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PostPosted: Fri Feb 11, 2011 9:25 am 
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Quasar wrote:
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The Universe originally being incredibly small arises from rolling the current observed expansion of the Universe back 13.7 billion years

You have said once again that the Universe was incredibly small. Going back to the time when it was 'incredibly small', which relative entity have you measured 'small' against?


Relative to the current size of the Universe.

If you aren't prepared to accept that something that has been expanding for billions of years was smaller in the past then this discussion becomes rather difficult !

Incidentally, the "singularity of an infinite size" that you refer to in your 2009 post is a contradiction in terms - singularity means having no size in any dimension. Having said that we should remember that the "singularity" referred to in the description of the Big Bang (and in black holes) is a mathematical singularity - our current knowledge of physics is unable to accurately describe the behaviour of matter/energy over extremely small distance scales


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PostPosted: Sat Feb 12, 2011 9:19 pm 
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David Frydman wrote:
You said the Universe is mathematically flat.
Prove it.
Show me your mathematical proof for your conclusion.
It is not sufficient to quote others.
Show me your line by line proof of this or your mathematical reasons for your hypothesis.

David.


This may help.

Proof that the universe is mathematically flat.

Parrallel lines never meet.
The angles of a triangle add up to 180 degrees.


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PostPosted: Sat Feb 12, 2011 9:41 pm 
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Are you saying we are two dimensional?

On a flat piece of paper the angles of a triangle add up to 180 degrees.

On a flat infinitely large piece of paper parallel lines don't meet. If that could exist.

How does that prove that the Universe is flat?

Presumably if you think the Universe is flat, then the Earth is also flat.

David.


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PostPosted: Sun Feb 13, 2011 10:21 am 
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Hi,

big_kev, what is the connection between parrallel lines and the Universe ?

What is parrallel in the Universe ?

All the best
Dave

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PostPosted: Sun Feb 13, 2011 12:05 pm 
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I think there is a good business opportunity here to set up the Flat Universe Society.
This would be grander than The Flat Earth Society, and you swould probably attract more members from across the Universe.
The fees would be payable in intergalactic monetary units redeemable in any universal bank, or the Post Office. The money would of course be flat money. No coins as these would be a bit to thick to be in keeping with the ideals of the Society.
Members would be recognisable as they would all wear flat caps, as worn by Andy Capp.

David.


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PostPosted: Sun Feb 13, 2011 12:23 pm 
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big_kev wrote:

Proof that the universe is mathematically flat.

Parrallel lines never meet.
The angles of a triangle add up to 180 degrees.


Rather than being a proof, these statements are a consequence of a "flat" Universe.

Although measurements to date have indicated that the large scale geometry of the Universe is "flat" (or very close to "flat"), it will never be possible to provide a 100% "proof" of the "flatness" of the geometry of the Universe - in the same way as it is not possible to absolutely "prove" Einstein's General Theory of Relativity.

All scientists can do is to carry out ever more detailed experiments to tie down the geometry of the Universe ever more accurately. These may continue to confirm the "flatness" or could possibly reveal some tiny divergence that cannot be detected due to the limitations of current measurements.


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PostPosted: Sun Feb 13, 2011 1:12 pm 
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Tony,
Am I correct that you are saying that the large scale geometry is flat or almost flat, but on the small scale such as the solar system or indeed a galaxy the geometry is not flat.
Or are you saying that the flatness extends even to local measurements even on the Earth.
Can you reiterate what the term flatness means in this context.
How does flatness react in the presence of dense and heavy objects that distort space?

David,


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PostPosted: Sun Feb 13, 2011 2:30 pm 
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Dear Tony,
I think part of what you are saying is that locally on the scale of the solar system, measrements would only be affected by flatness to a very small degree, so that flatness is not a major component of how we see our local neighbourhood.
It is only when we measure very large distances that flatness is seen/
Is this correct?

David.


