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How can the Planck length be claimed to be the smallest length?

  1. May 6, 2008 #1
    Many arxiv papers state that the Planck length
    is the smallest measureable length.

    On the other hand, the gravitational length
    L=2Gm/c^2
    associated with every electron or proton
    is 19 or 22 orders of magnitude smaller
    than the Planck length.
    Nobody seems to doubt either
    of the two statements.

    What is the exact answer to this paradox?
    One can imagine at least 3 solutions:

    1 - Lengths of objects can be smaller than L_Planck,
    but not positions.

    2 - Lengths can be smaller than L_Planck if
    one makes many measurements and then makes
    a statistical average.

    3 - There is an uncertainty relation between
    length L and position x:

    L x > L_Planck^2

    There might be other answers. What is the
    canonical answer by researchers to this question?

    Thanks!

    John
     
  2. jcsd
  3. May 6, 2008 #2
    On May 5, 1:28 pm, JohnMS <john_m_stan...@yahoo.co.uk> wrote:
    > Many arxiv papers state that the Planck length
    > is the smallest measureable length.
    >
    > On the other hand, the gravitational length
    > L=2Gm/c^2
    > associated with every electron or proton
    > is 19 or 22 orders of magnitude smaller
    > than the Planck length.
    > Nobody seems to doubt either
    > of the two statements.
    >
    > What is the exact answer to this paradox?
    > One can imagine at least 3 solutions:
    >
    > 1 - Lengths of objects can be smaller than L_Planck,
    > but not positions.
    >
    > 2 - Lengths can be smaller than L_Planck if
    > one makes many measurements and then makes
    > a statistical average.
    >
    > 3 - There is an uncertainty relation between
    > length L and position x:
    >
    > L x > L_Planck^2
    >
    > There might be other answers. What is the
    > canonical answer by researchers to this question?
    >
    > Thanks!
    >
    > John



    The length scale you describe is the radius in which you would have to
    fit the Compton wavelength of the particle for quantum gravitational
    effects to come into play.

    You provided a formula that gave a length scale smaller than the
    Planck length. The question is, does this formula describe anything
    physical?

    For the electron this length scale is 10^-57 m
    For comparison, the electron's classical radius is 10^-15 m

    I do not believe any laboratory experiments have confined an electron
    to the degree you require.
     
  4. May 6, 2008 #3
    On May 5, 1:28 pm, JohnMS <john_m_stan...@yahoo.co.uk> wrote:
    > Many arxiv papers state that the Planck length
    > is the smallest measureable length.


    Most of the time, this is merely a heuristic. The Planck length comes
    up as the scale beyond which quantum gravitational effects become non-
    negligible. This is shown using dimensional analysis, much in the same
    way as the Bohr radius, beyond which the full quantum mechanical
    description of the Hydrogen atom cannot be neglected. Note that the
    Bohr radius was derived before a modern quantum mechanical treatment
    of Hydrogen became available. A similar statement can be made about
    the Planck length.

    Current established theories neither require nor propose a minimal
    length. However, tentative models proposed for quantum gravity
    sometimes assume some kind of discreteness or granularity of space-
    time at the Planck scale. Thus, the nature of the Plank length as the
    smallest measurable one should be considered as one of the hypotheses
    assumed by these models. While there are arguments for the validity of
    this hypothesis, like all others, it must be subject to experimental
    verification.

    If you want a more detailed discussion of how to resolve your
    "paradox", you'll have to specify which model of quantum gravity you
    are assuming.

    Hope this helps.

    Igor
     
  5. May 7, 2008 #4
    JohnMS <john_m_stanton@yahoo.co.uk> wrote:

    > Many arxiv papers state that the Planck length
    > is the smallest measureable length.
    >
    > On the other hand, the gravitational length
    > L=2Gm/c^2
    > associated with every electron or proton
    > is 19 or 22 orders of magnitude smaller
    > than the Planck length.
    > Nobody seems to doubt either
    > of the two statements.
    >
    > What is the exact answer to this paradox?
    > One can imagine at least 3 solutions:
    >
    > 1 - Lengths of objects can be smaller than L_Planck,
    > but not positions.
    >
    > 2 - Lengths can be smaller than L_Planck if
    > one makes many measurements and then makes
    > a statistical average.
    >
    > 3 - There is an uncertainty relation between
    > length L and position x:
    >
    > L x > L_Planck^2
    >
    > There might be other answers. What is the
    > canonical answer by researchers to this question?


