Infinite vs Expanding Universe: A Physics Conundrum Explained

[Physics_Kid]

given all the great minds of physics, i still have trouble with this one.
"the uverse is infinitely big"
and
"the uverse is expanding"

my understanding is you can't have both, because to define expansion you need measurable differential on a boundary, thus expansion by definition infers changing finite regardless as to how fast the change is.

so which is it?

 

[fresh_42]

It is important to stop thinking the universe is expanding into somewhere. The universe itself is somewhere. It is the same difference as with any, let's say surface, because we can imagine surfaces. If we only knew our Earth and nothing about outer space, since the universe doesn't have an outer space, we would only knew the Earth's surface. Why shouldn't it get bigger and bigger without any reference to getting bigger into something? The surface is all we have, and it might get bigger. O.k. not the Earth as a solid rock, but for imagination it's sufficient.

The universe is estimated to have an expansion of about 45 billion light years in each direction (see Wikipedia). But that doesn't mean it's shaped like a ball. We simply don't know how it is shaped. All we know is, that it is almost flat, so either it is really big, or indeed flat. And it doesn't need a boundary as our Earth's surface doesn't have a boundary either. So infinitely big should better be read as without boundary.

 

[Blake Barr]

I tend to think of it as the universe is infinite, spatially, but the stuff in it is expanding. Love stuff.

 

[Physics_Kid]

hi Blake
so space in the space-time fabric is as any given time, infinite?
and for me, i don't see how to apply "expanding" to "stuff". what i can see though is that all "stuff" is moving away from all other "stuff", but by that observation i do not conclude "expanding".

example, let's take a large balloon, say 200x the size of the biggest weather balloon we know, inside there are a few atoms near the center and these atoms are moving away from each other at a rate of 1/1x10^100^100^100^100^100^100 m/1000yr, so from any point within the observation is that the "stuff" is just moving away from all other stuff, but you are not measuring any differential on any boundary since the boundaries that confine the stuff is the balloon, which is not changing.

now, if we want to talk about the density of "stuff" across a space, that would be an observable decrease by definition when the "stuff" becomes more distant from the other "stuff" within the "infinite" space.

if you blow up a balloon, the atoms up against the inside edge of the balloon are following the edge of the balloon, which infers that the edge of the balloon (aka boundary) has differential finite change of space, thus it is expanding.

 

[Blake Barr]

But the balloon itself is stuff. Your example assumes the universe, the actual space-time, has a boundary. Is space expanding to hold the stuff or is the stuff simply spreading out to fill the space?

 

[Khashishi]

to define expansion you need measurable differential on a boundary

No, another definition of expansion is metric expansion. If the distance between any comoving points is increasing, then space is expanding. And this is what we observe (Hubble's law).

 

[phinds]

Google "Hilbert's Hotel" for a discussion of how "expanding" and "infinite" are not in any way contradictory in the same context.

 

[Physics_Kid]

No, another definition of expansion is metric expansion. If the distance between any comoving points is increasing, then space is expanding. And this is what we observe (Hubble's law).

i will lookup hilbets, but Re: your point, localized "space" itself is not expanding (the box around which all your "stuff" is), if it were then you would have decreasing "space" density.
what you describe is nothing more than increasing distance between "stuff" within a confined non-changing "space".

"space" itself could be expanding at the boundaries, but that is like an expanding balloon, which at any time t has finite boundaries = not infinite.

 

[phinds]

But the balloon itself is stuff. Your example assumes the universe, the actual space-time, has a boundary. Is space expanding to hold the stuff or is the stuff simply spreading out to fill the space?

Really? Are you sure about that?

 

[Khashishi]

what you describe is nothing more than increasing distance between "stuff" within a confined non-changing "space".

In Euclidean space and Galilean relativity, there isn't really any difference between expanding space (i.e. the coordinate axes compressing) and everything moving apart within that space. Because there wouldn't be any way of measuring the difference. But we don't have Galilean relativity. We have General Relativity. In special and general relativity, nothing can travel faster than c relative to a local observer. But, we can measure that the distance to faraway galaxies is increasing faster than c. This isn't possible if space were just a static grid and everything was moving apart on that grid. Because it would mean all these faraway galaxies are traveling faster than c. No, rather, they are traveling fairly slowly** in their local space, but all of space is being expanded. This is what the equations tell us.

