Actual Infinity in Reality?

[pocaracas]

I just read your opening post. I don't know what has been presented.

You ask if something can exist "something concrete (not abstract)". -edit- that is infinite.

The theory of a Black-hole is just that. Is there an end to how dense a singularity can get? No. Theoretically it can continue to be more and more dense. At infinitude. There is nothing more "concrete" then matter its self. A black-hole is that mater condensed and can theoretically continue to condense more and more.

If you mean something that is proven beyond theory, then the idea of numbers. One can always count higher. There is no end to numbers. Count and count and count on. You'll always have another number to go to.

Ina black hole, you are talking about a property of being infinitely dense. That is not the same thing as having an infinite number of anything in real life.

Being able to count infinitely is a potential infinite. You can never actually arrive at infinity. The question the thread is concerned about is whether an actual infinite can exist (something real that has an infinite number of things).

Density is defined as "number of things per unit volume", so infinite density is equivalent to infinite number of things.
That is, if a black hole indeed has infinite density...

[Anomalocaris]

Ina black hole, you are talking about a property of being infinitely dense. That is not the same thing as having an infinite number of anything in real life.

Being able to count infinitely is a potential infinite. You can never actually arrive at infinity. The question the thread is concerned about is whether an actual infinite can exist (something real that has an infinite number of things).

Density is defined as "number of things per unit volume", so infinite density is equivalent to infinite number of things.
That is, if a black hole indeed has infinite density...

No. A finite number of things per zero volume is also infinite density.

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The lifespan of a photon in vacuum is regarded as being infinite though it would have to be predicated on two other factors
Namely that its journey is only ever through empty space and that the Universe itself is either temporally or spatially infinite

Actually, by relativity, time does not pass for a photon traveling through empty space. Hence it is meaningless to say what it’s lifespan is.

[pocaracas]

Density is defined as "number of things per unit volume", so infinite density is equivalent to infinite number of things.
That is, if a black hole indeed has infinite density...

No.  A finite number of things per zero volume is also infinite density.

Aren't we limited by Plack length?

[Jehanne]

No.  A finite number of things per zero volume is also infinite density.

Aren't we limited by Plack length?

Maybe.  (It's "Planck length", by the way).  On the other hand, space may be infinitely divisible ("Zeno's Paradox"), and so, there may be an infinite number of divisible points between any two finite points, which means that we are transversing actual infinites all the time!

[pocaracas]

Aren't we limited by Plack length?

(It's "Planck length", by the way). 

Lol... there are some days when my fingers just refuse to type properly. well spotted!

[Jehanne]

Someone like Donald Trump would have no idea who "Planck" was; consider yourself to be at least informed!

[polymath257]

Note -- A "singularity" is an actual infinite!!

If we have no other reason to suspect our theory that arrives at singularity is flawed, then we might think when the theory points to singularity, then an actual infinity is a probability to be taken seriously.

But in case of gravity and blackholes, we actually have strong reason to believe the theory of gravity breaks down well before things reach infinity.

Right. it is likely that quantum effects 'smooth out' the singularities, both at the Big bang and in Black Holes.

Of course, by doing so, you open up the possibility of an infinite past: the past can only be finite if there is a singularity.

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No.  A finite number of things per zero volume is also infinite density.

Aren't we limited by Plack length?

Answer: probably. Again, this is by quantum effects, which tend to smooth out those singularities. We are also probably limited by the Planck density, which is the Planck mass divided by the Planck volume.

If we had a tested theory of quantum gravity, I could give more definite answers, but we don't.

[Anomalocaris]

No.  A finite number of things per zero volume is also infinite density.

Aren't we limited by Plack length?

If we are, then there is no singularity.

In any case, the total number of things is conserved when a singularity forms. So if it didn’t start out with an infinite number of things before they all became a singularity, then there won’t be an infinite number of things in the singularity, assuming singularity exists at all.

[SteveII]

I think that is wrong. The standard model most ascribe to has a change in the singularity that resulted in the spacetime manifold we experience now. 

...

To get around the problem I brought up, all of those sequential spacetime manifolds (see where I quoted) have to already exist. That does not seem to be part of the theory. Please address this problem specifically. Most of your statements just seem to be assertions and not part of the model.

First, the singularity is NOT an event: it is a failure of the coordinate system to describe a situation. In this case, if you use standard general relativity, it describes a limit of infinite curvature.

I clearly did not say the singularity was an event. There was a change. Something started everything. 

Yes, it actually is part of the theory that the *previous* spacetimes already exist.

Note how you had to say *previous* when I said they have to all exist already--past and present. BECAUSE if all of them do not exist at once (in other words they exist sequentially as the theory clearly states), you have a very big problem of a past infinite. We could not have gotten to our current universe without an infinite amounts of universes already being created. We would still be waiting for an infinite amount of universe to be sparked before ours could be sparked--which will never happen, because there still needs to be an infinite more that need to come first. Why can't you address this!? You keep asserting that how it is. Explain why we could ever logically get to our current universe.  

[GrandizerII]

First, the singularity is NOT an event: it is a failure of the coordinate system to describe a situation. In this case, if you use standard general relativity, it describes a limit of infinite curvature.

I clearly did not say the singularity was an event. There was a change. Something started everything. 

Yes, it actually is part of the theory that the *previous* spacetimes already exist.

Note how you had to say *previous* when I said they have to all exist already--past and present. BECAUSE if all of them do not exist at once (in other words they exist sequentially as the theory clearly states), you have a very big problem of a past infinite. We could not have gotten to our current universe without an infinite amounts of universes already being created. We would still be waiting for an infinite amount of universe to be sparked before ours could be sparked--which will never happen, because there still needs to be an infinite more that need to come first. Why can't you address this!? You keep asserting that how it is. Explain why we could ever logically get to our current universe.  

1 is previous to 2 in the integer sequence. Doesn't mean they don't simultaneously exist.