Are the Big bang theory and the infinity of the universe mutually exclusive ?

[BonkingBal]

I've just got into astronomy with the purchase of my first telescope, and it has got me thinking about the universe etc., and my thought patterns have taken me through the following steps:

Assuming that the Big Bang theory is correct, the universe started expanding 13.8 Billion years ago.

All the particles of the universe are flying apart, but nothing can travel faster than the speed of light.

The most distance any particle can have travelled since the big bang is <13.8 Billion light years.

The furthest apart any 2 objects can be in the universe (assuming they travelled in opposite directions since the Big bang) is 27.6 Billion light years - a huge distance, but not infinity !

How can the universe therefore be considered to be infinite ?

I am guessing that a very much non-astrophysicist such as myself is missing some key points/element here, but if anyone can explain either the flaw in my logic, or what I have missed, I'd be interested to hear. It's not keeping me awake at night, but I am intrigued as to whether I have any sort of point here !

[michael.h.f.wilkinson]

One theoretical possibility is that the singularity that exploded was itself infinitely large in size (either that or it was infinitely small). An infinite object can expand. Another issue which allow the universe to exceed the size you describe is inflation. This would not make space inifinite in size. The size of 13.8 billion light years is the radius of our event horizon: the furthest we can see.

[red dwalf]

i`d like to know what we are expanding into.

[jnb]

Assuming that the Big Bang theory is correct, the universe started expanding 13.8 Billion years ago.

All the particles of the universe are flying apart, but nothing can travel faster than the speed of light.

The most distance any particle can have travelled since the big bang is <13.8 Billion light years.

The furthest apart any 2 objects can be in the universe (assuming they travelled in opposite directions since the Big bang) is 27.6 Billion light years - a huge distance, but not infinity !

How can the universe therefore be considered to be infinite ?

While nothing can travel through space faster than light, there is no limit to how fast space can move. By analogy consider a person running, they can do no more than perhaps 30km/h. Now consider them running inside a train. The train can travel at 200 km/h but the runner can still only move at a maximum of 30km/h. In that analogy there could be other trains moving away from us at more than 30km/h but we would never know because no message could get from them to us.

[jnb]

A closer analogy ...

Imagine one of those moving walkways, the sort you get in airports, and imagine someone running along it. That person can run at a maximum of perhaps 10m/s, that maximum speed has nothing to do with the speed of the walkway it is the maximum speed of the runner compared to the walkway. So that a runner 100m away could reach us in 10s, 200m away in 20s and so on.

Now imagine that if instead of the walkway moving it is stretching so that in 1 second a section that is 100m long grows to 101m. Now our runner will still reach us but it will take slightly longer because as the walkway stretches he has further to travel. As he starts from 100m he is moving away from us at 1m/s, if he started from 200m he would be moving away from us at 2m/s and so on. If he started from 800m away he would be moving away from us at 8m/s and take a lot longer. If he started from 1200m away he would be moving away from us at 12m/s but his maximum speed is 10m/s, he will never reach us. In that analogy 1000m is the local horizon, any runner on the walkway will only ever be able to reach things that are within 1000m of them when they start but the walkway itself could be much bigger.

By the same token as the big bang occured 13.8bn light years ago the we can only see objects that are within 13.8bn ly of us. That is our observable horizon but the universe could be much bigger.

[acey]

Start with infinite universe and make everything move closer to everything else, heating up as pressure increases, until everything meets and the whole lot disappears. Run that idea in reverse and you've got an infinite universe starting from a singularity. Where was the singularity? Everywhere (or nowhere). Why did it happen? No one knows (there are various ideas). What's everything expanding into? Nothing - if the universe is infinite there's no room left. It's just that all the large-scale bits (galaxy clusters) are moving ever further apart. Because the universe is of finite age, and the speed of light is finite, we can only see a finite part of it. So the observable universe is finite, but the whole universe is certainly bigger, and probably infinite.

Note that the distance to the edge of observable universe is not the age of the universe in light years, i.e. not 13.8 billion light years. It's more, because of cosmic expansion. Currently estimated to be 46-47 billion light years.

http://en.wikipedia.org/wiki/Observable_universe

[jnb]

Note that the distance to the edge of observable universe is not the age of the universe in light years, i.e. not 13.8 billion light years. It's more, because of cosmic expansion. Currently estimated to be 46-47 billion light years.

True but that's a detail I usually omit when describing this to people. The concept can be conveyed without going into that detail.

[ollypenrice]

Maybe we should distinguish betwwen 'infinite' and 'unbounded.' The surface of a shpere is not infinite in area because the sphere can expand. However, no point on the sphere is any different from any other point. The sphere's surface does not begin anywhere, nor does it end anywhere. It might be better to describe this as unbounded rather than infinite.

As a linguist rather than a mathematician I find the term 'infinite' to be a nightmare.

The universe bofore it expanded could be infinite just as an infinite number of matchboxes can each contain a hudnred matches.

I really don't like the word infinite!

Olly

[Cath]

The problem I guess is not the universe, the big band, the singularity, inifinity, time, space, et all, the problem has got to be with us and in how we're trying to explain to ourselves the universe et all in such a way that tries to fit into our extremely limited and biased and all to assuming and naive comprehensionability.

Wud not one fink ?

[ollypenrice]

The problem I guess is not the universe, the big band, the singularity, inifinity, time, space, et all, the problem has got to be with us and in how we're trying to explain to ourselves the universe et all in such a way that tries to fit into our extremely limited and biased and all to assuming and naive comprehensionability.

Wud not one fink ?

Yes, I agree. Our ability to conceptualize evolved in our local environment so its tools are not adequate for an extremely non-local thing like the universe. But we have to try simply because, like Everest, it is there.*

Olly

* Well, we think it is....