    The Planck length comes from dimensional analysis.
    If we agree to have c = \hbar = G = 1 and dimensionless,
    then lengths must be expressed in multiples of the Planck length.

    By it's very nature dimensional analysis
    has nothing to say about numerical factors.
    Neither does it stipulate that these factors must be of order one.
    To go beyond dimensional analysis (and get the factors)
    you need a physical theory.
    One that explains for example why the electron mass
    is so small in terms of the Planck mass.

    Since this is sadly lacking we do not know
    whether or not statements like:
    gravitational length = order 10^{-20} Plancks
    do or do not have physical meaning.
    Purely from dimensional analysis
    there is nothing wrong with them,
    hence no paradox.

    Best,

    Jan
     
  6. May 8, 2008 #5
    On 6 Mai, 19:19, nos...@de-ster.demon.nl (J. J. Lodder) wrote:
    > To go beyond dimensional analysis (and get the factors)
    > you need a physical theory.
    > One that explains for example why the electron mass
    > is so small in terms of the Planck mass.
    >
    > Since this is sadly lacking we do not know
    > whether or not statements like:
    > gravitational length = order 10^{-20} Plancks
    > do or do not have physical meaning.
    > Purely from dimensional analysis
    > there is nothing wrong with them,
    > hence no paradox.


    String theory is often claimed to have a minimum length
    (the Planck length or near it), so does loop quantum gravity,
    so do many other approaches. The theory-independent approaches
    argue convincingly that lengths below the Planck length
    cannot be measured by any known procedure or device.

    The electron mass is also well known, and
    R=2GM/c^2 is not in doubt, as electrons
    have gravitational effects. It seems difficult to say
    that R=2GM/c^2 is wrong
    for electrons.

    So in practice there IS a paradox, because
    electrons are known experimentally to
    have a gravitational length smaller than the
    Planck length.

    Is there no hint of a way out?

    John
     
  7. May 8, 2008 #6
    Thus spake JohnMS <john_m_stanton@yahoo.co.uk>
    >Many arxiv papers state that the Planck length
    >is the smallest measureable length.
    >
    >On the other hand, the gravitational length
    >L=2Gm/c^2
    >associated with every electron or proton
    >is 19 or 22 orders of magnitude smaller
    >than the Planck length.
    >Nobody seems to doubt either
    >of the two statements.
    >
    >What is the exact answer to this paradox?
    >One can imagine at least 3 solutions:
    >
    >1 - Lengths of objects can be smaller than L_Planck,
    >but not positions.
    >
    >2 - Lengths can be smaller than L_Planck if
    >one makes many measurements and then makes
    >a statistical average.
    >
    >3 - There is an uncertainty relation between
    >length L and position x:
    >
    > L x > L_Planck^2
    >
    >There might be other answers. What is the
    >canonical answer by researchers to this question?
    >

    Many researchers in quantum gravity assume Planck length as a
    fundamental length scale. This should be regarded as a hypothesis for a
    model, not as an established fact. It is well below the scale of
    measurable lengths. My own research hypothesises that L=2Gm/c^3 is a
    fundamental time. Of course, I think that is more promising. :-)

    Regards

    --
    Charles Francis
    moderator sci.physics.foundations.
    charles (dot) e (dot) h (dot) francis (at) googlemail.com (remove spaces and
    braces)

    http://www.teleconnection.info/rqg/MainIndex
     
  8. May 8, 2008 #7
    On May 7, 9:20 am, JohnMS <john_m_stan...@yahoo.co.uk> wrote:

    > String theory is often claimed to have a minimum length
    > (the Planck length or near it), so does loop quantum gravity,
    > so do many other approaches. The theory-independent approaches
    > argue convincingly that lengths below the Planck length
    > cannot be measured by any known procedure or device.


    Unfortunately, neither string theory nor loop quantum gravity enjoys
    the status of an experimentally verified theory. The theory-
    independent approaches are precisely the ones that use dimensional
    analysis, as discussed previously by J. J. Lodder and myself.

