If the universe is infinite, how is it expanding?

[howdydiddlydoo]

Also, you said infinity can accommodate "regional expansion." So what's the problem? When we talk about the universe expanding, we mean that galaxies are expanding away from one another.

Because regional expansion is quantifiable. ie you can measure the distance that galaxies are moving from each other.

They are however contained in infinity, which is not quantifiable.

Infinity can be described as a container for quantfiable measurements.

Infinity + 1 = Infinity. (meaning infintiy + 1 can not exist). If you add one more guest, then it means that the number of guests were not from an infinite set.


And more to the point to further invalidate this hotel analogy.....the hotel and guests have a clear starting point.....something that infinity does not. Basically the analogy is incorrect and misrepresentative of the concept of infinity.

[Garnier Fructis]

Because regional expansion is quantifiable. ie you can measure the distance that galaxies are moving from each other.

They are however contained in infinity, which is not quantifiable.

Infinity can be described as a container for quantfiable measurements.

Infinity + 1 = Infinity. (meaning infintiy + 1 can not exist). If you add one more guest, then it means that the number of guests were not from an infinite set.

By your own admission, Infinity + 1 = Infinity. Turn this around, and you have Infinity = Infinity + 1. So if infinity + 1 doesn't exist, then infinity does not exist because they are the same thing. You claim that because they are the same, infinity + 1 is nonexistent. That conclusion does not follow from the premise.

You're also still missing the crux of Hilbert's Hotel. You can't argue that there aren't an infinite number of guests. That's one of the basic premises from which the entire argument follows. There is no paradox in having an infinite number of guests. There only appears to be one because infinity is a subtle concept.

[Orlong]

The matter in the universe is expanding, not the boundary, we don't know if there is a boundary.B

There cant be a boundary because what would stop someone who theoretically had infinite fuel and infinite time to live, in a ship that could handle the trip, from continuing to travel in a straight line in space forever? A wall? then who built the wall, and even if ther WAS a wall there still has to be something on the other side. There cant be an end to "space". There could be a point at which nothing exists other than empty space, but there would still be room to keep moving away

[Garnier Fructis]

There cant be a boundary because what would stop someone who theoretically had infinite fuel and infinite time to live, in a ship that could handle the trip, from continuing to travel in a straight line in space forever? A wall? then who built the wall, and even if ther WAS a wall there still has to be something on the other side. There cant be an end to "space". There could be a point at which nothing exists other than empty space, but there would still be room to keep moving away

There can be a boundary, but you would never reach it in an expanding universe. The boundary would expand away from you faster than the speed of light, such that no matter how long you took or how much fuel you had, you would never reach it, because it would always be moving away from you and you will never go fast enough to compensate.

[howdydiddlydoo]

By your own admission, Infinity + 1 = Infinity. Turn this around, and you have Infinity = Infinity + 1. So if infinity + 1 doesn't exist, then infinity does not exist because they are the same thing. You claim that because they are the same, infinity + 1 is nonexistent. That conclusion does not follow from the premise.

You're also still missing the crux of Hilbert's Hotel. You can't argue that there aren't an infinite number of guests. That's one of the basic premises from which the entire argument follows. There is no paradox in having an infinite number of guests. There only appears to be one because infinity is a subtle concept.

I think you added this reply while i was making an addition, so i will draw your attention to it.

In the hotel analogy, the number of rooms and the numbers of guests have a clear starting point (at the bottom). This analogy to represent infinity is incorrect, because infinity does not have a starting point.

Hilberts hotel is basically misrepresenting the concept of infinity and "cheating" by use of a starting point. It makes the concept of adding 1 to infinity invalid.

---------- Post added 2013-01-05 at 12:27 AM ----------

There can be a boundary, but you would never reach it in an expanding universe. The boundary would expand away from you faster than the speed of light, such that no matter how long you took or how much fuel you had, you would never reach it, because it would always be moving away from you and you will never go fast enough to compensate.

This is nothing more than the concept of regional expansion.

Lets say that the Universe is expanding. And that it is expanding at a rate which you will never be able to reach. And that it will expand forever.

At any given moment in time, the universe does have a boundary, and it is quantifiable, measurable. Thus, not infinite at that particular moment in time.

The space that the univers is expanding into though MUST be infinite, to accomodate a limitless expansion.



