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Are these questions any good?

  1. Feb 5, 2004 #1
    Hi all,

    1.Exists a single (unified) geometric system which can and does accomodate the conditions of quanta and relitivity?

    2. If such a system exists, is it discrete or continuous? (Is there a discrete relitivity, and/or a continuous quanta? If so, how do the discrete parts relate to each other, and how does a quanta continue?)

    3.If no such system exists, can a system involving some duality or symmetry be constructed, in which the two or more parts may be said to interact where in conflict according to some definable rules of exchange?


    Thanks,

    Richard
     
  2. jcsd
  3. Feb 5, 2004 #2

    chroot

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    I'm sorry, Richard, I just can't decipher what you're asking.

    - Warren
     
  4. Feb 5, 2004 #3
    No need for sorrow. I have read some of your posts and I have great respect for your learning and dedication. Strangely, the questions seem quite bare and sensible to me. Is there some word that requires more definition? Or some phrase that conflicts itself?

    Thanks,

    Richard
     
  5. Feb 5, 2004 #4

    chroot

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    What's a unified geometric system? Are you asking Is there a theory which unifies quantum mechanics and relativity?

    If so, the answer is: not yet. People are working on several. The two largest candidates are string theory and loop quantum gravity. I will not go into a discussion of which is better.
    How can a system be discrete or continuous? By system I believe you mean theory, and it does not make any sense to apply the labels "discrete" or "continuous" to a theory itself. Are you asking In a unified theory, are space and time discrete or continuous?

    If so, the answer is: space and time would be discrete in a unified theory. (I believe -- if this is incorrect, somebody else, please interject.)
    Are you asking If there can be no unification of quantum mechanics and relativity, can the situation be remedied by relating the theories' disparate predictions through some set of rules?

    If so, the answer is: if two theories are in conflict, they are in conflict. That's pretty much the end of the story. Given the same experiment, two conflicting theories predict two different outcomes. If there were a way to make their predictions agree, then the puzzle will have been solved.

    - Warren
     
  6. Feb 5, 2004 #5
    Re: Re: Are these questions any good?

    perhaps you should say "we have two theories which combine quantum mechanics with relativity". in one case, it is unknown whether the theory reduces to classical GR, and in the other case, it is unknown whether there is a vacuum which describes our universe.

    but still, we have 2 theories which unify relativity and quantum mechanics.

    string theory, as currently formulated, lives on a smooth manifold.
     
    Last edited: Feb 5, 2004
  7. Feb 7, 2004 #6
    is this question any better?

    Amazing how slippery words can be. I have spent my life enamoured of the beautiful tools of language, yet when trying to speak of things most simple and profound, language fails me. Or perhaps it is not language that has failed me, but rather the other way around. Still, I will not bow to failure. I will try again. Onward and upward.

    Chroot has changed my question to Is there a theory which unifies quantum mechanics and relativity? Chroot said Yes, for example Super String Theory (SST) and Loop Quantum Gravity (LQG).


    "Is there" is the customary form for questions of existance. For example, " Is there a God?" or "Is there a reasonable doubt?" I intended to avoid this customary construction because 'there' brings up the question of 'where?" Since my question is intended to address a universal condition, I wanted to close the door to the idea of parallel universes with differing physical laws or physical constants. The word "does" has similar problems, relevant to time instead of space. By Occam, I decided to cut away this dross. So my unusual construction of the question of existance, which I prefer to keep.

    Also, geometry got lost somewhere. I wish to bring it back into the question.

    SST is described by the geometry of the Calabi-Yau manifold in ten dimensions. (I like the semantic construction "lives on" the manifold, as poetry, but it introduces divergent arguments about the meaning of "lives," so I toss it reluctantly and fondly into the dross bucket.) LQG uses the geometry of the sombrero to describe the energy of a false vacuum, but leaves unanswered the question of what a real vacuum might be.

