Extent of space (APOD 23 Mar 2006)

[cosgroved]

In a not too distant APOD, a model of the expansion of the universe since the big bang was posted. It brings up a question in my mind. As the universe expands, where does the space into which it expands originate? Was it alwys there? Is it infinite? This might seem a nonsense question, but current theories supported by observation indicate that space is not uniform, but can be changed locally by gravity. If this is just a construct to explain how objects can be viewed as relatively closer or farther away from each other, then this may not be important. But if space has some unknown fabric that is affected by gravity, then the question wold seem to be of importance. I have no answer, only the question.

[Nereid]

Perhaps the APOD you are referring to is Will the Universe End in a Big Rip? (21 Oct 2007)?

That the 'big bang' is some kind of explosion, from a point somewhere in space, is one of most common misconceptions; see, for example, this page for more detail.

More generally, the theory of General Relativity (GR) addresses the relationship between space, time, mass-energy, and gravity. It is both a very simple relationship and a highly counter-intuitive one. It has also been tested pretty thoroughly, and has passed every test to date, with flying colours.

The other great physics theory of the 20th century - quantum mechanics - is even more counter-intuitive! Interestingly, the two are mutually incompatible; sadly though the regimes in which the incompatibility would have easily detectable consequences - so amenable to scientific investigation, through observation and experiment - are way, way beyond anything we can probe today.

[cosgroved]

Actually, it was the APOD that showed a model beginning with the Big Bang depicted as a point. That is a misconception as I understand from following your links. Guess I will have to delve into the equations to understand better, but you have helped a lot.

[BMAONE23]

http://antwrp.gsfc.nasa.gov/apod/ap060323.html

[Dutchman]

So what's everyone's opinion on the extent of the universe? Finite or infinite?

[Sowndbyte]

Man is predisposed to place a boundary upon his surroundings. open your mind,and you will see infinity.

[Dutchman]

Oww, it hurts.

[Dr. Skeptic]

So what's everyone's opinion on the extent of the universe? Finite or infinite?

If quantum mechanics is true, the universe needs to be finite.

[BMAONE23]

MOOT,
We cannot and likely never will be able to travel there over the course of our species existance unless we learn to travel at the speed of thought. Still then not very likely since we cannot think of where we haven't seen.

[Qev]

So what's everyone's opinion on the extent of the universe? Finite or infinite?

If quantum mechanics is true, the universe needs to be finite.

I still don't see how quantization of spacetime necessarily requires a finite space.

[Dr. Skeptic]

So what's everyone's opinion on the extent of the universe? Finite or infinite?

If quantum mechanics is true, the universe needs to be finite.

I still don't see how quantization of spacetime necessarily requires a finite space.

If the universe is composed of strictly finite units, there cannot be an infinite amount of units or empirical measurements/data is meaningless.

Example:

Time

- The distance an object travels between two points take 1 second.

- Divide the second in half repeatedly until the smallest unit is reached.

- If quantum mechanics is true, there needs to be a quantum unit of time.

- If not, the result is 1/infinity seconds (mathematically undefined)

- The distance the object traveled in 100 billion seconds would = 100 B/infinity

- By definition, 1/infinity = 100B/infinity

- Because all empirical data can be extrapolated from another, distance, mass ... fall under the same flaw trying to introduce infinity into an empirical value.

[Qev]

So, you're effectively claiming the equivalent of saying the set of integers isn't infinite?

[rigelan]

I don't think a minimum size of object means that you must have a maximum number of objects.

Masswise, I think that there are only so many particles in the universe. Even though it goes beyond our perception of 14 billion years, I believe it exists. Whether that happens to be 10^50 particles or 10^100 or 10^1000, who knows.

Volumewise, I would say that the size which the universe COULD take up is infinite, but the amount it is currently taking up is not infinite, and it will never be infinite because it could always be larger.

[Dr. Skeptic]

So, you're effectively claiming the equivalent of saying the set of integers isn't infinite?

That is correct.

Quantum mechanics states everything in our 4 dimensions need to resolve as integers. Such as an electron is in one energy state or another but cannot and does not exist anywhere between the two states.

