BlackHole

But if space is a 2-dimensional plane, it is flat and infinite. AFAIK, there are really only two possibilites: a flat, infinite universe or a flat and finite universe with nontrivial topology in which the universe 'wraps around' spatially. http://arxiv.org/abs/astro-ph/9802012 http://arxiv.org/abs/gr-qc/0005128 http://arxiv.org/abs/gr-qc/9911049

True, space can be unbound and still have a size (like a sphere or a balloon) but if space is infinite (has no size and no age), i think it contradicts the big bang theory.

This might be the hardest question ever because it's questioning the size and dimensions of the universe. If the universe is infinite (space-time is flat and Euclidean), this simply means there never was a big bang at all. But if the universe is finite (space-time is curved and elliptic) but unbound (eternal but not infinite in size) then we, as 3D creatures, will never be able to see what lies beyond. A NewScientist article implies that the universe is finite but unbound.

This is all based on general relativity in which space-time can have a dynamic geometrical structure. I don't think there is aether in this case because nothing is moving through space-time. Also check out arXiv In GR there is no specific "preferred frame of reference", as in the classical field theory, therefore there is no aether.

It's so true. We know that our space is not empty. According to QFT there is energy in the vacuum. With energy comes pressure, since pressure is just the work done to change the volume of a box. In this case the pressure is negative, since increasing the volume of the box increases the energy. Therefore if space-time has a positive energy, the expansion will accelerate. The present model predicts that the present universe should also be filled with neutrinos, fundamental particles with no mass or electric charge. Another very hard question is what hapanned at and before Planck time (in the singularity). In GR space is dynamic but is it possible for anything physical to move in space-time? QFT (QED) and Heisenberg uncertainty principle. QCD was developed only after 1983. So the gravitational field is basically the curvature of space-time? There is string theory but it is currently untestable. True but we have yet to determine what prevailed before the big bang. If LISA will not detect gravitational radiation (also called ripples in space-time), would it shoot down GR? What is space and time are the two fundamental questions. Maybe in the future time will not be relevant, only energy will.

It's because general relativity generalizes special relativity. Special relativity is a "special" case because it deals with a special case of costant motion in a straight line (without any gravitational effects). Also according to the hot big bang model, space must expand with time.

No one knows. Cosmologists are convinced that there's a mysterious 'force' or 'dark energy' which is pushing the galaxies apart. Therefore it is reasonable to think that dark energy is causing space to expand (like a balloon) and when space expands, dark energy is created. Take note that all this could also hint to a failure of general relativity on very large distances.

It's called 'dark energy' but we don't know what it is. Future work in particle physics and space missions to come might finally provide an answer. This is how the expanding universe looks according to the standard big bang model: Special relativity does not apply to recession velocity so we are left with general relativity and the cosmological constant. Thanks for the explanation Martin. If the cosmos expands itself, new space is created. This means that before the big bang there was no space because the big bang was the explosion of space. Therefore if the galaxies are stationary and not moving through space, then the next question is: What is space? In this case i think the reasoning in ok because space is really expanding itself but the galaxies are not moving through space. Strange but that's all it is...

Special relativity sais that no physical signal (or no energy) can pass through space faster than light. This means that a peak can move faster than light speed (Four billion km/h) but the total energy of the pulse does not. Therefore Einstein's relativity is preserved and causality is not violated. Signals also get weaker and more distorted the faster they go, so in theory no useful information can get transmitted at faster-than-light speeds. But if so why is it said (within the context of general relativity which generalizes special relativity) that space itself can expand 50 times the speed of light? Is it possible that the distance between two objects is so great that the distance between them expands faster than the speed of light (locally)?

I think what i can't grasp is how space can be in motion. Therefore i say that space-time is an abstract 4-D geometrical structure, not a physical entity.

No doubt because space-time has a changeless nature but motion in space-time is impossible because the change is self-referential. Motion (a change in position) requires the existance of a time axis. If there is no motion an arrow of time is not required.

My question is why motion through space is necessarily essential to the progression of time (i take space-time as a non-physical, abstract mathematical construct). It's hard for me to believe that GR predicts motion through space-time. I believe we should think of time as an abstract parameter derived from change, not on the contrary.

How can anything physical move in space-time? Defining time by change in motion is problematic because time is progressing whether we move in space or not. According to this defintion, if the cosmos was static and not accelerating there would be no time. Time is a constant and does not change.

In Scientific American they say that the big-bang was the explosion of space itself. A thing which i can't grasp is how galaxies receed faster than light if there is nothing physical pushing faster than light? The result is that space can expands faster than light because SR does not apply to recession velocities.

