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4th dimension

  1. Sep 29, 2003 #1
    hey, anyone out there care to offer their thoughts on the fourth dimension? as in what would it be, all I have is that a fourth dimensional object would seem like a 3 dimensional object moving down and then disapearing?
     
  2. jcsd
  3. Sep 30, 2003 #2

    selfAdjoint

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    I suppose you mean fourth spatial dimension, rather than the Minkowski 3 space, 1 time geometry of relativity. For that, you should inquire on the relativity board.

    The best insight into a spatial fourth dimension is to read the delightful classic little book, "Flatland". Almost any library or bookstore should have it. It works on the analogy of an individual who lives in a two dimensional world - his name is "A. Square" - who learns about three dimensions.

    Another way to insight would be to look up "tesseract" on a search engine. Aside from hits on Madalyn L'engel's misuse of the term in her children's boooks (avoid her description), you should find many discussions on how to represent simple four dimensional objects in three dimensions, just as we represent three dimensional objects on a flat piece of paper with perspective.

    Four dimensions would have two directions that are perpendicular to our three dimensional world. They have been given the names "ana" for four dimensional "up" and "kata" for four dimensional "down" with respect to our space. Of course these are just the Greek words for up and down.

    So borrowing a description from Flatland, if a four dimensional sphere were to start anawards of our world and move through it in the kata direction, what we would see, as it intersected our world woild be first a tiny three dimensional sphere (cross section of the four dimensional sphere near its kata pole) which grows in size to a maximum (the "equator" passing through), and then decreases gradually again to its mini size before vanishing, having passed commpletely through our world and out the other side.
     
  4. Oct 2, 2003 #3
    You know, I had no idea that the two directions of the fourth spacial dimension had already been named. I once read a science fiction novel called "spaceland", wherein they called the two other directions "vin" and "vout" (for obvious reasons).
     
  5. Oct 2, 2003 #4

    selfAdjoint

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    Right around the year 1900 there was a little flurry of intellectual interest in "visualizing" the fourth dimension. Books appeared to teach it, or give an illusion of teaching it, and I believe it was they which gave the names ana and kata. At that remote epoch educated people were still expected to know a little classical Greek.
     
  6. Oct 5, 2003 #5
    as most know, 3 dimentional has an xyz...4 dimension can be a worm hole....a worm hole has a an xyz and time
     
  7. Oct 5, 2003 #6
    all dimensions have time, I dont' think time can be a dimension in itself, and time travel is most likely impossible unless in one direction, and that is forward if we were living in a 2D world we would still have time as a progression, what we did 15 minutes ago it can be plotted in a graph using x and Y coordinates, labeling each graph with a time signature,
     
  8. Oct 5, 2003 #7
    You are right. Dimensions must have two directions, which is where the "di-" in di-mension comes from. I think di means, two. People who say time is a dimension, and people who say there are four spacial dimensions are wrong, for the reason you gave, which is that time only moves in one direction.

    But string theory says there are ten dimensions. If you are in a 2D world, and you define that world as a group of points, when you lay down the points you must have separation between points. String theory says there is a separation between points: that points are really little strings. So if you take small strings, draw little lines and lay them out on a piece of paper, the most efficient arrangement of three strings is a triangle. If you continue to lay out strings, connecting them all, you continue to make triangles until you construct a space. Now if you travel from point to point, or string to string, you find you can only go in three directions. If we construct a plane out of strings, we can only travel in three directions from the string we are at, to the string next to it. All travel has to be from point to point, or string to string, and that limits travel to only three directions. Each direction back and forth is a dimension in this construction of strings.

    If you go from a random point A to a random B, you have to zigzag through the strings. To describe A to B you need an x and y axis. So this 2D space constructed from strings has five dimensions.

    In a 3D space constructed from strings, there are ten dimensions.
     
    Last edited: Oct 10, 2003
  9. Oct 5, 2003 #8
    Here is a diagram. The X's are points that have separation between them. To travel from A to B, it would look like

    oooXoooXoooAoooXoooX
    oXoooXoooKoooXoooXoo
    oooXoooXoooKoooXoooX
    oXoooXoooXoooKoooXoo
    oooXoooXoooKoooXoooX
    oXoooXoooBoooXoooXoo

    In the macro world, you would only see travel directly from A to B, but a photon or electron really has to zig zag through an arrangement of strings.
     
    Last edited: Oct 10, 2003
  10. Oct 6, 2003 #9
    In 3 dimensions, we all have an intuitive understanding of what length and angle mean, and it is not at all clear how to extend these concepts to higher dimensions.

    However, if we introduce coordinates and think about vectors, one can express both length and angle in terms of vector operations, and these operations readily generalize to any number of dimensions.

