0 Members and 1 Guest are viewing this topic.

Quote from: lean beanYou may remember my reply to you here.. Reply #24.Glad you mentioned that. I'd lost track of that thread. Going back over it may save some repetition.

You may remember my reply to you here.. Reply #24.

Same here.

What happens when we extrapolate back far enough is that the models start predicting ever increasing density--a density that tends to infinity at some point in the past. Most scientists take Bill's point of view here and believe that this infinity is an indication of a flaw in the model, not something that physically existed.

Infinities are funny things. Even with the equations predicting infinite density, you can still have an infinitely large universe that is ALSO infinitely dense. It remains infinitely large no matter how dense it is. That's one of the weird parts of infinity. If something is infinitely big and you compress it, it's still infinitely big, only denser!

If something is infinitely big and you compress it, it's still infinitely big, only denser!

Quote from: JPIf something is infinitely big and you compress it, it's still infinitely big, only denser! If you start with an infinite amount of low density and compress this to an infinite amount of high density, who/what "creates" the extra density? Where does it come from? OK, it's only theoretical, but what happens if you try to consider practical applications?

If you had an infinite amount of helium in the universe then how could you also have one hydrogen atom? That would mix finite and infinite.

Also having infinite helium would preclude having infinite electrons, protons and neutrons. You would have split infinities.

If you start with an infinite amount of low density and compress this to an infinite amount of high density, who/what "creates" the extra density? Where does it come from? OK, it's only theoretical, but what happens if you try to consider practical applications?

‘then what happens in the context of an infinit universe when it is run backwards so that each observable universe ‘closes down’ to its respected point? How many points in an infinite universe? The equations break down ‘everywhere’? singularity everywhere? My sentence ‘an infinite expanse in a state of singularity’ could read as ‘an infinite expanse in an indefinable state.’

If you had an infinite amount of helium in the universe then how could you also have one hydrogen atom? That would mix finite and infinite.Also having infinite helium would preclude having infinite electrons, protons and neutrons. You would have split infinities.

Why is this a problem? If the universe is actually infinite, it has an infinite amount of "stuff" so there would be no problem compressing it, having it get denser, and still having an infinite universe.

Quote from: JH If you had an infinite amount of helium in the universe then how could you also have one hydrogen atom? That would mix finite and infinite.Also having infinite helium would preclude having infinite electrons, protons and neutrons. You would have split infinities.Do I detect a hint of a "kindred spirit"; someone who has thought beyond mathematical infinities and found something astonishing?Are you a scientist?

If you had an infinite amount of helium in the universe then how could you also have one hydrogen atom?

I have been thinking about infinity since I was 12 and I'm now 53.

This infinity stuff is just so weird.

Quote from: JPWhy is this a problem? If the universe is actually infinite, it has an infinite amount of "stuff" so there would be no problem compressing it, having it get denser, and still having an infinite universe. By definition, compressing something is making it smaller, but leaving it with the same amount of “stuff”. If you could compress infinity; which I believe you can’t; you would produce a “smaller infinity”, which, outside mathematics, is nonsense. If you could do that, your “smaller infinity” would have to be contained in a “larger infinity”; again, nonsense; so more “stuff” would have to come from somewhere to fill the "larger infinity". Why can we not unite relativity and QM? It’s because infinity finds its way into the equations and produces nonsense.

Quote from: JHIf you had an infinite amount of helium in the universe then how could you also have one hydrogen atom?Please explain this, Jeffrey, I've been trying, on a number of discussion forums, for about three years, to make that point!Changing just one word in the above quote would take the argument to a whole different level, but let's take one step at a time.

The problem you've gotten yourself into here is that in the sense used to talk about the universe, compressing does not mean "getting smaller" by definition. I could take the set of all real numbers and divide each number in it by 2. I would be "compressing it" in that any two numbers will get closer to 0, but the set is still infinite and contains all real numbers.

I don't understand the problem you have with infinity

I think my “problem” with infinity is one of persuading people of science that there is a difference between mathematical infinities and physical infinity.

There is a strong tendency to think that anything outside mathematical infinities smacks of philosophy/theology, but such is not necessarily the case.

I agree with your explanations. I would take issue with nothing in your last post, but it doesn’t address the major point I am trying to make.

Time is very short at the moment, but I will come back to it later. Perhaps, if we can take one point at a time, we can achieve some clarity.

