Big bang and infinite space

[PurpleBuddha]

If true, that is the type of answer I am looking for. The 55 light year radius 200 seconds post birth, is also more or less the entire universe we can see now, correct? I had thought of it as the entire universe and that the parts now unobservable were simply the horizons that, while once visible, had slid past view. But I see what you are saying and it sounds to me like the right idea, assuming the universe is infinite.

If this is the correct idea, I now also see what Chrisspongob was saying on page one. The moment after the big bang the universe was infinite, and now space is simply stretching within that infinite size. Thinking about that too long might drive me crazy.

 

[chrisspringob]

If true, that is the type of answer I am looking for. The 55 light year radius 200 seconds post birth, is also more or less the entire universe we can see now, correct? I had thought of it as the entire universe and that the parts now unobservable were simply the horizons that, while once visible, had slid past view. But I see what you are saying and it sounds to me like the right idea, assuming the universe is infinite.

That's right. Unfortunately, many articles use the word "universe" when they really mean "observable universe". So yes, the 55 ly radius is just the size that the *current observable universe was back then*. The entire universe (meaning, not just the currently observable part, but everything), may well have been infinite, and would still be infinite.

There's a term that cosmologists use called the "scale factor" (denoted by the letter a), which is a measure of the distance between objects at any given time. It's normalized such that, at the present time, a=1.

Consider, at the present time, a galaxy that's 10 billion light years away. Back when the scale factor was 0.5 (several billion years ago), that galaxy was 5 billion light years away. When the scale factor reaches 2 (billions of years from now) it'll be 20 billion light years away. Likewise, a galaxy that's now 2 billion light years away was just 1 billion light years away when the scale factor was 0.5, etc.

[This is ignoring motions of the galaxies themselves relative to the underlying spacetime, which actually aren't all that significant when you're talking about scales that are that big.]

Now, if the universe is infinite, then there are actually galaxies at any arbitrary distance you can imagine, well beyond the limits of the *observable* universe. Let's say you have a galaxy at 100 bajillion (define bajillion however you like ) light years away. When the scale factor was 0.5, it was only 50 bajillion light years away, and so on.

The key here is that you have to envision spacetime as being a giant grid that extends to infinity in every direction. The distances between any two points on the grid are given by some comoving distance between them times the scale factor. The comoving distance never changes, just the scale factor. At the instant of the Big Bang, the scale factor was equal to zero, so if you like, that was the one time when the universe wasn't infinite. The Hubble constant is simply the present day growth rate of the scale factor:

http://en.wikipedia.org/wiki/Scale_factor_(Universe)

Most people don't really get this. The common misconception is that the Big Bang represents some kind of explosion, where the matter is bursting out from a center point into an empty void.

But no, there is no "center" to the universe in which an explosion took place, and there is no "empty" part of the universe that matter is moving into. It's just a big (more or less) homogeneous distribution of matter that's getting less and less dense over time as the spacetime that the matter occupies keeps getting more and more stretched out.

Here is an excellent explanation of this by my fellow former Cornell astro grad student Dave Rothstein:

http://curious.astro.cornell.edu/question.php?number=274

 

[Jadzia]

And somehow, nothingness has to mutate into what we have today. The crucial step... and perhaps the most mind bending concept in philosophy, is that nothingness must spontaneously change into something other than nothingness.

This is the part that makes my brain hurt.

Even if we introduce theology and say that god made it, then we have to ask the question of where god came from, and why it exists instead of something else. So that approach doesn't even give us an explanation.

I have been seeing more and more physicists rejecting the idea that before the big bang there was nothing, and then nothing turned into something. I find myself agreeing with them.

IIRC, there was a theory of Branes -- higher dimensional manifolds that our universe is embedded within.

Within that theory, a big bang was theorised to be a collision+recoil between two branes, that created a expanding shockwave of energy, that we perceive as our expanding spacetime manifold.

Our universe expanding into nothingness is then likened to a water ripple in a pond dispersing to nothingness after a rock is thrown into it.

at 200 seconds after birth, the radius of the universe was 55 light years. At 500,000 years after birth, when the universe was still a wee little baby, it was 1,500,000 light years.

Could the mass of the early universe have an effect on its apparent growth?

