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Author  Topic: Size of the universe  
cavediver Member (Idle past 1808 days) Posts: 4129 From: UK Joined: 
Good.
No, not in the mathematical sense of the word 'surface'. When I refer to a surface, the surface is all that exists  there is no above or below. So the surface of the Earth is a 2dimensional world that is finite but has no boundary. We call it a 2sphere. If you are a 2d creature constrained to live in this 2sphere, you can move forwards/backwards and left/right. If you go far enough you will arrive back where you started from without any deviation from your straight path. The solid Earth is a called 3ball  it is finite and bounded, and it is bounded by the 2sphere surface. A 3sphere is a 3dimensional space that is finite and unbounded. It is very difficult to visualise as we cannot build one in space. But if you lived in one, you could move in all three dimensions, and again, if you go far enough you will arrive back where you started from without any deviation from your straight path. Just to add, a 1sphere is a 1dimensional finite unbounded space that similarly loops back on itself. We call them circles. The interior of the circle is the finite bounded 2ball, or 2disc. And again, the boundary of the 2ball is the 1sphere (i.e. the boundary of a disc is a circle)
No! The Universe can be either finite or infinite, and it is without boundary. It could be infinite in all three spatial dimensions, in which case there is obviously no boundary, or it could be finite in all three spatial dimensions but wrapped into a 3sphere  again, no boundary. It could even be wrapped up into a 3torus, or something even more exotic, but in each case it is finite with *no* boundary. Now, there could be boundaries where the Universe as we know it merges into something else, and we consider this in highly speculative theoretical physics... but that's for another day.
 
cavediver Member (Idle past 1808 days) Posts: 4129 From: UK Joined: 
Typical! So to clear up the controvercy, Percy is quite correct in that the surface of the sphere (2sphere) *is* a boundary to the inside and outside of the sphere (3ball). BUT we can have the 2sphere quite independent of any notion of there being a 3ball to which it would be a boundary. In our everyday experience, this is not possible. Every 2sphere has an "inside"  but mathematically, and when we are talking about the geometry/topology of spacetime, this need not be the case. AND you were actually asking the more general question of whether a general surface is a boundary between that "above" and that "below". In this case, we can have a finite unbounded 2dimensional surface that does not form a boundary between an inside and an outside of a 3dimensional space! This is the famous Klein Bottle, whose inside and outside are joined, yet there is no break in the bottle, no opening... imagine a surreally twisted sphere that somehow manages to join its inside to its outside without any break in the sphere! This is another situation where we cannot actually construct a real Klein Bottle in the boring flat 3d space in which we live.
 
cavediver Member (Idle past 1808 days) Posts: 4129 From: UK Joined: 
Nor would I except when you quotemine me:
Admittedly, there should have been a colon there, not a full stop. And 2sphere should be in quotes.
 
cavediver Member (Idle past 1808 days) Posts: 4129 From: UK Joined: 
Not the way to think about it. Think of space as an ocean (the fields), and "things" as waves (field excitations). Everything is ocean, both the things, and the space between the things.
 
cavediver Member (Idle past 1808 days) Posts: 4129 From: UK Joined: 
Of course. That is inevitable as soon as you take Minkowski's work and allow the fixed metric to become a function of spacetime position, as with General Relativity. The past 100 years of quantum field theory simply enforces this view.
No wonder indeed.
 
cavediver Member (Idle past 1808 days) Posts: 4129 From: UK Joined: 
 
cavediver Member (Idle past 1808 days) Posts: 4129 From: UK Joined: 
 
cavediver Member (Idle past 1808 days) Posts: 4129 From: UK Joined: 
And just to point out that what Alfred says is contradicted by every professional phsyicist and cosmologist working today, every cosmology textbook, and every cosmology paper being published. But Alfred think's he's right  so we just pat him on the head, nod encouragingly, and then wait for him to nod back to sleep again... shouldn't take long.
 
cavediver Member (Idle past 1808 days) Posts: 4129 From: UK Joined:

