Fine Structure Constant

182 views
Skip to first unread message

Robert

unread,
Jul 22, 2007, 5:07:33 PM7/22/07
to
I am very happy to report that the Self-Similar Cosmological Paradigm,
aka the Discrete Fractal Paradigm, aka Discrete Scale Relativity, has
led to a highly appealing explanation for the long-standing enigma:
the dimensionless fine structure constant.

Since it is dimensionless, one can be reasonably confident that it
comes from a ratio. The question is: the ratio of what?

Numerically: alpha = e^2/4 pi epsilon h(bar) c.

Using the discrete fractal paradigm as an intuitive guide, I realized
through dimensional analysis that h(bar)c has the dimensions of
[gravitational charge]^2, or GM^2.

Then alpha is the ratio between the [fundamental EM charge]^2 and the
[fundamental GR charge]^2 for the Atomic Scale.

The key is knowing what G amd M are for the Atomic Scale, and this
information is given by the discrete self-similar scale transformation
equations of the SSCP, aka DFP, aka DSR.

A shortcut to these values can be found by going to www.amherst.edu/~rloldershaw
and clicking on "Technical Notes", then clicking on "Revised Planck
Scale". For the Atomic Scale, G = 2.18 x 10^31 cgs and the Planck
Mass is 1.2 x 10^-24 g.

When you plug the correct numbers into [e^2/4 pi epsilon] / [GM^2] you
get a close approximation to the fine structure constant. Unless I
have some bone-headed mistake.

At this point the numerical agreement is better than order of
magnitude, and at first glance appears to be within 20 % , or better.
This uncertainty is due to the fact that the scaling equations used to
derive G and M are still empirically-based and have a 1-10%
uncertainty.

However, in terms of intuitive concepts, and basic correctness, I
think you can bet the farm on this one.

Enjoy,

Rob
www.amherst.edu/~rloldershaw

PS: "Regards" to you too, Charles

Peter

unread,
Jul 24, 2007, 5:21:29 PM7/24/07
to
Robert <rlold...@amherst.edu> writes:

> On Jul 22, 5:07 pm, Robert <rlolders...@amherst.edu> wrote:
> > I am very happy to report that the Self-Similar Cosmological Paradigm,
> > aka the Discrete Fractal Paradigm, aka Discrete Scale Relativity, has
> > led to a highly appealing explanation for the long-standing enigma:
> > the dimensionless fine structure constant.
> >
> > Since it is dimensionless, one can be reasonably confident that it
> > comes from a ratio. The question is: the ratio of what?
> >
> > Numerically: alpha = e^2/4 pi epsilon h(bar) c.
> >
> > Using the discrete fractal paradigm as an intuitive guide, I realized
> > through dimensional analysis that h(bar)c has the dimensions of
> > [gravitational charge]^2, or GM^2.
> >
> > Then alpha is the ratio between the [fundamental EM charge]^2 and the
> > [fundamental GR charge]^2 for the Atomic Scale.
> >
> > The key is knowing what G amd M are for the Atomic Scale, and this
> > information is given by the discrete self-similar scale transformation
> > equations of the SSCP, aka DFP, aka DSR.
> >
> > A shortcut to these values can be found by going to
> www.amherst.edu/~rloldershaw
> > and clicking on "Technical Notes", then clicking on "Revised Planck
> > Scale". For the Atomic Scale, G = 2.18 x 10^31 cgs and the Planck
> > Mass is 1.2 x 10^-24 g.
> >
> > When you plug the correct numbers into [e^2/4 pi epsilon] / [GM^2] you
> > get a close approximation to the fine structure constant. Unless I

> > have made some bone-headed mistake.


> >
> > At this point the numerical agreement is better than order of
> > magnitude, and at first glance appears to be within 20 % , or better.
> > This uncertainty is due to the fact that the scaling equations used to
> > derive G and M are still empirically-based and have a 1-10%
> > uncertainty.
> >
> > However, in terms of intuitive concepts, and basic correctness, I
> > think you can bet the farm on this one.
> >
> > Enjoy,
> >
> > Rob
> > www.amherst.edu/~rloldershaw
> >
> > PS: "Regards" to you too, Charles
>
>
>

> Soooo...
>
> We have a newsgroup devoted to the foundations of physics.

yes :-)

> One person claims to have solved the fine structure constant puzzle,
> which has eluded every physicist since about 1920, and not for the
> lack of effort.

it's the benefit of this group to provide this possibility :-)

> In his Nobel Prize speech Pauli said that when he
> died, his first question to the Devil would be: "What is the meaning
> of the fine structure constant?".

I could not find this in the copy on www.nobel.se...

> No one else at SPF responds with a question, or points out a possible
> source of error?

perhaps, too many slogans have been used in your announcement

> Perhaps you are still looking for flaws.

rather waiting for an introduction that is easier to grasp than your
Technical Note dated April 2007 :-)

> Good Luck!