    > The electron mass is also well known, and
    > R=2GM/c^2 is not in doubt, as electrons
    > have gravitational effects. It seems difficult to say
    > that R=2GM/c^2 is wrong
    > for electrons.


    What would it mean for the above paragraph to be wrong? You've defined
    a length scale R. You can write down any length you want and call it
    R, no-one will argue with you solely on that basis.

    > So in practice there IS a paradox, because
    > electrons are known experimentally to
    > have a gravitational length smaller than the
    > Planck length.


    I see. And what is this experiment that has measured the gravitational
    length of the electron? None of the modern particle physics
    experiments have probed lengths that are even withing a few orders of
    magnitude from the Planck length, not to mention beyond it.

    Hope this helps.

    Igor
     
  9. May 8, 2008 #8
    On May 7, 6:20 am, JohnMS <john_m_stan...@yahoo.co.uk> wrote:
    > On 6 Mai, 19:19, nos...@de-ster.demon.nl (J. J. Lodder) wrote:
    >
    > > To go beyond dimensional analysis (and get the factors)
    > > you need a physical theory.
    > > One that explains for example why the electron mass
    > > is so small in terms of the Planck mass.

    >
    > > Since this is sadly lacking we do not know
    > > whether or not statements like:
    > > gravitational length = order 10^{-20} Plancks
    > > do or do not have physical meaning.
    > > Purely from dimensional analysis
    > > there is nothing wrong with them,
    > > hence no paradox.

    >
    > String theory is often claimed to have a minimum length
    > (the Planck length or near it), so does loop quantum gravity,
    > so do many other approaches. The theory-independent approaches
    > argue convincingly that lengths below the Planck length
    > cannot be measured by any known procedure or device.
    >
    > The electron mass is also well known, and
    > R=2GM/c^2 is not in doubt, as electrons
    > have gravitational effects. It seems difficult to say
    > that R=2GM/c^2 is wrong
    > for electrons.
    >
    > So in practice there IS a paradox, because
    > electrons are known experimentally to
    > have a gravitational length smaller than the
    > Planck length.
    >
    > Is there no hint of a way out?
    >
    > John


    Paradoxes point out a flawed argument.

    The relationship reality -> mathematical structure is one
    to many.

    The problem here is an assumption that the relationship
    (a particular mathematical structure) -> reality is one
    to one. There in lies the rub.

    Perhaps there is no hard reality for a minimum length, or
    Oh No's divide it by c to dimensionaly come up with a time.
    That does not mean it can't have some value in a model based
    representation. Just do not confuse the model with the singular
    notion of reality.

    Rick
     
  10. May 8, 2008 #9
    On May 6, 1:19 pm, nos...@de-ster.demon.nl (J. J. Lodder) wrote:
    >
    > The Planck length comes from dimensional analysis.
    > If we agree to have c = \hbar = G = 1 and dimensionless,
    > then lengths must be expressed in multiples of the Planck length.
    >
    > By it's very nature dimensional analysis
    > has nothing to say about numerical factors.
    > Neither does it stipulate that these factors must be of order one.
    > To go beyond dimensional analysis (and get the factors)
    > you need a physical theory.
    > One that explains for example why the electron mass
    > is so small in terms of the Planck mass.


    because the Bohr radius is

    a_0 = ((4 pi \epsilon_0) \hbar^2)/(m_e e^2)

    which is

    a_0 = (m_P/m_e) (1/ \alpha) l_P

    where m_P is the Planck mass, l_P is the Planck length, and \alpha is
    the Fine-structure constant (which is not a particularly huge or tiny
    number).

    it's been said that the reason gravity is so weak is really because
    the masses of particles are so small ( m_e <<<< m_P ). but the reason
    that particle masses are so small is the same reason that the size of
    atoms are so big ( l_P <<<< a_0 ) which is another what of saying that
    the Planck length is so small (compared to the sizes of atoms or even
    particles contained therein).