We all know how mass creates relativistic effects, such as time slowing down, and length contraction. Could this 55ly of growth in 200 seconds be because of that?

 

[Lindley]

Nice.

Come to think of it, that is a cool illustration of how space and time are connected.

Just goes to prove the old saying: The shortest distance between two points may involve time travel.

 

[STR]

Even if we introduce theology and say that god made it, then we have to ask the question of where god came from, and why it exists instead of something else. So that approach doesn't even give us an explanation.

Only because the human mind must force causality on everything. Causality is a function of time, time is a function of our 4D universe. To ask what was "before the universe" is to ask a meaningless question. The closest analogy I can think of is asking "how big is infinity?".

If there is an answer, you can only realize it in a frame of reference we do not exist in, assuming whatever higher/lower plane we're talking about here even has a frame of reference. Once you "leave the universe" the laws of physics might not be enforced.

And somehow, nothingness has to mutate into what we have today. The crucial step... and perhaps the most mind bending concept in philosophy, is that nothingness must spontaneously change into something other than nothingness.

This is the part that makes my brain hurt.

Put simply, the fact that you exist means that nothingness is not inevitable.

Best analogy is it's like playing the lotterly. Buy a ticket each week, and if you live long enough (statistically, were talking hundreds or thousands of years) you're going to win it once. This is, admittedly, a really bad analogy, but since English currently lacks the ability to articulate the kind of concepts we're dealing with here, it will get you closest to the right track.

 

[Jadzia]

Only because the human mind must force causality on everything. Causality is a function of time, time is a function of our 4D universe.

I'm not sure. Time allows for relationships between particles to change with some degree of continuity, but that doesn't necessarily make causality implicit with time.

In the same way that an implication is a thing of logic, not of time, even though it can be correlated with time when logic is applied to a continuously changing system. The question is truely probing a logical relationship, not a temporal one.

Asking why something is the way it is, is always a valid question.

 

[bryce]

Space can be "Closed" and yet infinite!!

Imagine if the universe was the size of a broom closet and you were in it, you could reach forward and touch your own back! And you would be standing on your own head!

I am thinking the universe is closed yet infinte!

Actually, I think that is called "finite but unbounded"...if I am not mistaken...

Travel in a seemingly straight line in 3D space you'd actually be traveling in a curve in 4 dimensions called a geodesic - because space is curved in this invisible 4th dimension.

You could sail around the universe in a "straight line" - and come back where you started.

Much like the surface of the Earth that way...it seems flat to us (on the surface) but travel around it and you see it's actually curved in a bigger space.

 

[STR]

Only because the human mind must force causality on everything. Causality is a function of time, time is a function of our 4D universe.

I'm not sure. Time allows for relationships between particles to change with some degree of continuity, but that doesn't necessarily make causality implicit with time.

In the same way that an implication is a thing of logic, not of time, even though it can be correlated with time when logic is applied to a continuously changing system. The question is truely probing a logical relationship, not a temporal one.

Asking why something is the way it is, is always a valid question.

I should qualify myself, that asking what came before the universe may be a meaningless question. Simple fact is that we don't know anything outside the scope of our universe. We (sentient beings, I certainly don't expect this to be solved in my lifetime) may never know, as our being inside the universe may preclude ever seeing outside of it. The rules of particle interaction, all the way to gravitation and space-time may or may not apply outside of existence. There indeed may be no "outside of existence" it's just the universe, and all our speculation is no different than ancient greeks speculating about Mt Olympus.

But for the love of God, truth, or that annoying spaghetti meme, yes, you should always be free to ask the question. Even if it is a pointless exercise. Scratch that, especially if.

=================================================
As for the infinite vs finite, I'm not sure if this was explained this way, but to put it simply:
*If the universe is finite, if you travel in a straight line away from Earth, given enough time, you will return to where you started. Almost like going around the world.
*If the universe is infinite, if you travel in a straight line away from Earth, you'll keep going forever. You'll never run out of space because space expands faster than you can travel.

 

[PurpleBuddha]

About the last sentence in your post. Space expanding faster than one can travel does not mean the universe is infinite.

 

[Trekker4747]

About the last sentence in your post. Space expanding faster than one can travel does not mean the universe is infinite.

