OT: Gravity, Dark Energy, Universal expansion

[Suicide Junkie]

The big bang didn't occur in some particular part of spacetime, but rather it is when everywhere was the all the same place.

It makes no sense to say that something is twice as far away as the big bang.

[MasterChiToes]

Suicide Junkie said:
It makes no sense to say that something is twice as far away as the big bang.

Yes it does... since in this context time = space (with a factor of c). The big bang was ~20 Billion years ago which makes it 20B*c far away [time] vs the farthest point in the universe which would be 20B*c*pi [space] (1/2 the circumference 2pi*r of the sphere described by r being the time since the BB [*c]).

[Suicide Junkie]

Come on, man.

Its not 20B light years away.
Its 20B years away.
Those are completely different units.

The size of the *visible* universe (roughly, time since photons were released * speed of light) is different from the size of the universe (which depends on its topology)!

Also, you are stating that there exists a farthest point in the universe from somewhere. This implies that you are assuming a closed universe. Why? Evidence indicates a flat or very slightly open universe last I checked.


The crux of the matter is that "speed of light perpendicular to 3-space" is nonsensical, since distance and speed are both undefined for that.

[MasterChiToes]

In my first post I said, "for the universe expanding at the speed of light"... which is an assumption. The rest follows from the balloon model of an expanding universe (the diagram above). In this case, the balloon model is an expanding 4-sphere [due to symmetry the number doesn't matter... it could be any n-sphere n>3], where the balloon's outer surface is 3-space.

Yes, the size of the visible universe is different from the size of the universe, which as I said, can make the universe untraversable... that is was one of my main points.

However, for an n-dimensional balloon model of the expanding universe, it does not by any means imply a closed universe, only a finite one... it can still be open if it expands forever. In any manifold/topology, any point can still have a farthest point... like two opposite sides of the balloon... it is a matter of spatial symmetry, and has nothing to do with the openness. Every point on a circle, or sphere, or n-sphere has a farthest point.

"speed of light perpendicular to 3-space" is not nonsensical, just non-physical... imagine a balloon who's radius is expanding at the speed of light. Mathematically, that perpendicular-ness allows speed and distance to be defined for more dimensions using the same symmetry that allows time being the 4th dimension (ie time= distance/c).

r^2 = x^2+y^2+z^2 where r=c*t (t being the age of the universe)
as t increases, any two "fixed" points (x1, y1, z1) and (x2, y2, z2) will be moving away from one another.

(Personally, I would like to draw the light cones for that diagram, but the curves are pretty hard to photoshop.)

[Suicide Junkie]

Presuming all of your topology and a fixed rate of expansion, why are you measuring "distances" through your time axis?

Go far enough back in time... and you start going forward again, but on the opposite side of the universe?

My problem is that you are mixing a space dimension with a time dimension.
You can't travel through the middle, since that is time travel. And you're measuring through to negative time which is definitely not right.

[MasterChiToes]

In polar or spherical coordinates, r is often constrained to the positive values. Space and Time can be 'mixable' in General Relativity, since the transformations and behavior of distance and duration are essentially the same... and especially since the radial coordinate axis is "unreal" and choosing a measure of space or time (which have a 1:1 correlation) is unimportant. The past doesn't exist anymore, and the old space doesn't exist either. Whether one of the two is more conceptually real is unimportant to the math.

Yes, you can't travel through the middle, only the surface of the sphere is the universe, there is nothing else, unless you want the philosophical definitions that inside of the balloon is the past and outside the balloon is the future. However, you can also choose the philosophical definitions that inside the balloon are old universes and outside are coming universes.

[Suicide Junkie]

So, back to my initial issue: "twice as far away as the big bang" is absurd.

[MasterChiToes]

There is a 1:1 correlation between space and time, especially in this example. From an observer, the big bang is seen through space, at a distance. However, the objective and unobservable size of the universe is larger than that... and it can be over twice that observed distance.

Still it is semantics... so don't worry about it. If you understand my example, it would be better to ask... can the universe be continuous if it is un-traversably large, or is there some sort of mega-macroscopic quantization going on, which could imply some sort of emergent macro-forces might exist.

[Suicide Junkie]

Aside from your negative time problem, I guess the issue is in trying to relate your model to reality when it is just too different.

[MasterChiToes]

There is no negative time problem for an expanding 4 sphere surface just like a pocketwatch doesn't prove time travel is possible.

http://www.astro.ucla.edu/~wright/Balloon2.html
http://en.wikipedia.org/wiki/Metric_..._balloon_model