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  1. Jan 25, 2004 #1
    Hi all.

    It is good to see all this beautiful work being done here. Thanks to Selfadjoint and all the mentors and moderators, as well as the contributers to this and the other physics forums.

    The mathematics of quanta seem to indicate that there is a smallest possible quantity to any measure. Not merely a smallest measurable amount, which may be made smaller by means of improvements in technology, but a physical minimum which cannot be said to be reducible in any meaningful manner. This quanta is represented by the Planck length, Planck time, Planck era, Planck mass, Planck quantum of change, and Planck sphere. Planck units are named for Max Planck, the physicist upon whose work quantum theory has its base. The Planck sphere is a unit in a geometric model of multidimensional spacetime for which I have some responsibility. My thanks to all those who have helped me develop this model.


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  3. Jan 26, 2004 #2
    Thanks for being here. If points in space can only be so close together, that produces a space in which you can only travel back and forth in no more than six directions. Those would be the six extra dimensions of string theory.
  4. Jan 26, 2004 #3
    Hi John. Good to hear from you.

    Motion is a very complicated idea. There must be an object which moves, an observer to register the motion, and a background against which the motion can be registered. Each of these three can be said to possess some degree of dimensionality. The object may be thought of as a point, as, for instance, the point of a pen or pencil. Of course a pen or pencil is a three dimensional object, but we can imagine that we are only interested in the zero dimensional "point" of the instrument, the rest of it being there only to indicate just where the point of movement actually is.

    We as observers generally imagine ourselves to be four dimensional, that is, we occupy and can manipulate a three dimensional space in one dimension of time. My personal goal is to see if the observer can comprehend higher dimensionalities, but let us leave that for now as a goal.

    Then there must be a background against which the object is to move. We might choose to wave the pencil about in the air, or to place it against a plane sheet of paper, or even to trace it along a stretched wire. The wire would represent a one dimensional background. The paper represents a two dimensional background, and the air is generally thought to be three dimensional.

    Now we may think of motion of a point as occuring in a one dimensional background, as along the wire. The wire, mathematically, is thought of as a series of points, and mathematically is infinitely divisible along any section of its length. However, we have determined that the moving point is not a mathematical point, but is more like a pencil point, and posseses some minimum measurable size. So we could make a mark on the wire, and another right next to it, and another next to that and so on, and give the points so marked names, Fred and Sam and Tom would do, but we like to put them in sequence and give them the names of our counting numbers, and this turns out to be very valuable in terms of calcualtions we may wish to make at some future time, such as distance, velocity, accelleration.

    Now in a one dimensional background, moving a one dimensional point, we three dimensional beings can define two directions of movement for the pencil point. It can go from a marked point on the wire that we might call zero to a marked point on the wire that we might call one, or it can go in the other direction to the point we might call negative one.

    In the case of a two dimensional background, as represented by the top side of a sheet of paper, we have more choices of which way to move the pencil. We might start by laying the wire down on the paper and drawing a line, since we already have explored how to do that in one dimension. Then with our pencil point on the paper, we see that we can still move along the line to 1 or -1, but we also can move on the background in some other directions which are not on the line. We can move our pencil point off the line, and make a mark that is no part of the one dimensional model we have now embedded in the two dimensional surface.

    We could move off the line and make a mark and give it a name like Sally or Linda, but it would be nice if we could retain the advantages of sequence, which allows calcualtions of two dimensional quantities like surface area and curvature of the line. There are a number of ways to do this, and we can name the points on the plane off the line using polar coordinates or degrees of angle or something, but the main change from the one dimensional model is that we now have to use two terms to specify a point on the plane. It is no longer good enough to say that it is one (mark from the zero), because there are a circle of points that are all one from the zero. We need to say that it is one mark from the zero at some angle or longitude. Or we can do something that was given to us by Descarte, if I remember my history lessons. Anyway it is called the cartesian method, and gives us a nameing system for points on the plane.

    This is done by defineing a second line, orthagonal to the first line in the plane, which just means that the angle from the new line to 1 on the old line is the same angle as from the new line to -1 on the old line. We call the first line x and the second line y, and name any point on the cartesian plane by calling it something like x1, y5. You see from this that to find the named point, you travel one mark on x in the positive direction, then make the orthagonal (90 degree) turn and move five marks on y in the positive direction, and you come to the place. To save writing, we always write the x first and the y second, and denote the place more simply as (1,5). Now we can name any point on the plane with two numbers, using the orthagonal basis lines x and y as referents.