    A further consideration is that the sombrero is a two dimensional surface with potential energy variations displayed in a third dimension. In my opinion, both the sombrero image from LQG and the GR 'bowling ball on a bedsheet' description of gravity suffer from attempting to picture three and four dimensional events on a two dimensional surface. It can be done, and is helpful at first, as an analogy, but the model must be carried into higher dimensions if it is to be useful as a means of finding common ground between quantum theory and GR.

    So, at this point I restate the question.

    1. Exists a geometry that describes both the theory of relativity and quantum theory?

    If yes, then GR and QT are not in conflict.

    If no, then we may be able to examine the geometry of GR as it conflicts with the geometry of QT and develop a sort of taxonomy of the conflict. In doing so we may be able to build a new geometry in which the conflict may be resolved.

    Am I any closer to a good question?

    Thanks,

    Richard
     
  8. Feb 7, 2004 #7
    Richard
    I was quite fascinated to read your take on LQG and GR . When you say that one resembles a sombrero and the other a bowling ball on a bed- sheet does this mean that in GR the space time continuum dips downwards to accommodate objects in the space time continuum , while in LQG they dip upwards ? Anyway I have some questions to put to you regarding the geometry of inner space in a manner of speaking . The question concerns inductive and radiative EM fields about which I had already made a post at this forum which , unfortunately , was so poorly worded that it has attracted only 7 views and no replies . Anyway I will try to explain the problem in a more lucid fashion. Suppose you have two electrical conductors placed close together but separated , one of which is carrying a current and can be referred to as the primary the other known as the secondary might be connected into a circuit but is not carrying a current. Now when an ac current is introduced in the primary a current is induced in the secondary which might have upto 98% of the value of the current in the primary. OK so big deal you say , that’s all old hat , what are you trying to get at ? Right so this is the problem , the computer you are using , the one I am using and most of the computers being used by other members of this forum are supplied with induced current using 60 Hz AC ,and transformers . Why ? Because higher voltage which is possible using induced currents and transformers is easier to shunt along long distances. Fine , you say , so what seems to be the problem ? The problem is this , the energy of the photon field in a 60 Hz current is only 2.48102 x 10 –13 eV. What’s wrong with that you ask ? At the heart of quantum physics is the idea that all electromagnetic energy is transferred in integer quantities of a fundamental unit, Planck's constant. Mathematically, you can state this concept as E=hf, where E is energy, h is Planck's constant, and f is the frequency of the photon. The energy levels for all physical processes at the atomic and molecular levels are quantized, and if there are no available quantized energy levels with spacings which match the quantum energy of the incident radiation, one of two things can happen , either the material will be transparent to that radiation, and it will pass through , or it will be opaque to the radiation and block it out completely , in either case no transfer of energy takes place . So how is this tiny amount of energy 2.48102 x 10 –13 e V in the 60 Hz field supposed to induce massive currents of several 100’s of amps and thousands of Volts . The answer is that it can’t , according to quantum mechanics it is impossible. So where does the Geometry come in you ask ? Right , suppose , just suppose for a moment that instead of these huge wave – lengths (50 Hz corresponds to a wave-length of 5000 Kms. ) which are supposed to originate in the electron , that there was a threshold on the maximum wave-length that an electron could emit and that this threshold was about 10 -6m. Then obviously all wave-lengths larger than this would have to be composed of these smaller wave-lengths linked together to form the larger wave-lengths . Thus all wave-lengths greater than this threshold wave-length of approx. 10 –6 m. would be composite wave-lengths . What is the advantage in this ? The advantage is that depending upon the manner in which these wave-lengths (photons ) are linked together , it would be possible to qualitatively change the energy of the field. Thus if the photons are linked serially they would give up their combined value , if linked in parallel they would give up their individual values. This gives an amazingly accurate figure for both the inductive and radiative fields . Suppose you have a current of 1 amp , and calculate that this give rise to an equal number of photons (i.e. one photon per electron 10 18 ) then if the value of the series connected composite wave length is 1.2 eV it would mean an energy of just under 1 joule . Similarly if the photons (wave-lengths are connected in parallel it would give rise to a radiated energy of 2.48102 eV which is correct. What do you think , could there be anything in it ?
     