[Cath]

But we have to try simply because, like Everest, it is there.

Most definitely.

A problem we have though, is that it's most likely a case of, our minds fitting into the universe, rather than the universe fitting into our minds.

Are we going to be able to fit the peas pod into the pea ?

[BonkingBal]

Very enlightening comments/replies folks - I'm not sure I fully follow all of it, but I think I get the gist (the expansion piece that I was missing, the conceptualisation of infinity (sorry, Ollypenrice, unbounded) within our known frames of reference etc). Glad to see that it sparked some comments and debate, rather than folks just shrugging and saying 'cos it is !'. 

[Piero]

I think that when people say the universe is infinite, they actually mean that 'it can expand infinitely'. 

One thing is the matter that we can detect, which seems finite, although this might be considered finite just because we do not know where exactly comes from...

Another thing is the 'space' containing the matter that we can detect, which seems to be infinite. I believe that beyond the 'borders' of our detectable matter, the emptiness can be infinite in all the direction, as well as you have emptiness between atoms somehow.

Whether this 'emptiness' or 'vacuum' is actually made of something else (dark matter?), who knows! 

Whether beyond our matter horizon, there is other matter, but the space has a certain shape preventing us to detect this other matter, who knows! 

To be fair, I love the concept of infinite (sorry Olly!  ), it makes me feel dizzy! As we have finite, I don't see why infinite cannot exist too. 

[Piero]

Very enlightening comments/replies folks - I'm not sure I fully follow all of it, but I think I get the gist (the expansion piece that I was missing, the conceptualisation of infinity (sorry, Ollypenrice, unbounded) within our known frames of reference etc). Glad to see that it sparked some comments and debate, rather than folks just shrugging and saying 'cos it is !'. 

You are welcome!

We like debating and comment! I think it is one of the major strength of this community! You started an interesting question btw! Let's see where it takes us now!   

[Cath]

Whether it's inifinite or otherwise brings in problems for our realm of thought.

I suspect the bottom line is, we don't have the foggiest idea about what either might be/mean, and if we do convince ourselves using our own arguments about which it has to be, can we be sure it isn't just a case of 'convincing' ourselves ?

[Piero]

I agree with you, we don't have any idea about it. 

I do not think there is anything wrong with stating an hypothesis though, as long as it is clearly stated that this is an hypothesis (and all the following ideas from this are based on an hypothesis). 

Unfortunately, this is not often the case, and arrogance of stating what is or what is not prevails quite often in science I have to say.. 

[Avo]

When does a finite distance become infinity ?

[michael.h.f.wilkinson]

When does a finite distance become infinity ?

By adding infinity

Maybe we should distinguish betwwen 'infinite' and 'unbounded.' The surface of a shpere is not infinite in area because the sphere can expand. However, no point on the sphere is any different from any other point. The sphere's surface does not begin anywhere, nor does it end anywhere. It might be better to describe this as unbounded rather than infinite.

As a linguist rather than a mathematician I find the term 'infinite' to be a nightmare.

The universe bofore it expanded could be infinite just as an infinite number of matchboxes can each contain a hudnred matches.

I really don't like the word infinite!

Olly

Being of quite a mathematical turn of mind, I find infinite interesting. Especially when you wonder if one infinity is more than another (it is , there are infinitely many, starting at ℵ₀)

Try looking up Hilbert's Hotel

[michael.h.f.wilkinson]

I think that when people say the universe is infinite, they actually mean that 'it can expand infinitely'. 

One thing is the matter that we can detect, which seems finite, although this might be considered finite just because we do not know where exactly comes from...

Another thing is the 'space' containing the matter that we can detect, which seems to be infinite. I believe that beyond the 'borders' of our detectable matter, the emptiness can be infinite in all the direction, as well as you have emptiness between atoms somehow.

Whether this 'emptiness' or 'vacuum' is actually made of something else (dark matter?), who knows! 

Whether beyond our matter horizon, there is other matter, but the space has a certain shape preventing us to detect this other matter, who knows! 

To be fair, I love the concept of infinite (sorry Olly!  ), it makes me feel dizzy! As we have finite, I don't see why infinite cannot exist too. 

Not sure about this one. Cosmologists actually do consider whether the universe can be infinite in the strict mathematical sense

[ollypenrice]

When does a finite distance become infinity ?

When you take one end and bend it round till it meets the other...

Oh no, that's unbounded again!

lly

[michael.h.f.wilkinson]

When you take one end and bend it round till it meets the other...

Oh no, that's unbounded again!

lly

An infinite set can be bounded

[Piero]

Not sure about this one. Cosmologists actually do consider whether the universe can be infinite in the strict mathematical sense

in the sense of infinite matter? 

or in the sense of universe of universes, in which ours is just one of the many?

can you explain a bit more, please? 

[michael.h.f.wilkinson]

in the sense of infinite matter? 

or in the sense of universe of universes, in which ours is just one of the many?

can you explain a bit more, please? 

In some models a single universe could have infinite matter (the inifinite singularity of infinite density is at least mathematically consistsent (either that or you have a finite amount of matter in a singularity of size zero). You could even have infinitely many of them.

[ollypenrice]

I can highly recommend John Barrow's The Book Of Nothing. It does deal with everything because nothing and everything very soon get into bed together in cosmology!

It's both erudite and entertaining. And just imagine how interesting John Barrow would be if he wrote abnout something!

Olly

[Piero]

In some models a single universe could have infinite matter (the inifinite singularity of infinite density is at least mathematically consistsent (either that or you have a finite amount of matter in a singularity of size zero). You could even have infinitely many of them.

Thanks! I wonder how this is likely though!