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Author Topic: If the universe is a 4-D sphere, are we just seeing the horizon?  (Read 504 times)

Offline Rachel A. H. Beckett

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I was talking to my daughter about space-time, and about the theory that it is like a 4-D sphere. I mentioned that, for me, it's a big conceptual problem because as you look back in time towards the big bang in any direction you are looking away from where we find ourselves - yet a circle should come back to where it started. Then I thought that this is like what happens with the spherical earth: at sea level it looks flat and you can see about 3 miles until the curvature makes the view 'disappear over the horizon'. The actual circle round the earth is 25,000 miles (8,333.3-recurring times longer than 3 miles). The three-mile figure, I suppose, depends on the height of a human being at sea level. Still, I thought you could use the same sort of logic with the universe. We can see 10,000 billion light years back to the 'early universe', but maybe this is just the 'horizon' before the curvature goes round and comes back to where it started (here). Using the same calculation as above, that would make the full circumference of the universe 8.3 trillion light years. It would actually depend on our 3-D 'height' which I suppose would consist in the volume (or the mass?) of the earth. I'm an editor, not a physicist, so of course there might be a huge hole in my logic, but I thought I should share it with you. If I'm wrong, tell me (in layman's terms), why I must be wrong.


 

Offline chris

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It's slightly more complicated than your Earth model because, unlike our planet, the Universe is largely transparent. So the idea of an inflating bubble with us sitting within that bubble as it expands is the simplest mental picture to grasp.
 

Offline Bill S

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Hi Rachel, welcome.   
Obviously, what Chris says is right, but does it answer your question? 

As I see it, your example of the surface of the Earth is just an analogy, which, by definition, differs from that to which it relates.  Your question opens up thoughts about the flatness of the Universe.  I am certainly not qualified to tackle this subject, but I know that current wisdom holds that the Universe is (as near as we can tell) flat. 

Pete (Pmbphy) will hopefully come in on this.  He occasionally shoots down my ideas by pointing out that they would not work in our flat Universe.   
 

Offline Rachel A. H. Beckett

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Hi, thank you both.

The first comment (by Chris) doesn't quite address my point. In a way I meant it as an analogy, but it was more an argument of the form 'Could it be that as A is to B, C is to D?'

I'm surprised when you say that current thinking is that the universe is flat. Is this something to do with the idea of a 'cosmological constant' holding it all in balance? Surely the concept of space-time being curved implies that the universe is also curved? It seems to me to be a bit too much of a coincidence that it should be flat rather than concave or convex. Of course if it were curved, then it would be logical to deduce that it is finite (bends back on itself) rather than infinite.

Although we humans are fascinated by infinity, I have come to the conclusion that it is a ridiculous concept. I feel that the onus is on those who believe in infinity (in the physical universe) to prove it to the rest of us, rather than the other way round. Today I was looking at a particular type of cauliflower that has a fractal pattern, the sort of thing that is considered 'infinitely' detailed. But of course, when you looked at the detail on the tiniest peaks, the pattern began to dissipate when it got to a minute scale, presumably because tiny environmental factors start to destabilise it. The same thing, it seems to me, applies to anything you can represent on a graph: surely any meaningful range of values must stop short before one variable reaches infinity?
 

Offline jeffreyH

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It has to do with what are called light cones. This is the 4-D representation that you are looking for. Since the universe is expanding the time taken by light to reach us is not only a function of the speed of light but also the rate of expansion over this time interval. The light cone itself actually describes an expanding sphere. It is the rate of expansion of the light sphere with respect to the expansion of space that is important.
 

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