This coincides precisely with the Hilberts hotel -

The space (hotel) is infinite, but the Universe (guests) is additionally growing.


Thus, infinity is a container that can hold regional expansion.

[Garnier Fructis]

I think you added this reply while i was making an addition, so i will draw your attention to it.

In the hotel analogy, the number of rooms and the numbers of guests have a clear starting point (at the bottom). This analogy to represent infinity is incorrect, because infinity does not have a starting point.

Hilberts hotel is basically misrepresenting the concept of infinity and "cheating" by use of a starting point. It makes the concept of adding 1 to infinity invalid.

Consider the set of all positive integers. This is the infinite set which consists of the following members: {1, 2, 3, ...}. There is clearly a starting point, and it is clearly infinite.

[howdydiddlydoo]

Consider the set of all positive integers. This is the infinite set which consists of the following members: {1, 2, 3, ...}. There is clearly a starting point, and it is clearly infinite.

Hmm good point. I concede on that one.

However, i will say these 3 points -

1) Shifting 1 guest to the next room would take an infinite amount of resources to do and thus is theoretically impossible to achieve.
2) Because an infinite amount of guests occupy an infinite amount of rooms, there is never an empty slot to fit another guest into.
3) Since the number of guests are already infinite, there is never a spare set of guests to use to add to the original set anyway. ie - you can not practically have two infinite sets of the same thing


These 3 points invalidate the hotel analogy imo.

[Garnier Fructis]

Hmm good point. I concede on that one.

However, i will say these 3 points -

1) Shifting 1 guest to the next room would take an infinite amount of resources to do and thus is theoretically impossible to achieve.
2) Because an infinite amount of guests occupy an infinite amount of rooms, there is never an empty slot to fit another guest into.
3) Since the number of guests are already infinite, there is never a spare set of guests to use to add to the original set anyway. ie - you can not practically have two infinite sets of the same thing


These 3 points invalidate the hotel analogy imo.

1. Of course it's unfeasible, but that's not the point of the hotel.
2. You create the empty slot at room 1 by reassigning all existing guests to the room n=n+1.
3. Think of it this way. You partition an infinite set into a finite group of subsets. As a result of the original set being infinite, at least one of the new subsets is infinite. Thus, you can have many subsets of an infinite set which are themselves infinite. You can apply this concept to the set of guests and easily come up with another set of infinite guests.

[howdydiddlydoo]

1. Of course it's unfeasible, but that's not the point of the hotel.
2. You create the empty slot at room 1 by reassigning all existing guests to the room n=n+1.
3. Think of it this way. You partition an infinite set into a finite group of subsets. As a result of the original set being infinite, at least one of the new subsets is infinite. Thus, you can have many subsets of an infinite set which are themselves infinite. You can apply this concept to the set of guests and easily come up with another set of infinite guests.

1) Ok. Well considering is is not feasible, then it cant apply to any real-world situation. Nevertheless, lets ignore this point for the sake of discussion.

2) n+1 creates an empty space at the start, it does not create space to move the end into though. There is no end. n itslef is an infinite. n+1 creates an infinite loop. n = n+1, they are the same thing. Lets ignore this too, i want to discuss point 3

3) In a positive set of infinite integers it is impossible to partition and create a subset of infinite integers. Since i conceded the point that a positive set of infinite integers has a beginning, as soon as you partition, your newly created set now has a beginning AND an end, thus meaning it is not, and can never be infinite. It is impossible for one of the new subsets to be infinite.

Thus, i stand firm with my belief that you can not practically have two infinite sets of the same thing. (meaning that the notion of adding another guest to an already infinite guest list is theoretically impossible).

[Frozen Death Knight]

The universe is infinite ~ The universe is expanding
You're talking about two different usages of the word here.
One is the totality of all existence - including everything we do not know and cannot observe.
The other is the observable universe. - What we CAN see (or theoretically could make observations ON (but not of - not from Earth)).
The diameter of the observable universe is estimated at 93 billion lightyears (yes, it can expand faster than the speed of light).

To us, it doesn't really make sense to talk about the universe we cannot observe, so while that MAY be infinite (there's no reason to say it is, and no reason to say it isn't), and that is certainly a popular statement, it is utterly pointless and meaningless.

The observable universe is NOT infinite, and IS expanding according to our currently accepted model.

