The Big Bang Bamma

No problem Please understand that you are delving into some very deep stuff here. I'm running out of analogies, as you can probably tell from my insertion of "technical" speak!Oh, just invented a new analogy! Electrons and photons are like bricks and mortar. Bricks do not bind to bricks and mortar just forms an amorphous splodge on its own. It takes the two together to create bound structures.

This is for any electron. It doesn't have a clue about ionic or covalent bonding, both of which occur at a much larger scale. It just experiences interactions with photons. Do you mean "too localised" rather than "too quantised"?In a sense this is true. It is interaction with other systems (multiple atomic systems in this case) that seems to bring about the ermergence of classical behaviour. Sort of... or I should say, each additional quantum mode increases the number of fermions by one. But there are no "different" fermions. You cannot distinguish two fermions... all you know is that there are two.This is far more fundemental and bizarre than it sounds... In normal probabilty, if you have two balls that you cannot distinguish, you have to still count the possibilities as ball1, ball2 and ball2, ball1. This is not true for electrons... there is only one state: two eletcrons. So the probablity counts differently to everyday experience. This is the source of the "statistics" weirdness. I haven't even mentioned the "spin" weirdness yet As fond as I am for the word "projection", in this case I would simply say the large scale observation of the field causes the interpretation of the electron to be an “object” Yes, that is exactly right. Sorry if I made it sound otherwise. Photons are neutral so they do not interact with themselves. They are also colourless, so they do not interact with gluons. So not strong force involved. They only interact with fermions with charge - electrons, muons, tauons, and the quarks. That's why the neutrinos are so damn elusive. They only interact via the weak... If you want to catch a particular neutrino, put an earth sized lump of lead in its path... you may just be lucky!This message has been edited by cavediver, 11-18-2005 02:13 PM

You are more than welcome Difficult, I know... it comes from living your life in flat space. Making this jump is like visualising your first 4d object: mind-blowing!The problem is your are still thinking of curvature as having something to do with "curves", which isn't too surprising, but not at all useful. A surface can have curvature without any concept of distance. In this case, no amount of extra dimensions is going to help you visualise what is happening, becasue you cannot (yet) even conceive of a distance-less surface. Yup Simple, where there is no higher diemensional space within which to have your extrinsic curvature! RP2 - Real Projective plane in 2d.How about this: take a globe. Conside all of the diameters of this globe. Each diameter can be represented simply by the position of one of its end-points on the surafce of the globe. What is the space of these end-points? Well, for a few local diameters in a bunch, their end-points will simply define a small 2d patch of the surafce of the globe. So their space is just 2d space. But what happens when you consider a larger bunch of diameters? The points spread out so they cover a larger and larger portion of the globe's surface. But then something strange happens. When you have points that are on opposite sides of the globe, you find that they represent the same diameter. So you only need half the globe to cover all of the diameters. Say we started at the north pole and spread outwards until we hit the equator. As we hit the equator, every equatorial point becomes identified with the equatorial point on the opposite side of the globe. So the space is like a disc with opposite points on the circumference identified. This 2d space is RP2. For contrast, the whole surface of a globe can be imagined as a disc with the circumference identified as a single pont, the south pole in our example. Think about this...So RP2 needs four dimensions to visualise properly without making identifications, but it most certainly exists in our 3d world, because diameters of globes certainly exist!This message has been edited by cavediver, 11-18-2005 06:18 PM

Well, I think I can But it wouldn't be in the way you think. However, before you can think of imagining 4d objects, you must learn to imagine 3d objects. You only have experience of flat 3d objects,which is rather restrictive. Take a 3-sphere, the possible topology of spatial sections of our universe. It is a very simple 3d space, but very difficult in conception. And we still haven't tackled the 2d spaces!I was digging around on wiki for some images to use, but found this all nicely presented here 2d spacesThe sphere one looks a bit odd, but the idea is that the entire perimeter of the square is one point. With RP2, diametrically opposite points are identified. The torus has points either side of the square identified. The Klein bottle is a mix of RP2 and the torus.These are your fundemental 2d compact spaces.Notice how all of them are completely flat. It is the identifications that introduce the curvature. To easily visualise the identifications, that is where you require the higher dimensions: 3d for the sphere and torus, 4d for the Klein bottle and RP2. But the diameters of a globe demonstrate RP2 in 3d, so clearly the 4d is not required for the existence of RP2. Interesting you ask this... by complex maths, do you mean strings of complicated equations? Because this is not the maths to which I am referring. By complex maths, I am talking about a way of thinking. Much of the maths here simply involves juggling images and concepts, without a single number, expression, or equation. It is extraordinarily simple... but it takes the years of study to get to the level of understanding where this can be done.