    This can easily be extended to three dimensions by adding a z line and nameing points in three dimensions something like (1,5, 7). Now we have the orthagonal cubic grid that is commonly used when comparing points in three dimensional space. Other methods are also used in special cases as in when talking about points on the surface of a sphere, but the other methods can always be converted to the cartesian coordinates without changing the physical qualities of the system under consideration.

    Ok. Now when you say "If points in space can only be so close together, that produces a space in which you can only travel back and forth in no more than six directions," I think you are refering to a two dimensional background. If the points are arranged in the usual othogonal cartesian plane, one might think that there are only four options for point to point movement in the plane. One could move the point from the origin (0,0) to the point (1,0), or to the point (0,1), or to (-1,0) or to (0,-1).

    There are problems with the cartesian plane method, and I think you have put your finger on the chief among them. It was designed to make calculation as easy as possible, which is a great advantage to those of us with innumeracy. However, it is an artifice, and can be misleading when trying to understand things like motion and dimensionality. For example, it is reasonable to assume that motion at its most basic level can be thought of as occuring along a line, from point to point. For motion to occur, one should not be allowed to skip points or just go at random from any point to any other point. Motion has to have some sense of continuity. We need to be able to imagine that the object that is moving is more or less the same object when we begin the move as it is when we finish moving. Motion would not be very meaningful if the object being moved were allowed to change itself along the way. We cant calculate the velocity of a jeep leaving Los Angeles and a Cadillac arriving in New York. The jeep might have a velocity and the Caddy might have a velocity but there is no meaningful way to talk about velocity when the object arriving and the object departing are two different objects.

    As it happens, there are non-orthagonal methods for nameing the points on the plane, but most of them are not very useful. We could name every point on the plane Tom or Sally or something, but there would be no easy way to tell from the names just how to move to get from where Tom is to where Sally is. I believe what you have done is to look at one of these other methods. You have observed (correct me if I am wrong) that a plane can be marked with points equally spaced in triangles, making a plane that is divided up into hexagons. This effect can be seen by tiling a table top with pennies or other coins. You can lay the coins out carefully in squares, but if you push on one side of the formation, you see that the square formation quickly and naturally collapes into the triangular formation. In fact, if the table top is vibrating, you will have to exert a lot of attention to maintain the square formation, because the coins will 'naturally' tend to the more densely packed triangular formation.

    Then, if you give in to nature and go ahead and lay the coins out on the table in the triangular formation, and if you then move your pencil from any one coin to any adjacent coin, you will find, as you have described, that there are six available next coins to which you can move. If I have mistated your argument, please do not be offended, but correct me, and I promise not to be offended either.

    I am less certain what you mean when you state that these six directions are the six "extra" dimensions of string theory, but it is possible as far as I know that you are correct. I am not sure what it means to add the usual three dimensions to the six directions on the non-orthagonal plane, or if they can be added meaningfully. And as for string theory, the higher dimensions mentioned there remain a mystery to me.

    In a three dimensional background, divided into a set of orthagonal points and lines, there are six possible directions of movement, say up down left right foreward backward. In the non-orthagonal dense packed sphere regime, variously known as the Kepler stack, the dymaxion, and the cubeoctahedron, there are twelve possible directions of movement. This seems by extension then to give a six dimensional space. I suppose one could superimpose the cartesian othagonal system on the natural Kepler stack, and come up with the additive result of nine dimensions, but this seems to be a little short of the ten or eleven dimensions I have seen mentioned in string theory.

    Anyway, it is good to be able to talk with you again, and, as always,

    thanks for being.

  5. Jan 26, 2004 #4
    When I first realized an array of points only allows you to move from point to point in seven directions, I added that to the three dimensions, and came up with ten dimensions/directions, an exciting number of dimensions, which agreed with string theory. The points within an object can only move in seven directions, but the object can move in any direction in the three classic dimensions. The point particles dance on seven dimensions/directions, which are the only directions they can move. It all made perfect sense. So I continued to pursue the idea and it kept making perfect sense.

    Then I discovered "a string theory point has six dimensions". And you agree: "the dymaxion, and the cubeoctahedron, there are twelve possible directions of movement. This seems by extension then to give a six dimensional space." By that time, I was so firm in my concepts it didn't bother me that six and three makes nine, one short of ten. I never considered time a dimension, but string theory does, so that gets us to ten with six extra string theory dimensions, not seven as I had long discussed.

