Branes, Branes and more Branes

[none]

from what I have been reading the universe is flat and not curved
and thinking about higher dimensional space, hyperspace or manifold where the universe might reside
and theory of multi universe mentions brane collision or brane interference producing universes
I was thinking that maybe hyperspace is curved and within hyperspace so to speak is multiple flat universes
that a curved hyperspace would break a causality chain because there would be a loop due to curvature
and that is what intrigues me that hyperspace could be curved and not flat
maybe I am conflating things here but I am actually enamored by the prospect of a curved hyperspace

 

[Malintent]

I think you are confusing your dimensions. "Curved" is a 3D term you are using to describe 12D space... The word has its limits and is invalid when you use it's 3D consequence to describe a potential 12D problem. It is like expressing a problem with the height of a line in 2D space (there is no height).

 

[Kharakov]

Except 4d spacetime is curved. Curves can exist in 2+ dimensions.

 

[fromderinside]

.

.. _

.... )

.... ▢

etc.

 

[none]

Except 4d spacetime is curved. Curves can exist in 2+ dimensions.

I think.... that you are confusing curvature within with the flat universe with curvature within a curved universe

 

[beero1000]

There's so much we still don't know, even in the simplest case of 3 geometric dimensions. Also, we all need to be super careful not to mistakenly embed the universe into a larger space. People intuitively tend to do this - it's hard to think of a shape without thinking about the space around it - but that's important when thinking about the universe, where the shape is all there is.

Curvature is a geometric concept and 'looping' is a topological one. Space could be curved, but as far as we've measured, it appears flat. No matter if it is curved or flat, it may or may not 'loop' - even in a flat universe, you could travel in a straight line and return to where you started (this is weird). Another property is orientability - it's possible you could travel on some path and return home reversed - heart on the right side, molecule chirality swapped, everything (this is weirder). For finite universes, you can make a list of the possible 3-manifolds (IIRC, there are 10 possible flat finite universes) and look at their properties. If the universe is finite, we probably live in one of those but it will be really hard to figure out which.

 

[Speakpigeon]

from what I have been reading the universe is flat and not curved

I've read that too but, hey, don't go believe eveything experts say. Friday 20th is near.

and thinking about higher dimensional space, hyperspace or manifold where the universe might reside

That' an idea.

and theory of multi universe mentions brane collision or brane interference producing universes
I was thinking that maybe hyperspace is curved and within hyperspace so to speak is multiple flat universes

Ok, I buy your idea of several universes drifting in a curved hyperspace but I think the topology of the hyperspace would necessarily be inherited by the various universes included in it so all the flatness you would ever get would be a universe being flat only when it would be located in a flat area of this otherwise curved hyperspace. It could in principle be transient flatness, one that would evaporate as the universe somehow drifted away into a curved area of hyperspace.

that a curved hyperspace would break a causality chain because there would be a loop due to curvature
and that is what intrigues me that hyperspace could be curved and not flat
maybe I am conflating things here but I am actually enamored by the prospect of a curved hyperspace

The prospect?! Whoa, come down, man. It's just an idea.

The only prospect you face right now is a very curved White House.

The loopness itself would also have to be transient in nature.

Will the goofiness of Trump prove transient too?
EB

 

[Speakpigeon]

Except 4d spacetime is curved. Curves can exist in 2+ dimensions.

I think.... that you are confusing curvature within with the flat universe with curvature within a curved universe

Interesting question.

I don't see how we could represent the curvature of a one-dimentional curve so that intuitively all curves have the same geometry as a straight line but I also don't see why curves, including straight lines, could not have a curved topology.

I suspect mathematicians haven't studied those. The notion of curvature being studied if I remember correctly is based on the notion of distance as measured within the considered space. In a curved space, there can be several possible minimal paths between two points but like for straight lines, there's just one possible route and therefore distance between two points on a one-dimentional curve. So, not curvature in the original sense. But may you could invent a different noion of curvature.
EB

 

[none]

Well if you put it like that then you could be right

 

[Speakpigeon]

Well if you put it like that then you could be right

It wasn't a curved ball you know.
EB

 

[Treedbear]

...
Curvature is a geometric concept and 'looping' is a topological one. Space could be curved, but as far as we've measured, it appears flat. No matter if it is curved or flat, it may or may not 'loop' - even in a flat universe, you could travel in a straight line and return to where you started (this is weird). Another property is orientability - it's possible you could travel on some path and return home reversed - heart on the right side, molecule chirality swapped, everything (this is weirder). ...