Space is infinite - the universe is not (or the other way around)
I don't think this helps the understaning. Space isn't really "that empty void which all the planets and stars and stuff is located in". That makes it too ... firm... or unalterable. Which it is not. It is space itself that is expanding, NOT the universe that expands into space.
- Galaxies aren't simply drifting further apart... The space between them is actually expanding (not simply increasing either - expanding - swelling, if you will).

tldr;
The known universe is finite and expanding.
Space itself is what is expanding.
Nothing outside of the known universe is relevant.

Ah, thanks for clearing it up for me (the definitions can really make it tricky to understand some of the more subtle differences). I am not as well read about the big bang and some of its predicted effects as I would like to be, so it helps when someone with a bit more insight corrects some of the misunderstandings and such.

[Orlong]

There can be a boundary, but you would never reach it in an expanding universe. The boundary would expand away from you faster than the speed of light, such that no matter how long you took or how much fuel you had, you would never reach it, because it would always be moving away from you and you will never go fast enough to compensate.

I disagree. How could there be a boundary even if we couldnt reach it, there is no such thing as a one sided object. There has to be something on the other side of it.

[Deleted]

I disagree. How could there be a boundary even if we couldnt reach it, there is no such thing as a one sided object. There has to be something on the other side of it.

But the universe isn't an object, or a single thing. The universe is everything that exist in our dimension(s).
It's a collective word for "everything" that exist. It doesn't have sides,corners, depth or width.


I think it's a pretty common misconception that the universe is a single entity/object.
It's referred to as just that in school, so it's not that odd.

[Frozen Death Knight]

Hmm good point. I concede on that one.

However, i will say these 3 points -

1) Shifting 1 guest to the next room would take an infinite amount of resources to do and thus is theoretically impossible to achieve.
2) Because an infinite amount of guests occupy an infinite amount of rooms, there is never an empty slot to fit another guest into.
3) Since the number of guests are already infinite, there is never a spare set of guests to use to add to the original set anyway. ie - you can not practically have two infinite sets of the same thing


These 3 points invalidate the hotel analogy imo.

Regarding number 2), there are more than one type of infinities, which in turn would make infinity + 1 = infinity actually valid, if I understand it correctly. Also, infinity can not measure anything, so saying that there are no more room for guests would actually put limitations on infinity itself, which is not the definition of infinity.

As for number 3), by limiting the amount of guests available you would have then put limitations on infinity itself in an attempt to measure it, which makes my first paragraph apply to this point as well.

[Aaldrus]

Aliens, obviously.

[Garnier Fructis]

3) In a positive set of infinite integers it is impossible to partition and create a subset of infinite integers. Since i conceded the point that a positive set of infinite integers has a beginning, as soon as you partition, your newly created set now has a beginning AND an end, thus meaning it is not, and can never be infinite. It is impossible for one of the new subsets to be infinite.

Thus, i stand firm with my belief that you can not practically have two infinite sets of the same thing. (meaning that the notion of adding another guest to an already infinite guest list is theoretically impossible).

Actually, it's impossible to partition an infinite set into a finite number of sets such that there is no infinite subset.

In fact, you could easily partition the set of all positive integers into two sets, both of which are themselves infinite, which consist of even positive integers and even odd integers.

Apply this to guests. Of the set of infinite guests, you take all the ones wearing blue and all the ones wearing red, and put them into their own sets. There are now two sets of infinite guests, both derived from the original infinite set of both.

I disagree. How could there be a boundary even if we couldnt reach it, there is no such thing as a one sided object. There has to be something on the other side of it.

Möbius strip only has one side.

[Orlong]

Möbius strip only has one side.

I disagree. Yes, its a neverending strip, but if you took a hole punch and punched a hole in it you could go from the front of the strip to the back of the strip and as such, if you could poke a hole in this imaginary edge of the universe what would be on the other side of the hole?

[Garnier Fructis]

I disagree. Yes, its a neverending strip, but if you took a hole punch and punched a hole in it you could go from the front of the strip to the back of the strip and as such, if you could poke a hole in this imaginary edge of the universe what would be on the other side of the hole?

Front = back, so punching a hole would accomplish nothing. The mobius strip has 1 side. It is a 1 sided surface. It's not something you disagree with. That's like disagreeing that a cube has 6 sides.

Does there need to be anything on the other side of the "edge" of the universe? If we take the definition of the universe to be the sum total of all matter and energy, then I imagine there's nothing but empty space beyond the edge.