Okay. Let's start with the point that you'd trying to make.

The question remains, and perhaps we should make it the first point: “Can there ever have been a time when there was nothing?”

Quote from: Bill SI think my “problem” with infinity is one of persuading people of science that there is a difference between mathematical infinities and physical infinity.In your mind, what is the difference between a mathematical one and a physical one.My own personal feeling is that this is no problem with scientists. In a strong sense of the phrase (and not to come off as too arrogant), we know better. We know that the answer all depends on definition. The author of the book I'm proof reading goes through great lengths to make sure the reader understands this regarding the event horizon of a black hole and the singularity at the center. The former is only a mathematical singularity which can be "transformed" away while the other is "real" and can't be transformed away.

Quote from: Pmb on 14/09/2013 15:17:27Quote from: Bill SI think my “problem” with infinity is one of persuading people of science that there is a difference between mathematical infinities and physical infinity.In your mind, what is the difference between a mathematical one and a physical one.My own personal feeling is that this is no problem with scientists. In a strong sense of the phrase (and not to come off as too arrogant), we know better. We know that the answer all depends on definition. The author of the book I'm proof reading goes through great lengths to make sure the reader understands this regarding the event horizon of a black hole and the singularity at the center. The former is only a mathematical singularity which can be "transformed" away while the other is "real" and can't be transformed away.Yes! That's the issue at the heart of this thread (and it surprises me it's gone on so long). I'd hope any physicist would admit that we don't know the answer to the question of whether infinities can exist in nature (examples would be the size of the universe, the infinitesimal sizes of point particles or the infinitesimal division of space if it is continuous). There's interesting arguments on both sides of the issue, but science is based on evidence, and so far there's nothing convincing either way. Certainly the lower or upper limit is so small or so large that we can plug infinities into many equations without introducing much error (indeed, the error must be so small that we can't currently measure it or we'd know the answer already!)What surprises me is seeing so many arguments against infinity based on personal intuition. Surely, intuition shouldn't guide debates in science. If we'd relied on intuition, we wouldn't have quantum mechanics or relativity! Surely it's not intuitive to anyone (at least anyone without serious training in those fields) that particles behave like waves or that time and distance measurements can vary between observers. Sure, infinity may not be able to exist in nature, but let's admit there's no proof either way, and certainly both equations with and without infinities can match our measurements. We keep infinities around because it's easier to use calculus than to compute everything in terms of finite differences.

I'm not sure the question makes sense. How can there be time if there is nothing (assuming 'nothing' is the absence of anything, not just 'empty' space)?

as far as reality is concerned, the idea of infinity vanishes, as in nature everything is finite.

In nature everything is finite. We cannot imagine infinite things, thus such in nature do not exist.

Yes! That's the issue at the heart of this thread (and it surprises me it's gone on so long). I'd hope any physicist would admit that we don't know the answer to the question of whether infinities can exist in nature

In a temporally open system the universe will expand forever, the size of it becoming larger and larger with time, increasing without limit.

That's the very meaning behind the term infinity.

The discussion of infinity can become one of philosophy rather than hard science

In a strong sense of the phrase (and not to come off as too arrogant), we know better.

Also the amount of material in a spatially open system is infinite, the amount of material being unbounded and hence infinite.

... Apart from dlorde’s attempt to brush it under the carpet, who has actually responded to the question: “Can there ever have been nothing”?

Quote from: Niebieskieucho as far as reality is concerned, the idea of infinity vanishes, as in nature everything is finite.QuoteI cannot agree that everything in nature is necessarily finite. Everything we see, we perceive as finite, but that is only our perception, which, as scientists frequently point out, “ain’t necessarily so”.What they consider could be infinite and on what grounds? Nature (the universe) cannot be infinite, but if scientists claim otherwise, then it would mean that:Finite matter of the universe is constantly expanding. It’s possible for some time.OrThe universe is readily infinite. But it’s impossible, as anything real can be closed in a solid. Infinite universe could be compared to a solid without walls. Obviously such solid cannot exist.

I cannot agree that everything in nature is necessarily finite. Everything we see, we perceive as finite, but that is only our perception, which, as scientists frequently point out, “ain’t necessarily so”.