Looping as with a Möbius strip? It's an interesting analogy in that a 3D version would be unbounded.

Could it be true that any set of dimensions would potentially have some amount of curvature from the perspective of the next higher dimension? I mean, a 2D plane can have curvature from the 3D perspective. And according to general relativity 3D space has curvature when the dimension ot time is considered. Just saying, as nothing is really perfect why assume our 4D universe is perfectly flat?

 

[beero1000]

...
Curvature is a geometric concept and 'looping' is a topological one. Space could be curved, but as far as we've measured, it appears flat. No matter if it is curved or flat, it may or may not 'loop' - even in a flat universe, you could travel in a straight line and return to where you started (this is weird). Another property is orientability - it's possible you could travel on some path and return home reversed - heart on the right side, molecule chirality swapped, everything (this is weirder). ...

Looping as with a Möbius strip? It's an interesting analogy in that a 3D version would be unbounded.

Well, more like a Klein bottle or a sphere or a torus. A Möbius strip has a boundary, which the universe does not appear to have (I think). Also, it might still be bounded.

Could it be true that any set of dimensions would potentially have some amount of curvature from the perspective of the next higher dimension? I mean, a 2D plane can have curvature from the 3D perspective. And according to general relativity 3D space has curvature when the dimension ot time is considered. Just saying, as nothing is really perfect why assume our 4D universe is perfectly flat?

It's not an assumption, it's an experimental result. We've measured the curvature from cosmic background radiation and the universe we can see appears to be flat (and uniformly so).

In terms of viewing the shape from a higher dimensional space - you need to distinguish between intrinsic curvature and extrinsic curvature. In other words, there's curvature that's inherent to the geometry of the shape (i.e. curvature we can measure as inhabitants of the shape), and there's curvature that's a result of the specific embedding chosen (i.e. curvature that can be measured from 'outside').

 

[Treedbear]

...
In terms of viewing the shape from a higher dimensional space - you need to distinguish between intrinsic curvature and extrinsic curvature. In other words, there's curvature that's inherent to the geometry of the shape (i.e. curvature we can measure as inhabitants of the shape), and there's curvature that's a result of the specific embedding chosen (i.e. curvature that can be measured from 'outside').

Got it. Sort of: What is the difference between intrinsic and extrinsic curvature?

So consider something like a circle drawn on a piece of paper. Then you roll the paper into a tube. The circle (like any shape, curve, whatever) drawn on the paper has an intrinsic curve property, regardless of the extrinsic curvature of the tube.

So I guess a beam of light will follow a curved path passing the Sun because space is intrinsically curved? Or is it that space-time is intrinscically curved? Or is it that space is extrinsically curved with respect to time? It seems the curvature is the result of the acceleration of gravity near the Sun. But acceleration is expressed in terms of distance divided by the square of time. So there's your 4th dimension.

 

[beero1000]

Got it. Sort of: What is the difference between intrinsic and extrinsic curvature?

So consider something like a circle drawn on a piece of paper. Then you roll the paper into a tube. The circle (like any shape, curve, whatever) drawn on the paper has an intrinsic curve property, regardless of the extrinsic curvature of the tube.

So I guess a beam of light will follow a curved path passing the Sun because space is intrinsically curved? Or is it that space-time is intrinscically curved? Or is it that space is extrinsically curved with respect to time? It seems the curvature is the result of the acceleration of gravity near the Sun. But acceleration is expressed in terms of distance divided by the square of time. So there's your 4th dimension.

For example, take the classic demonstration where we visualize spacetime as a rubber sheet:


Sure, mass introduces local deformation, but I'm talking about the global shape. You can ask, what if the natural surface the rubber defines is a sphere or a torus instead of a sheet? What if it's something weirder?

As far as we can tell, it has no intrinsic curvature to it, but we still don't know if it's finite or infinite, if it's orientable, etc.

 

[Treedbear]

...
For example, take the classic demonstration where we visualize spacetime as a rubber sheet:
View attachment 9535

Sure, mass introduces local deformation, but I'm talking about the global shape. You can ask, what if the natural surface the rubber defines is a sphere or a torus instead of a sheet? What if it's something weirder?

