what is the big bang and how do i understand it?

I sympathise... know only too well how that feels But you've still managed a post of Holmesian proportion so i will have to tackle it a bit at a time... Precisely This is the core of relativity. Special Relativity is simply the statement that space and time form a four-dimensional geomtry with distance function (metric)ds = -c.dt + dx + dy + dzThis IS just Pythagoras, with a strange minus sign in front of time. That is what "c" is... it's the conversion factor for converting our units of time into our units of space. We always set c=1, so the metric becomesds = -dt + dx + dy + dzSo, ok, I cheated a little... I kept a plus sign in my calculation, but it illustrates the point... and adding or subtracting 10^2 makes little difference to the dominating time component. Not at all. All units were rendered into metres, so it's just a simple piece of geomtry. They are radii of curvature. Remember when you used to calculate radii of curvature of some function? It's simply the radius of a circle that will "fit" the curve at that point. It is not a radius of anything, just a measure of curvature. Here we are simply comparing the two radii, and finding them equal.Now I've told you what SR is, I better tell you what GR is...take the simple distance function of a 2d plane:ds = dx + dy (Pythagoras)I can change to polar coordinates and I getds = dr + r dqNothing has changed.But what if I now choose a metricds = dr + sinr dqThis is now very different. This surface now has curvature, and in fact it is the distance on a sphere. Changing the coefficients of the differentials in the metric introduces curvature to our surface.So a theory of curved space-time simply takes the metric of SR and sticks in functions of the coordinates in front of each term of the metric... e.g.ds = -A(t,x,y,z)dt + B(t,x,y,z)dx + C(t,x,y,z)dy + D(t,x,y,z)dz (cross-terms are allowed as well, e.g. E(t,x,y,z)dt.dx )Now GR tells us what A, B, C, and D are allowed to beSo for example,ds = -(1-2M/r) dt + 1/(1-2M/r) dr + rdq + rsinqdfis allowed under GR and is the Schwarzschild space-time (black hole).As a general point to anyone reading this, notice how the space-time (existence) is given by the distance function. There is NO CONCEPT WHATSOEVER of anything "outside" the universe (including "before" and "after") The metric is all there is and it is totally contained within the reality it is describing. This is the amazing thing about GR. It is is completely self-contained and self-referential.This message has been edited by cavediver, 08-21-2005 12:29 PM

No, N is whatever it needs to be to make the theory actaully work in the first place. N=26 comes from the simplistic bosonic theory. The real string theories have N=10. There is no choice, it is not a free parameter. This is unlike GR, where N can be anything you want it to be. The maths works in all dimensions. This is a problem with GR... it doesn't tell us what the dimension of space-time should be. Most valid alternative gravitational theories have observational problems in one place or another. The lack of gravity waves in Ekpyrosis is only their imprint in the Cosmic Microwave Background. It is not that gravitational waves in general do not exist in Ekpyrosis. And as mentioned, Ekpyrosis is not a theory of gravity. It is a possible scenario within string/M-theory. It just pushes back the big questions... it doesn't answer any other than our standard cosmological questions. Well, if we're talking GR I would say that it is one of the most successfully tested theories ever... I'll be lazy and refer you to Tests of general relativity - Wikipedia No! The halo of the Galaxy, not the Solar System. Big difference. Apart from the Pioner Anomaly, there does not appear to be any deviation from GR in the Solar System. And given the size of the Pioneer Anomaly, I would take that as a measure of its success. The dark matter only reveals itself on the Galactic scale by the speed of rotation of the entire disc of the Galaxy. Who said this? Given that the galactic rotation curves require 90% dark matter, this has to be complete nonsense. The difference in rotation curve is A is prediction with luminous matter, B is the observed. You're not going to get that with the Pioneer Anomaly!