    but, out of ignorance, i dunno why anyone says that it's the smallest
    length. it's a quantity, we can always define a length much smaller.
    but such a teeny length might not be in the ballpark of any physical
    thing. hell, maybe not even the Planck length is comparable to any
    physical thing. but i think the reason that the Planck length is tiny
    compared to the radius of an atom is the same reason the Planck mass
    is huge compared to that of an atom.

    r b-j
     
  11. May 9, 2008 #10
    On May 7, 10:31 pm, robert bristow-johnson <r...@audioimagination.com>
    wrote:
    > On May 6, 1:19 pm, nos...@de-ster.demon.nl (J. J. Lodder) wrote:
    >
    >
    >
    > > The Planck length comes from dimensional analysis.
    > > If we agree to have c = \hbar = G = 1 and dimensionless,
    > > then lengths must be expressed in multiples of the Planck length.

    >
    > > By it's very nature dimensional analysis
    > > has nothing to say about numerical factors.
    > > Neither does it stipulate that these factors must be of order one.
    > > To go beyond dimensional analysis (and get the factors)
    > > you need a physical theory.
    > > One that explains for example why the electron mass
    > > is so small in terms of the Planck mass.

    >
    > because the Bohr radius is
    >
    > a_0 = ((4 pi \epsilon_0) \hbar^2)/(m_e e^2)
    >
    > which is
    >
    > a_0 = (m_P/m_e) (1/ \alpha) l_P
    >
    > where m_P is the Planck mass, l_P is the Planck length, and \alpha is
    > the Fine-structure constant (which is not a particularly huge or tiny
    > number).
    >
    > it's been said that the reason gravity is so weak is really because
    > the masses of particles are so small ( m_e <<<< m_P ). but the reason
    > that particle masses are so small is the same reason that the size of
    > atoms are so big ( l_P <<<< a_0 ) which is another what of saying that
    > the Planck length is so small (compared to the sizes of atoms or even
    > particles contained therein).
    >
    > but, out of ignorance, i dunno why anyone says that it's the smallest
    > length. it's a quantity, we can always define a length much smaller.
    > but such a teeny length might not be in the ballpark of any physical
    > thing. hell, maybe not even the Planck length is comparable to any
    > physical thing. but i think the reason that the Planck length is tiny
    > compared to the radius of an atom is the same reason the Planck mass
    > is huge compared to that of an atom.



    If gravity quantizes around the planck scale, then below that scale
    one does not have the convenience of a classical metric. Without a
    metric, how do you define length?
     
  12. May 9, 2008 #11
    On 8 Mai, 17:44, "Chris H. Fleming" <chris_h_flem...@yahoo.com> wrote:

    > If gravity quantizes around the planck scale, then below that scale
    > one does not have the convenience of a classical metric. Without a
    > metric, how do you define length?


    If one takes 10^24 atoms of silicon in a single
    crystal (around 1 kg)
    it is undisputed that the whole object has a
    measureable gravitational length.
    The crystal bends space-time around it and attracts
    other masses;
    that is easy to measure. And there is a definite
    metric in our environment.

    It is also undisputed that all atom masses
    in the crystal essentially add up
    (the crystal binding energy can be neglected here).
    Since the gravitational length of the silicon
    crystal is defined as R=2GM/c^2,
    it is very hard to avoid saying that every silicon atom
    has a gravitational length given by the
    same formula, this time using the atomic mass.

    However, the gravitational length calculated
    in this way for one atom is much smaller
    than the Planck length. (about 10^18 times smaller).

    So it does seem that much smaller lengths than a Planck
    length have a physical meaning...

    John
     
  13. May 9, 2008 #12
    On May 9, 2:47 am, JohnMS <john_m_stan...@yahoo.co.uk> wrote:

    > If one takes 10^24 atoms of silicon in a single
    > crystal (around 1 kg)
    > it is undisputed that the whole object has a
    > measureable gravitational length.
    > The crystal bends space-time around it and attracts
    > other masses;
    > that is easy to measure. And there is a definite
    > metric in our environment.
    >
    > It is also undisputed that all atom masses
    > in the crystal essentially add up
    > (the crystal binding energy can be neglected here).
    > Since the gravitational length of the silicon
    > crystal is defined as R=2GM/c^2,
    > it is very hard to avoid saying that every silicon atom
    > has a gravitational length given by the
    > same formula, this time using the atomic mass.