    But I think your approach to thought and my approach can affect the physics community and get people to see this idea of a structure to space itself.
    Last edited: Jan 27, 2004
  6. Jan 26, 2004 #5


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  7. Jan 27, 2004 #6
    I only read two-thirds of your reply before I answered. Then after reading the other third I realized I had answered the question you asked at the end, which was pretty surprising. Discussions can exist if people are thinking along the same lines.

    The motion of large objects ignores the underling six dimensions. The points within the object (points make up the large object but it is mostly empty space) those points have to travel only in the underlying six dimensions. The underlying six dimensions are the fabric of space, the way a TV screen is made of pixels. You notice some lines on a TV screen are squiggly, because of how the pixels line up, doesn't allow the line to exist except as a series of steps. But large images seem to move freely across the screen, ignoring the arrangement of pixels.

    In some cases, the arrangement of pixels becomes apparent. One thing we can do in physics today is look for places where the structure of space makes things look or act squiggly. I see the structure of space in snowflakes.
  8. Jan 27, 2004 #7
    Hi John, and Warren.

    I'm afraid that chroot is not pleased to find us resurrected here. As far as I know he is not required to participate in our discussions, but for my part, Warren, you are welcome as long as you can be civil. I am now and have for some time been trying to comprehend whatever I can of physics, and I think that should be evident from my communications. It is not helpful to my understanding to simply tell me I am wrong about something. If Warren wants a dialog, fine. If he has reason and authority to deny me access to this forum, I think at very least I deserve some explanation. However, I will continue until I hear or find otherwise from this forum's administrators.

    Meanwhile, greetings All and thanks for being here.

    I wish to reset and rebuild our thoughts from the most basic origins. It seems to me that semantic arguments can be useful to communication. We cannot simply throw up our hands and end a discussion by saying that it is an argument about semantics. If two parties are using a word differently, agreement may be easy to come by but hard to maintain. So defining our terms is certainly a valuable activity.

    In my post above this I used the term background, which may be a disputed term. I know I have read in other posts about the need for a model that is said to be "background independent," and people I generally respect have used this term. I am still somewhat confused as to what they mean exactly, since in the model I use, background is a necessary part of any observation. Clearly a change cannot occur unless there is a place for the change to occur in, and a definable object which changes, and we cannnot talk about this change without including the participation in the system of an observer. Without these three things, no discussion can take place, so I consider them to be indispensible elements. So when mentors speak of a background independent model, I must assume they mean something other than the association set the words evoke in my understanding. What do they mean when they say background independent? And, for my own thought process, what term do they prefer for the condition I have called background? I am perfectly willing to exchange words in the quest for better understanding. If there are better words for the three conditions of observation which I have tried to define here, I will be glad to use them.

    The central key to this misunderstanding seems to me to be the idea that space and time are in fact the same thing. I know that they do not seem to us usually to be the same, and there is a curious feature of observation that requires an arrow of time which does not allow the right of the observer to return to earlier observations. Causality, entropy, and being itself are caught up in the fabric of this argument. I believe much misunderstanding may be relieved by organizing and using a model of spacetime which acknowleges the rule of no return while seeking to explain phenomena of quantum mechanics and relitivity. I believe my model does this.

    Sorry to break this off here but as it happens, I have to go shovel snow. John, I will exchange an indulgence here for one of mine offered to you and redeemable next time you get a hurricane. Fair?


  9. Jan 27, 2004 #8


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    Background independence means the spacetime is part of the dynamics. Spcaetime geometry has an effect on matter and enrgy (through "curved geometry"), and matter and energy have their effect on spacetime (through "bending spacetime"). So instead of one dancer against a backdrop you have two dancers in a pas de deux.
  10. Jan 27, 2004 #9
    The background can't have the same importance as the dancer. But it's there. When we think we can mathematically manipulate reality with the ideas of relatvity, physics is mistaken.

    Mathematics actually breaks down, because the background and the things of our world have different levels of importance. You can't add 2 and 2 accurately, when one of the 2s is not as important as the other 2. The six underlying dimensions are not as important as the classic three dimensions. The underlying six make up the background.
  11. Jan 27, 2004 #10


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    2 + 2 = 5, for large values of 2.

    - Warren
  12. Jan 27, 2004 #11


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    Or even for small values of 5.
  13. Jan 27, 2004 #12
    Hi SelfAdjoint

    Yes, I was thinking about this as I shoveled out the woodpile. I seem to remember now that background independence has something to do with there being no preferred reference frame in general relitivity?