Space and time are just parts of abstract mathematical thinking.

The way i see it, time and space are mathematical entities. It's just a part of abstract mathematical thinking. In general relativity spacetime is the alternate name that physicists have given the gravitational field of the universe. There is no mathematical difference between the thing that we call 'spacetime' and the other thing that we call the gravitational field. Spacetime is the manifold and the curvature is the metric tensor. Because gravitational fields that act like the ones we know about cannot exist in more than four dimensions, this also means that spacetimes that lead to our kind of world cannot exist in other than four dimensions. Basically nothing moves in spacetime.

Therefore it was not a blunder at all. Einstein's mistake was not mathematical. It was philosophical.

Dark matter cannot interact with light (a phenomena of the electromagnetic force), therefore we can't see it. Dark matter is either baryonic (made up of protons, neutrons, etc) or non-baryonic (made up of exotic particles). Experts have suggested that dark matter could be made of WIMPs (Weakly interacting massive particles) or/and axions which interact only through the electroweak force and gravity. No one really knows what it is. Now dark energy is even more complex than dark matter. It is believed to be the driving 'force' behind the speeding up of the expansion of the universe. "Dark energy" probably isn't an entirely satisfactory way to describe this phenomenon. As of 2005, physicists have no other clue. Currently the Lambda-CDM model is the most consistent with all present observations.

QFT requires empty space to be filled with particles and anti-particles being continually created and annihilated. This could lead to a net density of the vacuum, which if present, would behave like a cosmological constant. When Einstein was told by Hubble that the universe is expanding, he introduced a cosmological constant into his equations for General Relativity. This term acts to counteract the gravitational pull of matter, and so it has been described as an anti-gravity effect. Astronomers plan to look at more distant high-redshift supernovae (far beyond the quasars)to precisely track how the universe’s expansion rate has changed, and this hopefully will narrow the dark energy alternatives. The Planck Surveyor and CLOVER array might also provide new results in 2007-2008. Hopefully LISA (in 2008) & Constellation-X will take place in 2016 or after. For now, ΛCDM is the best model to explain 'dark energy'.

I think i get the meaning (i'm not sure). String theory is strong but still baseless. The fact that it is almost solely based upon the flawed ancient notion of the discrete particle. The work of Einstein, Schrodinger, Clifford, Dirac proposes that matter must be a wave structure, continuous in the space it occupies (or is part of). To their view, our particle concepts are a result (not the cause) of the particle-like 'appearances' of the wave structures.

Is there any chance that the accelerating expansion of the universe is an illusion caused by relativistic redshift in stationary clouds of dust (see paper)? Such theories are unlikely because observations have almost firmly confirmed that the universe is accelerating based on CMB. The ΛCDM model is the best candidate. However cosmic inflation theory is still suspect. The graceful-exit problem is still not solved and again the only solution is string theory.

This is much more advanced than CM but basically, just as oscillating electric charges give out electromagnetic waves, general relativity (if it's a correct theory of nature) predicts that oscillating gravitational masses, such as double stars (also called binary stars), should give out gravitational waves. The discovery that the cosmos is accelerating (based on supernova Ia observations) has made things much more complicated. According to superstring theory (a favorite candidate for QG) gravitons -- hypothetical elementary particles transmitting gravitational forces -- can escape to other dimensions. This would cause leaks in gravity over large cosmic distances, what could also account for cosmic acceleration. Gravitons (as photons) have no mass and no charge. Superstring theory is the greatest challenge to dark energy. See also Physical review D and arXiv for much more technical information. * Also recent examinations reveal that the 'event horizon' is not as sharply defined as ones thought to be. Computer simulations indicate that information CAN get out of black holes. Also superstring theory can solve the singularity problem in the center.

Both QM and relativity (which uses mainly diffential geometry and tensors) require a thorough backround in CM and Electromagnetism (including classical electrodynamics). So Quantum Mechanics (non-relativistic) uses linear Algebra (especially complex numbers, matrix algebra and linear transformations), functional Analysis (Hilbert spaces), advanced calculus & diffential equations (ordinary diffential equations & partial differential equations). QM also uses Harmonic analysis using Fourier series & transforms. What else? Can someone give a little more information? Edit: So basically modern QM is a combination of Werner Heisenberg's matrix mechanics with Erwin's wave mechanics using Dirac's linear transformations.

I don't know but leaking gravity could solve the 'dark energy' puzzle. That's what i read on space.com. According to (super)string theory, the universe has more dimensions than the four we experience in every-day life and gravity may leak away to one of the other 6 microscopic dimensions. Another proposal is that dark energy and neutrinos might be connected.