Actual Infinity in Reality?

[Jehanne]

It seems that the fabric of space is expanding--like a loaf of raisin bread being cooked. Raisins are the galaxies and the space between them expands while it is being baked. Raisins move in the dough even as the dough is expanding. Everything is getting further apart but not from a center. 

Expanding means the volume is increasing so I don't understand your last sentence.

And in a flat spacetime, which is what seems to be the case, space is infinite in extent.

And yes, it is the case that expansion can happen with finite space. You are correct here.

My point is that expansion can also happen with (and, within) infinite space.  And, if the Universe is infinite in spatial extent, that does not change the fact that there is a finite distance between any two points.  Ditto for a beginningless Universe with respect to time!

[polymath257]

And in a flat spacetime, which is what seems to be the case, space is infinite in extent.

And yes, it is the case that expansion can happen with finite space. You are correct here.

My point is that expansion can also happen with (and, within) infinite space.  And, if the Universe is infinite in spatial extent, that does not change the fact that there is a finite distance between any two points.  Ditto for a beginningless Universe with respect to time!

Agreed.

[GrandizerII]

Okay, I think I finally understand your objection here.  You’re saying that time-flow is what’s throwing a wrench into translating an actual infinite from math to reality.  I get what you mean, but I am no physicist so I’ll let Grand and Poly continue on.  However I will say, as Grand has said, I don’t see how an actual infinity wouldn’t be logically possible if we assume B theory of time is correct.  Directionality of time wouldn’t be an issue in that case, if my understanding of the theory is correct.

I don't have much time today to comment (maybe later tonight past midnight if possible), but just to be clear, poly and I are not in disagreement here regarding actual infinity and such. Don't let Steve mislead anyone here into thinking we do.

Also, just in case anyone misreads what you said, I'm not a physicist.

[Jehanne]

Okay, I think I finally understand your objection here.  You’re saying that time-flow is what’s throwing a wrench into translating an actual infinite from math to reality.  I get what you mean, but I am no physicist so I’ll let Grand and Poly continue on.  However I will say, as Grand has said, I don’t see how an actual infinity wouldn’t be logically possible if we assume B theory of time is correct.  Directionality of time wouldn’t be an issue in that case, if my understanding of the theory is correct.

I don't have much time today to comment (maybe later tonight past midnight if possible), but just to be clear, poly and I are not in disagreement here regarding actual infinity and such. Don't let Steve mislead anyone here into thinking we do.

Also, just in case anyone misreads what you said, I'm not a physicist.

Neither is Steve (or, me).

Physicists do not have any "metaphysical qualms" about a beginningless Universe. They understand that what is true about space is also true of time.

[polymath257]

While I do not have a PhD in physics, I do have one in math and have taken the PhD qualifying exams in physics (and passed them the first time). I have about 60 hours of graduate physics classes under my belt. I haven't done a dissertation in physics, however.

No physicist that I have ever talked to has any qualms with either an infinite time into the past (or future) or an infinite amount of space, at least on the theoretical level. What happens in realty has to be determined through observation, however. But an infinite time or infinite space isn't a 'metaphysical' issue for working physicists. If anything, this goes double for cosmologists (which was the specialty I was going for before I stopped).

[SteveII]

It seems that the fabric of space is expanding--like a loaf of raisin bread being cooked. Raisins are the galaxies and the space between them expands while it is being baked. Raisins move in the dough even as the dough is expanding. Everything is getting further apart but not from a center. 

Expanding means the volume is increasing so I don't understand your last sentence.

Professional astronomers don't have a problem with space being an actual infinite:

The long explanation is below. However, if you just want a short answer, I'll say this: if the universe is infinitely big, then the answer is simply that it isn't expanding into anything; instead, what is happening is that every region of the universe, every distance between every pair of galaxies, is being "stretched", but the overall size of the universe was infinitely big to begin with and continues to remain infinitely big as time goes on, so the universe's size doesn't change, and therefore it doesn't expand into anything. If, on the other hand, the universe has a finite size, then it may be legitimate to claim that there is something "outside of the universe" that the universe is expanding into. However, because we are, by definition, stuck within the space that makes up our universe and have no way to observe anything outside of it, this ceases to be a question that can be answered scientifically. So the answer in that case is that we really don't know what, if anything, the universe is expanding into.

What is the universe expanding into? (Intermediate)

I just wanted your perspective on this question.

From a University of Cambridge conference series on the Philosophy of Cosmology, on the topic of "Do Infinities Exist in Nature" we get the conclusion at the end of the article:

And opinions are indeed divided. Both Barrow and Aguirre are happy with mathematical infinities and don't shut the door on physical ones either. "I think it's certainly true that we can develop theories that have infinity in them that can be perfectly useful," says Aguirre. "It's certainly true that as finite beings we can only experience a finite part of [the Universe], but I can't see any reason to place limits on whether the Universe can be finite or infinite in principle."

Ellis, on the other hand, does not believe that physical infinities exist and points to potential problems with using infinity in mathematical arguments pertaining to physics. He refers to a famous thought experiment due to the mathematician David Hilbert. Suppose you have a hotel with an infinite number of rooms, and suppose that the hotel is full. The paradox is that you can still fit a new person in; you simply move every person in the hotel one room along, so the person from room 1 goes into room 2, the person in room 2 goes into room 3, and so on. Since there isn't a largest number, you can do this without making anyone homeless and then you can fit the new person into room one.

Because of paradoxes like this one, Ellis thinks that you have to be very careful when you use infinities in a physical context. "I'll make a distinction; there are some times when people talk about infinity when all they really mean is a very large number, and they're just using infinity as a code word for a large number. In that case, I think it's more informative to make a guess what that large number is and to talk about that large number, not infinity. There are some cases where people use infinity in its deep sense; in the paradoxical sense. The paradoxical sense is, for instance, Hilbert's hotel. In my opinion, if a physics argument or any other argument depends on those paradoxical arguments, then this is a false argument and it should be replaced by something else."