As far as we can tell, it has no intrinsic curvature to it, but we still don't know if it's finite or infinite, if it's orientable, etc.

I have a problem accepting the classic visualization because it implies there is an extradimensional force pulling on the objects. In the demonstration that force is of course gravity acting on the ball moving around the depression. In reality the deformation occurs in 3 or 4 dimensions (I'm still not sure which) and so can't be represented visually. But still ... if the demonstration has any significance it surely calls for some additional force vector.

 

[beero1000]

...
For example, take the classic demonstration where we visualize spacetime as a rubber sheet:
View attachment 9535

Sure, mass introduces local deformation, but I'm talking about the global shape. You can ask, what if the natural surface the rubber defines is a sphere or a torus instead of a sheet? What if it's something weirder?

As far as we can tell, it has no intrinsic curvature to it, but we still don't know if it's finite or infinite, if it's orientable, etc.

I have a problem accepting the classic visualization because it implies there is an extradimensional force pulling on the objects. In the demonstration that force is of course gravity acting on the ball moving around the depression. In reality the deformation occurs in 3 or 4 dimensions (I'm still not sure which) and so can't be represented visually. But still ... if the demonstration has any significance it surely calls for some additional force vector.

Of course, it's an imperfect analogy. It's in a lower dimension and it uses gravity to create the deformation, etc. In actuality, per general relativity, mass/energy deforms the space-time around it without anything pulling on it (creating gravity). Still, it conveys the basic idea and my point was that we could just as easily imagine a rubber sphere, where the deformation occurs radially (or a torus, etc). That's what I meant by the shape of the universe.

 

[Treedbear]

I have a problem accepting the classic visualization because it implies there is an extradimensional force pulling on the objects. ...

Of course, it's an imperfect analogy. It's in a lower dimension and it uses gravity to create the deformation, etc. In actuality, per general relativity, mass/energy deforms the space-time around it without anything pulling on it (creating gravity). Still, it conveys the basic idea and my point was that we could just as easily imagine a rubber sphere, where the deformation occurs radially (or a torus, etc). That's what I meant by the shape of the universe.

Sorry if you'd rather not pursue this point further, but my main objection isn't that the deformation is due to gravity, but that the path of a ball in orbit around the mass requires the perpendicular force of gravity together with the force of the space-time plane in order to shape the circular path. Simply saying that space-time is deformed doesn't account for whatever influences the ball's path. It seems to introduce another unknown.

 

[beero1000]

Of course, it's an imperfect analogy. It's in a lower dimension and it uses gravity to create the deformation, etc. In actuality, per general relativity, mass/energy deforms the space-time around it without anything pulling on it (creating gravity). Still, it conveys the basic idea and my point was that we could just as easily imagine a rubber sphere, where the deformation occurs radially (or a torus, etc). That's what I meant by the shape of the universe.

Sorry if you'd rather not pursue this point further, but my main objection isn't that the deformation is due to gravity, but that the path of a ball in orbit around the mass requires the perpendicular force of gravity together with the force of the space-time plane in order to shape the circular path. Simply saying that space-time is deformed doesn't account for whatever influences the ball's path. It seems to introduce another unknown.

We're reaching the limits of the example, but I'm game if you are

In general relativity, nothing influences the ball's motion - it continues traveling in a 'straight line' (a geodesic) in space-time. Since space-time is curved due to the presence of mass, the path the ball takes in space also curves. The resulting change in velocity that we see is the effect we call gravity.

 

[Treedbear]

Sorry if you'd rather not pursue this point further, but my main objection isn't that the deformation is due to gravity, but that the path of a ball in orbit around the mass requires the perpendicular force of gravity together with the force of the space-time plane in order to shape the circular path. Simply saying that space-time is deformed doesn't account for whatever influences the ball's path. It seems to introduce another unknown.

We're reaching the limits of the example, but I'm game if you are

In general relativity, nothing influences the ball's motion - it continues traveling in a 'straight line' (a geodesic) in space-time. Since space-time is curved due to the presence of mass, the path the ball takes in space also curves. The resulting change in velocity that we see is the effect we call gravity.

So the space through which the Earth moves around the Sun is spherical? That doesn't seem rational to me.
ETA: Not only that but the orbital path is dependent on the Earth's speed. If it was traveling in a "straight line" why would the path change simply due to an increase in speed?