[Gheld]

I disagree. Yes, its a neverending strip, but if you took a hole punch and punched a hole in it you could go from the front of the strip to the back of the strip and as such, if you could poke a hole in this imaginary edge of the universe what would be on the other side of the hole?

A Möbius strip only has 1 continuous side but it occupies 3 dimensional space. So you end up in a different point in space surrounding the strip but you can still follow that side of the strip back to your original starting point. You've essentially just traveled half way down the strip.

Going by the most mainstream interpretations of quantum mechanics, if you were hypothetically able to reach and then exceed the 'edge' of the universe you must take into account the following postulates:

-The space outside of the universe has not interacted physically in any meaningful manner with the space within (it's 'unobserved' so to speak), therefore it has no knowable properties.
-Moving into that space means interacting with it (and thus 'observing it') and thus it has knowable properties.

So first, you are inside the universe, and nothing can interact with space outside the universe, so for all intents and purposes it doesn't exist. You leave the universe, you have now interacted with the space outside the universe, so for all intents and purposes it does exist.

EDIT: Also

Consider the set of all positive integers. This is the infinite set which consists of the following members: {1, 2, 3, ...}. There is clearly a starting point, and it is clearly infinite.

Infinity is not a scientifically valid concept. Science is based on observation and Maxwell Planck calculated the smallest possible units of time and space (Planck Time and Planck Length) that any meaningful observation could be made of. We also know mass and luminosity to come in quantities of fixed natural units as well.

So any possible observation you can make will be based on a finite quantity of natural units.

Infinity creates the "multiple infinities" paradox. If you start at a point and draw an infinite number of rays out of that point, you can draw concentric circles around that point and theoretically place even more rays in between the original rays. Somebody posted this hogwash on here before, by some mathematician that clearly had never dabbled in modern physics.

However, that point at the very best possible observation (of which we are nowhere near capable of) would occupy an area of 1 cubic Pl(Planck Length). You would be able to draw rays out from that point 1 Pl thick, The end result is that you could only draw a finite number of rays from that point. The density of the rays would decrease by a factor of 1/R^2 as you got further from the point. So even if you did keep drawing concentric circles and filling them up with additional rays, that number would ALWAYS be finite.

So the words "infinity and infinitesimal" have no place in a conversation about modern physics.

[semaphore]

Regarding number 2), there are more than one type of infinities, which in turn would make infinity + 1 = infinity actually valid, if I understand it correctly.

Well, ∞ + 1 = ∞ because we defined ∞ = ∞ + n (i.e. 1) to begin with.

Thus, i stand firm with my belief that you can not practically have two infinite sets of the same thing. (meaning that the notion of adding another guest to an already infinite guest list is theoretically impossible).

It might be more fruitful if you understand that infinity is not a real number.

[Garnier Fructis]

EDIT: Also


Infinity is not a scientifically valid concept. Science is based on observation and Maxwell Planck calculated the smallest possible units of time and space (Planck Time and Planck Length) that any meaningful observation could be made of. We also know mass and luminosity to come in quantities of fixed natural units as well.

So any possible observation you can make will be based on a finite quantity of natural units.

Infinity creates the "multiple infinities" paradox. If you start at a point and draw an infinite number of rays out of that point, you can draw concentric circles around that point and theoretically place even more rays in between the original rays. Somebody posted this hogwash on here before, by some mathematician that clearly had never dabbled in modern physics.

However, that point at the very best possible observation (of which we are nowhere near capable of) would occupy an area of 1 cubic Pl(Planck Length). You would be able to draw rays out from that point 1 Pl thick, The end result is that you could only draw a finite number of rays from that point. The density of the rays would decrease by a factor of 1/R^2 as you got further from the point. So even if you did keep drawing concentric circles and filling them up with additional rays, that number would ALWAYS be finite.

So the words "infinity and infinitesimal" have no place in a conversation about modern physics.

The whole set theory shenanigans arose because howdydiddlydoo decided to debate the mathematics of the hilbert hotel exercise, which at that point was already pretty far removed from talk of physics.

Now, you say that infinite is not a scientifically valid concept. If that assertion were so, then it boggles me why the finiteness of the universe is considered an important open question in cosmology. You said yourself that science is based on observation. Current astronomical observations do not rule out an infinitely vast universe. Also, I fail to see how considerations of the Planck length would do so.