The Curvature of spacetime?? how?

[dduckwessel]

Originally Posted by DanielFB

do you think it is possible for space time to be curved. If space could be curved then it wouldn't be space, it would be matter.

Space to me is a geometrical substratum supporting the universe, and it is not possible for it to be curved. If it was, it wouldn't be space, but a type of matter, like quantum foam.

danielfb

What is 'dark' matter then? Is that not the component which holds everything else in the universe together?

[dduckwessel]

Originally Posted by infamous

Are you suggesting that space is contracting now, or, that space will someday begin to contract?

Some astronomers have speculated that while the universe is expanding, it is also slowing down (search universetoday.com 2004 archives, now www.bautforum.com) and will act like a rubber band and recoil on itself!

[Tormod]

Not spam - I corrected the URL for dduckwessel.

[dduckwessel]

Originally Posted by Tormod

Not spam - I corrected the URL for dduckwessel.

Sorry Tormod,

infamous - how can a science site be considered spam???

[infamous]

Originally Posted by dduckwessel

Sorry Tormod,

infamous - how can a science site be considered spam???

When it appears as though someone is trying to sell merchandise.

[dduckwessel]

Originally Posted by infamous

When it appears as though someone is trying to sell merchandise.

The link is to a 'science forum' (a very good one too) - how on earth can that be interpreted as selling merchandise.

[DanielFB]

The idea incorporated into the theory of general relativity that gravity is the curvature of space-time implies that space is a physical medium for supporting all physical objects in the universe. Time is like space and the two are said to be connected inextricably. But time slows down at high speeds, and the effect is a time dilation, so here if you have derived that spaces physical property means that it is more like some type of 'ether' like medium and that our space in the geometrical terms we think of it is not an objectivity but much more of a subjective set of spatial relations just as philosophers thought of it, the possibility is that time, like space doesn't exist in an actual reality and that general relativity proves that the world actually doesn't possess physical attributes. The idea of space, to me, is self defining, so when we talk of bending space is sounds similar to an attempt to 'bend nothing'. The fact remains, if the strong force keeping us close to the ground is constructed of some kind of 'condensed nothing', then surely, a reappraisal of our definition of nothing is in order.

While the idea of curved space is possible in terms of a contraction of distance, or a dilation of distance, like the effects of time in motion, and indeed matter in motion, anything that can be curved is not nothing, because it only makes sense if another layer of space could be said to undulate movable space, and there must subsist in at least ideas a more fundamental structure to the universe, for example a polarity.

Essentially, a duality fabricates these notions; a fundamental substratum may be left out in concern of general relativity, it needn't be one or the other. Perhaps it is the case that two forms of space coexist at once? It could be the case. Essentially, I am dissappointed with the notion of what not just a mental subsistence can be affected by amounts that are seperate from anything mental. I see space like a football field whose dimensionjs cannot be altered no matter how many players fill it. Of course i could be wrong. This analogy is indeed philosophical.

But I am a believer in time dilation, so distance dilation should not seem so arbitrary, however, see the first paragraph for the confusion.

DanielFB

[modest]

...continued from Re: Alpha and Omega

Originally Posted by lawcat

I see. So, if one was sitting inside of the surface of the balloon, one would feel "negative curvature" towards the inside of the ballon, "positive curvature" towards the outside of the ballon, and "flat space" in a local area.

No. There is no inside of the balloon and there is no outside of the balloon. The balloon is 2-dimensional for this analogy. It is a manifold. A person on the balloon is also 2D. Such an observer can't feel a force towards the inside or outside of the 2D surface - as far as they are concerned such directions don't exist.

If you draw a triangle on a flat piece of paper then the angles add up to 180 degrees. If you draw a triangle on the surface of a sphere then the angles add up to greater than 180°. On a hyperbolic surface the angels add up to less than 180°. Check out this link:

Non-Euclidean geometry - Wikipedia, the free encyclopedia

The reason this is true is because these surfaces are curved. The surface of a globe is curved, so triangles don't have to add up to 180° and parallel lines intersect.