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PostPosted: Sun Feb 13, 2011 2:57 pm 
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I've always thought of it as the opposite; at small scales geometry appears flat (the horizon looks straight, the angles of a triangle add up to 180 degrees)) while at large scales, geometry could be positively curved (the horizon is actually curved and the angles of a triangle add up to more than 180 degrees). Or it could be negatively curved.

Another way of describing it is;
  • Positively curved = Closed/Spherical
  • Flat = Flat
  • Negatively curved = Open/Hyperbolic

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PostPosted: Sun Feb 13, 2011 4:19 pm 
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Are you saying that at large scales the Universe could be spherical, flat or open hyperbolic, yet at the same time large scale measurements could in each case indicate that the Universe is also flat?

David.


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PostPosted: Sun Feb 13, 2011 4:56 pm 
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Not also flat, it could be any of them. For example: measurements indicate that the universe is flat but it could be that we are only measuring a tiny fraction of the whole. It's like seeing the horizon as a straight line when in fact it's really a small part of the curvature of the Earth.

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PostPosted: Sun Feb 13, 2011 5:58 pm 
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So Joe,
You may not be entirely in agreement with others who maintain almost certainly that the Universe is flat.

I have not taken much interest in cosmology as I have had others things to busy myself with. It is not that it doesn't interest me, but it taxes the best human minds and I generally prefer more practical things.

Regards, David.


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PostPosted: Sun Feb 13, 2011 7:11 pm 
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David Frydman wrote:
Tony,
Am I correct that you are saying that the large scale geometry is flat or almost flat, but on the small scale such as the solar system or indeed a galaxy the geometry is not flat.
Or are you saying that the flatness extends even to local measurements even on the Earth.
Can you reiterate what the term flatness means in this context.
How does flatness react in the presence of dense and heavy objects that distort space?

I think part of what you are saying is that locally on the scale of the solar system, measrements would only be affected by flatness to a very small degree, so that flatness is not a major component of how we see our local neighbourhood.
It is only when we measure very large distances that flatness is seen/
Is this correct?

David,


David,

Most of our everyday experience is consistent with a "flat" geometry in which parallel lines don't converge and the angles of a triangle add up to 180 degrees.

However, on relatively "small" scales such as that of the solar system or our galaxy, the geometry can be distorted by the gravitational effect of objects such as stars, and this will cause parallel lines that pass close to such objects to diverge. Thus we can't easily test the "flatness" of the Universe by making "local" measurements, and tests of "flatness" have to involve much larger scales.

Obviously we can't draw triangles that have sides that are billions of light years in length, measure their angles and check whether these add up to exactly 180 degrees, so astronomers have to devise more indirect tests.

One such test is to measure the size of the tiny fluctuations seen in the Cosmic Microwave Background radiation. The Big Bang theory predicts the size (approx a degree across) that these fluctuations should be in a "flat" universe and measurements made by satellites such as WMAP have shown this to be the case (at least down to the accuracy possible using the available technology and time).

A "flat" Universe is also one which, in the absence of "dark energy", would have the density that would make it critically balanced between expanding forever and eventually contracting. Given that the most favoured versions of the Big Bang models actually predict the Universe to be "flat", cosmologists were very relieved to find this prediction confirmed by WMAP.

Tony


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PostPosted: Mon Feb 14, 2011 8:58 am 
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David Frydman wrote:
So Joe,
You may not be entirely in agreement with others who maintain almost certainly that the Universe is flat.


Ha! I wish I had the knowledge and courage to have an opinion on the matter. I just tag along with current thinking which seems to say that the universe appears flat but no one knows for certain.

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PostPosted: Mon Feb 14, 2011 9:19 am 
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I have looked at two of the book recommendations but at around 450 pages I am not prepared to invest the time in really getting to know the subject at least well enough to argue any opinions I might form.

I am looking for the book called Cosmology for Dummies.

It might exist but I realise it would be too shallow.

Regards, David.


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