  9. Feb 8, 2004 #8
    Hi McQueen. Good to hear from you again.

    I don't know.

    The sombrero and the bowling ball on a blanket are images I have seen and read about in many places, most recently as I was re-reading Alan H. Guth's book, The Inflationary Universe. I suppose you, or anyone interested in this kind of thing, will have seen them also. The sombrero is formed from a graph of energy density of two intersecting Higgs fields. For example see Guth, p. 140.

    I have just been trying to read Shadowitz, The Electromagnetic Field, published by Dover Press, which I found in the science section of my local B+N bookstore. I do not find it easy reading. Of course, electromagnetic field theory is classical and the results are hard to challenge by anyone using a computer. Obveously, the theory works. Any unified field theory has to include existing theories that are known to produce such spectacular results. So anyone hoping to provide insight into a unified field theory has to be familiar with the details of the theories involved, or be trapped in misconceptions. I suppose that is part of the reason some contributers and mentors on this forum disdain hobbyists. But I am trying seriously to understand these things and will not be put off by the scorn of people who fell into luckier circumstances.

    The idea that the fields dip up and down is an artifact of the model of a two dimensional surface in a gravity field. The model, as blanket or sombrero, represents energy density in terms of height, so that lower positions on the surface have less energy density. One is left to wonder about the source of the field which provides the sense of up and down.

    I suppose that up and down in the sombrero and blanket models could be replaced meaninfully by the use of colors to represent density, as is done when representing, for example, amounts of precipitation in a storm system or temperatures along a frontal line, which is common in television weather reports. Then one might be mislead into wondering why the rain prefers to fall in places that are colored red instead of green or blue? Someone might even build a field theory about how rain is repulsed by green and attracted by red. It could even be extremely accurate. But it wouldn't be correct. There aren't real red and green pixels in a storm cloud.

    I read your post in the other thread but didn't feel I had anything of value to contribute. You seem to know a lot more about the EM field theory than I do. Still, I am willing to give you what little I have.

    I thought your idea about the composite wavelengths was plausible, and the idea of series versus parallel waves makes sense to me. But I suspect I am merely playing with tinker toys. You can make a pretty fair model of a skyscraper with tinker toys, but real sky scrapers don't work like that.

    The textbooks talk about divergence and curl and the Laplacian operator and del operator and dirac operator and many other things which are only just beginning to make a vague sort of sense to me. I guess the strength of the field does not have to limit the strength of the forces that are carried by the field. For example, the surface tension of water is a kind of field, and it isn't very strong, you can stick your hand right through it. But water can still carry huge ships, carve coastlines, and carry away entire seacoast cities with one fell swoop of a tidal wave. Maybe field strength is measured when the field is quiet, as surface tension is measured when the sea is calm. The presense of a ship or a charged particle changes things dramatically. But I don't know. I am only guessing blindly. Maybe someone who knows more about field theory will help us here.



    Thanks,

    Richard
     
    Last edited: Feb 8, 2004
  10. Feb 9, 2004 #9
    Richard as you might have guessed I don’t really know much about the LQG theory and have only the vaguest idea of GR . But I have read something of Minkowski’s ideas on space , which were based on GR .
    Quote :
    -------------------------------
    Henceforth space by itself , and time by itself , are doomed to fade away into mere shadows , and only a kind of union of the two will preserve an independent reality. Hermann Minkowski
    --------------------------------------
    Minkowski made a simple diagram of space showing the mathematical relationship of past , present and future . The most striking aspect of the diagram is that all of the past and all of the present for each individual meet at one single point “now” or the present.
    Furthermore the “now” of each individual is specifically located , and will never be found in any other place , than “here”. (Wherever the observer is at.) What is fascinating in all this is how a potentially abstract subject such as the nature of space has been assimilated with even greater abstractions such as life forms and that the whole theory has been given a mathematical basis which can even be depicted diagrammatically.

