The Universe - infinite or not ?

[George Jones]

I know this is very counter-intuitive, but I really did mean what I wrote in posts #52 and #55.

How will it "turn around" Can you please clarify this point.

Thanks for pushing me for further explanation, as this has forced me to think more conceptually about what happens.

This can happen because the Hubble constant decreases with time (more on this near the end of this post) in the standard cosmological model for our universe. Consider the following diagram:

O                                B        A        C
*                                *        *        **                    *     *     *
O                    B     A     C

The bottom row of asterisks represents the positions in space (proper distances) of us (O) and galaxies B, A, and C, all at the same instant of cosmic time, $t_e$. The top row of asterisks represents the positions in space of us (O) and galaxies B, A, and C, all at some later instant of cosmic time, $t$. Notice that space has "expanded" between times $t_e$ and $t$.

Suppose that at time $t_e$: 1) galaxy A has recession speed (from us) greater than c; 2) galaxy A fires a laser pulse directed at us. Also suppose that at time $t$, galaxy B receives this laser pulse. In other words, the pulse was emitted from A in the bottom row and received by B in the top row. Because A's recession speed at time $t_e$ is greater than c, the pulse fired towards us has actually moved away from us between times $t_e$ and $t$.

Now, suppose that the distance from us to galaxy B at time $t$ is the same as the distance to galaxy C at time $t_e$. Even though the distances are the same, the recession speed of B at time $t$ is less than than the recession speed of C at time $t_e$ because:

1) recession speed equals the Hubble constant multiplied by distance;

2) the value of the Hubble constant decreases between times $t_e$ and $t$.

Since A's recession speed at time $t_e$ is greater than c, and galaxy C is farther than A, galaxy C's recession speed at time $t_e$ also is greater than c. If, however, the Hubble constant decreases enough between times $t_e$ and $t$, then B's recession speed at time $t$ can be less than c. If this is the case, then at time $t$ (and spatial position B), the pulse is moving towards us, i.e., the pulse "turned around" at some time between times $t_e$ and $t$.

If the value of the Hubble constant changes with time, what does the "constant" part of "Hubble constant" mean? It means constant in space. At time $t_e$, galaxies O, B, A, and C all perceive the same value for the Hubble constant. At time $t$, galaxies O, B, A, and C all perceive the same value for the Hubble constant. But these two values are different.

Probably some of my explanation is unclear. If so, please ask more questions.

 

[Astralos]

The universe is mathematically approaching the concept of infinity, but is, and will never be, itself infinite. Nothing quantitative in the known universe can be infinite.

 

[Cosmo Novice]

I know this is very counter-intuitive, but I really did mean what I wrote in posts #52 and #55.


Thanks for pushing me for further explanation, as this has forced me to think more conceptually about what happens.

This can happen because the Hubble constant decreases with time (more on this near the end of this post) in the standard cosmological model for our universe. Consider the following diagram:

O                                B        A        C
*                                *        *        *


*                    *     *     *
O                    B     A     C

The bottom row of asterisks represents the positions in space (proper distances) of us (O) and galaxies B, A, and C, all at the same instant of cosmic time, $t_e$. The top row of asterisks represents the positions in space of us (O) and galaxies B, A, and C, all at some later instant of cosmic time, $t$. Notice that space has "expanded" between times $t_e$ and $t$.

Suppose that at time $t_e$: 1) galaxy A has recession speed (from us) greater than c; 2) galaxy A fires a laser pulse directed at us. Also suppose that at time $t$, galaxy B receives this laser pulse. In other words, the pulse was emitted from A in the bottom row and received by B in the top row. Because B's recession speed at time $t_e$ is greater than c, the pulse fired towards us has actually moved away from us between times $t_e$ and $t$.

Now, suppose that the distance from us to galaxy B at time $t$ is the same as the distance to galaxy C at time $t_e$. Even though the distances are the same, the recession speed of B at time $t$ is less than than the recession speed of C at time $t_e$ because:

1) recession speed equals the Hubble constant multiplied by distance;

2) the value of the Hubble constant decreases between times $t_e$ and $t$.

Since B's recession speed at time $t_e$ is greater than c, galaxy C's recession speed at time $t_e$ also is greater than c. If, however, the Hubble constant decreases enough between times $t_e$ and $t$, then B's recession speed at time $t$ can be less than c. If this is the case, then at time $t$ (and spatial position B), the pulse is moving towards us, i.e., the pulse "turned around" at some time between times $t_e$ and $t$.