In summary there is as yet no consensus as to whether infinities exist in the physical world. In the absence of concrete scientific answers it makes sense to turn to philosophers. "I think it's very important to get physicists and philosophers together," says Aguirre. "I think there's a reaction that a lot of my physics colleagues have about philosophers which is that they don't know any physics. They're just saying things about physics and they don't really know what they're talking about, and criticising physics but they don't really understand it. I think there may once have been some truth to that and I'm sure that there is now, but the philosophers that I talk to all know lots of physics. I see them as being specialists in thinking about the intellectual foundations of those questions, looking at them from a slightly bigger and different point of view than a more empirically or pragmatically engaged physicist would. I think that's incredibly valuable."

Emphasis added

The whole article is very interesting. Also distinguishes early on between actual infinities and potential infinities.

[Jehanne]

The article is just someone's opinion. Even Professor George Ellis (who is a believer, a Quaker), who is one of several thousand practicing cosmologists, has expressed "reservations" about physical actual infinites, but this is an example of where you and WLC are cherry picking your sources. I could make equivalent claims about New Testament history by citing Professor Bart Ehrman.

But, let me ask you this, "If space is a physical actual infinite, how did we arrive at our present location?"

[LadyForCamus]

There could not have been that many events already (because events are things that can be counted backwards one before the other and by definition, you can't get to infinity by successive addition). Even if you still can't wrap your head around the standard definitions of infinity, doesn't the fact that there still has to be an infinite amount more events that have to happen before "any point in time" give you pause? By the very definition of infinity, you cannot traverse it to get to the events of today. There will always and forever be more events that must happen first!

You can't simply treat infinity as one thing that you can throw into a sentence because mathematicians use it in set theory. You are talking about an infinite series of events. These events have substance and are real things. You make a claim when you say there are an infinite series of events and you have to tell us how, against all logic, that is even possible. 

Doesn't it seem odd to you that you can't find an article to explain this for you? 

Unless you have something new, this is the last time I am going to say the same thing. 20 times is my limit.

---

How do I know if Penrose even believes his theory to be the best one? Even if he got the math right, that does not imply in the least that an actual infinity exists. 

Do you think that every scientific paper that gets published is true or that even the authors think it is true?

Are you asking if space is an actual infinite of distance or substance, then no. If you are asking is space a potential infinite of distance or substance -- that seems possible. 

It seem to me that different potential infinities can accumulate more quickly so there should be some mathematical differentiation for that, but at the end of the day, there is no upper limit so it does not make sense when talking about real objects--and that is the topic of this thread and what I intend to discuss.

Why are you counting *backwards*? Time moves forward! Nobody is counting backwards from today to the infinite past.

I'm not sure what you mean by there having to be an infinite number of *more* events before any particular moment of time. Where is the 'more'?

So, what we do *NOT* have is a situation

start----infinite time----now.

Instead, we have the situation for any point in the past,

infinite time----point in the past---finite time---now.

Bold mine.

I think what Steve means is, if we have time moving in a forward direction, how do we get to that one point in time from an infinite past?  How do you get to that single event in time without beginning somewhere?  If events are happening in succession, and time is infinite into the past, how would we ever arrive at a singular point in time?  Wouldn’t you have to start somewhere to get there?   I’m confused! Lol

[polymath257]

Why are you counting *backwards*? Time moves forward! Nobody is counting backwards from today to the infinite past.

I'm not sure what you mean by there having to be an infinite number of *more* events before any particular moment of time. Where is the 'more'?

So, what we do *NOT* have is a situation

start----infinite time----now.

Instead, we have the situation for any point in the past,

infinite time----point in the past---finite time---now.

Bold mine.

I think what Steve means is, if we have time moving in a forward direction, how do we get to that one point in time from an infinite past?  How do you get to that single event in time without beginning somewhere?  If events are happening in succession, and time is infinite into the past, how would we ever arrive at a singular point in time?  Wouldn’t you have to start somewhere to get there?   I’m confused! Lol

Well, and that is the whole point. There is NOT a start. It is always going on. Any time you 'set down' will always have an infinite amount of time in its past.

So, yes, the basic issue is that there is not a start. There isn't a contradiction there, just a mind bender.

[SteveII]

The article is just someone's opinion.  Even Professor George Ellis (who is a believer, a Quaker), who is one of several thousand practicing cosmologists, has expressed "reservations" about physical actual infinites, but this is an example of where you and WLC are cherry picking your sources.  I could make equivalent claims about New Testament history by citing Professor Bart Ehrman.

But, let me ask you this, "If space is a physical actual infinite, how did we arrive at our present location?"

What part of that was cherry picking? 

1. The Cambridge University Conference or
2. The +Plus Mathematics Magazine and the article authors or 
3. George Francis Rayner Ellis, FRS, Hon. FRSSAf (born 11 August 1939), is the Emeritus Distinguished Professor of Complex Systems in the Department of Mathematics and Applied Mathematics at the University of Cape Town in South Africa. He co-authored The Large Scale Structure of Space-Time with University of Cambridge physicist Stephen Hawking, published in 1973, and is considered one of the world's leading theorists in cosmology.[1] He is an active Quaker and in 2004 he won the Templeton Prize.[2] From 1989 to 1992 he served as President of the International Society on General Relativity and Gravitation. He is a past President of the International Society for Science and Religion. He is an A-rated researcher with the NRF.

Perhaps I should have found someone who did not co-author a book with Hawking? 

No one has claimed space in an actual infinite. It might be potentially infinite. Read the article.