Hello, John. Welcome to Hypography.
I would disagree slightly with some of your reasoning and conclusions, but I think you are very much on the right track.
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Originally Posted by johngetup
The Universe we exist in (as to our own perception) is the 3 dimensional Universe, and coupled with the theory of the Big Bang is finite.
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Big Bang cosmology has three possible geometries of space: spherical, flat, and hyperbolic. The geometry is determined by density and determines the topology which is open in the case of flat and hyperbolic, and closed in the case of spherical:
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The density of the universe also determines its geometry. If the density of the universe exceeds the critical density, then the geometry of space is closed and positively curved like the surface of a sphere. This implies that initially parallel photon paths converge slowly, eventually cross, and return back to their starting point (if the universe lasts long enough). If the density of the universe is less than the critical density, then the geometry of space is open, negatively curved like the surface of a saddle. If the density of the universe exactly equals the critical density, then the geometry of the universe is flat like a sheet of paper. Thus, there is a direct link between the geometry of the universe and its fate.
The simplest version of the inflationary theory, an extension of the Big Bang theory, predicts that the density of the universe is very close to the critical density, and that the geometry of the universe is flat, like a sheet of paper. That is the result confirmed by the WMAP science.
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WMAP- Shape of the Universe
Big bang does not, then, necessitate that space be finite. If the density of matter and energy is low then the typology is open and space is infinite.
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Originally Posted by johngetup
It started at a single point in space, and expands form this position...or does it?
From measurements of the speed in which the Galaxies are moving away from one another, we find that each is accelerating and thus we live in and accelerating Universe.
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I agree, though I would word it a bit differently and say that expansion is
currently accelerating. There's also no way to look at a galaxy and tell if it is accelerating away from us or if it has a steady velocity. To determine that the rate of expansion is recently (last couple billion years) accelerating requires supernovae standard candles and a model capable of interpreting redshift vs. brightness data.
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Originally Posted by johngetup
If you imagine for the time being that the Milk Way is stationary, and looking through a telescope we see two more Galaxies in line with each other which we will call A and B; A being the closest and B the furthest away; then this model of the Universe would suggest that B was moving faster away from us than A. As Galaxy A travels, let’s say, at the speed of 10mph away from us, Galaxy B is travelling 10mph away from A. Then to our perception B would be moving 20 mph from us.
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I agree. This assumes that B is the same distance from A as A is from us. More importantly, it assumes that the distance you're talking about is the comoving distance. In special-relativistic coordinates the same would not be true which is why the comoving velocity of an observable galaxy can be greater than c while the special relativistic velocity cannot be. This explains in some detail:
Many Distances
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Originally Posted by johngetup
If we added 1000 more Galaxies in this scenario, imagine how fast the one at the end of the line must be travelling...basically 10 to the power of 1000.
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If all the 1,000 galaxies are each the same distance from the one next to it then the final velocity would not be 10 to the power of 1,000, but rather 10 times 1,000. But, regardless, I don't quite agree with your reasoning in the following:
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Originally Posted by johngetup
This is impossible, so where have we gone wrong.
How can Galaxies be moving at equal speeds away from one another?
The answer must therefore be that the space between the Galaxies is expanding...
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I see what you are saying: that the further away something is the faster it is going away from us. As those distances get arbitrarily large so too must the velocity get arbitrarily large. But, that would be impossible because things can't go faster than the speed of light.
It is, however, necessary to note that things cannot go faster than the speed of light *in special relativity*. But, in special relativity velocities are not added such that AB = 10 and BC = 10 therefore AC = 20. Velocities should rather be added according to:
where
AB = u
BC = v
AC = w
It's explained in detail here:
Relativistic Velocities
I, therefore, would not agree with your method of concluding that space must be expanding. It's more appropriate to say that space is expanding in the
Robertson Walker metric which big bang cosmology uses to model the evolution of the universe according to the Friedmann equation. In that metric velocities can be greater than c, but as it defines simultaneity differently than special relativity there is no problem with arbitrarily large velocities.
Essentially: expanding space versus things moving through space ends up being a coordinate choice. This is supported here:
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Are galaxies really moving away from us or is space just expanding?
This depends on how you measure things, or your choice of coordinates. In one view, the spatial positions of galaxies are changing, and this causes the redshift. In another view, the galaxies are at fixed coordinates, but the distance between fixed points increases with time, and this causes the redshift. General relativity explains how to transform from one view to the other, and the observable effects like the redshift are the same in both views. Part 3 of the tutorial shows space-time diagrams for the Universe drawn in both ways.
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Frequently Asked Questions in Cosmology
and explained in more depth here:
What Causes the Hubble Redshift?
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Originally Posted by johngetup
But how can this be the case as the laws of a 3 dimensional Universe negate such a conclusion (If two cars are racing each other then the one in front must be travelling faster than the one in second place). Referring back to the expanding balloon mentioned by 'EWright' above, if the ant was stationary then it would perceive other stationary ants on the same balloon expanding away from him at an equal rate. The 2 dimensional space is expanding, while the ants remain still. This seems to be a good explanation, but while the balloon is 2 dimensional the ants remain 3rd dimension, just like the matter (information) of our Universe, therefore such a conclusion cannot apply in the 3 dimensional world.
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The link I gave on special relativistic velocity addition will explain the race car thing. The balloon example is best understood with 2-dimensional beings while the third dimension is either non-existent or unobservable. A better analogy, I think, since we're talking about infinite space is to imagine an infinitely large rubber sheet with dots on it. The distance between any two dots increases with time.
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Originally Posted by johngetup
Think about the ant again, if he walked around the balloon (his 2 dimensional space) he will not find an edge, but instead will eventually end up back where he began. His Universe is then infinite to him, but has clear set boundaries to us in the 3rd dimension.
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The balloon is an example of spherical geometry. If the density in our universe were greater than
(and the cosmological constant were zero) then the geometry would be spherical and the universe would be closed like the balloon. Assuming expansion were not too great we could shine a laser in any direction and it would eventually hit the back of our head—like you say. I would disagree with your use of the word infinite however. A closed universe is said to be "spatially finite and unbound". That is to say: there's only so much space, but you can move around without ever bumping into a boundary.
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Originally Posted by johngetup
As the space in our Universe expands, as is the case with the balloon, there is no set point in which it is expanding from. Therefore if we flew in a straight line faster than this expansion, we will end up back where we started.
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The current standard cosmological model which fits best with astronomical evidence (
ΛCDM) says that the universe is flat or nearly flat. In that case space is infinite and unbound. Shine a laser and it will continue forever never coming back around to hit you in the back of the head.
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Originally Posted by johngetup
Hence forth, our Universe become infinite to us, but finite to the 4th dimension... So to answer your question, the 3rd dimension is both finite and infinite according to perception....
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I think it would avoid confusion to call a universe with three spatial dimensions, closed topology, and extrinsic curvature into a 4th unseen spatial dimension:
"spatially finite in both 3 and 4 dimensions"
and
"unbound in the third dimension but bound in the fourth"
You certainly do hit the correct topics, so don't think I'm entirely disagreeing with you
"Be glad of life, because it gives you the chance to love and to work and to play and to look up at the stars." ~Henry Van Dyke
~modest