If the value of the Hubble constant changes with time, what does the "constant" part of "Hubble constant" mean? It means constant in space. At time $t_e$, galaxies O, B, A, and C all perceive the same value for the Hubble constant. At time $t$, galaxies O, B, A, and C all perceive the same value for the Hubble constant. But these two values are different.

Probably some of my explanation is unclear. If so, please ask more questions.

Thankyou for taking the time to explain. This does make complete sense except one thing:

This assumes that for galaxies whose recession>c for their photons to reach us then there must be a decrease in the Hubble constant. I thought the Hubble constant was the rate of acceleration of expansion and as such would always increase? I understand the constant referes to spatially constant (any given point in space will be the same constant as any other place at the same time) but am unclear whether this is increasing/decreasing.

I am a complete novice so appreciate the simpligied explanation you gave.

Thanks

 

[George Jones]

This assumes that for galaxies whose recession>c for their photons to reach us then there must be a decrease in the Hubble constant. I thought the Hubble constant was the rate of acceleration of expansion and as such would always increase? I understand the constant referes to spatially constant (any given point in space will be the same constant as any other place at the same time) but am unclear whether this is increasing/decreasing.

The definition of the Hubble constant $H$ is
$$H = \frac{\mbox{rate at which scale increases}}{\mbox{scale of the universe}}.$$
The universe expands with time, so the scale of the universe increases with time. Accelerated expansion means that the rate at which the scale increases itself increases, i.e., the rate tomorrow at which the scale increases is greater than rate today at which the scale increases. If, over a given period of time, the increase in the scale of the universe is proportionately greater than the increase in the rate at which the scale increases, then the Hubble constant decreases with time (since the denominator increases faster than the numerator. Observations indicate that this true now, and that this will remain true in the future.

I might later post a specific example.

 

[Cosmo Novice]

The definition of the Hubble constant $H$ is
$$H = \frac{\mbox{rate at which scale increases}}{\mbox{scale of the universe}}.$$
The universe expands with time, so the scale of the universe increases with time. Accelerated expansion means that the rate at which the scale increases itself increases, i.e., the rate tomorrow at which the scale increases is greater than rate today at which the scale increases. If, over a given period of time, the increase in the scale of the universe is proportionately greater than the increase in the rate at which the scale increases, then the Hubble constant decreases with time (since the denominator increases faster than the numerator. Observations indicate that this true now, and that this will remain true in the future.

I might later post a specific example.

Thankyou for the explanation. Although I still find this very counter-intuitive, although I can see the logic behind galaxies whose recession>c photons still reaching us. I do not think I require a specfic example in this case but thankyou.

Ok so while I know see the logic in galaxies with recession>c light reaching us - giving certain circusmtance. Am I safe in assuming that beyond the OU current cosmological models indicate galaxies so far away and receeding so much >c that their light will never reach us?

I guess the core question I am posing is: Beyond our OU, is there a cutoff point, in terms off recession speeds>c where we will no longer receive photons from galaxies further out than this cutoff point?

 

[Lost in Space]

Aren't scales just another example of the strong anthropic principle?

 

[Chronos]

Only to the extent necessary for the universe to be sufficiently large and ancient to permit our existence at this point in its history. Our efforts to measure scale factors is motivated by curiosity about the origins and destiny of the universe, not anthropic principles.

 

[Lost in Space]

Only to the extent necessary for the universe to be sufficiently large and ancient to permit our existence at this point in its history. Our efforts to measure scale factors is motivated by curiosity about the origins and destiny of the universe, not anthropic principles.

But if the laws of physics break down at the boundaries, aren't these scale factors merely reduced to a human perspective and, given that, are they any closer to describing reality or are they merely a reflection on what we consider important in relation to ourselves?

 

[Fortnum]

Since the Big Bang took place a finite time ago, the Universe would have had to expand at an infinite rate to reach an infinite size. Unless it was already infinite at the time of the Big Bang.

 

[bcrowell]

I guess the core question I am posing is: Beyond our OU, is there a cutoff point, in terms off recession speeds>c where we will no longer receive photons from galaxies further out than this cutoff point?

If the universe is spatially infinite, then yes.

But if the laws of physics break down at the boundaries, aren't these scale factors merely reduced to a human perspective and, given that, are they any closer to describing reality or are they merely a reflection on what we consider important in relation to ourselves?

The universe doesn't have a boundary. The observable universe has a boundary. The laws of physics don't break down at the boundary of the observable universe. The boundary of the observable universe is not a place with special physical properties. It's simply the set of all points from which light has just barely had time to reach our own planet since the Big Bang. Tomorrow, that boundary will be about 3 light-days farther from us than it is today, so a certain volume of space will have become newly available to us for observation.