    It is true that a kilogram of silicon has a measurable gravitational
    field. This field corresponds to space-time curvature of order 1/L,
    where L is some length. We know for a fact that these gravitational
    effects are very weak, which in turn implies that L must be very
    large. When we measure gravitational effects due to this hunk of
    silicon, it is L that we measure, not the R that you've defined above.
    R would be the size of the hunk of silicon if it were dense enough to
    become a black hole. Since it is not a black hole, we have another
    demonstration that R is irrelevant to the physical situation.

    In short, your paradox is avoided because, no matter how small R is,
    it never comes up as an experimental measurement; only L does. And L
    is of regular macroscopic proportions.

    Hope this helps.

    Igor
     
  14. May 11, 2008 #13
    On May 5, 12:28�pm, JohnMS <john_m_stan...@yahoo.co.uk> wrote:
    > Many arxiv papers state that the Planck length
    > is the smallest measureable length.
    >
    > On the other hand, the gravitational length
    > L=2Gm/c^2
    > associated with every electron or proton
    > is 19 or 22 orders of magnitude smaller
    > than the Planck length.
    > Nobody seems to doubt either
    > of the two statements.
    >
    > What is the exact answer to this paradox?
    > One can imagine at least 3 solutions:
    >
    > 1 - Lengths of objects can be smaller than L_Planck,
    > but not positions.
    >
    > 2 - Lengths can be smaller than L_Planck if
    > one makes many measurements and then makes
    > a statistical average.
    >
    > 3 - There is an uncertainty relation between
    > length L and position x:
    >
    > � � � � �L x > L_Planck^2
    >
    > There might be other answers. What is the
    > canonical answer by researchers to this question?
    >
    > Thanks!
    >
    > John


    Hello John; Let us suppose that the gravitational length (radius) of
    the electron is L: where L = 3Gm/c^2. This is the photon orbit radius
    for the electron mass. Next, suppose that the shortest meaningful
    distance is Planck length times the square root of (3/2). The
    circumference is 2pi (radius). A circumference is (2pi) (Planck
    length) (3/2)^1/2. This value is (3pi h G/c^3)^1/2. When a photon with
    energy equal to the mass energy of one electron plus one positron is
    gravitationally blue shifted to the wavelength (3pi h G/c^3)^1/2, the
    size reduction factor is (L/L)^2 rather than (L/L). This is because
    distance is shortened to match time dilation. The observable length
    will then be equal to the photon orbit circumference, 2pi (3Gm/c^2),
    while the radius is 3Gm/c^2. This is discussed in "Talk:Black hole
    electron", Wikipedia.

    Don Stevens
     
  15. May 13, 2008 #14
    Planck length - the finest scale?

    If the Planck scale were considered as the finest measurement scale; still the general concept of a non-differentiable, no longer smooth manifold, might still be descriptive for a still finer scale. The breaking up of a manifold is just an assumption. After all mathematicians start with the generality of a manifold, and then subsequently add structure such as a metric etc.
     
  16. May 16, 2008 #15
    On May 7, 11:07am, Igor Khavkine <igor...@gmail.com> wrote:
    > On May 7, 9:20 am, JohnMS <john_m_stan...@yahoo.co.uk> wrote:
    >
    > > String theory is often claimed to have a minimum length
    > > (the Planck length or near it), so does loop quantum gravity,
    > > so do many other approaches. The theory-independent approaches
    > > argue convincingly that lengths below the Planck length
    > > cannot be measured by any known procedure or device.

    >
    > Unfortunately, neither string theory nor loop quantum gravity enjoys
    > the status of an experimentally verified theory. The theory-
    > independent approaches are precisely the ones that use dimensional
    > analysis, as discussed previously by J. J. Lodder and myself.
    >
    > > The electron mass is also well known, and
    > > R=2GM/c^2 is not in doubt, as electrons
    > > have gravitational effects. It seems difficult to say
    > > that R=2GM/c^2 is wrong
    > > for electrons.

    >
    > What would it mean for the above paragraph to be wrong? You've defined
    > a length scale R. You can write down any length you want and call it
    > R, no-one will argue with you solely on that basis.
    >
    > > So in practice there IS a paradox, because
    > > electrons are known experimentally to
    > > have a gravitational length smaller than the
    > > Planck length.

