what are space curvatures exactly

[Money]

Einstein's general relativity says that all the planets

and our earth actually travel in a "straight line"

within a curved space-time.

 

Put another way....GR can show that the earth is not orbiting the sun, rather the earth is travelling a straight path and space/time is wrapped/curved around the sun.

 

So gravity = space-time curvature.

 

That is from another topic in this forum if this is true

are we not heloicentric?

 

does "everything" in the universe follow the curvatures?

does even light follow the space curvatures?

what are the curvatures exactly?

[lakmilis]

Yup, that sums up the notion of the topology of GR.

 

WE as in Earth? and yes, the Solar system is heliocentric. Kepler's laws still hold. The straight path following curves is basically the same notion which explains the centrifugal pseudoforce. An orbiting object due to inertia will travel in a straight line unless some force (centripetal for example) affects its path. The straight path analogy of curved space simply says that instead of hmm assigning an inherent gravitational force of mass in Newtonian mechanics, GR is saying that mass has the inherent ability to curve space.. in that case the same effect happens as Newtons force, and one can say that an object is travelling in a straight line in curved space.

 

This intuitively makes perfect sense. If you magically removed the Earth instantenously, the moon would then keep moving but now in a straight line in flat space (disregarding the gravity curvature from other masses like the planets and the sun).

 

Same thing as if you kept spinning a ball on a rope around you and cut the rope weeeeeeeee, ball flies off in a straight line (well, a trajectory but if we again disregard other masses, in this case the earth + drag, it would be a straight line).

 

It is merely a geometrical interpretation of forces, in this case the Newtonian law of gravitation.

 

About the 'Everything'. The answer is a lenient yes. Yes, because as far as we know, with regards to normal matter and light, this should follow the laws of physics , and all forms of energy are affected by the curvature of which it is embedded in. Yup, that includes light.

 

However, why the leniency? Well, you get things such as virtual particles, quantum tunnelling, dark matter, etc which hmm does say, exceptions might exist. But for example, dark matter I think is said to neither emit, absorb or reflect light. This is the definition of matter per se (as in at a metaphysical, not necessarily scientific level). But this violates E = Mc^2 ; what happens if a photon hits dark matter??? completely bizarre to think about. But it is part of current cosmology and experimental physics. So the former yes must be given a lenient rather than strict connotation.

 

WHAT the curvatures are.... This for various people in the scientific world (and on this forum) will entice many different opinions. But what most I would say agree on on a fundamental level, is that the curvatures is a geometrical understanding from differential geometry(topology) defined by Riemann, Einstein, Minkowski, bunch of others but the exact relation is probably the more specific Einstein tensor.

 

What the opinions which are deduced though from this is where I say many vary on the interpretation....i.e. the quality of the continuum, which is the 'what' you are asking.

 

If you want to get an idea, get popular non mathematical books like Hawkings, or Einsteins book relativity, hmm I have two good books I read when younger , Eric Damm (Norwegian astrophysicist but it is in Norwegian only I guess), and hmm whats his name again....Kaiko? hypercube something something dunno :X

 

You see the what question relates a bit to the fact the continuum expands into something, which in the past was intuitively the universe...now we say the universe in contained in this continuum which curves... the question is then , is is inherently different from the hmm space it expands into or is that where it expands something we just can not imagine...or total nothingness?

 

Will this imply if the space curves, and is not the same as nothingness, given virtual particles, it must necessarily be non zero Kelvin and have an energy density of positive semi-definite form or so

 

there, something to work from, and probably others again rebounding some of what I said, saying no no no , that is not a correct interpretation

 

hope this helps

 

lak

[ajb]

Particles and light rays follow what are know as geodesics if they are acted on by no forces other than gravity. Geodesics are in effect the "straight-lines" on a curved space; they are the shortest distance between points.

 

What is curvature? That is a hard question to answer exactly without some differential geometry, which I won't give here.

 

But basically if you take a vector [math]X_{0}[/math] at the point [math]p[/math] and parallel transport it along to different paths [math]C[/math] and [math]C'[/math] to the point [math]r[/math] you obtain two (in general) different vectors [math]X_{C}®[/math] and [math]X_{C'}®[/math] The curvature is defined in essence to be the difference of these two vectors.

 

With some differential geometry you can make what I said more meaningful.

 

Try a simple experiment on [math]\mathbb{R}^{2}[/math] i.e. a sheet of paper and [math]S^{1}[/math] i.e. a ball.

 

In these cases parallel transport just means moving a vector along a path such that it keeps pointing in the same direction. So on your sheet draw a loop and trace your vector along it keeping it pointing in the same direction. You will see it returns to your original vector. Thus our sheet is indeed "flat".

 

Now try it on a sphere, a football or something. You will see that the vector does not come back to the same vector, but it is rotated by 90 degrees. This is the "curvature".

 

You can do the same thing on any space-time (or more generally any manifold) provided you define how to parallel transport vectors. This requires some extra structure and this is part of differential geometry.

 

From this curvature you can calculate geodesics, but this is more involved so I won't tell you how.