**relative to the cosmic microwave background

 

[Khashishi]

In relativity, there's a concept called parallel transport. Let's consider what it means to have expanding space.
Let point A be the origin of an inertial reference frame. Take an object at rest at point A and then move it to point B, far away. It is possible to keep track of all the accelerations that you have made on the object using an inertial guidance system, so in principle, it is possible to accelerate up to a velocity v, travel to B, and then decelerate back to velocity 0, relative to your original inertial motion which is calibrated to be 0 velocity.

Now, after decelerating back to "0 velocity", is the object at B moving relative to point A? We could infer this motion by sending radio signals back and forth. What you would be measuring is the distance between B and A. And if space is expanding, that distance is growing, even though your inertial guidance system is telling you that you aren't moving.

 

[Comeback City]

if you blow up a balloon, the atoms up against the inside edge of the balloon are following the edge of the balloon, which infers that the edge of the balloon (aka boundary) has differential finite change of space, thus it is expanding.

The Balloon Analogy shows that when you inflate the balloon, the stuff on the surface of the balloon will expand. It isn't talking about the atoms inside it. So if you have point X and point Y on the surface of the balloon, the distance between point X and point Y will grow during the time that the balloon is being inflated. This is expansion on the 2 dimensional level. The problem with this analogy is that it only works on a 2 dimensional scale. Enter: the universe... 3 spatial dimensions, not to mention the time dimension which collectively make up spacetime. It would be VERY challenging to come up with an analogy to fit spacetime expansion.

It has been stated that the galaxies themselves are getting further apart, but they themselves are NOT moving. Khashishi explained this well in post #10. So to go back to the Balloon Analogy, imagine that point X and point Y are galaxies. They themselves are not moving. The expansion of the balloon is moving them, which translates to the expansion of the universe moving the galaxies farther apart.

 

[Physics_Kid]

ok, i see some good info for me to chomp on.
but, balloon analogy of the particles of the balloon itself, you are the observing differential in boundary, thus would be saying that "space" is not infinite, but rather finite at any given time. however, if i look at that in 2-dimensional view, from surface, i can see where it look like the stretching or "expanding" of space.

i see Suskind u-toob video for this example, a simple cut rubberband with a few equally spaced dots on it (not unlike balloon analogy, but 1-dim), stretch the rubber in linear fashion and the dots get further apart yet there is no actual movement of the dots relative to their dot location on the rubber. but most things will disappear if you stretch then for a long time, so how can "space" itself stretch continuously at speed of c ?

 

[Comeback City]

but most things will disappear if you stretch then for a long time, so how can "space" itself stretch continuously at speed of c ?

What do you mean by they disappear?

 

[Physics_Kid]

What do you mean by they disappear?

i mean, stretch something, stretch it more, more more, what eventually happens? take the individual atoms and increase the space between them at a constant rate, what you wind up with is a single atom with all the rest infinitely far away.

"space" doesn't seem to work like that, it can stretch at the speed of light for infinite amount of time? So does "space" just fill itself in when it gets thin? do black holes form because the forces created there are strong enough to rupture "space"? and this odd "space" will stretch like that no matter where the observer is, an observer in this "space" seems to alway be at the center point of the 3D expansion, yet, if that's the case then we have conflict when analyzing the data from two observers because when combined the "space" would seem to be expanding towards each other, how can that be?

example, me at xyz, joe at x+1 y-2 z+3, to me space is expanding in 3D as if I am the center, for joe, space is expanding in 3D as if he was the center, but that means space is expanding towards me and joe at the same time. if this model is false then the expansion of "space" has a singularity origin, so where is that?

 

[Khashishi]

You have all these preconceptions about what space is, and that's why it doesn't make sense to you. Space is not a substance that can get thin. It is just a mathematical framework for assigning positions and measuring distances between things or events. We describe space in terms of the topology and the metric. You need to forget everything and just start reading. All your questions are of the form: if this then that. how can that be? Well, the answer is that your deductions are based on some incorrect assumptions. If you find a contradiction between two things you have read, then please ask, and we'll try and figure it out. But if there's a contradiction between something you read and one of your preconceptions, your preconception is probably off.

