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Coulomb's Force Law and the Fine Structure Constant - Variance?

  1. Aug 28, 2004 #1
    *** PART I. ***

    The value of the constant "K" in what appears to be the "ORIGINAL" Coulomb's Law depends upon the nature of the medium.
    [ K = 1/4pi*epsilon ] where epsilon is the "absolute permittivity of the medium".

    In many modern books, I find that "K" is defined as:
    [ K = 1/4pi*epsilon(zero) ] where epsilon(zero) is the "permittivity of free space".

    In 2 physics dictionaries (Oxford's publ'd in 2000 and Penguin's publ'd in 1991), Henri Semat's book "Intro to Atomic & Nuclear Physics" (1960) and on one web-site ( http://www.plus2physics.com/electrostatics/study_material.asp [Broken] ) I find "K" defined as: [ K = 1/4pi*epsilon ] where "epsilon" is the "absolute permittivity of the medium".

    QUESTION #1:
    Which of these equations for Coulomb's Law is correct?

    QUESTION #2:
    What is the definition of "free space"?

    Continuing on:
    Relative permittivity is defined as epsilon(r), where: [ epsilon(r) = epsilon / epsilon(zero) ]
    and Epsilon(r) is the "Dielectric Constant".

    The "Epsilon of the absolute permittivity of the medium" is often assumed to be equal to the "epsilon(zero) of the permittivity of free space" which, until recently, seemed like a reasonable approximation, but recent measurements of dielectric constants reveal that Epsilon(r) values can be much larger than 1.

    Dielectric constants (epsilon(r) values) for gases and liquids range from 1 to 20 normally, but for some materials (eg ice and some liquids) the dielectric constant rises to 100-200. For some Inorganic Compounds the dielectric constant is much much higher.

    For example:
    SnTe has epsilon(r) = 1,770
    SbSI has epsilon(r) = 2,000
    SrTiO3 has epsilon(r) = 2,080
    Ferroelectric materials have dielectric constants >4,000
    Pb3MgNb2O9 has epsilon(r) = 10,000
    KSrNbO3 has a dielectric constant or epsilon(r) = 34,000 !!!

    QUESTION #3:
    Since the difference in results of Coulomb's Force law can decrease the Force by a factor of 10-5,000 or more even, what are the ramifications for forces calculated from the interactions between the proton and the electron in the hydrogen as an initial test case? (More complex atoms will naturally be different.)

    *** PART II ***

    The " Fine Structure Constant " seems to be directly dependent on the Coulomb's Force Law constant "K" as defined by Sommerfeld's original set of ratio'd constants:

    [ alpha = e*e / 4pi*epsilon(zero)*hbar*c ]

    The Fine Structure Constant (FSC) is one of the key constants in QED and it is used / involved in many QM calculations. It serves as a kind of foundation rock for QED. For that reason many scientists have used various methods to improve the precision of the FSC. As a result the FSC has been derived from various measurements and now enjoys much greater precision.

    Below are the known FSC values as measured (but without uncertainties):

    TABLE I: Inverse values of the fine stucture constant measured from:
    1. de Broglie wavelength of slow neutrons----------------137.03601082
    2. AC Josephson effect in superconductor junction--------137.059770
    3. Quantum Hall effect-----------------------------------137.0360037
    4. Anomalous magnetic moment of electron---------------137.03599976
    5. Anomalous magnetic moment of positron---------------137.03599976
    6. Muonium atom----------------------------------------137.0359940
    7. Helium spectrum--------------------------------------137.035853
    8. Velocity of hydrogen 1s electron /velocity of light-------137.0388

    (All values were obtained from book called "Hydrogen" published by Harvard University Press in 2002 by John S. Rigden)

    If Coulomb's law should be using "epsilon(zero)" then everything should be safe and correct, and we can ignore the following two questions.
    If, however, Coulomb's law should be using "epsilon" and not "epsilon(zero)", then the questions are:

    QUESTION #3:
    What are the effects on the Fine Structure Constant?

    QUESTION #4:
    What are the effects on the rest of QED?

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    Last edited by a moderator: May 1, 2017
  2. jcsd
  3. Aug 29, 2004 #2
    What's the exclamation icon for?

    I don't see what the fuss is about for k and epsilon. Coulomb's law is that F is proportionnal to Qq/r2. The proportionnality constant is different for each medium, and called k. A factor 4Pi turns this into epsilon. In free space, the value is epsilon = epsilon 0. Just consider k as a function of epsilon. Use k0 when epsilon = epsilon0 if this k confuses you.

    Free space is just what it sounds like. No charge, no medium, nothing existing except the charges your are working with. If you really want to be strict, free space only contains things that don't matter to your system.