    The formula for the length of a 3-dimensional vector (x,y,z) is also easily obtained: you draw a right-angled triangle whose hypotenuse is the vector (x,y,z) and whose other two sides are (x,y,0) (whose length is x² + y²since it's really just a 2-d vector) and (0,0,z) (whose length is just |z|).


    For example, a vector in 4-dimensional space can be given by four coordinates as (x,y,z,w), and its length is defined to be by analogy to the length formula in two and three dimensions.

    This, then, gives a definition of what the concept of length means in four and higher dimensions.

    The other main geometric concept is that of angle. Again, we have an intuitive understanding of what it means in our 3-dimensional world, and it's not at first clear how to generalize it to higher dimensions.

    However, if you apply the law of cosines to the three vectors u, v, and u- v, the angle between u and v satisfies the equation.
     
  11. Oct 7, 2003 #10
    What would space be like if it was made of points like a TV screen is made of pixels?

    Today, the newest TV cameras form three light rays out of every bright light source, because the light is spilling out along the three lines that the pixels line up in. If you have an old computer screen, not a flat screen, you can look at its pixels and see how they line up in three directions. And of course you can see how, in some places, straight lines are squiggly.

    Physical points have to arrange themselves in triangles on a TV screen. I thought, "How can physical points arrange themselves in 3D space?" They would arrange themselves in tetrahedrons. Two tetrahedrons base to base have lines going in seven directions. When you look at a star, you can see rays going in six or seven different directions, just like you see light spilling out in three directions on a TV screen due to the arrangement of pixels. Old cameras had two rays, which is called a lensing effect. New cameras have three rays, which is not due to the lens, but due to the arrangement of pixels. Stars have six or seven rays, which is just what I would expect since I realized the arrangement of points in space line up in seven directions. In 3D space, one ray might be pointing straight at you so you would not see it. If you see a star with five rays, which is rare, the rays are very clearly defined, since two rays are more or less pointing at you, and the other five are very flat and evenly spaced to your line of sight. Sometimes, on big lights you see rays and the lensing effect. And the number of rays changes depending on when you look. Space has an absolute structure, and the earth is rotating through it. The way to count the rays is to count all the rays on one half of the star or bright light. A bright light in a TV camera has three rays on one half of the light source, and those three rays continue on the other side in the same direction.

    I think the rays of a star, and of a light source on a TV screen show us how the multiple dimensions work. They are an arrangement of points that form the minute structure of space. And on a TV screen, certain lines are not straight, but squiggly. From enough distance, they can look straight. Photons have to travel along the points that line up in seven directions, seven lines of dimension. When they go in certain direction, they go very squiggly, which is no problem when you understand that light does not hurtle through space, but is pulled through space from point to point; it can change directions and change back without losing energy; it can be slowed down and regain its speed. So it is pulled along from point to point. They are points arranged in seven directions, seven dimensions since they are the only seven directions that are possible in the smallest structure of space. Photons spill out over those seven dimensions near a bright light source, not due to a lensing effect, but for the same reason there are three rays in a new TV camera from a bright light source. It's a "dimensional effect".
     
  12. Oct 7, 2003 #11
    oooRoooXoooXoooXoooXoooRoo
    oXoooRoooXoooXoooXoooRoooX
    oooXoooRoooXoooXoooRoooXoo
    oXoooXoooRoooXoooRoooXoooX
    oooXoooXoooRoooRoooXoooXoo
    RoooRoooRoooRoooRoooRoooR
    oooXoooXoooRoooRoooXoooXoo
    oXoooXoooRoooXoooRoooXoooX
    oooXoooRoooXoooXoooRoooXoo
    oXoooRoooXoooXoooXoooRoooX
    oooRoooXoooXoooXoooXoooRoo

    Dimensional spillover effect, look for it on a TV screen.

    X's are pixels, R's rays
     
  13. Oct 15, 2003 #12
    according to Flatland (and numerical logic) the fouth spatial dimension would have 16 terminal points and 8 sides.

    ...just thought i should add...
     
  14. Oct 17, 2003 #13
    Logic says something is a straight line, but if the points can have varying degrees of separation, the straight line can curve. If you make a very smooth marble table and call that flat, but look at it through a microscope, it is very rough. The points that make up space are not perfectly orderly, just like nothing else is perfectly orderly.
     
    Last edited: Oct 29, 2003
  15. Oct 17, 2003 #14
    If you are looking from the macro to micro or micro to macro there is space between points whether it is logical or not. The atom is a point to us but there is a lot of space between the neuton and its electrons. When the hubble telescope looks at 1 arc second of the sky where nothing is visisble and thousands of galaxies appear there is most certainly space between the galaxies.
    When invisioning dimensions it is geometrically difficult for the human mind to put it togetter. The first second and third are easy to invision because we see them every day. But imagine that there is a limit to small, the plank lenght. From the plank lenght extends a dimension that leaves each point in 360 degrees outward as a cone to infinity, each time becoming larger. Anywhere on the 360 degree circle is the distance of the plank lenght or width if you may. Following the plank length to infinity you can observe the universe in all its sizes. I have always called this dimension simply the big small dimension.
    Only by reaching the speed of light can you experience this dimension.
    From outside the universe an observer would have to view this dimension as an infinite amount of plank lenght points converting into infinite cones curling back on themselves. It would have to form a solid ball yet from inside the ball there would still have to be space between the plank lenghts. Why is the plank lenght mathematically the samllest unit possible?
     
