B 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.

 

[phinds]

A territory is just a different type of map.

I don't agree. A map is a DESCRIPTION. A territory is reality.

 

[Ken G]

So when you talk about atoms and forces and other aspects of science, are you talking about maps or territories? And in this thread, when you talk about the universe being finite or infinite, are you doing description or reality? My point is, descriptions are all we ever get, and all science can do with them is test them. We don't tell them in advance what they are allowed to do, we just test them and see what the ones that work actually do. If the equations of general relativity say that the scale factor in an initially finite universe can go infinite in a finite time (I don't know that they can but I don't see why not), then it is not for us to say that cannot happen, any more than it is not for us to say that event horizons cannot form or particles cannot be entangled. All those things are descriptions, none of them are realities, but they are what go into the models and are the only things we could ever test.

 

[phinds]

My point is, descriptions are all we ever get, and all science can do with them is test them.

No argument there, my point is just that (and this is true even GIVEN that all we ever have, really, is maps) it's important not to think that the map IS the reality. I agree that the goal of science is to make maps that are as accurate as possible, I just think it's important to make the distinction. That's particularly true in the case of this discussion because while I can believe that it is possible for math to describe something that goes from finite to infinite, I don't think (and I realize you don't agree w/ me) that reality can do that in a finite amount of time. So in this case, in my point of view anyway, the map can describe something that will never be the territory.

 

[Ken G]

I certainly agree that one's views about differences between maps and territories comes under their personal philosophy, I'm merely saying that this should never impose on the models that we allow ourselves to use to describe reality. If a model tests out well that solves some equations that have the scale parameter going infinite in a finite time, then so be it, that becomes our map. In science, anyway, there should never be a different criteria applied to a map, than to a reality, since the maps are how we understand reality, even if you think those are two different things.

 

[phinds]

I certainly agree that one's views about differences between maps and territories comes under their personal philosophy, I'm merely saying that this should never impose on the models that we allow ourselves to use to describe reality. If a model tests out well that solves some equations that have the scale parameter going infinite in a finite time, then so be it, that becomes our map. In science, anyway, there should never be a different criteria applied to a map, than to a reality, since the maps are how we understand reality, even if you think those are two different things.

Again, no argument, except I would point out that our map of reality includes singularities (black holes, big bang) for which we do NOT say about the math "so be it", we say "this is an unphysical math result".

 

[m k]

"the uverse is infinitely big"
and
"the uverse is expanding"

my understanding is you can't have both

What if you combine two infinities, positives and negatives?

 

[phinds]

What if you combine two infinities, positives and negatives?

You are trying to treat infinity as a number. There ARE areas of math where that works, sort of, but this is not one of them.

 

[Drakkith]

What if you combine two infinities, positives and negatives?

Depends on what you mean by "combine two infinities". For example:
$y=x^2-x$ could represent two infinities as $x→∞$, one positive and one negative. But the combination ($y$) is still a positive infinity because the positive term is squared while the negative term is linear. This is still true if $x→-∞$. You can immediately see this if you graph it, as it's just a parabola that opens upwards.

 

[Ken G]

Again, no argument, except I would point out that our map of reality includes singularities (black holes, big bang) for which we do NOT say about the math "so be it", we say "this is an unphysical math result".

But that's just it, we don't always say that. For example, no lesser expert on general relativity than Kip Thorne takes entirely seriously the singularity that the mathematics says forms in a black hole. He holds that if the mathematics says it is so, and the mathematics seems to be a reliable guide, then so be it, there is a singularity in a black hole. Others think there are all kinds of things behind the veil of an event horizon, even dragons there. But no one can say with any confidence that there isn't a singularity inside a black hole, simply on the grounds that it would be "unphysical." Our track record for telling our mathematics when it is doing something impossible is not very good, as it includes things like Einstein telling Bohr that God doesn't play dice, or Eddington telling Chandrasekhar that white dwarfs cannot undergo unstable gravitational collapse.

On the other hand, I grant you that no one could ever do an observation and say, "see, there really is a singularity there," but they could say, "there is no better way to treat this result than as a singularity." We have things like photons that are moving in frames that no observer is allowed to enter, and some might say "that means photons can't really have zero rest mass and can't really move at the speed of light", but that isn't actually what we say. We seem rather arbitrary about what types of singularities we will tolerate, and what types we will regard as unphysical, but our best theories still do include singularities, whether we disbelieve them or not.

 

[nikkkom]

Actually, BH singularity is somewhat problematic. Mathematically, it represents a boundary on the space-time manifold: for objects inside horizon, any possible future worldline ends on the singularity. The problem is that it really ENDS there, it does not continue (it does not have any valid continuation after it hits singularity). The time coordinate just stops there.

Imagine that someone tells you that today, after 23:59:59, tomorrow will not arrive. Time will just... end. 23:59:59 second will be the last second of time, ever.
Sounds ridiculous, right?

 

[Ken G]

I don't see anything necessarily ridiculous about that, I only see people who are used to thinking in one particular way. And isn't that exactly what people say about the origin of the universe in the Big Bang model? Certainly there are those who attempt to "continue" existence before the origin, but most people accept that the most striking feature of the Big Bang model is that it implies a time origin, before which time might not make sense. So how is that any more problematic running forward than backward? The point is, we are students of reality, and all our understanding of it comes from models that seem to work. But as soon as we say one model "could not be," all it means is that we are already married to a different model. And the track record of that style of thinking, in science, is pretty spotty!

 

[nikkkom]

I don't see anything necessarily ridiculous about that, I only see people who are used to thinking in one particular way. And isn't that exactly what people say about the origin of the universe in the Big Bang model? Certainly there are those who attempt to "continue" existence before the origin, but most people accept that the most striking feature of the Big Bang model is that it implies a time origin, before which time might not make sense. So how is that any more problematic running forward than backward?

It is equally problematic, and there is no reason to think that such approximation backwards is valid. Standard Model's math certainly breaks down at _finite_ density and thus loses its validity at this point. We don't have reliable predictions before this moment.

 

[Ken G]

The issue is not if there is a reason to think it is valid, it is if there is a reason to think it is not valid. Falsification is the beating heart of science. The evidence in favor of a model is all a model ever has going for it, we never get evidence that the model is correct. All we do is, use a model until found to be contradicted by observation, and that's just as true for atoms as it is for black hole singularities.

 

[nikkkom]

The issue is not if there is a reason to think it is valid, it is if there is a reason to think it is not valid.

Hey, check this out. I did a little experiment:
When I run "dd bs=1024 count=9 </dev/urandom >FILE", this creates FILE 9 kbytes long.
When I run "dd bs=1024 count=99 </dev/urandom >FILE", this creates FILE 99 kbytes long.
When I run "dd bs=1024 count=9999 </dev/urandom >FILE", this creates FILE 9999 kbytes long.

It's obvious!
Clearly, if I'd run
"dd bs=1024 count=99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 </dev/urandom >FILE",
this will surely create FILE 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 kbytes long.

What can possibly go wrong? Why should I think there might be some "new" things at play if I'd go this far?

 

[Ken G]

I can't tell if you are trying to be ironic, or if you are being serious. Of course a computer can hit a limit and be unable to function beyond that. That's my point-- the same could happen to the universe, and if the math of our best theory predicts that will happen (hypothetically), then we would have no logical basis to claim no it won't! That was Einstein's error, that was Eddington's error.