In relativity, you don't have a universal grid with nice x, y, z coordinates that work for everybody. Space is curved, so parallel lines may diverge or converge in some places. What you can do is create local x, y, and z coordinates for a specific observer for a small area around the observer. And you can have another set for another observer. You can calculate how to transform between the coordinates, but you'll find that one set of coordinates don't work well for the whole universe.

 

[Comeback City]

do black holes form because the forces created there are strong enough to rupture "space"?

This is not why black holes form.

if this model is false then the expansion of "space" has a singularity origin, so where is that?

There is not a single spot in the universe where you can say the universe started, according to Big Bang Theory.

 

[Physics_Kid]

Khashishi

ok, take for example two local observers A&B who each have access to hubble, each observer looks at different distant objects to determine that those objects are moving away from each other, and, that they themselves (objects) are moving very slowly but their apparent differential speed is quite high, thus each observer concluded that it must be space that is expanding, however, when each observer makes their reference the distant object it would appear that all the other "stuff" is moving away from that reference point, but observer B sees the same thing in another place, so wouldn't the apparent directions of expansion conflict?

also, if space itself was a thing of infinitely tight folds, like a roll of paper towel unrolling onto table and it folds back and forth on top of itself, you could have infinite distance in a infinitely small space ? the u verse as we see it, could possibly be within the smallest thing ever.

 

[phinds]

Khashishi

ok, take for example two local observers A&B who each have access to hubble, each observer looks at different distant objects to determine that those objects are moving away from each other, and, that they themselves (objects) are moving very slowly but their apparent differential speed is quite high, thus each observer concluded that it must be space that is expanding, however, when each observer makes their reference the distant object it would appear that all the other "stuff" is moving away from that reference point, but observer B sees the same thing in another place, so wouldn't the apparent directions of expansion conflict?

also, if space itself was a thing of infinitely tight folds, like a roll of paper towel unrolling onto table and it folds back and forth on top of itself, you could have infinite distance in a infinitely small space ? the u verse as we see it, could possibly be within the smallest thing ever.

You really need to pay attention to what's being said to you:

You have all these preconceptions about what space is, and that's why it doesn't make sense to you. ... You need to forget everything and just start reading.

 

[Physics_Kid]

yeah yeah, i know, i know that i don't know, just me throwing up some wild questions.

 

[Comeback City]

yeah yeah, i know, i know that i don't know, just me throwing up some wild questions.

And we're just throwing back some wild answers

 

[phinds]

yeah yeah, i know, i know that i don't know, just me throwing up some wild questions.

Sure, and that might be entertaining, but it's a pretty poor way to really learn anything. We're not trying to give you a hard time here, it's just that we recognize that you need to get more systematic in your acquisition of knowledge.

 

[Physics_Kid]

And we're just throwing back some wild answers

not really, the A's were mostly "your understanding of it is wrong, go read up", etc.
i know its not all correct, and my wild Q's if answered in basic ways would actually be helpful to me
cheers

 

[russ_watters]

given all the great minds of physics, i still have trouble with this one.
"the uverse is infinitely big"
and
"the uverse is expanding"

my understanding is you can't have both, because to define expansion you need measurable differential on a boundary, thus expansion by definition infers changing finite regardless as to how fast the change is.

so which is it?

I'm sorry if I skimmed through and missed it, but I didn't see treatment of this from a math point of view, which appears to me to be the main issue:

Many people think of "infinity" as just being "the biggest number possible", which would mean you can't go any bigger. But it actually just means "unbounded", so it really does mean something infinite could continue increasing.

"Infinity" is not a limitation, it is the absence of limitation.

 

[Comeback City]

not really, the A's were mostly "your understanding of it is wrong, go read up", etc.
i know its not all correct, and my wild Q's if answered in basic ways would actually be helpful to me
cheers

Your questions have definitely been answered. Which questions do you have from the original post that you feel have not been answered?

 

[Khashishi]

wouldn't the apparent directions of expansion conflict?

From an observer at point A, everything is moving away from point A. From an observer at point B, everything is moving away from point B. A and B are getting farther apart. I don't see the conflict here.