Quote from: niebieskieuchoIn nature everything is finite. We cannot imagine infinite things, thus such in nature do not exist.QuoteThat's not necessarily true. At this point in time we don't know either way which is true and which is false.There is no problem to make a diagnosis. If one cannot sketch an infinite universe (no matter scale and accuracy) such universe does not exist (as any real things can be sketched). QuoteIn a temporally open system the universe will expand forever, the size of it becoming larger and larger with time, increasing without limit. That's the very meaning behind the term infinity.I need not to refer to needless, so-called parameter omega. The universe does not expand. It’s a closed system. I realize that it’s hard to imagine “empty” space ending sharp, but there is no other feasibility. It must end sharp. The problem is, that we cannot see spatial structure from the perspective of physical entities of the micro-world hence such limitation gives the impression that the universe is infinite which is impossible. Such is my stance and I am not going to change it. QuoteAlso the amount of material in a spatially open system is infinite, the amount of material being unbounded and hence infinite.As I said earlier it’s only our human (due to natural limitations) perception. In reality space =/= nothing (lack of space). That implies finiteness of the universe, in other words both the universal space and its content.

That's not necessarily true. At this point in time we don't know either way which is true and which is false.

In a temporally open system the universe will expand forever, the size of it becoming larger and larger with time, increasing without limit. That's the very meaning behind the term infinity.

Quote from: PmbIn a strong sense of the phrase (and not to come off as too arrogant), we know better.This is one reason why "hitch-hikers" like me come to people like you, looking for answers, and why we are sometimes disappointed when questions seem to be evaded.

It is important to realize that the Schwarzschild “singularity” at r = r_{S} is not a physical singularity. The “singularity in Eqs. (8.2) and (8.3) is spurious – it is a pseudosingularity or coordinate singularity. It arises from an inappropriate choice of coordinates and can be eliminated by a change of coordinates.

An infinite series (sequence) exists only in the (presumably finite) mind of the mathematician as a useful concept.

I simply call attention to the fact that infinity is not a number,..

…the concept of infinity is of singular importance in thinking about the origin of the Universe.

Quote from: PmbAlso the amount of material in a spatially open system is infinite, the amount of material being unbounded and hence infinite.You might demonstrate that the amount of material in a spatially open system is unbounded; you might theorise that it could be infinite; but could you prove that it was infinite?

Infinite - (1) having no limits (2) extremely large or great (3) extending indefinitely (4) endless <infinite space> (5) immeasurably

I have not offered to scan and post this as I'm sure it would infringe copyright.

Quote from: JPYes! That's the issue at the heart of this thread (and it surprises me it's gone on so long). I'd hope any physicist would admit that we don't know the answer to the question of whether infinities can exist in natureOne of the reasons it has gone on so long is that we tend to talk across one another. Apart from dlorde’s attempt to brush it under the carpet, who has actually responded to the question: “Can there ever have been nothing”?Does infinity exist in nature? I neither know, nor pretend to know.Does nature exist in infinity? The answer to that depends on the answer to “Can there ever have been nothing”?

That wasn't the question I responded to, and rather than trying to sweep it under the carpet, I was hoping you might be able to explain how it made sense at all. You couldn't, so you changed the question to one that makes no more sense to me than the previous one.How can nothing 'be'?

I'm not entirely sure I understand what you mean here. But if I do then I don't think that you're being exactly fair here, Bill.

I know the difference between a mathematical singularity and a physical one.

Pete, I apologise if my answer offended you, I certainly intended nothing personal.

However, if you were to look back through this and other threads in which infinity has been discussed, I think you will find that almost every point I have tried to make about physical infinity has been countered by arguments involving mathematical infinities.

isn’t it possible that it’s you who don’t know the difference?

I’ve asked you to explain them to me above and you went off on something you called a etymological diversion

Real to a physicist means something doesn’t exist.

Quote from: Pmb isn't it possible that it's you who don't know the difference?Yes, it is quite possible.

isn't it possible that it's you who don't know the difference?

I've asked you to explain them to me above and you went off on something you called a etymological diversion.

Pete, if you would remind me of the context (and post) in which I used the term etymological diversion in response to a question from you I will gladly try to clarify it.

Quote from: PmbReal to a physicist means something doesn't exist.You have lost me there, Pete.

Real to a physicist means something doesn't exist.

I will infer that you are not really trying to sink the discussion in a see of semantics.

Picking up on your last question, may I ask what "is" when no thing exists?