Infinities in science

[Aos Si]

The expansion is speeding up and what if that does not stop? Perhaps a randomly occuring bit of something(the universe) is dispersing into a infinite sea of nothing(the emptiverse)?

If the expansion is infinite, then the entire Universe freezes to absolute zero and nll life will cease to exist.

Indeed although absolute zero as a temperature is forbidden by the uncertainty principle in quantum mechanics, it will approach 0K asymptotically in fact, heat death means that no processes at the atomic or chemical level can happen, hence no biochemistry, all process will therefore be mediated by quantum phenomena such as gravitation and electromagnetisms effects which will still exist.

Yes. It would be more accurate to state that it will freeze to a fraction above absolute zero. And while life as we know it will cease to exist, the simplest and most primitive type - bacteria - may not. Experiments have been conducted that demonstrate that it can survive in such extreme environmemts. It has already been discovered in outer space and radioactive matter. Also, helium is the only gas that can't freeze at absolute zero. So it isn't true to state that nothing will srvive, but that virtually nothing will, But I was referencing this in general rather than specific terms.

Yeah well it will not be able to biochemically do anything so such an existence will be as the torpor of death anyway. So semantically no life will be able to synthesise, metabolise, or reproduce, meaning it will not really be alive anyway. Not that that matters. If 5 billion years is inconceivable the heat death of the Universe is just completely mind blowingly far off. To the order of magnitude in the squillions perhaps even bazillions.

Nothing will survive in the sense that nothing will exhibit any characteristics we know as life at heat death, and will eventually break down into its constituent atoms as even they decay, and then even the protons and neutrons do, even subatomic particles such as that have a lifespan. This will leave a sea of mostly photons and other leptons and not much else, a quantum foam of almost nothing as even blackholes evaporate.

[surreptitious57]

The expansion is speeding up and what if that does not stop? Perhaps a randomly occuring bit of something(the universe) is dispersing into a infinite sea of nothing(the emptiverse)?

If the expansion is infinite, then the entire Universe freezes to absolute zero and nll life will cease to exist.

Indeed although absolute zero as a temperature is forbidden by the uncertainty principle in quantum mechanics, it will approach 0K asymptotically in fact, heat death means that no processes at the atomic or chemical level can happen, hence no biochemistry, all process will therefore be mediated by quantum phenomena such as gravitation and electromagnetisms effects which will still exist.

Yes. It would be more accurate to state that it will freeze to a fraction above absolute zero. And while life as we know it will cease to exist, the simplest and most primitive type - bacteria - may not. Experiments have been conducted that demonstrate that it can survive in such extreme environmemts. It has already been discovered in outer space and radioactive matter. Also, helium is the only gas that can't freeze at absolute zero. So it isn't true to state that nothing will srvive, but that virtually nothing will, But I was referencing this in general rather than specific terms.

Yeah well it will not be able to biochemically do anything so such an existence will be as the torpor of death anyway. So semantically no life will be able to synthesise, metabolise, or reproduce, meaning it will not really be alive anyway. Not that that matters. If 5 billion years is inconceivable the heat death of the Universe is just completely mind blowingly far off. To the order of magnitude in the squillions perhaps even bazillions.

The Universe cares not one jot about our existence or even it's own. And we think we are important !

[Aos Si]

Yeah well it will not be able to biochemically do anything so such an existence will be as the torpor of death anyway. So semantically no life will be able to synthesise, metabolise, or reproduce, meaning it will not really be alive anyway. Not that that matters. If 5 billion years is inconceivable the heat death of the Universe is just completely mind blowingly far off. To the order of magnitude in the squillions perhaps even bazillions.

The Universe cares not one jot about our existence or even it's own. And we think we are important !

A truism that is one because it is true.

I think I always sum it up by saying I don't think reality gives a shit what you think.

[mistermack]

To be honest, I think it's impossible for an infinity to exist. Because the two words are incompatible. If something exists, it's finite.
But the nature of existence is not quite what it seems. The universe seems gigantic, but it was once smaller than a pinhead. Matter is nothing but energy. So the word "exist" does not mean what we intuitively think. It's not about solid objects but events.

So you can say that no infinities exist, but the reality might be that nothing "exists" at all. In that context, you can can have all the infinities you like. An infinity of nothing is perfectly possible.

[Svartalf]

Iz infinitely funny, trying to read through this thread without reading the posts made by OP

[Svartalf]

Same with Euclidian geometry. Just cause you draw an arrow on a line...

Actually, Euclidian geometry is an illusion, or planes would go straight from Paris to New York instead of going over the Pole and Canada.

Talk to me of luminaries like Bolyai, Lobachevsky and Riemann

[Feck]

no no NO ! there is One parallel line all other lines will meet the first Lobachevsky

[hackenslash]

I voted 'other', and here's why:

The first thing to talk about is what infinity actually is, and that's a difficult topic to broach. So what is infinity?

Well, in physics, it just means 'a really big number'. That might sound a bit woolly, until you think about what infinity actually is. It's a number that is beyond the scope of computability. In other words, it's simply a number that we can't deal with properly. It doesn't necessarily mean 'without limit', although it can, because any number without limit is necessarily infinity, because we can't deal with it. This is why you can't arrive at infinity by the successive addition of integers. All that happens when you successively add integers is that you get a finite number, albeit really huge, but one that can be dealt with in reasonable terms.