Looking forward,
Peter

Robert

unread,
Jul 24, 2007, 3:43:53 PM7/24/07
to
On Jul 22, 5:07 pm, Robert <rlolders...@amherst.edu> wrote:
> I am very happy to report that the Self-Similar Cosmological Paradigm,
> aka the Discrete Fractal Paradigm, aka Discrete Scale Relativity, has
> led to a highly appealing explanation for the long-standing enigma:
> the dimensionless fine structure constant.
>
> Since it is dimensionless, one can be reasonably confident that it
> comes from a ratio. The question is: the ratio of what?
>
> Numerically: alpha = e^2/4 pi epsilon h(bar) c.
>
> Using the discrete fractal paradigm as an intuitive guide, I realized
> through dimensional analysis that h(bar)c has the dimensions of
> [gravitational charge]^2, or GM^2.
>
> Then alpha is the ratio between the [fundamental EM charge]^2 and the
> [fundamental GR charge]^2 for the Atomic Scale.
>
> The key is knowing what G amd M are for the Atomic Scale, and this
> information is given by the discrete self-similar scale transformation
> equations of the SSCP, aka DFP, aka DSR.
>
> A shortcut to these values can be found by going to www.amherst.edu/~rloldershaw
> and clicking on "Technical Notes", then clicking on "Revised Planck
> Scale". For the Atomic Scale, G = 2.18 x 10^31 cgs and the Planck
> Mass is 1.2 x 10^-24 g.
>
> When you plug the correct numbers into [e^2/4 pi epsilon] / [GM^2] you
> get a close approximation to the fine structure constant. Unless I
> have made some bone-headed mistake.

>
> At this point the numerical agreement is better than order of
> magnitude, and at first glance appears to be within 20 % , or better.
> This uncertainty is due to the fact that the scaling equations used to
> derive G and M are still empirically-based and have a 1-10%
> uncertainty.
>
> However, in terms of intuitive concepts, and basic correctness, I
> think you can bet the farm on this one.
>
> Enjoy,
>
> Rob
> www.amherst.edu/~rloldershaw
>
> PS: "Regards" to you too, Charles

Soooo...

We have a newsgroup devoted to the foundations of physics.

One person claims to have solved the fine structure constant puzzle,


which has eluded every physicist since about 1920, and not for the

lack of effort. In his Nobel Prize speech Pauli said that when he


died, his first question to the Devil would be: "What is the meaning
of the fine structure constant?".

No one else at SPF responds with a question, or points out a possible
source of error?

Perhaps you are still looking for flaws.

Good Luck!

Rob
www.amherst.edu/~rloldershaw

Robert

unread,
Jul 25, 2007, 12:53:16 AM7/25/07
to
On Jul 24, 5:21 pm, Peter <end...@dekasges.de> wrote:
>
> > In his Nobel Prize speech Pauli said that when he
> > died, his first question to the Devil would be: "What is the meaning
> > of the fine structure constant?".
>
> I could not find this in the copy onwww.nobel.se...


The source of this anecdote is Christoph Schiller's interesting
physics "web-book" called "Motion Mountain". He claims that Pauli
expressed this sentiment on at least two separate occasions, one of
which was part of his receiving the Nobel Prize.


> > No one else at SPF responds with a question, or points out a possible
> > source of error?
>
> perhaps, too many slogans have been used in your announcement

I am not sure I know what you mean. Maybe the content is a wee bit
more important than the style, no?


>
> > Perhaps you are still looking for flaws.
>
> rather waiting for an introduction that is easier to grasp than your
> Technical Note dated April 2007 :-)

Now I am really confused. The "Revised Planck Scale" technical note
on www.amherst.edu/~rloldershaw is written at a level that should be
readily understandable to a high school student who has a basic
understanding of science.

Could you be more specific about what the difficulty is?

I am more than willing to walk people through the reasoning involved
in the Discrete Fractal Paradigm, how it leads to a revised Planck
scale, and how the revised Planck scale leads to an understanding of
the fine structure constant. But you have to make some effort too.
If you ask specific questions, or pose specific potential problems,
then we will have something to work with.

Rob

Ray Tomes

unread,
Jul 25, 2007, 8:34:40 AM7/25/07
to
Hi Rob

The photographs and comparisons on your web page are compelling.
Certainly it gives something to think about. To some extent this is to
be expected because at different scales we have inverse square laws
operating and so similar solutions must exist to the equations.

However use of phrases like "Self-Similar Cosmological Paradigm" and
"Discrete Fractal Paradigm" mean to me that similarity should exist at
multiple scales. Certainly at a very crude level of similarity we may
say that a galaxy is like a solar system in having a lump in the
middle and stuff approximately in a plane going around it one way. And
this same type of thing for planetary system and an atom.

However each has very definite differences. The galaxy has a huge
number of stars and extends a much greater percentage of the way to
the next galaxy compared to the other systems. Also, a star is very
different to the other centres in terms of the huge outpouring of
energy from it. I hope that so far you would agree.

The question is then, if there is to be a single law for the universe
(which I think is why a group such as sci.physics.foundations exists),
why if the whole thing is fractal do some levels of structure behave
so differently?