  16. Oct 17, 2003 #15
    The Bible says, In the beginning, the world (universe) was without form, and the Spirit of God brooded above the waves of the abyss. I did some thinking and realized matter cannot be compressed, but it can easily be pulled apart. I realized by looking at what matter does, the most basic form of matter had to be like water, impossible to compress and easy to pull apart. When I concluded that, I remembered the first line of the Bible, which describes the initial state of the unvierse as a sea. We know this was the universe and not the earth because, next God created light.

    So I had invisioned a sea of matter surrounded by the vacuum. The gods, whose bodies are made of fire, heated up the matter. The "drops" of liquid matter are dispersed throughout space. They are in a perpetual state of expansion with the vacuum pushing inward. The vacuum creates the strong force. Space itself is expanding against the strong force, not gravity. These drops of matter become the points of space. All movement at the particle level can only go from point to point, and the points have to be arranged in a matrix that only allows seven directions. These seven underlying directions are the seven hidden dimensions.
     
    Last edited: Oct 29, 2003
  17. Oct 18, 2003 #16
  18. Oct 19, 2003 #17
    The real change comes when you construct a plane or a cubic space with strings. You suddenly realize you can only travel in seven directions in the cubic space, if you only travel along the strings. Since the strings represent points, then you can ONLY travel back and forth in seven directions. These directions become dimensions, but you still have the three classic dimensions. A straight line from point A to point B is not really straight. It has to zigzag through multiple dimensions in the underlying structure.
     
    Last edited: Oct 29, 2003
  19. Oct 21, 2003 #18

    I am having dificulty with the zig zagging that you are demonstrating.

    Differiential structures

    How do you explain your zig zagging here?

    Sol
     
  20. Oct 24, 2003 #19
    Imagine a small square drawn on a sheet of paper. You are at a point in that box.

    Math says there are an infinite number of non-dimensional points in that box. So you can go in an infinite number of directions to a point next to the point you are at. But what if there are only four points in the box?

    With only four points in the box, you can only go from the point you are at in three directions. That means the flat box has three dimensions instead of two, because those are the only three directions possible.

    Now imagine the universe has a finite number of points. So at the smallest level, just like being in a box with only four points, there are only a limited number of directions. Those limited directions become dimensions.

    It is not logical to assume this line ______________ and this line __ both have the same number of points. They are different lengths, yet supposedly, they have the same infinite number of points. If they each have a different number of points, then they each must contain a finite number of points. Lines that we know are two different lengths cannot both contain the same infinite number of points! Therefore, since they must have a finite number of points, in a square or cubic space you can only go in a limited number of directions. The question becomes, how many points can you stack around one point? Draw points on a flat piece of paper. Start from any point and go to a point beside it. Now go from the original point to a different point. Find another point that you can go directly to from the original point. These are three lines of dimension on this plane constructed from points. In cubic space there are seven lines of dimension in a space constructed from points.
     
    Last edited: Oct 29, 2003
  21. Oct 25, 2003 #20
    Buky Fuller says that the physical Universe is not macro-infinite but micro infinite inas
    much-as the rock --.or quark--- potentially is break apartable into infinitly smaller parts.

    I think if there can be micro-infinite somthingess then there also must be marco-infinite
    somethingess ergo there will exist infinite multi-verses or the infinite bubble-like Universes.

    However, i think neither are true in the sense that there is both a micro-quantisizing limit
    --i.e. the quantum graviton planck or sub-planck limit--
    and the larger finite macro-physical Universe.

    Where does the many varying concepts of geometrical "dimension" and mathematical "powers" fit into these scenarios ive laid out above? Im not sure.

    Dicussion of dimension is like 'time' in some ways in that it seem to have so many varying concepts surrounding it as well as some overlap or no overlap that it nearly makes for paradoxes and/or recursive/recycling loops spiraling in or/then out of our ability to make senae of it.

    The proof is in the pudding even if the pudding is still only a probaility without causal geomtric visuals to to help explain the deeper nature --i.e triangulated/structr-- of those probalities.

    Jabob Bekenstien in his August article "Scieitific American" might argue this by saing thatt our brains percevie a 3-D world which is really only 2-D visual --i.e. screen-like of non-seeable holographic world.

    Now that really blows --or compresses-- my mind if his --and Hawkings-- mathamtical black hole studies are correct.

    Rybo
     
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