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 Posted: Fri Jun 27, 2008 11:32 am Post subject: Running of the fine structure constant - how exactly? |
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The fine structure constant alpha is said to be running
with energy as (from various QED textbooks)
1/alpha(E) = 1/alpha - (1/3 pi) ln (E^2/m^2)
where m is the electron mass, ln the natural logarithm,
and alpha without index is 1/137.036.
But many papers mention that at 90 Gev, alpha is around 1/128.
This is in contradiction with the above formula, which would give
a value of around 133 at 90 GeV.
Is the discrepancy due to the fact that the formula
misses the hadronic corrections?
As a result, what value is expected for alpha at
10^19GeV? Where can one look this up?
Frank |
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tnlockyer@aol.com
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| Posted: Sat Jun 28, 2008 3:52 pm Post subject: Re: Running of the fine structure constant - how exactly? |
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On Jun 27, 4:32�am, frank_k_shel...@yahoo.co.uk wrote:
| Quote: |
The fine structure constant alpha is said to be running
with energy as (from various QED textbooks)
1/alpha(E) = 1/alpha - (1/3 pi) ln (E^2/m^2)
where m is the electron mass, ln the natural logarithm,
and alpha without index is 1/137.036.
But many papers mention that at 90 Gev, alpha is around 1/128.
This is in contradiction with the above formula, which would give
a value of around 133 at 90 GeV.
Is the discrepancy due to the fact that the formula
misses the hadronic corrections?
As a result, what value is expected for alpha at
10^19GeV? Where can one look this up?
Frank
|
Frank, the fine structure constant is, by definition, the
dimensionless ratio between the electron's electrical potential energy
and rest mass energy. It is unlikely that alpha could "run" with
energy because it is set by the geometry of the electron.
There is another famous dimensionless constant "PI" that is also an
irrational number (goes on forevver without end) that shows these
constants are based on geometric ratios.
I think you are on the right path in looking for some correction to
the measurement methods. The running of their measurement has to be
an artifact of their measurement methods.
See; http://members.aol.com/tnlockyer/CHARGESPIN.pdf
Hope the link works,
Regards, Tom |
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John C. Polasek
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| Posted: Sun Jun 29, 2008 6:50 am Post subject: Re: Running of the fine structure constant - how exactly? |
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On Sat, 28 Jun 2008 08:52:40 -0700 (PDT), "tnlockyer@aol.com"
<tnlockyer@aol.com> wrote:
| Quote: |
On Jun 27, 4:32?am, frank_k_shel...@yahoo.co.uk wrote:
The fine structure constant alpha is said to be running
with energy as (from various QED textbooks)
snip
Frank, the fine structure constant is, by definition, the
dimensionless ratio between the electron's electrical potential energy
and rest mass energy. It is unlikely that alpha could "run" with
energy because it is set by the geometry of the electron.
|
It might be instructive if you stated the two quantities whose ratio
is alpha. I have alpha = e^2/2hceps0 but can't see your ratio there.
| Quote: |
There is another famous dimensionless constant "PI" that is also an
irrational number (goes on forevver without end) that shows these
constants are based on geometric ratios.
I think you are on the right path in looking for some correction to
the measurement methods. The running of their measurement has to be
an artifact of their measurement methods.
See; http://members.aol.com/tnlockyer/CHARGESPIN.pdf
Hope the link works,
Regards, Tom |
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tnlockyer@aol.com
Guest
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| Posted: Sun Jun 29, 2008 5:18 pm Post subject: Re: Running of the fine structure constant - how exactly? |
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On Jun 28, 6:50�pm, John C. Polasek <jpola...@cfl.rr.com> wrote:
| Quote: |
On Sat, 28 Jun 2008 08:52:40 -0700 (PDT), "tnlock...@aol.com"
tnlock...@aol.com> wrote:
On Jun 27, 4:32?am, frank_k_shel...@yahoo.co.uk wrote:
The fine structure constant alpha is said to be running
with energy as (from various QED textbooks)
snip
Frank, the fine structure constant is, by definition, the
dimensionless ratio between the electron's electrical potential energy
and rest mass energy. � It is unlikely that alpha could "run" with
energy because it is set by the geometry of �the electron.
|
Frank says;
| Quote: |
It might be instructive if you stated the two quantities whose ratio
is alpha. I have alpha = e^2/2hceps0 but can't see your ratio there.
|
Your equation is in obselete cgs units, Frank.
