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Fundamental Unit of Mass

  1. Jul 19, 2011 #1
    I have always been critical of the idea of Planck units. They seem to be something conjured from numerology - particularly in view of the fact that it is possible to arrive at diffeent values of the so called fundamental dimension(s) by combiing different constants. But I recently had reason to rethink a relationship I derived a number of years ago in connection with a quantum theory of space. What fell out of the result was a unit of mass =
    H(hbar)/2c^2 The value is about about 10^-69 kgm - which works out to be about what is needed to bring omega = 1 if the spatial units have a sphere of influence approximately equal to the classical electron radius

    Anyway, when first derived H would not have qualified as a legitimate constant (everyone knew the universe was decelerating and H was a long term variable.

    But in 1998 things changed - our universe appears to have long ago entered a de Sitter phase, an Lo, H can now be a regarded as a legitimate constant - so the question is whether the relationship
    (H)(hbar)/c^2 might have significance as a fundamental dimension

    Any Thoughts
     
  2. jcsd
  3. Jul 19, 2011 #2

    Chronos

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    I don't think mass is a fundamental unit in nature. In strictly planckian terms, the planck mass [which is absolutely enormous] is fundamental, but, obviously trivial since particles of far less mass are known to exist.
     
  4. Jul 20, 2011 #3

    Chalnoth

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    H can't be regarded as a legitimate constant period, because it is changing and will continue to change. So you're just looking at the rate of expansion in different units.
     
  5. Jul 20, 2011 #4
    In a pure exponential expansion, once the Hubble has reached a de Sitter horizon, R is constant and therefore so is H.

    Weinberg has discovered another relationship that involves G,
    H, c and ž. The value arrived at by combining these factors is very close to that of the Pion.
    Mass = [(ž)2(H)/Gc]1/3- correction that z should be hbar and bracket raised to the 1/3 power
     
    Last edited: Jul 20, 2011
  6. Jul 21, 2011 #5
    let me try that again. Weinberg's Mass = [(hbar^2)H/Gc]^1/3
     
  7. Jul 21, 2011 #6

    Chalnoth

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    Try using [noparse][tex][/tex][/noparse] brackets for writing equations, and [noparse][itex][/itex][/noparse] brackets for equations within text.

    Anyway, I just don't think these sorts of manipulations mean anything.
     
  8. Jul 22, 2011 #7
    That was sort of my point in the first post - so why should Planck's unit if mass be any better than Yogi's unit of mass or Weinberg's unit of mass - yet its hard to find an authority that doesn't endorse Planck units
     
  9. Jul 22, 2011 #8

    Chalnoth

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    Because H only has a single unit (inverse time), it can be effectively used to make whatever set of units you want.

    By contrast, actually fundamental constants, such as the speed of light, tend to be relationships between two or more sets of unit conventions. What this means, basically, is that Planck units cannot be composed in arbitrary ways, but are actually quite limited and fundamental.
     
  10. Jul 22, 2011 #9
    These are not Planck units. You need to use c, [itex]\hbar[/itex] and G to construct a physical quantity of an arbitrary (physical) dimension. The Hubble parameter is not among these three units. You may construct a combination with the same dimension as the Hubble parameter (inverse time) and find the ratio of the two to get a dimensionless number, but that's just measuring the Hubble parameter in a different system of units.
     
  11. Jul 22, 2011 #10

    Chalnoth

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    Don't forget Boltzmann's constant and the Coulomb constant!
     
  12. Jul 22, 2011 #11
    Boltzmann constant is used to convert temperature in energy units and Coulomb constant is used to give electromagnetic physical quantities a dimension w.r.t. electric current. Thus, they are not fundamental constants, but merely conversion factors fixed by the choice of our system of units.
     
  13. Jul 22, 2011 #12

    Chalnoth

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    That's also true of the Gravitational constant, the speed of light, and Planck's constant.

    The only fundamental constants in this way of looking at things are dimensionless constants, such as the fine structure constant.
     
  14. Jul 22, 2011 #13
    c is also a conversion number because of the way the meter is defined, but, since there is no fundamental unit of mass, the Planck constant and the gravitational constant are not simple conversion numbers, but there is an inherent uncertainty associated with their measurement. The fine structure constant is not dependent on the gravitational constant.
     
  15. Jul 22, 2011 #14

    Chalnoth

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    Because they have units at all, they can't be anything but conversion factors. It is only dimensionless ratios that can truly be constant in the sense you pointed out.

    But why did you point out that the fine structure constant is not dependent on the gravitational constant?
     
  16. Jul 22, 2011 #15
    It's a curious fact that gravity is 'orthogonal' to electromagnetism. :tongue:
     
  17. Jul 22, 2011 #16

    Chalnoth

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    I'm not entirely sure how curious that is. I'm pretty sure the strong force is also orthogonal to E&M. The different forces just have different sources is all. The source of gravity is the stress-energy tensor. The source of E&M is electromagnetic charge. The source of the strong force is color charge. There is some mixture between the electromagnetic and weak forces, but then that's to be expected because of the way that symmetry was broken. But I'm pretty sure all the others are mutually orthogonal.
     
  18. Jul 22, 2011 #17
    So, doesn't the electromagnetic field generate a stress-energy tensor?
     
  19. Jul 22, 2011 #18

    Chalnoth

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    Um, yes. As does the strong force. But that just means that gravity couples to photons as well as electrons and protons. I don't see how it's particularly special that photons only couple to electromagnetic charge.
     
  20. Jul 22, 2011 #19
    You might be right. Since all the gauge theories are developed without any mention of gravitation, it is only logical that the corresponding coupling constants (like the fine structure constant in QED) should not depend on G.

    On the other hand, G would only enter through the Lagrangian density of the gravitational field as it appears in the Hilbert-Einstein action. As far as I know, such a theory is non re-normalizable. Thus, it can be considered an effective field theory at best, but no one knows what is the more fundamental theory.

    No one even knows what mass is, or whether G is truly a fundamental constant or an artifice of the approximate theory that we are using nowadays.
     
  21. Jul 22, 2011 #20

    Chalnoth

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    I definitely wouldn't say nobody knows what mass is. Mass is the energy of the internal degrees of freedom of an object. We may not necessarily know where all of this energy comes from, but I don't think there is any arguing with that definition.

    For a proton, for example, the majority of the mass is due to the strong force interaction between the quarks which results in a binding energy. For more fundamental particles, I believe we generally think that interactions with the Higgs field provide their masses, though we need some more experimental evidence to be sure.
     
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