Yes. This club is usually known as "all the physics and cosmology departments in the world".
We can. We do. We have done. A billion times since Einstein. It is just you who has not gained the ability to understand.
Yes Alfred, every physicist and mathematician involved in relativity and cosmology is completely inept. All of us. And you are not. Alfred's world sounds like a nice play to be.
Your laughing? What, while it us to that takes all the grant money? Us, that get to build and play with the largest machines ever buily by man? Us, that are approached for our scientific and mathematical ability? Us, that after our scientific careers, are employed around the world in some of the highest paying jobs? Keep laughing Alfred... keep laughing
 
cavediver Member (Idle past 1808 days) Posts: 4129 From: UK Joined: 
Not required for a black hole.
Not required for a black hole
Not required for a black hole
Not required for a black hole Once again, Alfred, you wear your ignorance like a badge of honour.
 
cavediver Member (Idle past 1808 days) Posts: 4129 From: UK Joined:

I don't want to say that  that is simply the way it is. And we don't even need the event horizon, as we could never have the globally required god'seye view to determine if it exists. An apparent horizon is good enough.
I certainly must not know, as it is blatently untrue. Depending on context, gravity is the reaction of the metric to itself and the stressenegy distribution (essentially the mathematics of General Relativity); or it is the reaction of a test body to the metric (essentially the physics of General Relativity.)
Yes, if we are talking about Newtonian gravity and mechanics. But as we are discussing black holes, we are actually talking about General Relativity and have left such basic concepts long behind.
Gravity does not "cross" anything. The spacetime metric has a particular form around the black hole, and external bodies will move according to that form. There is no gravity "force" at this level of discussion, and gravity cannot be "trapped" inside the horizon  although one could look at propagating fluctuations in the metric (gravitational waves) and these are indeed trapped. Actually, an almost identical situation occurs with the electromagnetic field, where propagating fluctuations are trapped (i.e. light cannot escape), but static field configurations can straddle the horizon as we see with electrically and magnetically charged (ReissnerNordstrom) black holes.
Information does become trapped until the point where the black hole evaporates away. But we are now moving through semiclassical relativity into quantum gravity, and this certainly does not belong in a discussion that is still clinging to Newtonian concepts and terminology. Edited by cavediver, : No reason given.
 
cavediver Member (Idle past 1808 days) Posts: 4129 From: UK Joined: 
Yep, ignore the naysayers  I've always used this as a "see, we are at the centre of everything" smartarse comment Have I missed much?
 
cavediver Member (Idle past 1808 days) Posts: 4129 From: UK Joined:

Yeah, I guess I should have been here for that. I have to say that on the announcement, I punched the air and welled up a fair bit. I surpised myself at my own reaction
 
cavediver Member (Idle past 1808 days) Posts: 4129 From: UK Joined:

Couldn't put it better myself. Ok, I could, but it's close enough.
That would be rather incredible if true, given that Einstein died in '55 and John (Wheeler) didn't coin the term Black Hole until '67 (although there are reports of the term as early as '64) In 1939, when Einstein wrote the paper of which you are so fond, it had only recently been appreciated that the Schwarzschild "singularity" (at r=2M in geometric units) was not actually a real singularity, but merely a coordinate singularity (such as r=0 in polar coordinates) and later became known as the Schwarzschild radius. Oppenheimer with his student Snyder started looking at collapse to and through the Schwarzschild radius, but Einstein was dubious as to such an extreme area existing physically. Einstein attacks the problem by building the mass for his Schwarzschild solution out of orbiting bodies. He discovers that even before the Schwarzschild radius could be reached, his orbiting bodies were being forced to orbit at the speed of light, which of course is impossible. He reasons that this behaviour amongst others will prevent collapse down to the radii in the region of the Schwarzschild radius. His error is assuming that he can build such a mass out of orbiting bodies in the vicinity of the Schwarzschild radius. It is not possible as there are no stable orbits for massive objects close to the Schwarzschild radius. So his reasoning is incomplete and incorrect. Next?



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