The International MetricSystem (SI) is the modern language of science,
and I find it more intuitive.
See the following link I gave you, Figure 4, left panel bottom
calculation.
The fine structure constant can be derived from a number of different
math equations but all are traceable to the geometry, as demonstrated
by the derivation shown.
Alpha= (Flux x 2 x e)/ h
| Quote: |
snip
I think you are on the right path in looking for some correction to
the measurement methods. �The running of their measurement has to be
an artifact of their measurement methods.
See; � �http://members.aol.com/tnlockyer/CHARGESPIN.pdf
Hope the link works,
Regards, Tom- -
|
P.S. See; www.amazon.com 096315463X for more information. |
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John C. Polasek
Guest
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| Posted: Mon Jun 30, 2008 8:21 am Post subject: Re: Running of the fine structure constant - how exactly? |
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On Sun, 29 Jun 2008 10:18:28 -0700 (PDT), "tnlockyer@aol.com"
<tnlockyer@aol.com> wrote:
| Quote: |
On Jun 28, 6:50?pm, John C. Polasek <jpola...@cfl.rr.com> wrote:
On Sat, 28 Jun 2008 08:52:40 -0700 (PDT), "tnlock...@aol.com"
tnlock...@aol.com> wrote:
On Jun 27, 4:32?am, frank_k_shel...@yahoo.co.uk wrote:
The fine structure constant alpha is said to be running
with energy as (from various QED textbooks)
snip
Frank, the fine structure constant is, by definition, the
dimensionless ratio between the electron's electrical potential energy
and rest mass energy. ? It is unlikely that alpha could "run" with
energy because it is set by the geometry of ?the electron.
Frank says;
It might be instructive if you stated the two quantities whose ratio
is alpha. I have alpha = e^2/2hceps0 but can't see your ratio there.
Your equation is in obselete cgs units, Frank.
The International MetricSystem (SI) is the modern language of science,
and I find it more intuitive.
See the following link I gave you, Figure 4, left panel bottom
calculation.
The fine structure constant can be derived from a number of different
math equations but all are traceable to the geometry, as demonstrated
by the derivation shown.
Alpha= (Flux x 2 x e)/ h
snip
I think you are on the right path in looking for some correction to
the measurement methods. ?The running of their measurement has to be
an artifact of their measurement methods.
See; ? ?http://members.aol.com/tnlockyer/CHARGESPIN.pdf
Hope the link works,
Regards, Tom- -
P.S. See; www.amazon.com 096315463X for more information.
The link doesnt work. |
John Polasek |
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tnlockyer@aol.com
Guest
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| Posted: Mon Jun 30, 2008 4:47 pm Post subject: Re: Running of the fine structure constant - how exactly? |
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On Jun 29, 8:21�pm, John C. Polasek <jpola...@cfl.rr.com> wrote:
| Quote: |
On Sun, 29 Jun 2008 10:18:28 -0700 (PDT), "tnlock...@aol.com"
tnlock...@aol.com> wrote:
On Jun 28, 6:50?pm, John C. Polasek <jpola...@cfl.rr.com> wrote:
On Sat, 28 Jun 2008 08:52:40 -0700 (PDT), "tnlock...@aol.com"
tnlock...@aol.com> wrote:
On Jun 27, 4:32?am, frank_k_shel...@yahoo.co.uk wrote:
The fine structure constant alpha is said to be running
with energy as (from various QED textbooks)
snip
Frank, the fine structure constant is, by definition, the
dimensionless ratio between the electron's electrical potential energy
and rest mass energy. ? It is unlikely that alpha could "run" with
energy because it is set by the geometry of ?the electron.
Frank says;
It might be instructive if you stated the two quantities whose ratio
is alpha. I have alpha = e^2/2hceps0 but can't see your ratio there.
Your equation is in obselete cgs units, Frank.
The International MetricSystem (SI) is the modern language of science,
and I find it more intuitive.
