A time machine from a science fiction TV show? Really???The only example I know of, is the TARDIS - Wikipedia
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The first cause argument
- Thread starter firedragon
- Start date
You keep missing my point by going back to geometry. You can't build a house by doing geometry. You are missing my point.
Then you've answered my question; one of the differences between empty space and nothing at all is space has gravity, nothing at all would not. Thanks for answering my question.
ratiocinator
Lightly seared on the reality grill.
How do you know how big you expect it to be inside, i.e. how much volume it 'should' contain?
It doesn't matter! The inside is always smaller than the outside.
muhammad_isa
Veteran Member
In this context, 'finite' means 'having a finite volume'. And, as usual, 'infinite' means 'not finite'.
First, even defining what that means is problematic.
The situation is that you have a 'boundary' (like the walls of the house) that divides space into an 'inside' and an 'outside'.
Q1: How do you distinguish between inside and outside?
For example, suppose I draw a circle on the Earth. That circle will divide the surface of the Earth into two pieces. Which do you designate as the inside and which as the outside?
So, if I draw the circle at 45 degrees north latitude, which is the 'inside' and which is the 'outside'? How about if I draw a circle at 45 south latitude? how about at the equator?
And yes, there are three dimensional analogs to this two dimensional (surface) situation on the Earth.
When you say the 'inside' is always smaller than the 'outside', it is likely you *really* mean that the volume inside is bounded by the *area* of the walls in a predictable way. And yes, that is a property of space.
You can't build a stable house without doing geometry.
mikkel_the_dane
My own religion
That depends on what you mean by all words.
muhammad_isa
Veteran Member
Oh, really?
In mathematics, transfinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers, yet not necessarily absolutely infinite.
Transfinite number - Wikipedia
So which is it, when you refer to an "infinite universe"?
ratiocinator
Lightly seared on the reality grill.
Of course it matters, otherwise saying it's smaller on the inside has no meaning. You've got to compare a boundary (which is all you see from the outside) with a volume it encloses. Unless you have some expectation of how the boundary relates to the volume it encloses (which needs geometry) then you have no way to say it must be smaller.
If we are talking about volumes, we are not talking about transfinite numbers (cardinals or ordinals). We are talking about 'extended real numbers'--the decimal numbers with infinity as an upper limit point. And no, it has nothing to do with Cantor's 'absolute infinite' (which is simply a proper class as opposed to a set).
Finite volume means a real number (not a counting number, necessarily) that represents the total volume.
Infinite, in this context, means 'not finite'.
I'm sorry, but you are confusing several different uses of the word 'infinity'. Which happens since there *are* several distinct ways the term is used in math and physics.
if you are asking how many points are in a set, you are asking about cardinality.
If you are asking about length, area, volume, etc, you are asking about extended real numbers.
If you are asking about infinite density, you are likely to be asking about a limit (in the mathematical sense---see calculus).
There are also several commonly confused terms:
Finite cardinality: there is a natural number that represents the number of elements in the set.
Infinite cardinality: the number of elements in the set is not finite.
Finite length: a line segment with a real number as its length.
Finite area: similar to 'finite length' but instead with area.
Finite volume: simular to finite length and finite volume but using volume instead.
So, for example, a line segment of length 3 has finite length, but there are infinitely many points on it, so it has infinite (and, in fact, uncountably infinite) cardinality.
A square whose sides are 3 units has an area of 9 square units, and so has finite area.
A cube whose sides are 5 units has a volume of 125 cubic units and so has a finite volume.
But, for example, the Euclidean plane has infinite area: any finite region you select has parts of the plane outside of it. A straight line can have infinite length. Both of these are different than having infinite cardinality.
The term 'bounded' as a number of possible uses so needs to be defined when used. Often, it means having an enclosing boundary. But, in cosmology, that is NOT what it means. The cosmological definition is simply that space has a total volume that is finite.
And, again, it is possible to be unbounded (in the sense of not having an enclosing boundary), have finite volume (and so, to be bounded in the cosmological sense) and to have infinite cardinality (the number of individual points is infinite). These are distinct concepts that need to be kept straight.
muhammad_isa
Veteran Member
That makes no sense.
You said: "If it is infinite now, it was infinite before. If it is finite now, it was finite before."
How can the volume of the universe be infinite before inflation, and be the same volume i.e. infinite, after inflation.
That makes no sense.
You said: "If it is infinite now, it was infinite before. If it is finite now, it was finite before."
How can the volume of the universe be infinite before inflation, and be the same volume i.e. infinite, after inflation.
Because if you inflate an infinite volume (or deflate it), the volume is still infinite.
5*infinity=infinity
On the other hand, if you follow *comoving* finite volumes, their volumes increase over time.
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muhammad_isa
Veteran Member
Hmm .. An infinite universe implies an infinite amount of heavenly bodies, which in turn implies infinite mass etc.
The big-bang theory intuitively implies a finite universe, imo.
It makes a lot less sense to me, than being finite and bounded in some way due to topography.
There is no point in something that inflates / expands, if it is infinite in volume in the first place. It is just mathematical rhubarb.
Yes. But not an infinite density.
Funny that specialists disagree with you.
If you want to learn more, I can suggest some books.
We Never Know
No Slack
If I may ask.... Doesn't several, if not many things being discussed here depend on whether the universe is finite or infinite, which really isnt yet known to my knowledge.
But don't let me interupt, I enjoy reading your alls posts. They are interesting and educating.
Not as much as you might initially think.
For example, whether the universe is spatially infinite or not has little consequence on whether it is temporally infinite into the past or not.
It *does* have relevant as to whether the universe is infinite into the future or not, although some models that are cyclic are more likely to happen in a spatially finite case.
Both expansion and inflation can happen in either a spatially infinite or spatially finite universe.
Quantum gravity does not differ substantially based on whether the universe is spatially infinite or not.
muhammad_isa
Veteran Member
No. I want you to explain, how something that is infinite in the first place, can actually expand.
You just admitted that they would be the same volume before and after inflation.