How can a big bang expand to an infinite size?

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22 minutes ago, geordief said:

does the light ray  with which we see the boat disappear exist  in  an embedding 3rd dimension making the surface extrinsic after all?

Yes, this is it. If the light were somehow tied to the 2D surface and went strictly along it, the ship would not disappear. A straight line on the surface of Earth is a great circle. But the light ray does not follow it - it rather follows a straight line in the 3D space.

Consider the example of a cylinder again. Imagine that the planet has a cylindrical shape. Unless the ship goes in the direction of the cylinder's axis, it will be disappearing behind the horizon as usual. But we know that the intrinsic curvature of the cylinder is 0. So, the disappearance of the ship over the horizon is a consequence of the extrinsic curvature, i.e., of how the surface is curved in the embedding space.

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Very helpful @Genady, thanks.  Intrinsic and extrinsic are clarified for me now.

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In simple terms, intrinsic curvature implies there is no 'outside' dimensions embedding the curvature.
Since there is no 'outside' you cannot 'see' a ship dropping below the horizon as your view is confined to the curved surface.
The Earth's surface is extrinsic because you can go 'inside' the curvature by boring a hole between two points connecting the ends of an arc, or 'outside' the curvature to see the top of the mast of the ship dropping below the horizon.

21 hours ago, Markus Hanke said:

Actually, it doesn’t - they are separate concepts. GR determines only local geometry, but not global topology.

Not sur I agree.
Global geometry is also determined by the  mass/energy content of the universe, and this global curvature constrains possible topologies.
As an example, a negatively curved universe can not close on itself, and has to be infinite.
A flat universe can either be infinite or finite, as there are flat closed topologies like a flat torus.
A positively curved universe has only closed topologies, like hyperspheres or toruses, available which are necessarily finite.

If the universe is homogenous and isotropic, we may be able to use the local curvature of the observable universe as an indication of the global curvature of the universe, and all measurements indicate it is very nearly flat.
That could mean the universe is finite but many orders of magnitude larger than the observable universe; much like the floors of your house are flat on a curved Earth, or it could actually be flat and infinite.

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1 hour ago, MigL said:

Not sur I agree.
Global geometry is also determined by the  mass/energy content of the universe, and this global curvature constrains possible topologies.

You are right in that it constrains the set of all possible global topologies, but what I attempted to point out is that it doesn’t uniquely determine it, at least not in 4D. More precisely, globally different topologies  can be compatible with the same local geometry, so local measurements of curvature alone don’t necessarily give this information. The reverse is also true - manifolds can have the same global topology, yet different geometries. So this issue is subtle.

The interesting exception is in 2D - here, the Ricci scalar is also the Euler characteristic, so gravity is entirely topological.

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On 1/4/2024 at 5:15 PM, geordief said:

Is this a space with no time component?

A space that is ready to be populated with objects?

I think I am more familiar with a space that is created by objects reconfiguring themselves(in an overall expansionist way as per observations)

I think that is the orthodox view even if I am not up to speed with it.

It still seems difficult for me to imagine  the 3d universe existing on the 2d surface of the sphere

There doesn't seem to be room for the 3 dimensions.

Is it just an analogy?

And the universe is not hollowed out ,is it?)unless the "hollow" is somehow the past history-surely not that)

I was wondering if time can exist without matter?  This is what I found:

"GR states that spacetime is the field produced by matter just like the electromagnetic field is produced by charges. Vacuum solutions are unphysical, they don’t exist in reality."

Does that mean that if the big bang has a finite size, the outer 3d limits of the expansion could be expanding at ANY speed (assuming there is no infinite speed), and beyond that limit could be a region of no matter and therefore no spacetime, just "space" if you will?  No more spacetime, just space, until you encounter another big bang coming from another direction?

I thought one way to explain an accelerating expansion of the universe is our observable universe is located inside a great void, like a bubble surrounded by unimaginably great masses pulling our region of spacetime apart from all directions.

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33 minutes ago, Airbrush said:

I thought one way to explain an accelerating expansion of the universe is our observable universe is located inside a great void, like a bubble surrounded by unimaginably great masses pulling our region of spacetime apart from all directions.

No, according to Birkhoff's theorem, the spacetime inside a non-rotating spherical shell of matter is flat.

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2 hours ago, Airbrush said:

I was wondering if time can exist without matter?  This is what I found:

"GR states that spacetime is the field produced by matter just like the electromagnetic field is produced by charges. Vacuum solutions are unphysical, they don’t exist in reality."

Does that mean that if the big bang has a finite size, the outer 3d limits of the expansion could be expanding at ANY speed (assuming there is no infinite speed), and beyond that limit could be a region of no matter and therefore no spacetime, just "space" if you will?  No more spacetime, just space, until you encounter another big bang coming from another direction?

I thought one way to explain an accelerating expansion of the universe is our observable universe is located inside a great void, like a bubble surrounded by unimaginably great masses pulling our region of spacetime apart from all directions.

Don't really know what to think.

But I don't think the observable universe is surrounded by a great void as in my understanding it is surrounded by "more of the same"  but that we have no idea how much of this "more of the same" there or-or what it is doing.

The only reason we don't  see this "more of the same" is that it is receding from us faster than the speed of light and so has become invisible to us.