The universe just is. It's energy did not come from anywhere, it is just a property of the universe. It does not matter whether there was a Big Bang 14 billion years ago, or whether the universe has always existed. Either way, the universe is a self-contained whole. It did not come from anywhere and it's not going anywhere. It just exists. The big bang is not an explanation of why the universe exists. It is merely a description of one end of the universe. The big crunch, or perpetual expansion, are descriptions of the other end of the universe. But neither explain why we have a universe. If the universe has always been here, that does not answer the question either...

One way to start is to take the regular polytopes. These are the regular polygons, the platonic solids and then the higher dimensional analogues. Think of the simplex, which starts as the point, line, triangle, tetrahedron, 4-simplex. Each time you add a point equidistant from the others, and join with lines. Think about it... The 2d projection (with no hidden line removal) of the n-simplex is an (n+1)-gon with all internal lines present. Look at the 4-simplex this way (pentagon), and appreciate the five tetrahedrons that make up the "surface" of the 4-simplex.Next, the cubes: point, line, square, cube, hyper-cube. Each time add a second copy a unit distance away from the first and join with lines... Appreciate the six cubes that make up the "surface" of the hypercube.Cook your brain for several months and hey-presto! You'll be seeing 4-d Seriously, you can really start visualising 4d objects this way, but it takes time. You can look at a 2d projection of a 3d object, but see it as real and rotate it in your mind. You can do the same for 4d.BTW, I fogot to mention something wonderfully fundemental...There are an infinite number of regular polygons. There are only five Platonic solids... what about the other infinitude of dimensions? How many perfect regular polytopes in each dimension? That's your homework d=2 infinite
d=3 5
d=4 ?
d=5 ?
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.This message has been edited by cavediver, 11-26-2005 08:15 AM

That's it If you do the above you get the 4d hypercube, not a 3d projection (a tesseract) Only becasue of perspective. They are regular cubes. Try this for a non-perspective 2d projection: hypercube 2d projectionNo supposedly about it, but you do make me think that I may have said 6 in my message above... yep, I did. Bugger That's right.There's plenty out there on this subject. Can you answer my homework problem yet?

Ok, if you've played polytope generation, what about the 24-cell? Have you looked into that? It's the magic polytope in 4d. It's one of the reasons that 4d is special out of all possible dimensions.I'm looking on the net for a picture of my favourite representation but I can't find it. It's probably the construction that gave me the most insite. Esentially you take an octohedron, a truncated cube (space-station from Elite if you're old enough ), and another octahedron. They sit unit distance apart in the fourth dimension, and you join lines to construct additional octohedrons in your mind. So the top vertex of the first octo, the square face on the top of the trunc cube, and the top vertex of the other octo. That forms another octohedron "side" to the 4-solid.

Thanks for the links! A couple of new ones there for me...re the Klein bottle. Remember that it is perfectly regular and smooth. The twisting is just an artifact of trying to represent it. 4d is maximal for regular polytopes (excluding the trivial 2d case). There are six regular polytopes in 4d, five in 3d, and only three in 5d and up. The first 5 of 4d are just pure 4d analogues of the 5 from 3d. Then there is the 24-cell, which sits on its own, unique in 4d. Just about. Notice the octahedron start and end slices, and the trunc cube in the middle (where the six square faces just touch). These are the three to which I referred.Have you thought about the spheres? Do you know how to build higher d spheres?