 

[Ken G]

I think part of the problem here is that many times, people are given pictures to help them understand the mathematics of general relativity, since the mathematics is very difficult and the pictures are much easier. But then they have problems with the pictures, there's something about them they don't like, but they were only pictures in the first place-- they were never general relativity. General relativity does not have a theory of space that you could test if space is expanding or not, instead it has what Khashishi described so eloquently-- rules for linking up the local coordinates of widely separated observers, where the local coordinates are like those of special relativity, unaffected by gravity. You could think of it as special relativity applying locally, and general relativity telling you how to link up all those special relativistic local coordinates based on what gravity is doing to those connections. This is one way to interpret the meaning of the all-important "equivalence principle", which states that the local coordinates are always those of special relativity, which then have to be cobbled together into a global story that took Einstein many years to piece together, even after he had his lynchpin equivalence principle.

So when you understand that "space is expanding" is just a useful picture, and not a statement of fact about the universe, you are more free to adopt a different picture that you may prefer. But it must connect to general relativity-- a picture that violates general relativity will not serve you. Still, you have a lot of different pictures that can work. For example, general relativity provides a formal way to say that spacetime is curved, but a curved spacetime does not necessarily include an expanding space, it's just a curved spacetime that you can coordinatize in many different ways. If you say that distances are increasing with time, you are using what are known as "comoving coordinates", which means you take as your time coordinate the local proper age of the universe for the material in each region you are coordinatizing. That's a very natural thing to do, we are imagining hypothetical clocks that were created with that material and stayed with it all this time, but we could use an entirely different set of clocks for our time coordinates, These different coordinates are giving us different languages for talking about what is happening, different pictures, but they are all saying the same thing in terms of what we would observe. For example, if you choose a coordinate system where the Earth is at the origin, then the Earth is at the center of your universe, but it doesn't mean that it is actually at a special place, only that you have coordinatized it that way. Space is like that too, we often mistake how we are coordinatizing it for the "real thing."

A classic example of this is if we decide to picture Khashishi's parallel transport experiment by saying that rulers and clocks and all bound systems are shrinking with age, this is what the universal gravity is "doing," in our picture. Then we also understand why the rocket, after accelerating and decelerating completely symmetrically, continues to have its distance from us increase with age-- it's because our rulers are shrinking with age. No experiment adjudicates these pictures, as long as we make them all consistent with general relativity. Some people might like one picture and dislike another, but notice that if you regard bound systems as shrinking with age, you have no trouble answering how an infinite universe could require more and more rulers to span between galaxy clusters as it ages. Indeed, I might argue this is the most important lesson of relativity-- our pictures are not unique descriptions of "what is really happening." The truth is, in itself, in some sense relative, in the sense of being subordinated to a choice of coordinate language.

 

[Blake Barr]

Really? Are you sure about that?

I am not sure I understand your question. Are you asking if I am sure that his example would require that space-time has a boundary? Or did you interpret this as me saying that space-time has a boundary?

 

[phinds]

I am not sure I understand your question. Are you asking if I am sure that his example would require that space-time has a boundary? Or did you interpret this as me saying that space-time has a boundary?

Ah ... I misread your post and thought that YOU were saying that it has a boundary. Sorry.

 

[lifeonmercury]

Could someone please tell me if this statement is correct or is at least believed to be true by some cosmologists?

If the universe is infinite now, it was also infinite one second after the Big Bang.

 

[Bandersnatch]

this statement is correct

It is.

 

[phinds]

Could someone please tell me if this statement is correct or is at least believed to be true by some cosmologists?

If the universe is infinite now, it was also infinite one second after the Big Bang.

Yes, as Bandersnatch said, it is true. Finite things can't become infinite and infinite things can't become finite. Whichever one something is, it always has been that way and always will be that way (this statement gets a bit problematic if you allow infinite time but let's not go there).

 

[Ken G]

We should be careful though, there may be types of expansion laws that are solutions to general relativity under the cosmological principle that reach an infinite scale parameter in a finite time, starting from a finite universe. I think the mathematics could allow that, so I don't know that we can say it is logically impossible. But it certainly isn't a type of solution that is under any serious consideration at present. Perhaps all such solutions are open solutions anyway, so could not start out finite.

 

[phinds]

I think the mathematics could allow that, so I don't know that we can say it is logically impossible

The map is not the territory. Not all mathematics can be realized physically. I don't see how something physically finite could become infinite in a finite amount of time.

 

[Ken G]

Yet that's the kind of reasoning we have to watch out for, it's the kind of thing people say when they say they don't understand how an infinite universe could come into being in the first place. A territory is just a different type of map.