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Planck Scale and Unification of Forces- new research studies

  1. Nov 26, 2008 #1
    How do Planck's photon theories relate to the belief that all forces may be unified at high speeds?

    I understand that light waves can act as particles, and particles can act as light waves. Waves/particles emit energy. And Planck's scale is believed to be around the length of convergence of all forces. But besides this, is there a connection between Planck/Einstein's theories and the work being done to speed up particles in an attempt to clash them?
     
  2. jcsd
  3. Nov 26, 2008 #2
    You've asked a wide range of questions..may be better to try one at a time so you get to sort things out...but here goes.

    I can't think of a "Planck photon theory" at the moment. Maxwell did the field equations for light (electromagnetic waves);Schrodinger the wave equation; Einstein the photoelectric effect...;beam splitter "double split" type experiments; that's all that come to mind.

    The unification of three of four forces (strong,weak, electromagnetic) has been done (at least to some degree) and so far seems pretty good. But it can't be the final answer because gravity remains outside and general relativity )GR) and quantum gravity are not yet unfied. Nobody knows how all four forces were apparently once "unified" during the very early moments of our universe when energies and temperatures were almost incomprehensibly high. And there may be another basic field:Higgs which imparts mass to particles and may be found at the Large Hadron Collider (LHC,currently being repaired).

    Planck scale sets some apparent minimum size to space and time, that is discreteness, but also envisions extremely high energies on such small scales....nothing likes to be confined and gets "jittery", "uncertain". Quantum theory relates to the small and discrete; general relativity more a classical and continuous wave perspective; but there are quantum field theories as well. There are many varieties quantum theories; relativity is, I think, more uniformely accepted. Loop quantum gravity is the one, I believe, which offers the hope of unification with GR; but that's very speculative.

    High Planck scale energies may be the factor that prevents us from accurately measuring sub atomic paramaters to arbitrary accuracy like energy and time, or momentum and position...the Heisenbery uncertainty principle. Whatever the obstacle, both quantum theory and GR breakdown at the extremes of the origin of the universe and inside black holes.

    Light has a dual nature of wave and particle like other sub atomic particles. Sometimes it appears one way, sometimes another. The forces were believed unified at extremely high temperatures: I don't believe it's known for certain if Planck scale constraints played a role other than that happened to be when the extreme energies existed. As things cooled, a phase transition switched to a lower energy universe and the four (or five) fields (forces) split and became distinct.
    I have not read that the LHC is probing anything specifically related tp Planck Scale; maybe others can comment. Nor do I know if any aspect of relativity is planned for additional testing.

    I believe most would agree relativity and quantum theory have been pretty well proven experimentally, at least under the limited conditions we can create; I don't think anything near Planck scale has been experimentally confirmed.
     
    Last edited: Nov 26, 2008
  4. Nov 26, 2008 #3
    um, this all seems a little muddled to me. What photon theory by planck? Basically, the planck scale is considered to be one at which gravity will have an expected affect upon quantum theories because of dimensional analysis.

    Length scales can be computed which will give some idea of which factors have to be taken into account at which scales. For example, if there is no interaction (such as electromagnetic, weak, etc), the length scale will be that of the compton radius, given by the reciprocal of the mass (in natural units). If there is an interaction, a coupling constant comes into play. For a rough calculation of the scattering cross section of a photon by an electron, we need to consider the compton radius and the electromagnetic interaction. The stronger the interaction the higher the cross section, so the fine structure constant (the interaction term) should be in the numerator. However there are still effects die to the compton radius of an electron, so the electron mass should be in the denominator. This is all that comes into play, so a rough value for the x-section can be given by [tex]\alpha \over m_e[/tex]. At length scales several times greater than this length (i.e. radio-waves), the scattering by electrons will be unimportant.

    Carrying this further, we want typical length scales for the gravitational interaction. So we want the equivalent of the fine structure constant for gravity. This can be found roughly by comparing the gravitational potential (Newtonian) to the coulombic potential. It's a bit loose and hand-wavy, but it produces energies near the planck energy and lengths near the planck length. At length scales greater than the planck length, gravitational effects will be unimportant.

    So to summarise, a theory which unifies all the forces will only be needed at the planck length (which we're a long way from - Planck energy = 10^19 GeV. The LHC will only get up to about 10^3 GeVs, so we're a long way off observing quantum gravity). Or the unification of forces will only be observed near the planck scale.
     
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