I Infinite Universe from Dimensionless SIngularity

[Lucifuge Rofocale]

A significant number of physicists today postulate that the universe we reside in is infinite in size. It's also thought that if we extrapolate back in time to the big bang that the universe was a singularity of infinite density. Singularities are commonly thought of as a dimensionless point, therefore, how can the universe exist as a dimensionless point with no spatial extent and then a fraction of a second later extend to infinite in 3 dimensions.

 

[Chalnoth]

A significant number of physicists today postulate that the universe we reside in is infinite in size. It's also thought that if we extrapolate back in time to the big bang that the universe was a singularity of infinite density. Singularities are commonly thought of as a dimensionless point, therefore, how can the universe exist as a dimensionless point with no spatial extent and then a fraction of a second later extend to infinite in 3 dimensions.

The singularity is a mathematical quirk that can't really have existed. The problem is that it's the equivalent of dividing by zero.

So the existence of that singularity in the math indicates that our mathematical model for the early universe isn't entirely correct.

 

[Fervent Freyja]

how can the universe exist as a dimensionless point with no spatial extent and then a fraction of a second later extend to infinite in 3 dimensions.

In that cold and frigid isolation, He shivered...

We will never know for sure. Humans are incapable of truly comprehending this point.

 

[Drakkith]

In that cold and frigid isolation, He shivered...

We will never know for sure. Humans are incapable of truly comprehending this point.

I'm not sure I agree. We can say with some degree of confidence that the fact that our models give us a mathematical singularity means they don't describe real physics beyond a certain point in the past. We certainly can't say with absolute certainty what happened, but I see no reason why we can't say that something. After all, can we "truly comprehend" anything? We can never know with completely certainty that our understanding of physics is correct, only that our laws and theories are accurate to some amount of certainty.

 

[Lucifuge Rofocale]

Well we have a high level of confidence in the notion that the density of our universe increases as we extrapolate backwards in time. If we take into consideration a universe of infinite size, is it therefore correct to assume that at some point in the past the universe had a density equal to or near infinity and extending indefinitely in all three dimensions (therefore not being a true dimensionless singularity).

 

[phinds]

Well we have a high level of confidence in the notion that the density of our universe increases as we extrapolate backwards in time. If we take into consideration a universe of infinite size, is it therefore correct to assume that at some point in the past the universe had a density equal to or near infinity and extending indefinitely in all three dimensions (therefore not being a true dimensionless singularity).

Do you understand that "equal to infinity" and "near infinity" are not even CLOSE to being the same thing and that "near infinity" is not really a meaningful concept?

Give me a number that is as hugely gigantic as you can make it, with things to the power to the power to the power ... and so forth, and it is approximately zero relative to infinity. If you then take that number to the power of itself, it is STILL approximately zero relative to infinity.

SO ... rather than saying "near infinity" it is more appropriate to say "asymptotically approaching" infinity.

Also, despite what you may have seen in pop-science programs, "singularity" does NOT mean "dimensionless point" it just means, as Chalnoth already pointed out, "the place where the math model breaks down and we don't know what is going on".

 

[phinds]

In that cold and frigid isolation, He shivered...

Let's not bring religious nonsense into a discussion of science.

 

[Lucifuge Rofocale]

Do you understand that "equal to infinity" and "near infinity" are not even CLOSE to being the same thing and that "near infinity" is not really a meaningful concept?

Give me a number that is as hugely gigantic as you can make it, with things to the power to the power to the power ... and so forth, and it is approximately zero relative to infinity. If you then take that number to the power of itself, it is STILL approximately zero relative to infinity.

SO ... rather than saying "near infinity" it is more appropriate to say "asymptotically approaching" infinity.

You're playing semantics. I'm sure you all knew what I meant however, yes, I should have articulated that better. I understand that "near infinity" has no meaning. More to the point, I guess what I'm truly trying to understand here is how a space extending to infinity emerged, as cosmologists state that space itself emerged at the point of creation. Doesn't this imply that an infinity (space) emerged from a non-infinity (singularity or whatever you want to call it). The only way this makes sense to me is if this starting state (singularity) always extended to infinity in 3 dimensions exactly like the universe does in it's current state (if the universe truly does go on indefinitely that is of course).