BTW, we have a new entry on this topic in the cosmology forum's sticky FAQ thread.

 

[Lost in Space]

If the universe is spatially infinite, then yes.


The universe doesn't have a boundary. The observable universe has a boundary. The laws of physics don't break down at the boundary of the observable universe. The boundary of the observable universe is not a place with special physical properties. It's simply the set of all points from which light has just barely had time to reach our own planet since the Big Bang. Tomorrow, that boundary will be about 3 light-days farther from us than it is today, so a certain volume of space will have become newly available to us for observation.

BTW, we have a new entry on this topic in the cosmology forum's sticky FAQ thread.

Pardon my confusion, but I've been given to understand that the Big Bang is a boundary where the laws of physics break down? What about event horizons of black holes? And isn't the present an ever moving and growing boundary as well as we cannot view future events, only events in the past?

 

[Lost in Space]

Since the Big Bang took place a finite time ago, the Universe would have had to expand at an infinite rate to reach an infinite size. Unless it was already infinite at the time of the Big Bang.

Is it finite, or is it just us measuring a portion of time relative to our own existence? Can time be divided into infinite pieces? In other words is there a state in which the 'finite' time we perceive since the Big Bang can be said to be 'infinite'?

 

[Cosmo Novice]

If the universe is spatially infinite, then yes.

Ok. Can you please clarify.

I would suggest that even if U was spatially finite then it would probably be large enough for their to be photon emitting objects so far away that the expansion and scale factor of the intervening space would result in the photon never reaching us.

 

[Shenstar]

I find an infinite universe impossible to comprehend.

 

[thekushal276]

I can't agree with you more, Mentat. I would say, maybe, that the universe is on the verge of infinity?[?]

i don't think that universe is infinite. logic behind this is: as we know that infinite is not a real number. that means infinite is not reality. it is our imagination. the thing which cannot be counted we refer it as INFINITE. something imaginary, not real or uncountable. but that do not means that the universe is infinite. the thing is that we are not able enough to explore it and define the size of it...

 

[bcrowell]

I would suggest that even if U was spatially finite then it would probably be large enough for their to be photon emitting objects so far away that the expansion and scale factor of the intervening space would result in the photon never reaching us.

I didn't quite get that right. For a closed universe with zero cosmological constant, you get a recollapse, so nothing is ever permanently hidden from any observer. But we know that the cosmological constant isn't zero, and recollapse is ruled out.

Pardon my confusion, but I've been given to understand that the Big Bang is a boundary where the laws of physics break down? What about event horizons of black holes? And isn't the present an ever moving and growing boundary as well as we cannot view future events, only events in the past?

These are all different cases. The Big Bang is a physical singularity (not just a coordinate singularity). The event horizons of black holes are not physical singularities. The boundary between past and present isn't a uniquely defined thing in relativity. I thought you were talking about the boundary of the observable universe, which is still another thing.

 

[bcrowell]

i don't think that universe is infinite. logic behind this is: as we know that infinite is not a real number. that means infinite is not reality. it is our imagination. the thing which cannot be counted we refer it as INFINITE. something imaginary, not real or uncountable. but that do not means that the universe is infinite. the thing is that we are not able enough to explore it and define the size of it...

Please read the FAQ entry "Is the universe finite, or is it infinite?" in the thread titled "Frequently Asked Questions (FAQ) about Cosmology" at the top of the cosmology forum.

 

[Lost in Space]

These are all different cases. The Big Bang is a physical singularity (not just a coordinate singularity). The event horizons of black holes are not physical singularities. The boundary between past and present isn't a uniquely defined thing in relativity. I thought you were talking about the boundary of the observable universe, which is still another thing.

But aren't black holes physical singularities bounded by event horizons? And they're part of the observable universe are they not?

 

[bcrowell]

But aren't black holes physical singularities bounded by event horizons? And they're part of the observable universe are they not?

The physical (non-coordinate) singularity is at the black hole's center, not at its event horizon.

 

[Lost in Space]

The physical (non-coordinate) singularity is at the black hole's center, not at its event horizon.

Yes, I understand this much but surely the boundary of the black hole is its event horizon which separates us from it? Although we cannot observe the singularity at the black hole's centre, we are still aware that it's there, so isn't the event horizon in this case a boundary within the observable universe?

 

[narrator]

I find an infinite universe impossible to comprehend.

I find it difficult but not impossible. We live our lives by many paradigms and when confronted with one that's different we think "contradiction" or even "contravention".