    So in physics we usually select our own frame to be the rest frame, and think of all else as under the conditions of motion?

    However, I am not sure that any of this ballet has to do much with the Planck Sphere model. Here is why. When talking about events at the Planck scale, we are considering times so short as to be instantaneous for all practical purposes. What is the Planck time, 10^-43 seconds? That is, there are ten with 43 zeros after it Planck times in every second. That would be 1000000000000000000000000000000000000000000000.0 Planck times in every second. The decimal point is a meaningful indicator of precision in this mumber since the theory demands that there be an integral number of Planck units in any system.

    There is no time for anything to change in a single Planck sphere. That is why I have suggested that the Planck sphere model have a basic unit that is at least three Planck spheres in diameter. This would be the cubeoctahedron, with 12 spheres around a central one. Then it would be possible to consider what we might mean when we speak of a least quanta of change. I hope you see that the cubeocathedron becomes the background here, and that any change we speak of within the cubeoctahedron is short enough to be effectively background independent?

    I have no problem thinking of the Planck spheres as undergoing change in a uniform way, as if they all expand together to make a kind of pseudogravity. But that feature is not at risk when talking about instantaneous events on the Planck scale, which occur in such a small amount of time that gravity is unappreciable.

    Are we in agreement about the meaning of background independence, and how it is not a problem to the consideration of the background of Planck spheres?


  14. Jan 28, 2004 #13


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    Einstein used the term General Covariance. This means that the laws of physics have to be unchanged by any smooth (diffeomorphic) change of coordinates. So yes you can pick your frame of reference, and if something is nonzero in one coordinate frame but zero in another one, then it's not "real". An example is the force of gravity. Certainly as you stand on a solid object you feel its force, but if you are falling ("free fall") you don't. This is a change of spacetime coordinates for you that makes the force vanish, so it is not a basic part of physics but just an "inertial" one, on the same level as centrifugal force.

    The freedom to pick a frame thus has a sting in it; if you pick the wrong one you can see and feel things that others will say are not really there!

    If this was all there was to it - diffeomorphism invariance, in modern lingo - it wouldn't be background independence, there would still be that "real" spacetime background. But Einstein went farther. His basic field equation has a mathematical description of spacetime curvature on one side, and a description of the local energy, momentum, and stress on the other. Each side determines the other one. You can't say spacetime is where physics happens anymore; spacetime is determined by the other physics. Hence the dance I spoke of.

    So if spacetime has crossed the line from backdrop to physics , what is left as background? Nothing! That is background independence.
  15. Jan 28, 2004 #14
    Einstein very elegantly connected the math to show us that things are not what they seem, and because his math made the connections, his ideas were accepted. And he was right.

    But there may be a relationship between background, and physics that is much less connected than any amount of math can describe. Here is a simple picture. It looks like every particle shower looks, but there is NO REASON why the particles would be making angular changes in direction, unless they are following an underlying set of dimensions, described as Planck Spheres. There is no math here, just observation of what is there, and imagination, trying to figfure out why they move like they do.

  16. Jan 28, 2004 #15


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    Okay, John. I have to say it: you have no idea what you're looking at in that picture, or how it is supposed to be interpreted.

    - Warren
  17. Jan 28, 2004 #16
    Warren, you seem to imply that you do understand what is going on in that picture. I myself think I have some rather vague ideas about it, and I would really appreciate some elucidation, should you feel up to it here. I don't think I know enough to argue with anyone about it, though.

    The text seems to be saying that this is a simulation of a typical shower under the stated conditions as it would occur in a concrete media. I am not sure how experimentalists could check on the validity of the simulation, or what relationship the lines shown have to the paths that actual photons and electrons and positrons might be expected to follow. I am generally a trusting person and will assume, since I know no better, that the computer simulation folks and their physics mentors at SLAC have done their jobs and that there is no significant inaccuracy.

    The dimensions of the simulation space, if I may call it that, are evidently 10x20x20 cm, altho the target is said to be cylindrical. The boundaries of the target are not indicated in the simulation space, but I suppose it is roughly centered in the space and that the injection point is centered on one end of the cylinder.

    That leaves a question seemingly unanswered about the length of time of the "exposure". I assume that it is much less than a second, but much more than a Planck time. In fact, I would be interested to know how many Planck times are superimposed in this one simulation. I would be very curious to see the development of the shower Planck by Planck. For example, I assume the photons pretty much all start at the left, near the injection point, and move generally toward the right. And the electrons, they must do likewise. But what about the positrons? Would they move generally from left to right or from right to left? Feynman suggested that the positrons are just electrons moving backward in time. But I can't seem to decide if this means that they should enter the picture stage left or right.