General relativity models our spacetime as curved and cosmology that's based on general relativity has possible curvature. This means a very big triangle may not have angles that add up to 180° and parallel lines may diverge (if global geometry is hyperbolic) or they may intersect (if global geometry is elliptical).

Here's the tricky part: we can tell the balloon is curved because it's curved in our 3D perception. This is called "extrinsic" curvature. A line is one dimensional. It can be curved by adding a second dimension and making it a circle. The circle can be curved by adding a third dimension and making a sphere. Curving coordinates into a higher dimension like this is extrinsic curvature. This is how humans understand curvature, but there's no reason why there would have to be a higher dimension. If mass curves 4-dimensional spacetime, there's no reason why there would have to be a 5th dimension that spacetime is being curved into. It could just be intrinsically curved.

This is where the balloon analogy breaks down, because the two dimensional surface of the balloon is being expanded into our three dimensional perception. From our 3D perspective there is a center to the balloon. But, if our spacetime is being curved into a higher dimension we don't see it. It is completely imperceptible. If it is curved as general relativity tells us it is then it is intrinsically curved. There's no 5th dimension - just 4 curved dimensions.

Originally Posted by lawcat

Modest,

I did not understand your geodesic graph and this sim http://www.adamtoons.de/physics/relativity.swf

If an object falls, and fallows the curvature, it traverses space at a constant rate, to meet the surface.

I think the graph you're talking about is this one:



You'll notice the red line isn't traveling at a constant rate toward the green one. It accelerates toward it.

Originally Posted by lawcat

Both the object and the surface travel through time, but only the ibject travels through space.

You've got that backwards. Notice the red line only intersects the horizontal lines on the grid. The green line (surface of the planet) intersects both the horizontal and vertical grid lines. The red (free-falling) observer is traveling through time only. The green observer on the surface of the planet is traveling through (in fact, accelerating through) space and time. But, keep in mind, this is only a quick representation of an idea and not mathematically accurate.

~modest

[lawcat]

MOdest,

So, if I am understainding correctly, when an object accelerates due to gravitation, it stops moving through space, and it only moves through time.

Also, the vertical green line really makes it difficult to see how an observer can possibly be accelerating (linearly; not angularly.)

(This appears to be limited by the initial conditino of where you enter the gravitational field.)

[modest]

Originally Posted by lawcat

So, if I am understainding correctly, when an object accelerates due to gravitation, it stops moving through space, and it only moves through time.

Not exactly. When red looks at green, green appears to be accelerating (from red's perspective). When green looks at red, red appears to be accelerating (from green's perspective). So, which is actually accelerating?

Einstein introduced the equivalence principle that says a person standing on a planet is accelerating just like a person in a rocket who is accelerating with no planet or any other gravity source nearby. This is possible because spacetime is curved somewhat like the pic above (or below).

It also makes some intuitive sense. A person on a planet feels acceleration just like a person accelerating in a rocket. You might say that a person on the surface of a planet has spacetime accelerating through them because of the mass of the planet while a person in a rocket is accelerating through spacetime because of the impulse of the engine.

So, according to relativity, the answer to your question is that the surface of the planet is accelerating while the free-falling observer is not.

Originally Posted by lawcat

Also, the vertical green line really makes it difficult to see how an observer can possibly be accelerating (linearly; not angularly.)

It may be more intuitive like this,



Crossing a vertical line means moving through space. Crossing a horizontal line means moving through time. The green line crosses both while the red line crosses only the horizontal lines. The surface feels acceleration by more and more quickly crossing vertical lines. The free-falling object does not cross horizontal lines and feels no acceleration.

I stress again that this is just a depiction of the idea and not exactly accurate to GR. The reasons for that along with background info to this whole idea can be found at this site:

Relativity Tutorial

~modest