See the following link I gave you, Figure 4, left panel bottom
calculation.
The fine structure constant can be derived from a number of different
math equations but all are traceable to the geometry, as demonstrated
by the derivation shown.
Alpha= (Flux x 2 x e)/ h
snip
I think you are on the right path in looking for some correction to
the measurement methods. ?The running of their measurement has to be
an artifact of their measurement methods.
See; ? ?http://members.aol.com/tnlockyer/CHARGESPIN.pdf
Hope the link works,
Regards, Tom- �-
P.S. �See; �www.amazon.com� � 096315463X � for more information.
The link doesnt work.
John Polasek- Hide quoted text -
- Show quoted text -
|
John, The link requires you type
096315463X
in the top search block on the Amazon opening page, that should bring
up the book page.
Regards: Tom |
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Sue...
Guest
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| Posted: Mon Jun 30, 2008 11:56 pm Post subject: Re: Running of the fine structure constant - how exactly? |
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On Jun 27, 7:32 am, frank_k_shel...@yahoo.co.uk wrote:
| Quote: |
The fine structure constant alpha is said to be running
with energy as (from various QED textbooks)
1/alpha(E) = 1/alpha - (1/3 pi) ln (E^2/m^2)
where m is the electron mass, ln the natural logarithm,
and alpha without index is 1/137.036.
But many papers mention that at 90 Gev, alpha is around 1/128.
This is in contradiction with the above formula, which would give
a value of around 133 at 90 GeV.
Is the discrepancy due to the fact that the formula
misses the hadronic corrections?
As a result, what value is expected for alpha at
10^19GeV? Where can one look this up?
|
http://physics.nist.gov/cuu/Constants/alpha.html
Sue...
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tnlockyer@aol.com
Guest
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| Posted: Tue Jul 01, 2008 12:52 am Post subject: Re: Running of the fine structure constant - how exactly? |
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On Jun 30, 4:50�pm, John C. Polasek <jpola...@cfl.rr.com> wrote:
John, cannot ubderstand why. The link works for me. Do you have a pdf
reader?
Try also;
http://www.members.aol.com/tnlockyer/CHARGESPIN.pdf
Regards; Tom. |
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Jay Bala
Guest
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| Posted: Tue Jul 01, 2008 2:55 am Post subject: Re: Running of the fine structure constant - how exactly? |
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A while back, I came up with something that defined alpha, the fine
structure constant, in terms of geometry and Chaos Theory constants:
Its an irrational number:
alpha=7.29 735 257 240 051 31... x10^-3
1/alpha=137.035 999 025 471 68...
Regards,
Jay Bala.
| Quote: |
There is another famous dimensionless constant "PI" that is also an
irrational number (goes on forevver without end) that shows these
constants are based on geometric ratios. |
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Jay Bala
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| Posted: Tue Jul 01, 2008 3:22 am Post subject: Chaos Theory and Quantum Mechanics (was: Re: Running of ...) |
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Let me give you the equation:
Lets define,
1) 1/alphaPrime=((180*Phi)^2)/(20*pi^3)
2) For period doubling, as the limit approching infinity in chaos
theory:
Feigenbaum constant delta:
deltaF=delta Feigenbaum constant=4.66920....
3) For period doubling reduced from one doubling to the next,
converges to:
Feigenbaum constant alpha:
alphaF=alpha Feigenbaum constant=2.50290...
then,
1/alpha=1/alphaPrime+alphaF/10+sqrt(10/deltaF)
Rearranging the alphaPrime shows that its in fact a product of radians
and the golden ratio.
Regards,
Jay Bala.
On Jun 30, 10:55 pm, Jay Bala <jay1b...@aol.com> wrote:
| Quote: |
A while back, I came up with something that defined alpha, the fine
structure constant, in terms of geometry and Chaos Theory constants:
Its an irrational number:
alpha=7.29 735 257 240 051 31... x10^-3
1/alpha=137.035 999 025 471 68...
Regards,
Jay Bala.
