Actual Infinity in Reality?

[Anomalocaris]

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.

That come back to how does one define time. Here it seems to me that we are arguing from a hazy, notional perception of time, rather than from a more rigorous definition of time that could usefully define a direction of time. It is necessary to first define what constitute direction of time before arguing whether time could stretch infinitely along that direction.

For time to be useful concept with specific direction, there must be some mechanism to mark the directional progress of time. Time has no meaning if either nothing whatsoever changes, or if all changes are purely random such that defining time as going one way is utterly indistinguishable from defining time as going in the opposite direction.

All physical laws except one do indeed seem to work just as well going one way in time as going in the other. So nothing else in our physical universe can be used to consistently mark the progress of time. Anything the law says can happen going one way the same law says can go in the other.

The only exception seems to be to be the law of entropy. So that suggest the increase in entropy marks direction of time. This makes it problematic to say time extends infinitely back into the past, because to trace time backwards is to trace reduction in entropy. Entropy can not go negative, and is likely to be quantized. So while one might notionally imaging time going back forever, beyond a certain point time no longer has meaning. So one might say meaning time does not stretch back forever.

[polymath257]

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



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.

And again, the Hilbert Hotel is a *paradox* and not an actual logical problem. But let's face it, physics alone has many paradoxical issues: paradoxes concerning rapidly rotating objects, the twin paradox, paradoxes concerning entropy, paradoxes concerning the relationship between quantum theory and gravity, etc. To have a paradox just means our initial intuition is incorrect and needs to be corrected. it is an opportunity to learn.

From my experience, philosophers know a fair amount about *popularizations* of physics, but very little *actual* physics. Most would not be able to compute a quantum probability in any way. Most cannot solve a differential equation. And, I am sorry, but unless you can do both of those with some fluency, you simply do NOT understand the physics. And I certainly do NOT consider philosophers as any sort of experts on infinity. For that, you should go to mathematicians.

[Jehanne]

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.

What is true of time is also true of space; if space is infinite, how did any of us arrive at this point??

I would like Steve (or, individuals with his Aristotelian mentality) to explain to me how a ray of light can behave as both a particle and a wave, both at the same time. And, why he's at it, explain how an electron can move from one point to another without crossing the intervening space between.

Dozens of these paradoxes exist, and no one doubts them, except religious fundamentalists and the outlier scholars they can cherry pick and quote (often, out of context) to support their extremist views.

[polymath257]

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.

That come back to how does one define time.   Here it seems to me that we are arguing from a hazy, notional perception of time, rather than from a more rigorous definition of time that could usefully define a direction of time.  It is necessary to first define what constitute direction of time before arguing whether time could stretch infinitely along that direction.

For time to be useful concept with specific direction, there must be some mechanism to mark the directional progress of time.   Time has no meaning if either nothing whatsoever changes, or if all changes are purely random such that defining time as going one way is utterly indistinguishable from defining time as going in the opposite direction.

All physical laws except one do indeed seem to work just as well going one way in time as going in the other.  So nothing else in our physical universe can be used to consistently mark the progress of time.   Anything the law says can happen going one way the same law says can go in the other.  

The only exception seems to be to be the law of entropy.  So that suggest the increase in entropy marks direction of time.   This makes it problematic to say time extends infinitely back into the past, because to trace time backwards is to trace reduction in entropy.   Entropy can not go negative, and is likely to be quantized.   So while one might notionally imaging time going back forever, beyond a certain point time no longer has meaning.   So one might say meaning time does not stretch back forever.

Some aspects of the weak force are time anti-symmetric, but they are unlikely to be relevant here.

The problem with entropy is that it is not fundamental. It is a statistical construct based on the loss of information in going from a low level (microscopic) description to a high level (macroscopic) description. This is the whole point of the various 'ensembles' of statistical mechanics.

There are two main physical arrows of time: entropy increase, and universal expansion. There seems to be no good reason for the two to be the same. So, in a pre-Big bang scenario, it is *possible* to have a contracting universe with increasing entropy. And some versions of quantum gravity have exactly that. We may also have long periods of expansion with zero entropy production (which satisfies your requirement for change to give a sense of time direction).

Another aspect of this is that most scenarios where time goes infinitely into the past are in some sort of multiverse model. In this, the entropy of the multiverse need not directly correlate to that of particular universes (there is the randomness between universes to consider). This allows for a very different entropy picture that the one we see locally.