    Well I have a lot of other questions about partical showers, but I should wait and see if my autodidaction needs serious revision.


  18. Jan 28, 2004 #17
    Hi, SelfAdjoint. And thanks for the reply.

    Are you saying that gravity is a pseudoforce? I tried to prove that to a science methods class in secondary education but only succeeded in making a fool of myself in front of a lot of blank stares. Oh well. Maybe I will find more sympathy here, at least. Would you say that this is a commonly held view in physics today? Or is it partisan? Or are we just a bannished outpost?

    The Planck scale is incredibly small compared to the scale on which we do physics. Even in the Feynman diagrams time reversals and spatial discontinuities seem to exist. Is it not possible that Feynman diagrams are a horizon beyond which time reversals and spatial discontinuities are the norm? I think it must be so and have taken a peek over that horizon. At the Planck scale, times stand still and other directions in time become evident. I speculate that the missing mass in the famous cosmological problem can be accounted for in the Planck time. Gravity starts at the Planck scale, and there are ten times as many mass events in the Planck least space as there are represented in any single time history. I have come to this conclusion since there are thirteen Planck spheres in the least relational grouping, and any mass event history must occupy three of the available spheres, leaving ten that are not counted in the mass event. The ten uncounted Planck spheres may be thought of as the progenitors of divergent time lines, which fall outside the light cone of the three spheres that make up the least mass event in any timeline.

    Getting late. Hope to hear more from this company. Thanks.

  19. Jan 29, 2004 #18

    Well somebody must have some very comfortable explanations for why the small particles don't go in straight or curving lines, but spiral around and make angular changes in direction. That isn't supposed to happen. It does happen, though, in my six-dimensional model of underlying space.

    Notice the larger particles are following the paths we would expect: a fan-like shower of gently curving lines. But the small particles seem to be obeying their own personal laws of physics. Okay, explain it.
  20. Jan 29, 2004 #19


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    The particles fan out because of conservation of momentum and they curve around because the scientists have deliberately put a magnetic field across the chamber to make the particles curve.

    When faced with a puzzling picture like this there are two strategies:
    1) Use google and the public library to find more information and train yourself to see the perfectly well explained things going on. If that doesn't help you could ask for an explanation down on the Particle forum.

    2) Sit back and dream up a fancy explanation of your own and then try to sell it.

    Which one do you think is more likely to reach a successfull answer?
  21. Jan 29, 2004 #20
    Hi John and selfAdjoint

    Are we looking at different pictures? My impression is that this is not a photo of any actual reaction, but a computer generated simulation. The conditions of the simulation seem to be a high energy partical entering a concrete media.

    I don't see where the electromagnetic field is specified. I thought the path changes were due to partical interactions with the media.

    I am still wondering about the time length of the simulation. I suppose one could assume that the photons are traveling at c, then measure the paths and try to come up with a travel time.

    John, the scale of the simulation is about twenty centimeters across. The spacetime matrice is trillions of trillions of times smaller. The changes in direction you see are probably events where the photon is absorbed by an electron, and then a very, very short time later, it or another like it is re-emitted. Since there is a time delay, and the electrons are changing position in the atom, the re-emitted photon leaves the electron at a different place (too small to detect the image) from where it was absorbed, and it travels away from the electron, and the atom, in a different direction from the way it was moving when it arrived. We don't see the atom or the electron that absorbs the photon because they are too small to show up in the image.

    In a medium like concrete, the atoms are mostly randomly placed, although I am sure there is some crystalline structure in local regions. A purely crystalline medium would diffract the photons in a more regular pattern, as you can see in diagrams of xray crystalline interferography, which has been used for many years to get information about crystalline structure of materials at the atomic scale. As a result, the emitted photon can leave the electron and its atom in almost any direction. The divergence of the spray is a result of the photons becoming less energetic with each interaction. The less energetic the photon is, the more likely it is that it will be scattered at an acute angle. I imagine this is because higher energy photons tend to be re-emitted at more oblique angles, because the electron and its atom hold on to them for shorter times, meaning that the change in orientation of the atom and electron in the medium is generally less, so the re-emitted photon leaves on a path closer to the path of the absorbed photon.

    Well this is what I have gleaned from the leavings of the more academic among us. Perhaps Chroot or SelfAdjoint will correct me.


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