    >
    > I see. And what is this experiment that has measured the gravitational
    > length of the electron? None of the modern particle physics
    > experiments have probed lengths that are even withing a few orders of
    > magnitude from the Planck length, not to mention beyond it.
    >
    > Hope this helps.
    >
    > Igor


    Hi Igor; Some photon wavelength equations relate the Planck length to
    the electron mass.

    L1/L2 = L2/L3

    L1 = (L2)^2 (1/L3) = 2pi (3/2)^1/2 (Planck length)

    Where L2 is the photon wavelength with energy equal to the mass energy
    of one electron plus one positron and the wavelength L3 is (2pi)^2 (c)
    (one second). The L2 length is then equal to [(L1) (L3)]^1/2. When L2
    is defined, the electron mass energy can have only one quantized
    value.

    Don Stevens
     
  17. May 17, 2008 #16
    On May 15, 5:51 pm, donjstev...@aol.com wrote:
    > On May 7, 11:07am, Igor Khavkine <igor...@gmail.com> wrote:
    >
    >
    >
    > > On May 7, 9:20 am, JohnMS <john_m_stan...@yahoo.co.uk> wrote:

    >
    > > > String theory is often claimed to have a minimum length
    > > > (the Planck length or near it), so does loop quantum gravity,
    > > > so do many other approaches. The theory-independent approaches
    > > > argue convincingly that lengths below the Planck length
    > > > cannot be measured by any known procedure or device.

    >
    > > Unfortunately, neither string theory nor loop quantum gravity enjoys
    > > the status of an experimentally verified theory. The theory-
    > > independent approaches are precisely the ones that use dimensional
    > > analysis, as discussed previously by J. J. Lodder and myself.

    >
    > > > The electron mass is also well known, and
    > > > R=2GM/c^2 is not in doubt, as electrons
    > > > have gravitational effects. It seems difficult to say
    > > > that R=2GM/c^2 is wrong
    > > > for electrons.

    >
    > > What would it mean for the above paragraph to be wrong? You've defined
    > > a length scale R. You can write down any length you want and call it
    > > R, no-one will argue with you solely on that basis.

    >
    > > > So in practice there IS a paradox, because
    > > > electrons are known experimentally to
    > > > have a gravitational length smaller than the
    > > > Planck length.

    >
    > > I see. And what is this experiment that has measured the gravitational
    > > length of the electron? None of the modern particle physics
    > > experiments have probed lengths that are even withing a few orders of
    > > magnitude from the Planck length, not to mention beyond it.

    >
    > > Hope this helps.

    >
    > > Igor

    >
    > Hi Igor; Some photon wavelength equations relate the Planck length to
    > the electron mass.
    >
    > L1/L2 = L2/L3
    >
    > L1 = (L2)^2 (1/L3) = 2pi (3/2)^1/2 (Planck length)
    >
    > Where L2 is the photon wavelength with energy equal to the mass energy
    > of one electron plus one positron
    > and the wavelength L3 is (2pi)^2 (c)(one second).


    so, if human beings decided to use a different unit of time than a
    second, L3 (and then L1) would come out to be a different physical
    value?

    i have trouble imagining that physical reality gives a rat's ass what
    unit of time we humans happen to use. or the aliens on the planet
    Zog.

    r b-j
     
  18. Jun 6, 2008 #17
    Reply regarding aliens on planet Zog.

    I will redefine the length values so that any advanced people would know their physical value. The L2 value was previously defined as 1/2 of the electron Compton wavelength. The L2 value is also equal to (h/2 mc) where m is the electron mass. The next value needed is L4, defined as (2pi) times the photon sphere radius for the electron mass. In our system, L4 is (2pi) (3Gm/c^2). The L1 value may then be derived from ratio equations as shown.

    L1/L2 = L4/L1

    L1 = [(L4) (L2)]^1/2 = [(L4) (h/2mc)]^1/2 = (3pi hG/c^3)^1/2

    L1 = 2pi (Planck length) (3/2)^1/2

    The L3 value is derived from the physical values L1 and L2 with ratio equations. Values L1/L2 will equal L2/L3.