Also, ∞ is not an integer, in fact it is not a number - it is a non empirical conceptual limit.

[Qev]

Well, then, I'm afraid you're wrong. The set of integers is defined as countably infinite. That a set has a smallest indivisible unit says nothing about its extent.

[NoelC]

Maybe it's not expanding at all, but time is varying. Maybe it just takes longer for the light to travel from one point to another now than it did then. Of course, now and then are relative too...

Just goes to show that it's difficult to observe something when a part of it and inside it.

-Noel

[Dr. Skeptic]

Well, then, I'm afraid you're wrong. The set of integers is defined as countably infinite. That a set has a smallest indivisible unit says nothing about its extent.

Isn't the "extent" just the reciprocal of the "unit division"?

Infinity as an integer has an unobtainable value so its value cannot be defined - other than an abstract concept.

Infinity doesn't exist in the universe, if it did mathematics would be meaningless. (That would also include infinity itself.)

[Qev]

Doesn't the reciprocal of the unit division depend on how you're expressing the unit division, though? If I define it as 1, its reciprocal is 1.

Infinity is unobtainable as a value, certainly... it's defined as greater than any assigned value. It can be treated as a number in certain ways, but isn't the same 'kind' of number than say an integer or real. I don't see how the presence of infinity in the integer set invalidates mathematics using integers; that's where you're losing me, I think.

[Dr. Skeptic]

Doesn't the reciprocal of the unit division depend on how you're expressing the unit division, though? If I define it as 1, its reciprocal is 1.

Infinity is unobtainable as a value, certainly... it's defined as greater than any assigned value. It can be treated as a number in certain ways, but isn't the same 'kind' of number than say an integer or real. I don't see how the presence of infinity in the integer set invalidates mathematics using integers; that's where you're losing me, I think.

Infinity is a non empirical value, injecting infinity into an empirical statement produces a non empirical result, or, it changes a quantitative product into a qualitative product.

Am I helping or confusing you?

[Qev]

Just to be clear, I'm not claiming that infinity is an integer in the set of integers, but rather that the set of integers itself is infinite, ie. it increases without bound. There exists no 'largest integer'.

I do agree that when mis-applied, infinities lead to nonsense results. They're not 'normal' numbers.

[Dr. Skeptic]

Just to be clear, I'm not claiming that infinity is an integer in the set of integers, but rather that the set of integers itself is infinite, ie. it increases without bound. There exists no 'largest integer'.

I do agree that when mis-applied, infinities lead to nonsense results. They're not 'normal' numbers.

That is correct, there is no largest integer, but, there is a finite limit to quantum units in the universe.

Saying there is an infinite number of integers is applying a conceptual limit to empirical numbers, its not a real limit because infinity is not a number, thus empirically cannot be a defined as a limit. Applying this logic, the universe cannot be infinite because infinity is not a real limit.

Logic: (An infinite universe would then not be real????)

[Qev]

Well, I'll certainly agree that we're not likely to ever be able to observe that the universe is infinite (or finite), I still disagree that it can be ruled out by the logic you're giving. Aren't you basically arguing that (going back to the numbers example) since we can't count to infinity, integers can't be infinite in extent?

[BMAONE23]

Mathematically speaking, the only set of problems that can include infinity as te product must have infinity as the basis.
Infinity (I)
I+I=I
I-I=I
IxI=I
I/I=1
Otherwise the product of any whole number will be just another whole number.

There are no 2 whole numbers whose product = I

[Pete]

"Infinity" is certainly not a particular number and can't be thrown into equations like that; you get obvious contradictions like

1/infinity = 100B/infinity

implying 1 = 100B.

[Dr. Skeptic]

Well, I'll certainly agree that we're not likely to ever be able to observe that the universe is infinite (or finite), I still disagree that it can be ruled out by the logic you're giving. Aren't you basically arguing that (going back to the numbers example) since we can't count to infinity, integers can't be infinite in extent?

Well, in a way.

Empirical data cannot reach the limit of infinity. Remember, infinity is a (non?) limit not a number.