# The Universe - infinite or not ?

by drag
Tags: infinite, universe
Mentor
P: 5,893
 Quote by Cosmo Novice What is a cosmological event horizon?
Consider the following two disjoint subsets of spacetime:

1) those events that we have seen, or that we will see;

2) those events that we will never see.

The cosmological event horizon is the boundary between these two subsets of spacetime.
 Quote by Cosmo Novice What I meant was that our OU will eventually (billions of years) consist of less galaxies as once a distant galaxy receeds>C and all light emiited prior to a recession>C reaches us then we will no longer see said galaxy.
As I said above this isn't true. It is true that recession speeds of galaxies that we now see will eventually exceed c, but it is not true that we loose sight of a galaxy once its recession speed exceeds c. If we see a galaxy now, then we will (in principle) always see the galaxy, even when its recession speed exceeds c. It might seem that moving to a recession speed of c represents a transition from subset 1) to subset 2), but this isn't the case.

Suppose we now see galaxy A. Assume that at time t in the future, A's recession speed is greater than c, and that at this time someone in galaxy A fires a laser pulse directly at us. Even though the pulse is fired directly at us, the proper distance between us and the pulse will initially increase. After a while, however, the pulse will "turn around", and the proper distance between us and the pulse will decrease, and the pulse will reach us, i.e., we still see galaxy A.
 P: 743 BB doesn't say if the universe is finite or infinite. The expansion of the universe is formulated as a scaling of distances, not an increase in the size of the universe. You can have a scaling of distances in a finite or infinite universe. That said, an infinite universe can't have positive curvature (and be homogeneous, isotropic). Maybe dark energy is the universe constraining itself to not become positively curved, pushing back against the pull of gravity.
P: 167
 Quote by George Jones Consider the following two disjoint subsets of spacetime: Suppose we now see galaxy A. Assume that at time t in the future, A's recession speed is greater than c, and that at this time someone in galaxy A fires a laser pulse directly at us. Even though the pulse is fired directly at us, the proper distance between us and the pulse will initially increase. After a while, however, the pulse will "turn around", and the proper distance between us and the pulse will decrease, and the pulse will reach us, i.e., we still see galaxy A.
Probably not correct. I argued with a few people in another forum whether photons have inertia or not. Eventually I realized it creates more problems, specially in experimental results with light, if we assume moving frames have no effect on photons.

Which means photons of galaxies receding with FTL speed may be traveling with the galaxies with FTL speed but photons speed inside the galaxy would remain the same c.

Btw, my logical mind says galaxies are not moving at FTL speed.
Mentor
P: 5,893
 Quote by Neandethal00 Probably not correct.
This result can be derived from the stuff in the thread

 Quote by Neandethal00 I argued with a few people in another forum whether photons have inertia or not. Eventually I realized it creates more problems, specially in experimental results with light, if we assume moving frames have no effect on photons. Which means photons of galaxies receding with FTL speed may be traveling with the galaxies with FTL speed but photons speed inside the galaxy would remain the same c. Btw, my logical mind says galaxies are not moving at FTL speed.
P: 366
 Quote by George Jones As I said above this isn't true. It is true that recession speeds of galaxies that we now see will eventually exceed c, but it is not true that we loose sight of a galaxy once its recession speed exceeds c. If we see a galaxy now, then we will (in principle) always see the galaxy, even when its recession speed exceeds c. It might seem that moving to a recession speed of c represents a transition from subset 1) to subset 2), but this isn't the case. Suppose we now see galaxy A. Assume that at time t in the future, A's recession speed is greater than c, and that at this time someone in galaxy A fires a laser pulse directly at us. Even though the pulse is fired directly at us, the proper distance between us and the pulse will initially increase. After a while, however, the pulse will "turn around", and the proper distance between us and the pulse will decrease, and the pulse will reach us, i.e., we still see galaxy A.
How will it "turn around" Can you please clarify this point.

I am in galaxy A looking at Galaxy B. At some point t in the future Galaxy B recession speed exceeds c. So surely at t the last photon ever released prior to galaxy B crossing the threshold into expansion>c is released. Once this photon gets to us would this not be the last photon we would ever see from Galaxy B?

In understand light will get redshifted, but assumed this requires expansion<c otherwise it would not be measurable.

If you can clarify this for me I would greatly appreciate this.
 P: 125 If something is finite it can be quantified. Einstein suggested that the universe was finite but had an infinite boundary. And if something is finite the question is, is it confined to or contained in a bigger state of finity (and so on ad infinitum), or is infinity its ultimate container?
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P: 5,893
I know this is very counter-intuitive, but I really did mean what I wrote in posts #52 and #55.
 Quote by Cosmo Novice 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.
 P: 10 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.
P: 366
 Quote by George Jones 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
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P: 5,893
 Quote by Cosmo Novice 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.
P: 366
 Quote by George Jones 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 recieve photons from galaxies further out than this cutoff point?
 P: 125 Aren't scales just another example of the strong anthropic principle?
 PF Patron Sci Advisor P: 8,880 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.
P: 125
 Quote by 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.
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?
 P: 2 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.
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P: 5,305
 Quote by Cosmo Novice 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 recieve photons from galaxies further out than this cutoff point?
If the universe is spatially infinite, then yes.

 Quote by Lost in Space 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.
P: 125
 Quote by bcrowell 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?
P: 125
 Quote by 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.
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'?

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