The Curvature of spacetime?? how?

[DanielFB]

do you think it is possible for space time to be curved. If space could be curved then it :eek2: 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

[Dark Mind]

I don't think space is "literally" being curved... That's just a type of metaphor used to describe the intensity of gravity, I believe. The bigger the "curve" in towards an object, the more pwerful the gravity is.

 

Essentially it is a type of "quantum foam"... metaphorically...

 

:eek2:

[HydrogenBond]

Space has distance and time components; this is what curves. Since gravity is connected to the attraction between matter than if space didn't have substance than it would imply that gravity can bend distance and time without mass. That would really screw with the laws of physics because nothing would be stationary as space pulsates in space and time. Space having some mass makes more sense. Space mass probally comes as a biproduct of fusion, which is why space contraction occurs where matter is highly pressurized. Space is gaining substance which diffuses to uniformly fill space. This makes the final universe state one of contraction.

[infamous]

This makes the final universe state one of contraction.

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

[Dark Mind]

I believe "Now".

 

...But not positive, just really sure :eek2:.

[DanielFB]

this sounds good, but however, I regret to say that if space is now physical it can no longer be space. I like to think of it in terms of a football field and it's boundaries. Now, it matters not :eek2: how many players there are in the field, the boundaries never increase. What happens is new. The players fill over the edges, but the boundaries remain really fixed into reality. The same applies to space. But if general relaitivity is right, space must now be thought of as a mental construct, and nothing physical, say.

[Erasmus00]

Space has distance and time components; this is what curves. Since gravity is connected to the attraction between matter than if space didn't have substance than it would imply that gravity can bend distance and time without mass.

 

Thats not true. According to general relativity, mass curves the space around it. The idea of curvature is then connected to mass, but it does not require space to have any "substance" in the way you mean.

 

Space having some mass makes more sense. Space mass probally comes as a biproduct of fusion, which is why space contraction occurs where matter is highly pressurized. Space is gaining substance which diffuses to uniformly fill space. This makes the final universe state one of contraction.

 

Space mass coming as a biproduct of fusion doesn't make any sense. The sun would then be gaining mass. Also, the expansion of the universe would be decelerating, not accelerating as observed. Not to mention that the most accurate theory of gravity we thus far have (general relativity) predicts that, if nonzero, the curvature of empty space creates a sort of anti-gravitational effect.

-Will

[Dark Mind]

:lol:

 

... Like I keep telling myself... Someday, someday I'll know this stuff...

 

:)

[Qfwfq]

Space to me is a geometrical substratum supporting the universe, and it is not possible for it to be curved.

Have you studied differential geometry?

 

As far as we currently can observe, the geometric interpretation can't be really verified. It is simply a logical consequence of the principle of equivalence. Actually, gravity can be viewed as a curvature of space-time and not necessarily of space. Observing the lare scale geometry of the universe it might, however, prove to have a global topology that isn't possible for a flat space.

[UncleAl]

Why should spacetime be Euclidean? Because you learned 2-D plane geometry in high school? Euclid won't even work on the surface of the Earth (surveying, navigation). You have a choice of eight fundamental 3-D geometries,

 

WP Thurston, "Three-dimensional geometry and topology," Vol. 1. Princeton Mathematical Press, Princeton, NJ, 1997

 

Given a nice laser and two mirrors. You make an arbitrary optical triangle with sides each a few million miles long in free fall orbiting the sun. The laser shoots a light beam to the first plane mirror, it reflects to the second plane mirror, and that reflects back to the laser. You add up the sum of the interior angles of the triangle. Three possiblities:

 

1) The sum is exactly 180 degrees. Plane (Euclid) geometry. The circumference divided by the diameter of a circle is exactly pi. Given a point not on a given line, there can be drawn only ONE line through that point parallel to the given line. Flat sheet of paper.

 

2) The sum is more than 180 degrees. Elliptic (Bolyai-Lobechevsky) geometry. The circumference divided by the diameter of a circle is less than pi. Given a point not on a given line, there can be drawn ZERO lines through that point parallel to the given line. Surface of the Earth.

 

3) The sum is less than 180 degrees. Hyperbolic (Riemann) geometry. The circumference divided by the diameter of a circle is more than pi. Given a point not on a given line, there can be drawn an INFINITE number of lines through that point parallel to the given line. Surface of a nuclear power plant cooling tower.

 

If you do the laser experiment, (2) not (1) will obtain. This can be modeled as gravitation arising from either spacetime curvature (Einstein, metric theories of gravitation) or spacetime torsion (Weitzenböck, affine/teleparallel theories of gravitation). Spacetime curvature and spacetime torsion give identical predictions for all gravitational phenomena at all scales. However, they are measurably different based on their assumptions.

 

http://arxiv.org/abs/gr-qc/0505092

http://arxiv.org/abs/gr-qc/0412034

 

Metric gravitation postulates the Equivalence Principle: all local bodies fall identically in vacuum. Affine gravitation makes no additional postulate. If you can provide two lumps that fall differently in vacuum, Einstein was wrong. Folks have looked,

 

http://www.mazepath.com/uncleal/eotvos.htm#b22

 

given the menu of ways of being fundamentally different,

 

http://www.mazepath.com/uncleal/eotvos.htm#b21

 

The last possiblity for measurable metric/affine theory divergence will have its empirical experiment completed in mid-September. What makes you think there are only three material dimensions?

 

http://arXiv.org/abs/astro-ph/0508572

[Tormod]

Not spam - I corrected the URL for dduckwessel.

[infamous]

Sorry Tormod,

 

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

When it appears as though someone is trying to sell 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

 

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.

 

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.

 

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]

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.

 

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

[maddog]

DanielFB,

 

Between Qfwfq and UncleAl I feel answered adequately your first post. However

the one below needs a bit more.

 

this sounds good, but however, I regret to say that if space is now physical it can no longer be space. I like to think of it in terms of a football field and it's boundaries. Now, it matters not :) how many players there are in the field, the boundaries never increase. What happens is new. The players fill over the edges, but the boundaries remain really fixed into reality. The same applies to space. But if general relaitivity is right, space must now be thought of as a mental construct, and nothing physical, say.

 

I have reread this a few times and am now not sure of your position.

 

Space is "physical" or not. [may you meant to not for now]

 

The space we live in is only a metric (like the boundries in your example) or

a measure. Whenever we represent a system by some graph or picture, it

is always a mental construct (GR or otherwise). We define a set of

coordinates and scale to assist with our graph and orient it appropriately.

It maybe you are not aware of Differential Geometry as Qfwfq mention or

considering other forms of Geometry than that of Euclid as UncleAl said.

Non-Euclidian geometry has been with us since about the 1850s or so. It is

true it was not fully utilized in physics until General Relativity. This is the

modern view today though.

 

Do a google search on "Differential Geometry" or "Noneuclidian geometry",

goto Wolfrom website or Mathworld or something. Learning new things is

good.

 

maddog