    L3 = (L2)^2 (1/L1)

    In our units, L3 will be very close to (2pi)^2 (c) (one second). Then the L2 value is equal to [(L1) (L3)]^1/2. The L2 is then equal to 2pi (3pi hG/c)^1/4. If this is precisely correct, the applicable G value must be very close to 6.6717456x10^-11. The ratio equations allow L3 to be developed from physical values.
     
  19. Jun 14, 2008 #18
    John M S, you asked "Is there no hint of a way out?"

    A way out was suggested by John A. Wheeler when he proposed that the electron is "--a fossil from -- gravitational collapse". The pattern of equal ratios (below) supports the Wheeler suggestion.

    L1/L2 = L2/L3 = L4/L1 = (L4/L2)^1/2 = (L4/L3)^1/3

    The ratio L4/L2 is also equal to (3/2)^1/2 times (Planck time) divided by (2pi seconds). These ratios are all equal when the gravitational constant value is 6.6717456x10^-11.

    We can now see that L4 and L1 are essentially the same. With gravitational collapse, the L2 photon wavelength is blue shifted to the L1 wavelength. When the twin effect of gravitational length shortening (to match time dilation) is included, the length that is observable from a distance is L4. There is no known reason why these ratios should apply to electrons if electrons are not gravitationally confined (gravitationally collapsed) particles.

    Don Stevens
     
  20. Jun 24, 2008 #19
    Many persons have viewed these posts, so it may be appropriate to add some information.

    Much of the work needed, to show that a self-confined, single wavelength photon, has the fundamental properties of an electron was done by J. G. Williamson and M. B. van der Mark. Their paper "Is the electron a photon with toroidal topology?" (1997) shows that the electron charge can arise from the toroidal topology of the photon path, in combination with the photon electric field. A left-handed flow produces an electron while a right-handed flow produces a positron. Explanations are provided for half-integer spin, gyromagnetic ratio and de Broglie wavelength. When gravitational collapse is included in this concept, the new model defines the quantized electron mass value and defines a specific relationship to the Planck mass.

    electron mass = (h/4pi c) (c/3pi hG)^1/4

    Don Stevens
     
  21. Jul 6, 2008 #20
    Hi,

    I have always felt that Planck units are trying to tell us something fundamental but that view is often undermined by frequent mentions that are is nothing physical or fundamental about the Planck length. In other words the Planck length does not represent a minimum distance. It is easy to see how a discrete Planckian coordinate system falls apart. Imagine a grid of coordinates of based on units of one Planck length. A diagonal can not be made of a whole number of units. The circumference of a circle with radius of one Planck unit is not a whole number of Planck units. Even if we "square off" a circle at the Planck scale to give it a "circumference" of 4 Planck units the diagonals are no longer a whole number. One way out of this dilemma is to forget about the discreteness of distance at the Planck scale and consider the Planck unit of time or its inverse (frequency) as being the more fundamental minimum unit. With time as the discrete unit the problem of Planck circles or diagonals disappears if no longer insist on distance as being discrete. The wavelength of a photon still comes in discrete units of Planck length but that is side effect that is completely determined by the discreteness of time and the constancy of the speed of light. Knowing the frequency of a photon (which is always a discrete inverse multiple of time units) determines the discreteness of its other physical qualities such as energy and momentum. You can also think of the temperature and mass of a Planckian black hole in terms of a characteristic frequency.

    You may be familiar with Peter Linde's solution to the Zeno paradoxes which was that time is smooth and continuous and that there is no such thing as an instant of time. He did not make it clear whether he meant that there is no such thing as interval of zero time or no such thing as a minimum discrete interval of time. My suggestion of a worthwhile path of investigation is that distance is smooth and continuous but the quantum discreteness comes about by discreteness of a minimum time interval. I believe it is harder to find processes that can be proven to happen in less than a Planck interval of time than it is to find examples that seem to contradict the limit set by the Planck interval of distance or examples of at the Planck scale that do not appear to be quantisized as whole units of Planck length. Retaining the fundamental discreteness of the Planck time interval while rejecting the discreteness of length solves some of the geometrical problems at the Planck scale while retaining it discrete quantum nature.
     
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