    Coming back to the inductive and radiative fields which I was referring to . I don’t know if I can agree with your statement that :
    Quote:
    ------------------------------------
    Of course, electromagnetic field theory is classical and the results are hard to challenge by anyone using a computer. Obveously, the theory works.
    ------------------------------
    The point is that a statement made in physics as for instance saying that the boundary between inductive and radiative electromagnetic fields exists at a distance of ((wave-length )/ Pi x2 )from the conductor carrying an alternating current , is an observation of a relationship it does not really explain why this happens and it certainly does not differentiate between the type of fields. The point is that even though this is just an observation of a relationship , it still works extremely well. It is probably possible to detect some kind of inductive influence within the distance specified by this relationship but it does not explain how the energy can drop of by such a huge factor at the boundary. Again the terms you had used such as divergence , curl the Laplacian operator dirac operator etc., are used not to describe an inductive electromagnetic field but rather to formulate how electromagnetic waves are propagated . If there does exist any other explanation for the presence of an inductive field it certainly , to the best of my knowledge , does not include any qualitative change in the field . Maybe as you had suggested some one else can come up with a better explanation. In any case I have found the post quite interesting.
     
  11. Feb 10, 2004 #10

    arivero

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    Supose that I postulate a linear discrete lattice where you can always insert a new point in the middle of two old ones. Should you call such system discrete or continuous?
     
  12. Feb 10, 2004 #11
    Some thoughts

    Linear discrete lattice. Just curious, how many dimensions?

    Well, a lattice in zero dimensions wouldn't be arguable. One, hmm, a line of points, each point a lattice element, but that would not be linear. So two dimensions, anyway, where a lattice is a trellis-like object, wide and tall but of minimal thickness for the desired application. Or a snow flake, eh, or a binary convergent rivine system. Then in three dimensions a capillary bed, or an intertwined branching as in the crown of a healthy and mature forest. But this last is a thing few in our day have ever seen. Think of that. So we must abandon the tree of life and move to some other image to reveal the meaning. Lets see. What do we know today? Some kind of three dimensional landscape. An office building, a tower? A mall? A city?

    You see a one dimensional linear object only has one discrete line available. A point by itself does not make a line. I posit along with the fifth of Euclid that a linear object considered as its own universe can only have one line, no matter how many dimensions it is viewed in or from. You can't bend it or change its quantum state from within its own definition. You may see or project that there is a space for the one dimensional object to bend in, but that is your propery and the property of the background, not the property of the object in question. From within a one dimensional universe, there is no sense in the idea of bending. So, every line definable in a one dimensional universe is a subset of the single infinite line of the one dimensional universe.

    I wonder if I have made a clear argument that a one dimensional universe cannot be a linear discrete lattice?

    So in two dimensions we have the trellis, the branching structure such as that which is used in gardens to support vineing flowers like morning glory. Or the River system seen from map view as a series of convergent streams.

    Three dimensions. A child's jungle gym? Crystallography?

    Anyway it seems any dimension can be built adding up ones and twos.
    But the main thing in the idea of a linear discrete lattice is that it contains discrete lines. I suppose ten dimensions then to be built up of a ten dimensional lattice of linear discrete lines. Each line, within its own definition, its own universe, each line, so to speak, within itself, is perfectly straight and infinite.

    A ten dimensional system, I should think, would be made up of ten internally consistant one dimensional lines (these would be basis lines in a non-orthagonal geometry?). But before we attempt to build a ten dimensional structure, lets talk some more about what dimensions are. Or, what are these one dimensional universes that collectively make up some kind of lattice that we exist upon?

    Space and time are spoken of as the most basic of dimensions. I should think all measures should be reducible to space and time, or, more simply, to spacetime itself, (Minkowski?)

    I meant not to blog here, but am doing it anyway. Usual apologies and explanations offered.

    Thanks,

    Richard
     
  13. Feb 10, 2004 #12
     
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