 

[bcrowell]

Yes, I understand this much but surely the boundary of the black hole is its event horizon which separates us from it? Although we cannot observe the singularity at the black hole's centre, we are still aware that it's there, so isn't the event horizon in this case a boundary within the observable universe?

The boundary between the US and Canada is also a boundary within the observable universe. In your earlier post, you refer to "a boundary where the laws of physics break down:"

Pardon my confusion, but I've been given to understand that the Big Bang is a boundary where the laws of physics break down? What about event horizons of black holes? And isn't the present an ever moving and growing boundary as well as we cannot view future events, only events in the past?

When people refer to the laws of physics breaking down in GR, they usually mean singularities. You've been lumping together a lot of different things.

 

[DavidMcC]

I find it difficult but not impossible. We live our lives by many paradigms and when confronted with one that's different we think "contradiction" or even "contravention".

That doesn't make an infinite big bang a physical possibility, though. The only way the universe could be infinite is if it never had a beginning, ie that its beginning was an infinite time ago. Not plausible.

 

[Cosmo Novice]

That doesn't make an infinite big bang a physical possibility, though. The only way the universe could be infinite is if it never had a beginning, ie that its beginning was an infinite time ago. Not plausible.

I don't think this is necessarily true, as I understand it something does not require infinite age to be spatially infinite. If the U is infinite now, then essentially it was infinite at the moment of the BB, so you could say if the U is open and spatially flat it is temporally finite but spatially infinite.

 

[DavidMcC]

I don't think this is necessarily true, as I understand it something does not require infinite age to be spatially infinite. If the U is infinite now, then essentially it was infinite at the moment of the BB, so you could say if the U is open and spatially flat it is temporally finite but spatially infinite.

You may have to re-invent physics for that, Cosmo!

 

[narrator]

You may have to re-invent physics for that, Cosmo!

That depends on your understanding of physics. Even of those of us who understand everyday physics, very few understand the physics of black holes (for example).

As a simplistic example, under the right conditions, a fog appears everywhere with no starting point. Sure, the analogy breaks down if you get into the nitty gritty, but to me, it's a very rough analog of how the universe formed - one difference being that the "right conditions" were not localized.

The other aspect of this is that these theories have come from actual "science", not from untested fantasy.

 

[DavidMcC]

I see a fog descending on this thread, narrator!

 

[Neandethal00]

I don't think this is necessarily true, as I understand it something does not require infinite age to be spatially infinite. If the U is infinite now, then essentially it was infinite at the moment of the BB, so you could say if the U is open and spatially flat it is temporally finite but spatially infinite.

I have a growing feeling some of you are mixing up observable universe (OU) and container of the OU. OU is the region which holds galaxies , us. There may even be objects in our OU which are beyond our observation limits at this time. If the U is really expanding, it is expanding into another region, which I call container. We have absolutely ZERO knowledge about this container, which may or may not be infinite, we can only speculate about this container, our speculation would probably be light years away from 'reality'. But OU can not be infinite to humans.

My personal opinion is our 'sensory systems' are playing a big tricks on us.

 

[bcrowell]

I don't think this is necessarily true, as I understand it something does not require infinite age to be spatially infinite. If the U is infinite now, then essentially it was infinite at the moment of the BB, so you could say if the U is open and spatially flat it is temporally finite but spatially infinite.

You may have to re-invent physics for that, Cosmo!

Cosmo Novice is correct. Standard spatially flat models of the universe are spatially infinite but have only existed for a finite time.

If the U is really expanding, it is expanding into another region

This is incorrect. Here is a good explanation: http://www.astro.ucla.edu/~wright/cosmology_faq.html#XIN

 

[Ken G]

My own feeling is we immediately err whenever we choose to use language like "the universe is...", regardless of how we finish the sentence. It simply isn't scientific. Instead, we must ask "we gain the following benefits by modeling the universe as A, and these other benefits by modeling it as B." This language stresses two important things about science:
1) our "knowledge" is constantly changing, and
2) we have a purpose for favoring the models we favor.
So in terms of the size of the universe, we would say that we observe no spatial curvature so the model with the fewest added assumptions is one that is spatially infinite. This in no way means that the universe is infinite, nor does it make any difference if we are incredulous about it being infinite (the history of science is wall-to-wall suspension of incredulity), it just means an infinite model keeps us from having to say anything else about our model that would be completely arbitrary. It's not even a question that the universe "either is or isn't infinite", because terms like "infinite" apply to models, not to the universe itself. If we can't measure a size, even in principle, then the universe doesn't have one, neither finite nor infinite-- it is the models that are one or the other. The sole scientific statement we can make is that we have never been able to detect any curvature that would suggest a size to the universe, the rest is just model-favoring.