Ok, skipping your middle section just for now... I understand your picture, but there is much deeper connection between the extra dimensions and "particles". For instance, in Kaluza-Klein theory, we have GR in five dimensions. We roll one dimension up into a small circle, to give us our usual 3+1 dimensions. You do the maths, and instead of just gravity in 4 dimensions, we have magically got electromagnetism as well! AND another "scalar" field of the type required by inflation and quintessence. So the photon in this picture is just a residue of the 5 dimensional graviton, as is this scalar particle. Now that's not bad from one extra dimension! Ok, you're mixing ideas here... namely 3d Newtonian ideas with 4d GR ideas. There is no gravitational attraction, there is no gravitational force. There is only curvature of space-time. The time lines, if not actively accelerating, will follow the straightest path through space-time. These "straight" paths will be distorted by the presence of mass. I explained this recently in the "What is Space and Time" thread so I'll just add it in here

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What track through space-time do we take? Well, just like everyday experience we follow "straight" lines. We call these geodesics. Think of the aircraft following a great circle path around the earth... it's not straight in the usual definition, but it is the straighest path over a curved globe. It is the path something will move along if pushed and then does not subsequently accelerate.

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Mass/energy curves space-time, so the geodesics are curved away from naive ideas of straight. Discovery has just returned from following a straight line which happens to be so curved it closes up into a "circular" path all the way around the earth. The orthogonal straight line (geodesic) to the orbit is a path straight towards the earth. If you "fall" along these paths, you are following the curvature of space-time. You experience no acceleration, no force. Hence being weightless both in orbit and in free-fall (ignoring air-resistance). To deviate from a geodesic, you need to exert a force.

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This is the crux... it led Einstein to GR. The 1g we experience on the earth is not gravity. It is the up-push from the earth forcing us off our preferred geodesic which is to "fall" to the centre of the earth.

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If we increase this force, by use of Discovery for instance, we increase this 1g force and we move further away from the geodesic. In fact, with Discovery, we exert sufficient force to move us onto a new orbital geodesic.

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If you jump out of plane, nothing accelerates. You just move naturally. It is, as you say, the surface of the earth accelerating towards you.

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It's nothing to do with not being there to observe time after the big crunch. Think of my globe analogy. Time points along lines of longitude towards the south pole (big crunch). Very close to the south pole, the arrows of time are pointing inwards towards the south pole. If you push your time arrow through the big crunch singularity, it remains on the same globe, just now moving back towards the north pole. There is no mechanism for the arrow to leap off this globe onto another globe, even if you say they are touching. The big cruch is not an edge, beyond which we say "what comes after" It is just a badly behaved point on an otherwise smooth surface. The only thing beyond the big crunch are those moments before it. What is south of the south pole?

Thanks for the tip... however, on my screen the images are identical! Both have a white background???BTW, was this a "ps" to a post you've made, as I don't have any other replies to my posts 42-44?

There is a confusion here between Space, space-time and distance. Distance betwen points in the universe is given by a field called the metric. By field, I mean a thing that takes a value at every point in the universe. In the case of the metric, it is not a single value but a matrix of values at each point (it is a 2nd rank tensor field in the language of mathematics). The metric tells us the distance between infinitesimally separated points in the universe. You can add up (integrate) the metric along a path to find the total distance between two points.If the distance is negative, it means the points are separated by what we call time. But this division into space and time is not fundemental to the universe, simply a property of the metric.Between certain points (those possibly connected by a light-ray), the distance comes out as zero - not separated by space or time. But this doesn't mean the actual Space of the universe has been "eliminated", just that this distance function has value zero. Our experience of time and distance are simply measurements of the metric.

Busy as hell... so quicklyThere's confusion over to which G you're both referring. Unhelpfully, there are three "g"s in the Einstein Equation! G_ab is the Einstein Tensor, g_ab is the metric tensor, and G (on the rhs of the equation) is Newton's Garvitational Constant. SG is referring to G_ab and RAZD is only referring to G, as it appears both in F=GMm/r^2 and G_ab=8piG/c^2T_ab.I wil come back to the rest, but I will just add here that at the level of quantum gravity there is confusion over what is reality and what is model. Outside of this arena it is very easy to think of reality as being built up of smaller bits of reality. In quantum gravity we seem to run out of reality and all we seem to be left with is the mathmatics. Check out the thread "God and Mathematics" in the coffee shop for my thoughts. I still must get back to that thread sometime as I left it hanging in the middle of my A-level exam marking.In terms of predictions and falsification tests, that's easy. Whatever we theorise must reduce to observed reality in a low energy limit. If it doesn't, it's falsified. Observations at the high-energy limit are very difficult: either technologically infeasible or potentially devastating to the universe And I'm not kidding!