    Between an proton and an electron of a hydrogen atom, what could there be besides free space? Certainly not KSrNbO3! So you use epsilon 0, and then k = 1/4Piepsilon(0).
  4. Aug 29, 2004 #3


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    Both. It's wrong to assume that because there are 2 different forms, that one is correct and the other incorrect. Read this to learn about polarizability, and how to correctly apply the laws.
    ...and you are welcome to them!!!
  5. Aug 29, 2004 #4
  6. Aug 29, 2004 #5
    Effects on the fine structure constant

    Electromagnetic interactions appear stronger when investigated at high energies. This means the value of the fine structure constant increases when investigated at high energies. Also at short distances Coulombs law has to be modified slightly by taking account of electron-positron pairs that appear for short periods of time in empty space (even empty space inside an atom).

    I don't fully understand this myself yet.
  7. Aug 29, 2004 #6
    Just to get attention. Does it mean something extra special to the members of this forum? If so, I will restrict my use of it.
    Epsilon(0) = 8.8e-12 Farads/meter = 8.8e-12 Coulombs/Volt*meter
    Since the value is not zero or one, does this mean that the space between the electron and the proton has a medium. If we call the space between them a medium then shouldn't that space be defined to have an Epsilon(R) value, a dielectric constant?

    The questions, in another sense, are:
    Q1: Can we really use Epsilon(0) to define the dielectric interactions between the electron, which is highly delocalized around the proton, and the proton sphere in hydrogen?
    Q2: Can we use this approach for the other orthagonal orbits, p,d and f-orbitals?
  8. Aug 29, 2004 #7
    If you have a reference to that increase in FSC, I would appreciate a copy or a link. I too have read something to that effect, and IIRC the number is 1/128.

    Excellent note:
    The potential presence of electron-positron (virtual) pairs between the electron and the proton is one of the reasons that I posted this question and the reason that I included the various very large epsilon(R) values that I found in the CRC handbook of Chem & Physics. These large epsilon(R) values might serve as a rough guide as to what might be happening in the "free space" between the proton and the electron in hydrogen.

    In addition to the "potential" presence of these virtual pairs, we need to "consider the possibility" that the electron and the proton move around in a relative motion in response to the fields of each other, which IIRC is an already expected behavior. Then we have to consider the Zwitterbewegnung (ZBW) effect which is or is related to the above IIRC.
  9. Aug 29, 2004 #8
    Do you by chance have a reference to the definition of "free space"? I have my idea as to what it means, but would like a detailed definition so I don't get confused. Thanks!
  10. Aug 29, 2004 #9
    FSC is 1/128 at 100GeV. I'm new to quantum physics, and I don't really understand free space either. If it is nothing, then that must mean there is no particles, no photons, no charge, no energy. Doesn't this mean that free space would be at absolute zero.
  11. Aug 29, 2004 #10
    I don't think the exclamation has a special use, I just wonder whenever I see someone use it. It makes me feel as if the user is pressuring me, when there is obviously no hurry. Personally, an ! won't attract me more than an interesting question I believe I can contribute to.

    As for the topic, the epsilon(0) comes first, and all other epsilon(r) are defined relative to it. These epsilon(r) are defined for bulk matter, not atoms. They lose meaning at the atom (quantum) level. Only epsilon 0 still has meaning at this level. Macroscopic charges in space behave as epsilon 0, so there is no reason to believe epsilon 0 changes if the seperating distance is as small as the atom (10E-10 m). Just like there is no reason to believe c changes on the Moon. Besides, c=1/sqrt(mu 0 * epsilon 0), which brings that attacking the constance of epsilon 0 is attacking Relativity.

    The fact that it works for the hydrogen (and any one electron atom I think) atom is probably what convinces people of the localized nature of the electron at this level. Even though it is may not be obvious that Coulomb's law should work with an electron cloud or orbital.
    Last edited by a moderator: Aug 29, 2004
  12. Aug 30, 2004 #11


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    FSC changes with the energy scale due to QED's charge renormalization of the electron. The Feynman graphs that contribute to it are those in which a virtual particle-antiparticle pair appears on the virtual photon propagator.
    Unfortunately, https://www.physicsforums.com/showthread.php?t=5374 says :
  13. Aug 30, 2004 #12


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    Hilarious. I doubt you have any worries about anyone stealing your 'work'.
  14. Aug 30, 2004 #13
    Recently I have noticed a rash of irrationality within quite a number of members within this forum. Even so, it is necessary as a fellow human to be kind to irrational creatures who have never had a chance to develop manners or reasonable social behavior.

    Pray tell me what exactly do you think Greg Bernhardt is attempting to do by the following:

    https://www.physicsforums.com/showthread.php?t=5374 says :
    Originally Posted by Greg Bernhardt
    "All content posted on this site is copyrighted to Physics Forums."

    And to add to your state of despondent humor, I suggest you read my open letter to Greg. I'm sure you are intelligent enough to find it without my providing specific directions.
  15. Aug 30, 2004 #14
    Many thanks for opening my eyes to this dubious statement.
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