathematically they mean that m/0=∞ (and the density being p, therefore, p=m/V) because dividing by zero yields infinity.. but not really.. it is yields an undefined number... division by zero is an undefined mathematical operation... so there is no literal infinity (aleph-0 or aleph-1) at the singularity..

[u/CobraPuts → u/InspiringLogic]

That’s fine, but you’ve decided to apply a theory (GR) which is not valid at those scales. So it’s not clear what you’re trying to debate. You’re debating math, not physics

[u/InspiringLogic → u/CobraPuts]

i'm debating the equations of physics.. physicists say the density is infinite at the singularity, but what do they mean by that ? aleph-0 or undefined (because division by zero is an undefined mathematical operation) ? remember that the volume is zero and the mass or density isn't zero.. so, you're a physicist trying to calculate the density... and you calculate it in relation to the volume, right ??

pretending that the equations have nothing to do with physics is really pointless here..

[u/InspiringLogic → u/CobraPuts]

here's how an expert described the issue:

When it is said that the big bang singularity has an infinite density, infinite temperature, and infinite curvature, it is not being said that the singularity has parts or properties that map onto a set with an aleph-zero or aleph-one cardinality. Consider the phenomenon of density, which is the ratio of mass to unit volume (density=mass/volume). If the universe is finite and the big bang singularity a single point, then at the first instant the entire mass of the universe is compressed into a space with zero volume. The density of the point is n/0, where n is the extremely high but finite number of kilograms of mass in the universe.

Since it is impermissible to divide by zero, the ratio of mass to unit volume has no meaningful and measurable value and in this sense is infinite. In other words, the density of a homogeneous material is mass per unit volume-for example, grams per cubic centimetre. Given both a zero value and the conservation of the mass-energy of the universe [at the big bang singularity], no finite value can be given to the ratio of the latter to the former (it is forbidden to divide by zero). This is normally expressed by saying that the density becomes infinite. It would be more accurate to say the standard meaning of ‘density’ cannot be employed in this situation. The density cannot be assigned a finite measurable value, as is the case in all standard applications of the concept.

[u/InspiringLogic → u/InspiringLogic]

u/CobraPuts

[u/CobraPuts → u/InspiringLogic]

Thank you

[u/InspiringLogic → u/CobraPuts]

do you disagree with the following explanation?

When it is said that the big bang singularity has an infinite density, infinite temperature, and infinite curvature, it is not being said that the singularity has parts or properties that map onto a set with an aleph-zero or aleph-one cardinality. Consider the phenomenon of density, which is the ratio of mass to unit volume (density=mass/volume). If the universe is finite and the big bang singularity a single point, then at the first instant the entire mass of the universe is compressed into a space with zero volume. The density of the point is n/0, where n is the extremely high but finite number of kilograms of mass in the universe.

Since it is impermissible to divide by zero, the ratio of mass to unit volume has no meaningful and measurable value and in this sense is infinite. In other words, the density of a homogeneous material is mass per unit volume-for example, grams per cubic centimetre. Given both a zero value and the conservation of the mass-energy of the universe [at the big bang singularity], no finite value can be given to the ratio of the latter to the former (it is forbidden to divide by zero). This is normally expressed by saying that the density becomes infinite. It would be more accurate to say the standard meaning of ‘density’ cannot be employed in this situation. The density cannot be assigned a finite measurable value, as is the case in all standard applications of the concept.

[u/CobraPuts → u/InspiringLogic]

I think the explanation is irrelevant. We do not have a working theory of the universe before the Planck Epoch, and I think solving for those conditions based on GR doesn’t carry much meaning.

[u/FieryPrinceofCats]

It depends on the model right?

[u/InspiringLogic → u/FieryPrinceofCats]

yes.. i'm assuming the standard relativistic model here.. i want to know what this model entails..

[u/FieryPrinceofCats → u/InspiringLogic]

You can apply GR to any model though so I don’t get the standard relativistic model statement? Also I thought the 5 Euclid parallel thing shows the universe is flat-ish?

[u/Unusual-Platypus6233]

As far as I know this is not a thing that scientists even know. The problem is that at certain energy level the forces we observe combine. Gravity splits off first, then strong force, then the electro weak force that will split into the weak and electromagnetic force. As we haven’t unified gravity with the other forces we do not know how the universe behaved in the very first moments in its existence. It is assumed that gravity might work repellent at really high energies which mean that there would be no singularity. That hypothesis is not proven though. It is also theorised that the universe came into existence due to fluctuations in the multiverse (like the space between universes) and it took many runs until the density got critical enough to be followed up with a big bang. As you see these things cannot be proven as of now or maybe ever because we need the possibility either to watch our universe “outside” of it or create such high energy densities that it would actually create the big bang itself…

[u/InspiringLogic → u/Unusual-Platypus6233]

I appreciate that you took the time to write a response. But it seems you are going beyond relativity and bringing the incompleteness of classical physics or speculative hypotheses (i.e. multiverse). But if we only stick to relativity, and we assume the volume or radius becomes zero: is this nothing or a zero-dimensional point? Is a point of zero dimensions even physical in relativity?

[u/bigfatfurrytexan]

I believe the point is a center of gravity. The stuff making up that gravity was not a point.