There is another famous dimensionless constant "PI" that is also an
irrational number (goes on forevver without end) that shows these
constants are based on geometric ratios. |
|
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John C. Polasek
Guest
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| Posted: Tue Jul 01, 2008 4:50 am Post subject: Re: Running of the fine structure constant - how exactly? |
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On Mon, 30 Jun 2008 09:47:23 -0700 (PDT), "tnlockyer@aol.com"
<tnlockyer@aol.com> wrote:
| Quote: |
http://members.aol.com/tnlockyer/CHARGESPIN.pdf
Nope: did not recognize the link |
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Rock Brentwood
Guest
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| Posted: Wed Jul 02, 2008 7:33 am Post subject: Re: Running of the fine structure constant - how exactly? |
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On Jun 30, 9:55 pm, Jay Bala <jay1b...@aol.com> wrote:
| Quote: |
alpha=7.29 735 257 240 051 31... x10^-3
1/alpha=137.035 999 025 471 68...
|
That's the low energy asymptotic value. As you ramp up the energy in a
scattering process and probe deeper into the field of a source, the
effective value of alpha increases. This occurs because the source
being probed by a scatting process actually deviates from Coulomb, as
you probe deeper into it. For electromagnetism, the effective
potential goes faster than 1/r, though it's 1/r when far-removed from
the source. There's a huge industry that is (and has long been around)
dedicated to the question of the inverse scattering problem
(reconstructing an image, here, the profile of the potential
surrounding a source, from the results of scattering done off the
source). One actually sees the effective alpha go up at high energies.
It's widely believed (but not a complete consensus) that theory
predicts, in fact, that it would approach infinity at a finite
positive radius. That's called the Landau Pole.
To some extent this may be classically modelled. On general
principles, one would expect an effective dynamics for the dielectric
coefficient epsilon to be given by an equation of the form
[] log(epsilon_0) = -K epsilon_0 (E^2 - B^2 c^2)
for some positive constant K. This translates directly into an
equation d^2(log alpha)/d(1/r)^2 = k alpha, for some constant k. From
this you can get any of a wide variety of phases, including one that
replicates the features of the Landau Pole.
Other solutions, interestingly, include a phase where the effective
field E approaches a constant as r -> infinity, and alpha -> 0 as r ->
0. These features are called, respectively, "infrared slavery" and
"asymptotic freedom". For non-Abelian gauge fields (SU(3), here) it's
the basis of confinement that rules out the existence of monopole
sources. In this phase, sources with bounded fields can only exist as
dipoles or higher order multipoles (which includes, in SU(3), the 3-
body neutral sources with 3 charges bound to each other).
The 3-Way Kiss -- the Real Life Version
http://www.flickr.com/photos/confusedamused/20988689/ |
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Jay Bala
Guest
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| Posted: Wed Jul 02, 2008 4:33 pm Post subject: Re: Chaos Theory and Quantum Mechanics (was: Re: Running of |
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Rather, steradian: (180/pi)^2
Jay Bala.
On Jun 30, 11:22 pm, Jay Bala <jay1b...@aol.com> wrote:
| Quote: |
Lets define,
1) 1/alphaPrime=((180*Phi)^2)/(20*pi^3)
.. |
..
..
| Quote: |
Rearranging the alphaPrime shows that its in fact a product of radians
and the golden ratio.
Regards,
Jay Bala. |
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Jay Bala
Guest
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| Posted: Fri Jul 04, 2008 11:46 pm Post subject: Re: Chaos Theory and Quantum Mechanics (was: Re: Running of |
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On Jun 30, 11:22 pm, Jay Bala <jay1b...@aol.com> wrote:
| Quote: |
Let me give you the equation:
Lets define,
1) 1/alphaPrime=((180*Phi)^2)/(20*pi^3)
2) For period doubling, as the limit approching infinity in chaos
theory:
Feigenbaum constant delta:
deltaF=delta Feigenbaum constant=4.66920....
3) For period doubling reduced from one doubling to the next,
converges to:
Feigenbaum constant alpha:
alphaF=alpha Feigenbaum constant=2.50290...
then,
1/alpha=1/alphaPrime+alphaF/10+sqrt(10/deltaF)
|
Correction: 1/alpha=1/alphaPrime+alphaF/10+sqrt(10/deltaF)x10^-5
Regards,
Jay Bala. |
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