Exactly. There is no self-intersection. It was really an internet/Wikipedia assignment rather than "work it out for yourself" !!! I would be impressed if you had reasoned it out from first principles. That said, it's not too hard in 3d. Obviously to be regular, each face must be a regular polygon. So start with the simplest polygon, look at how many you can fit around it to start building your solid. Why is not worth looking at hexagons and beyond?The magic of 3d and 4d is the existence of the dodecahedron/icosahedron and the 4d equivalent. The extra magic of 4d is the 24-cell. In 5d+ all you have are the n-simplices, the hypercubes and their duals (octahedron in 3d). Do you appreciate the concept of dual solids? Yep, it's unique to 4d. So you can see that just from a matter of mathematical symmetry, 3d and 4d are special compared to all other dimensions. Relevent to reality? I'd be surprised if it wasn't... You've got it. If you look closely, the cuboctahedron is just the special case of the trunc cube where the squares touch. It is halfway between the transformation of a cube into an octahedron. Flip back to where I was asking you to visualise the 24-cell as an octahedron either side of the cuboctahedron: The top vertex of the top octo, the top square of the cubo and the top vertex of the bottom octo make up one of the other octahedrons. Likewise with the bottom, and the four sides. So that makes 8 octahedrons forming the eight solid "faces" of the 24-cell. Ok, that will do it... but not what I was thinking:The sphere is known as the 2-sphere as it is a 2d surface, despite the fact that we usually think of it as a 3d object. The 3d filled 2-sphere is actually called the 3-ball.0-sphere is two distinct points (the poles)fill in between the points - line segment
add another line-segment and identify the boundaries (end-points)
(in other words, lay them next to each other and pinch the ends together)
Infalte. This gives a circle1-sphere is the circleFill in the circle to get the disc or 2-ball. Take a second 2-ball and place on top of each other. Identify the boundaries (pinch the edges together)
Inflate. This gives a 2-sphere2-sphere is the globeFill in the 2-sphere to get the 3-ball. Take a second 3-ball and place on top of each other. Identify the boundaries
Inflate. This gives a 3-sphereContinue ad-nauseum.

In many ways, yes. You have to have change in order for there to be a perception of time, and the predominant form of change is elecron/photon interaction. There's no real processing. It's just a case of adding two functions together: e1(x) + p(x) = e2(x) True, but what this does is challanege what we mean by single electrons and time. Yes, but this is simple absorption and re-emission. Well, yes they do. This is a very important process. We have the "bare" photon propagator, but it is "dressed" by considering one electron loop in its path, two loops, two loops interacting, 3 loops, etc. The real photon is the infinite sum of all of these possibilites:~~~~ + ~~O~~ + ~~O~~O~~ + ~~<|>~~ + ...

Let's do it backwards: Take a globe made of stretchy-stuff. Punch a hole at the south pole, squeeze your fingers in, now stretch the whole thing flat. You should have a disc, with the north pole at the centre, and the circumference is the south pole seriously stretched out.Does that help?

Depends on context. When I say Klein bottle, I mean the 2d mathematical entity. Others may mean the twisted, self-intersecting 3d representations of the Klein bottle. I think in this case, tesseract refers to the 3d representation only. The 4d object itself is the 4d-cube, or hypercube. Ok, what's the minimum number of hexagons with which you can surround a hexagon? Six sides need neighbours so six surrounding hexagons needed. Stick them together and what do you find? They tesselate (tile) flat space perfectly. There's no room to fold up the surrounding haxagons as they are already touching. Heptagons and higher will always overlap when you try to surround them with like polygons. So in flat space, pentagons are going to be the highest polygon that can be used in a regular solid.The pentagon has five surrounding pentagons, that do not touch when laid flat. But the spaces do not allow for any more pentagons to fit in-between. So five surrounding pentagons is all you can have. Fold them up until they touch and you have the bottom half of a dodecahedron.The square can have four surrounding squares: one for each face. It can also fit another 4 squares between those squares to form a 3 by 3 grid. But like the hexagons, this is now tiling the flat surface and there is no space to fold them up. So with just the four surrounding squares, fold them up to form the obvious box, and just add the top square: the cube.The triangle can be surrounded by 3 triangles (one for each face), 6 triangles (1 in each gap), 9 triangles (2 in each gap), and 12 triangles (3 in each gap). The last one tiles the flat surface so has no room to fold up. The first folds up to the tetrahedron. The second folds up to the lower half of an octahedron. And the third folds up to give the lower half of the icosahedron. Keep at it