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3 hours ago, Airbrush said:

I was wondering if time can exist without matter?  This is what I found:

"GR states that spacetime is the field produced by matter just like the electromagnetic field is produced by charges. Vacuum solutions are unphysical, they don’t exist in reality."

That doesn't seem a reasonable assumption.
It would mean space-time is an emergent property of the matter in it, as if separations and durations are 'encoded' in the particles of matter themselves ( in a hidden variable sort of way ).

My understanding is that the geometry of space-time is the field, not space-time itself. Space-time devoid of geometry is equally un-physical.
The reason vacuum solutions are un-physical is because there is no true vacuum devoid of anything.

But ... I could be wrong.

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1 hour ago, geordief said:

it is receding from us faster than the speed of light and so has become invisible to us.

This is a common misconception. In fact, we can and do see light coming to us from sources which recede faster than $$c$$. It is so because as the emitted light moves away from its source along the line connecting us to the source, it gets to parts which recede from us slower than the source. Eventually, it gets to parts which recede slower than $$c$$.

Here is a more detailed description:

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4 hours ago, Airbrush said:

I was wondering if time can exist without matter?  This is what I found:

"GR states that spacetime is the field produced by matter just like the electromagnetic field is produced by charges. Vacuum solutions are unphysical, they don’t exist in reality."

Where did you find it? Is it a credible source?

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Posted (edited)
48 minutes ago, Genady said:

This is a common misconception. In fact, we can and do see light coming to us from sources which recede faster than c . It is so because as the emitted light moves away from its source along the line connecting us to the source, it gets to parts which recede from us slower than the source. Eventually, it gets to parts which recede slower than c .

Here is a more detailed description:

Thanks.Probably a bit too hard for my brain to get around but I will accept it for now

Not sure how it affects the point I was trying to make.

Does it mean there isn't  an unobservable universe  beyond  the  observable  universe?

8 minutes ago, swansont said:

Where did you find it? Is it a credible source?

I think I found it here in physics stackexchange (by googling)

Edited by geordief
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19 minutes ago, geordief said:

Not sure how it affects the point I was trying to make.

It removes the consideration of superluminal expansion from the point you were trying to make.

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49 minutes ago, geordief said:

I think I found it here in physics stackexchange (by googling)

Some guy on substack, where others disagree, is probably not to be taken as authoritative. But i’d like Airbrush to answer.

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Posted (edited)
16 hours ago, swansont said:

Where did you find it? Is it a credible source?

Most of this is beyond my understanding.

"Time and energy are Fourier conjugates (or more generally, spacetime and energy-momentum) and cannot exist in the physical reality without each other. In other words, GR states that spacetime is the field produced by matter just like the electromagnetic field is produced by charges. Vacuum solutions are unphysical, they don’t exist in reality. Their flaw is that the equations are solved without realistic physical initial conditions. This approach and resulting solutions are physically meaningless."

But then there is also this from the same source:

"No, general relativity doesn't make any claim as to whether matter must exist or not. In fact, the simplest of the solutions to the Einstein equations are vacuum solutions. For example, the Kerr-Newman blackholes and their special cases such as the Schwarzschild blackholes and Kerr blackholes. The dimensionality of spacetime is still 4D in these solutions with one dimension being time-like."

Edited by Airbrush
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35 minutes ago, Airbrush said:

Most of this is beyond my understanding.

"Time and energy are Fourier conjugates (or more generally, spacetime and energy-momentum) and cannot exist in the physical reality without each other. In other words, GR states that spacetime is the field produced by matter just like the electromagnetic field is produced by charges. Vacuum solutions are unphysical, they don’t exist in reality. Their flaw is that the equations are solved without realistic physical initial conditions. This approach and resulting solutions are physically meaningless."

But then there is also this from the same source:

"No, general relativity doesn't make any claim as to whether matter must exist or not. In fact, the simplest of the solutions to the Einstein equations are vacuum solutions. For example, the Kerr-Newman blackholes and their special cases such as the Schwarzschild blackholes and Kerr blackholes. The dimensionality of spacetime is still 4D in these solutions with one dimension being time-like."

Time and energy being Fourier conjugates doesn’t come from relativity, and it’s a leap to say that this means something about the existence of spacetime and energy-momentum.

Anyway, just because someone claims something does not make it true.

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2 hours ago, Airbrush said:

Most of this is beyond my understanding.

"Time and energy are Fourier conjugates (or more generally, spacetime and energy-momentum) and cannot exist in the physical reality without each other. In other words, GR states that spacetime is the field produced by matter just like the electromagnetic field is produced by charges. Vacuum solutions are unphysical, they don’t exist in reality. Their flaw is that the equations are solved without realistic physical initial conditions. This approach and resulting solutions are physically meaningless."

But then there is also this from the same source:

"No, general relativity doesn't make any claim as to whether matter must exist or not. In fact, the simplest of the solutions to the Einstein equations are vacuum solutions. For example, the Kerr-Newman blackholes and their special cases such as the Schwarzschild blackholes and Kerr blackholes. The dimensionality of spacetime is still 4D in these solutions with one dimension being time-like."

The central postulate of general relativity is that local physics is physics of special relativity. And special relativity does not make any claims about matter.

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14 hours ago, Airbrush said:

GR states that spacetime is the field produced by matter

This is absolutely untrue, on all levels.

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