[lakmilis]

ajb, I studied at Warwick in the past, there is exactly 2 months between us in age. Completely useless fact but hey, I'm a personal kind of guy ;p

[Spyman]

are we not heloicentric?

In astronomy, heliocentrism is the idea that the sun is at the center of the Universe and/or the Solar System.

http://en.wikipedia.org/wiki/Heliocentric

 

All celestial objects inside the Solar system are in freefall, (orbit), around the Solar systems center of mass, since the Sun have about 99 percent of the total mass, the center of mass is inside the Sun.

http://en.wikipedia.org/wiki/Solar_system

 

The Solar system is in freefall, (orbit), around the center of mass of Milky Way, which is moving towards the Great Attractor in the direction of the Hydra and Centaurus constellations.

 

In the general sense, the absolute velocity of any object through space is not a meaningful question according to Einstein's Special Theory of Relativity, which declares that there is no "preferred" inertial frame of reference in space with which to compare the galaxy's motion. (Motion must always be specified with respect to another object.)

 

With this in mind, many astronomers believe the galaxy is moving through space at approximately 600km per second relative to the observed locations of other nearby galaxies. Most recent estimates range from 130 km/s to 1,000 km/s. If indeed the Milky Way is moving at 600 km per second, we are traveling 51.84 million km per day, or more than 18.9 billion km per year. For comparison, this would mean that each year, we are traveling about 4.5 times the distance that Pluto lies from the Earth (at its closest). The Milky Way is thought to be moving in the direction of the constellation Hydra, and may someday become a close-knit member of the Virgo cluster of galaxies.

 

Another reference frame is provided by the Cosmic microwave background (CMB). The Milky Way is moving at around 552 km/s with respect to the photons of the CMB. This can be observed by satellites such as COBE and WMAP as a dipole contribution to the CMB, as photons in equilibrium at the CMB frame get blue-shifted in the direction of the motion and red-shifted in the opposite direction.

http://en.wikipedia.org/wiki/Milkyway

 

The Great Attractor is a gravity anomaly in intergalactic space within the range of the Centaurus Supercluster that reveals the existence of a localised concentration of mass equivalent to tens of thousands of galaxies, observable by its effect on the motion of galaxies and their associated clusters over a region hundreds of millions of light years across.

 

These galaxies are all redshifted, in accordance with the Hubble Flow, indicating that they are receding relative to us and to each other, but the variations in their redshift are sufficient to reveal the existence of the anomaly. The variations in their redshifts are known as peculiar velocities, and cover a range from about +700 km/s to -700 km/s, depending on the angular deviation from the direction to the Great Attractor.

http://en.wikipedia.org/wiki/Great_Attractor

 

Are we at the center of the Universe? No, I don't think so and one should be careful with such claims, it could start an Intergalactic War since those pesky little green men also can make such claims for the same reasons.

 

The mainstream science of today don't consider the Universe to have a center.

(At least not in our common 3 dimensions.)

 

Wherever you are in the Universe the expansion are thought to look likewise.

 

If the large-scale universe appears isotropic as viewed from Earth, the cosmological principle can be derived from the simpler Copernican principle, which states that there is no preferred (or special) observer or vantage point. To this end, the cosmological principle has been confirmed to a level of 10-5 via observations of the CMB. The universe has been measured to be homogeneous on the largest scales at the 10% level.

http://en.wikipedia.org/wiki/Big_bang

 

In cosmology, the Copernican principle, named after Nicolaus Copernicus, states the Earth is not in a central, specially favoured position.

http://en.wikipedia.org/wiki/Copernican_principle

 

does "everything" in the universe follow the curvatures?

Yes, if no force is acting upon the object.

 

does even light follow the space curvatures?

Yes, and both mass and energy curves space, so light curves space also.

 

what are the curvatures exactly?

An popular analogy describing gravity is a two-dimensional map where the third dimension is presented as the curvature or gravity.

http://en.wikipedia.org/wiki/Image:Spacetime_curvature.png

 

So the bending of space-time could be viewed as the altitude lines in a topographic map.

http://en.wikipedia.org/wiki/Image:Topographic-Relief-perspective-sample.jpg

 

Modern physics describes gravitation using the general theory of relativity, but the much simpler Newton's law of universal gravitation provides an excellent approximation in most cases.

http://en.wikipedia.org/wiki/Gravitation

 

In this theory, spacetime is treated as a 4-dimensional Lorentzian manifold which is curved by the presence of mass, energy and momentum (or stress-energy) within it. The relationship between stress-energy and the curvature of spacetime is described by the Einstein field equations. The motion of objects being influenced solely by the geometry of spacetime (inertial motion) occurs along special paths called timelike and null geodesics of spacetime.

 

One of the defining features of general relativity is the idea that gravitational 'force' is replaced by geometry. In general relativity, phenomena that in classical mechanics are ascribed to the action of the force of gravity (such as free-fall, orbital motion, and spacecraft trajectories) are taken in general relativity to represent inertial motion in a curved spacetime. So what people standing on the surface of the Earth perceive as the 'force of gravity' is a result of their undergoing a continuous physical acceleration caused by the mechanical resistance of the surface on which they are standing.

http://en.wikipedia.org/wiki/General_relativity