[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?"

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.

Professor Ellis is outlier; most cosmologists are atheistic:

Why (Almost All) Cosmologists are Atheists

If the Universe is only a "potential infinite", then it may have an edge or boundary (it probably doesn't), a geographical center and, hence, a center of mass (again, probably not), but most importantly, at what "expense" is the Universe expanding into?  Are there just layers of "potential infinities" that go on forever??  Sounds like an actual infinite to me!  But, again, the FLRW metric (just Google) works just fine with actual infinities!

[SteveII]

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.

Professor Ellis is outlier; most cosmologists are atheistic:

Why (Almost All) Cosmologists are Atheists

If the Universe is only a "potential infinite", then it may have an edge or boundary (it probably doesn't), a geographical center and, hence, a center of mass (again, probably not), but most importantly, at what "expense" is the Universe expanding into?  Are there just layers of "potential infinities" that go on forever??  Sounds like an actual infinite to me!  But, again, the FLRW metric (just Google) works just fine with actual infinities!

Textbook ad hominem attack. Who cares if he an atheist or not.  We are talking about cosmology and mathematics--subjects he is super well qualified to speak about. One does not speak at conferences at Cambridge University by being an "outlier". 

The universe may have an edge or not. Maybe it is curved around like a sphere. Who knows. You don't get to declare an actual infinite exists. The very laws of physics prohibit us from ever finding out. In addition, if the universe was bounded at one time (big bang/inflationary universe), then it could only be potentially infinite. It could never be an actual infinite.

[Jehanne]

Processor Ellis is entitled to his opinions; there are other cosmologists and mathematicians who disagree with him:

https://m.phys.org/news/2015-02-big-quan...verse.html

[SteveII]

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

You correctly understand my point. Polymath does not because he is so sure that there is not problem with an infinite chain of evens that he doesn't even see the metaphysical impossibility of his statements. He just states them over and over because his math background says you can do math with potentially infinite sets so an actual infinite must exist. If it wasn't so frustrating, it would be a fascinating example on why Philosophy of Science should be the first course math and physics majors should take.

---

Processor Ellis is entitled to his opinions; there are other cosmologists and mathematicians who disagree with him:

https://m.phys.org/news/2015-02-big-quan...verse.html

LOL. Sure there are. BTW, you are failing to prove that actual infinities exist. You bring up some potential infinities candidates or that potential infinities are used in some equations--but that is not the same, is it.

[Jehanne]

Processor Ellis is entitled to his opinions; there are other cosmologists and mathematicians who disagree with him:

https://m.phys.org/news/2015-02-big-quan...verse.html

LOL. Sure there are. BTW, you are failing to prove that actual infinities exist. You bring up some potential infinities candidates or that potential infinities are used in some equations--but that is not the same, is it.

And, so, if no one can prove that actual infinities exist, that makes their existence "impossible"??

[polymath257]

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

You correctly understand my point. Polymath does not because he is so sure that there is not problem with an infinite chain of evens that he doesn't even see the metaphysical impossibility of his statements. He just states them over and over because his math background says you can do math with potentially infinite sets so an actual infinite must exist. If it wasn't so frustrating, it would be a fascinating example on why Philosophy of Science should be the first course math and physics majors should take.

---

I can see the paradox: it is counter-intuitive to not have a start since we are accustomed to things having one. But why does that lead to an *impossibility*?
And I would say this is why math and physics should come first and philosophy later: most people simply haven't developed their intuitions prior to learning how things actually are or can be.

---

You correctly understand my point. Polymath does not because he is so sure that there is not problem with an infinite chain of evens that he doesn't even see the metaphysical impossibility of his statements. He just states them over and over because his math background says you can do math with potentially infinite sets so an actual infinite must exist. If it wasn't so frustrating, it would be a fascinating example on why Philosophy of Science should be the first course math and physics majors should take.

---

I can see the paradox: it is counter-intuitive to not have a start since we are accustomed to things having one. But why does that lead to an *impossibility*?
And I would say this is why math and physics should come first and philosophy later: most people simply haven't developed their intuitions prior to learning how things actually are or can be.

Essentially, as far as I can see, you are assuming that any process in the real world must have a start. Does that correctly state your position?

So, why do you think this is necessary?