Now, when infinity turns up as the solution to a mathematical problem in physics, it is usually taken as a sign that whatever hypothesis generates that solution is on the wrong track. It isn't actually the case that it's necessarily on the wrong track, it's just that we expect our theories to be within the boundaries of computability. There isn't actually any requirement in nature for this to be the case, however.

Moving on to something that has already been brought up, lets' talk about black holes:

A black hole singularity is thought to have infinite density and infinite curvature. But what does that actually mean? Well, it means that curves are so tight that they are beyond any measurement. Infinite density is similar. The problem arises here in dealing with what a singularity actually is, and this is a more difficult topic still. In reality, a singularity is an event that defies description under our current understanding. It' a point where our theories quite literally break. The reason that our treatment of black holes and, indeed, the big bang singularity (if indeed there was such a thing), render infinities is that they constitute quantum events with relativistic mass. In other words, they are really tiny, but they have the mass of really big thing, to put it in vernacular terms. This means that they require a marriage of QM and GR for their description. Every time the equations of General Relativity have been married with the equations of Quantum Mechanics, the result is infinity. This has been taken to be a sign that the theories are (or at least one of them is) incomplete. It could very well be, however, that they are complete, and that the infinities that fall out of these marriages are real infinities. I doubt that, however. I suspect that at least one of them is incomplete. Most people think that it is GR that will have to be modified to take quantum effects into account, but there are those, most notably Roger Penrose, who suspect that it is QM that will have to be modified to take relativistic effects into account.

As for the Big Bang, it is far from clear that it even involved a singularity, either a physical singularity or a mathematical singularity. Indeed, one of the two models currently considered to be the front-runners for cosmic instantiation removes the singularity altogether, although it has problems of its own. Both of the front-runners, incidentally, consider time to be infinite, which should be a clue.

In summary, there is no known barrier to an actual infinite existing in nature, and anybody who says it isn't possible is talking shite.

[mistermack]

A black hole singularity is thought to have infinite density and infinite curvature. But what does that actually mean? Well, it means that curves are so tight that they are beyond any measurement. Infinite density is similar. The problem arises here in dealing with what a singularity actually is, and this is a more difficult topic still. In reality, a singularity is an event that defies description under our current understanding. It' a point where our theories quite literally break.

As far as I can see, the meaning is quite obvious.
As a black hole has a finite mass, if we say it has infinite density or curvature, we are saying that it has zero volume. Zero width, length and thickness. Anything less than zero would lead to finite values.
So it's not just that these parameters are beyond our measurement. They have to be zero.

[Aos Si]

As for the Big Bang, it is far from clear that it even involved a singularity, either a physical singularity or a mathematical singularity. Indeed, one of the two models currently considered to be the front-runners for cosmic instantiation removes the singularity altogether, although it has problems of its own. Both of the front-runners, incidentally, consider time to be infinite, which should be a clue.

Schwarzchild metric where an extra dimension that is set to 0 is introduced; suffices for now.

An even more interesting question is does renormalisation of integers actually reflect anything? Does what we expect mean a damn to reality?

Infinity does not exist any more than 0 does though of that I can be sure. And yes I also agree that infinity in a science equation means you have got something wrong.

[mistermack]

Hackenslash wrote that, not me.

It seems to me that when we get stuck, we always throw in infinity as an easy answer to difficult questions.
God is infinitely powerful. He explains everything. That's keeping it simple.
But then real science came along, and over and over again explained what we used to think had to involve infinity.
So I think the singularity falls into that catagory. Things defy description by the current theories. So you say that something is infinite in some way, and you can proceed.

But the problem is, when you say something is infinite in some way, you haven't explained anything.
Saying that a singularity is infinitely small, is like saying that god did it.

I don't think that time is something. It's a property of something. A property of energy. So saying that time is infinite, is simply re-stating the thermodynamic law, that energy cannot be created or destroyed, and is therefore infinitely old, and will get infinitely older. It's a law that works, that we can rely on, but it's not an explanation, it's just a tool.

[JimC]

A black hole singularity is thought to have infinite density and infinite curvature. But what does that actually mean? Well, it means that curves are so tight that they are beyond any measurement. Infinite density is similar. The problem arises here in dealing with what a singularity actually is, and this is a more difficult topic still. In reality, a singularity is an event that defies description under our current understanding. It' a point where our theories quite literally break.

As far as I can see, the meaning is quite obvious.
As a black hole has a finite mass, if we say it has infinite density or curvature, we are saying that it has zero volume. Zero width, length and thickness. Anything less than zero would lead to finite values.
So it's not just that these parameters are beyond our measurement. They have to be zero.

It certainly has a finite mass (usually a few stellar masses), and, if we use the event horizon, a non-zero volume. So, the average density inside the event horizen is finite and calculable.

At the "centre", however, the singularity may well be described in classical terms as aprroaching zero AS A LIMIT...

Perhaps quantum theory gives us an out. If the Planck length is in fact a measure of space which is discrete, and no smaller length is possible, there may be a "smallest possible volume"

In that case, the maximum possible density at a singularity may be a few stellar masses divided by the Planck volume; huge, but finite, and avoiding those pesky infinities...

[mistermack]

That sounds about right. I would like to know if the plank length is a constant, or is it expanding, along with spacetime?

[JimC]

That sounds about right. I would like to know if the plank length is a constant, or is it expanding, along with spacetime?

Good point about the expansion aspect; not sure...

[Svartalf]

That sounds about right. I would like to know if the plank length is a constant, or is it expanding, along with spacetime?

given that a plank length is generally macro thather than quantic in scale, its dimensions are pretty much constant