Of course it does! I'm an infinite distance away from my far wall! You are too!

Try it! Walk half way to the wall.

Ok, walk half way to it again (half the new distance, that is), now keep doing that until you reach the wall.

You NEVER WILL!!



Your wall is an infinite distance away!

 

[Lindley]

About the last sentence in your post. Space expanding faster than one can travel does not mean the universe is infinite.

Of course it does! I'm an infinite distance away from my far wall! You are too!

Try it! Walk half way to the wall.

Ok, walk half way to it again (half the new distance, that is), now keep doing that until you reach the wall.

You NEVER WILL!!



Your wall is an infinite distance away!

That actually fails for two reasons:
1) You will reach the wall in finite time, since each movement takes less time. Basically, you're screwed by the fact that
lim x->inf Sum y=1_x 1/2^x = 1.
It may take an infinite number of steps, but towards the end each step takes an infinitely small amount of time, so the two actually cancel each other out.

2) According to some therories, you can't execute the experiment in practice, since you could never move a distance shorter than the Plank length. That isn't widely accepted, however.

 

[Trekker4747]

About the last sentence in your post. Space expanding faster than one can travel does not mean the universe is infinite.

Of course it does! I'm an infinite distance away from my far wall! You are too!

Try it! Walk half way to the wall.

Ok, walk half way to it again (half the new distance, that is), now keep doing that until you reach the wall.

You NEVER WILL!!



Your wall is an infinite distance away!

That actually fails for two reasons:
1) You will reach the wall in finite time, since each movement takes less time. Basically, you're screwed by the fact that
lim x->inf Sum y=1_x 1/2^x = 1.
It may take an infinite number of steps, but towards the end each step takes an infinitely small amount of time, so the two actually cancel each other out.

2) According to some therories, you can't execute the experiment in practice, since you could never move a distance shorter than the Plank length. That isn't widely accepted, however.

It was a joke, dear.

 

[Lindley]

Yes, but the math major in me couldn't resist.

 

[Trekker4747]

Yes, but the math major in me couldn't resist.

Well, then at the very least you realize you can always divide a number in half. Even if my "wall analogy" wouldn't really work.

 

[Lindley]

Actually, what's really interesting is that if you walk half a mile, then a third of a mile, then a quarter of a mile, then a fifth of a mile and so on.....you really will cover an infinite distance.

It's only when you start increasing the denominator faster, that you enter a situation where you'll only travel a finite distance in infinite time.

 

[RoJoHen]

I was trying to remember the term "limits." Haven't taken Calc in a while.

 

[Jadzia]

Let me show you some maths now

To begin, an infinite geometric series is one where each term is generated from the previous one by multiplying it by a fixed amount (r).

ie, a + a.r + a.r^2 + a.r^3 + ...

= a * (1+r+r^2+r^3+...)

So in Trekker's example, the first term (a= 1/2), and each subsequent term is (x1/2) the previous term (r=1/2), so the series is (1/2) + (1/4) + (1/8) + ...


notice that (1-r) * (1+r+r^2+r^3+...) = 1 , since alternate terms cancel in the expansion. This is only true where it is an infinite series.

So
Total Length = a * (1+r+r^2+r^3+...) = a/(1-r)

and applying that to Trekker's example with a=1/2 and r=1/2, the total Length Trekker walks =(1/2) / (1 - 1/2) = (1/2) / (1/2) = 1 = the distance to the wall.



The interesting thing is what happens if r>1,

eg, if a=5 and r=1.5, then Total Length = 5/(1-1.5) = -10 !! Surely not.

It's interesting why this formula lies to us in some situations, yet works other times. How can we be sure it is working properly at all? And the answer to that is within complex analysis, even though we're dealing with real numbers, because the formula applies to complex numbers just as well.

eg, a=3+2i, r=1/2 - i/2

Total length = a/(1-r) = (3+2i) / (1 - 1/2 + i/2) = (6+4i)/(i - 1)


more on that later...

 

[All Seeing Eye]

My head just exploded.

 

[Trekker4747]

My head just exploded.

I though you were brilliant, knew everything, and was the smartest man on this board? This math should be childs play to such an individal.

 

[Silvercrest]

My head just exploded.

Ladies and gentlemen... The Big Bang.