Quite When our accelerators start producing energies higher than the most energetic cosmic rays and gamma ray bursts... worry!

What? You mean you don't think you've been like this already...??? Oh dear...

I promise I will get round to my HUGE reply to all of this, but for now... No one is saying that GR is absolutely correct. Everyone accepts that GR will be superceded by a higher level theory, but in most cases this will not change the gross nature of GR.What do you think I was trying to do for all those years as a mathematican/theorectical physicist? Hanging with my friends, saying how great GR is? Forgive me RAZD, but I feel like an evolutionary biologist sparring with a creationist In this field, no stone is left unturned. The sheer number of papers pursuing every conceivable modification or alternative to GR is amazing... it started ninety years ago, and continues unabated to this day. To suggest that us comsologists and theo/math physicists are blinded by our devotion to GR is verging on insulting... it's not our fault that nothing has come close to replacing GR. But it's not that surprising when you understand the concepts. Hmmm, this is EXACTLY like sparring with a creationist You seem to think that cosmologists have postulated two large epicycles -lambda and CDM - and left it there. Please understand that no-one is happy with this situation. The task is on to explain why we have a lambda (not that a constant lambda needs explaining from the POV of GR) and what is CDM... this is major research. At the same time, there is major research into models that produce the same effects without lambda and CDM... this is where ekpyrosis comes from.I think I need to devote an entire topic to teaching GR and demolishing distorted views bred by the popular "science" press.

Yes, true, in the same way that evolution is just a notch up from Genesis 1 on explaining diversity of species, and so much more cumbersome with the understanding.I'll put this with my collection of Tal's eloquent evolution critiques

Bullseye! Couldn't have said it better myself... well, perhaps I won't go quite that far but right to the heart of the matter.I will still expand on this when I've got a moment's break.The key point is that GR, unlike Newton, is not a theory. It is a theory of theories, a mini-TOE in its own right. Every problem that RAZD has talked about are problems with theories (or solutions as we would refer to them) that sit within the framework of GR. SG is quite right when he says that nothing contradicts GR, we just have some problems identifying the correct solutions within GR.(as an aside... Platonistic-type thinking arises precisely because of this theory-of-theories nature of reality)RAZD is looking for aesthetics of the solutions , where-as the aesthetics lies in the orginal equations. This is no more evident than in the standard model of particle physics. QCD and electroweak are mind-blowingly aesthetic... but look at the low-energy results and it's ugly as hell. RAZD, if you think we have epicycles in cosmology, you should take a look at the standard model Lagrangian... it's over a page long. Compare that to GR: L = sqrt(g)R. You cannot get more simple than GR.One of the reasons you aren't too convinced with GR is because you aren't convinced about SR. If you understood what SR implies, you would understand that we are stuck with some form of GR-type theory. And don't forget that SR is tested to unbelievable accuracy every day at CERN and Fermilab amongst others. That is why we hang on to a GR-type framework... we are forced to. GR not only has to reduce to Newton, but it must reduce to SR. To reduce to Newton is exceptionally simple. To reduce to SR pretty much dictates what GR must be.

Hey, you should try being an evolutionist in a church full of creationists... then you'd learn about tag-teaming I've realised how disjointed all of this is. I'm used to teaching GR, not defending it. Thus my arguments are not as streamlined as I would like. However, my last post started to get to the root problems. I will try to put this all back together into a coherent whole.Have a good trip!

Easy, it's not! This is the big misunderstanding with SR. Velocities do not add. Naively: we see a spacecraft (mass M, velocity V<~c) exert thrust F for time T. The spacecraft deltaV is F/M x T, so we expect to see new velocity = V + F/M x T. We don't because veocities don't add. We see something smaller than this. The false conclusion is that M has increased. This is the key. In different 4d coordinate systems, 4d vectors (and tensors) will have different components, and if we are measuring one of these components as if it were a scalar, we get upset when it changes in odd ways (length intervals, time intervals). The trick is to look for real 4d scalars that do not change when we change coordinate system. Curvature is one, measured by the Ricci curvature scalar. You can relate this directly to your excess radius. You can then relate that to your mass. So your "mass" when measured correctly, will not change in different coord systems - as in, different frames of reference - as in, when moving at different velocities.

Look like you've got it! Yep, that's pretty much it.