 

[Chalnoth]

You're playing semantics. I'm sure you all knew what I meant however, yes, I should have articulated that better. I understand that "near infinity" has no meaning. More to the point, I guess what I'm truly trying to understand here is how a space extending to infinity emerged, as cosmologists state that space itself emerged at the point of creation. Doesn't this imply that an infinity (space) emerged from a non-infinity (singularity or whatever you want to call it). The only way this makes sense to me is if this starting state (singularity) always extended to infinity in 3 dimensions exactly like the universe does in it's current state (if the universe truly does go on indefinitely that is of course).

There never was a singularity. Whether space is infinite or not is unknown.

 

[Drakkith]

More to the point, I guess what I'm truly trying to understand here is how a space extending to infinity emerged, as cosmologists state that space itself emerged at the point of creation.

Contrary to what you've read or heard from popular media, this is not true. The modern Big Bang Theory does not say that time and space emerged from a singularity, and any theories that do are extremely speculative and should not be taken as correct at this time.

 

[phinds]

Doesn't this imply that an infinity (space) emerged from a non-infinity (singularity or whatever you want to call it).

You are correct that you can't get a universe of infinite extent by starting with a finite volume. If the universe is infinite in extent now, then it has always been infinite. If it is finite now, then it has always been finite. The singularity may have been infinite or finite.

 

[PeterDonis]

The singularity may have been infinite or finite.

No, the singularity is not part of spacetime at all; it's a mathematical artifact. Please don't reintroduce a confusion that has already been clarified.

 

[Fervent Freyja]

Let's not bring religious nonsense into a discussion of science.

He...

 

[Fervent Freyja]

I'm not sure I agree. We can say with some degree of confidence that the fact that our models give us a mathematical singularity means they don't describe real physics beyond a certain point in the past. We certainly can't say with absolute certainty what happened, but I see no reason why we can't say that something. After all, can we "truly comprehend" anything? We can never know with completely certainty that our understanding of physics is correct, only that our laws and theories are accurate to some amount of certainty.

He is referring to a point for which no physical law exists. That is why I said, "this point", I was not arguing against understanding what happened after that point...

 

[Drakkith]

He is referring to a point for which no physical law exists. That is why I said, "this point", I was not arguing against understanding what happened after that point...

Ah, okay.

 

[Lucifuge Rofocale]

You are correct that you can't get a universe of infinite extent by starting with a finite volume. If the universe is infinite in extent now, then it has always been infinite. If it is finite now, then it has always been finite. The singularity may have been infinite or finite.

Fair enough.

 

[nikkkom]

Well we have a high level of confidence in the notion that the density of our universe increases as we extrapolate backwards in time. If we take into consideration a universe of infinite size, is it therefore correct to assume that at some point in the past the universe had a density equal to or near infinity and extending indefinitely in all three dimensions (therefore not being a true dimensionless singularity).

In general, extrapolating to the infinite density is questionable. Imagine you detect a very weak radio signal seemingly coming from a distant location in space. You fly a rocket and measure the strength of the signal. The signal strength increases as distance^-2 to its apparent source.

If you extrapolate your observations, you may assume that at the source there is a point with infinitely strong radio signal.

But then you reach the source and discover that it's a horn antenna. The singularity with infinitely strong radio signal does not exist, it is the imaginary location where conical portion of the antenna has its apex:

With Big Bang, it's similar. "Naive" extrapolation gives you singularity. Almost certainly, that's not what really was there.

 

[phinds]

No, the singularity is not part of spacetime at all; it's a mathematical artifact. Please don't reintroduce a confusion that has already been clarified.

OOPS. Thanks Peter. I should have said that the universe might have been infinite at the point where the big bang theory takes hold, not at the point where the model breaks down, which of course I agree w/ you about.