Have you ever seen anyone give a sensible answer to this question?
There is an answer, provided by the harmonics theory, http://ray.tomes.biz/maths.html
which follows simply and logically from a single non-linear wave
equation that explains why structures form at a scale ratio of about
10^4.5 just as we observe. Note that the sequence of distance scales:
Hubble scale, galaxies, stars, planets, moons, x, y, z, atoms,
nucleons has a common ratio of around 10^4.5 between them. This
typical ratio is predicted from a single principle by the harmonics
theory as explained in the referenced page.

Note also that the FSC of 1/137.036 can be interpretd as the speed of
an electron in a hydrogen atom (c/137.036) and appear in expressions
of energy (approx (1/2)v^2) or (1/2)*alpha^2 which has a value of
37557.73 or close to 10^4.5 and I suggest that this is connected with
this series of scale ratios in the universe.

However the harmonics theory does not predict a constant ratio at each
scale and very specifically gives a clear reason why each scale is
different because the pattern of energy predicted by the theory is
only somewhat similar and not actually self-similar at different
scales. No other theory can explain this approximate similarity as
deriving from a single law.

regards
Ray Tomes
http://ray.tomes.biz

Robert

unread,
Jul 25, 2007, 1:53:01 PM7/25/07
to
On Jul 25, 8:34 am, Ray Tomes <r...@tomes.biz> wrote:
> Hi Rob
>
> The photographs and comparisons on your web page are compelling.
> Certainly it gives something to think about. To some extent this is to
> be expected because at different scales we have inverse square laws
> operating and so similar solutions must exist to the equations.
>
> However use of phrases like "Self-Similar Cosmological Paradigm" and
> "Discrete Fractal Paradigm" mean to me that similarity should exist at
> multiple scales. Certainly at a very crude level of similarity we may
> say that a galaxy is like a solar system in having a lump in the
> middle and stuff approximately in a plane going around it one way. And
> this same type of thing for planetary system and an atom.
>
> However each has very definite differences. The galaxy has a huge
> number of stars and extends a much greater percentage of the way to
> the next galaxy compared to the other systems. Also, a star is very
> different to the other centres in terms of the huge outpouring of
> energy from it. I hope that so far you would agree.


Whoa! Let's stop right here and straighten out a misunderstanding.

Stars and the Solar System are discrete self-similar analogues of
atoms in various excited states.

Galaxies are discrete self-similar analogues of Atomic Scale particles
and nuclei, or equivalently neutron stars, pulsars, dark matter
objects, microquasars, etc. on the Stellar Scale, in various states of
excitation.

You have set off comparing the Solar System and the Galaxy. Not a bad
start, and a mistake that I also made at the beginning. But I found
that these are not proper analogues.

It is crucial to master the scaling and the correct analogues proposed
by the SSCP before you start to look for problems. It is really easy
to do that. Go to www.amherst.edu/~rloldershaw and click on "Selected
Papers". If you read Papers #1 and #2 nice and slowly, with an open
mind and the willingness to tentatively accept someone else's ideas,
you will get a good working understanding of the SSCP in 1-4 hours. I
think it is well worth that reasonable amount of effort.

Tonight I will look at the rest of your post and I will possibly post
a follow-up response. But I think those two papers will get you
started on the right track for answering most of your own questions.
If there are burning issues that remain, post away. I'll do my best
provide answers or admit that the issue is still to be worked out.

Sincere thanks for the positive comments and your effort so far.

Rob

Peter

unread,
Jul 25, 2007, 2:23:30 PM7/25/07
to
Robert <rlold...@amherst.edu> writes:

> > > In his Nobel Prize speech Pauli said that when he
> > > died, his first question to the Devil would be: "What is the meaning
> > > of the fine structure constant?".

> > I could not find this in the copy on www.nobel.se...

> The source of this anecdote is Christoph Schiller's interesting
> physics "web-book" called "Motion Mountain". He claims that Pauli
> expressed this sentiment on at least two separate occasions, one of
> which was part of his receiving the Nobel Prize.

Then, perhaps, during small talk at this event or as a spontaneous addition
to the speech - the written version can be downloaded for free from that URL
(many speeches contain a lot of interesting material, where one has to be
cautious against certain details, of course).


> > > No one else at SPF responds with a question, or points out a possible
> > > source of error?

> > perhaps, too many slogans have been used in your announcement

> I am not sure I know what you mean...

I didn't found in 'babylon' an appropriate translation of 'Schlagwörter',
sorry.

> ...Maybe the content is a wee bit more important than the style, no?

Maybe, yes - often, not ;-)


> > > Perhaps you are still looking for flaws.

> > rather waiting for an introduction that is easier to grasp than your
> > Technical Note dated April 2007 :-)

> Now I am really confused. The "Revised Planck Scale" technical note
> on www.amherst.edu/~rloldershaw is written at a level that should be
> readily understandable to a high school student who has a basic
> understanding of science.

I have only a Dr. habil. in Theoretical Physics, thus, am, obviously, far
below your requirements. However, since I'm not the only layman in this
group, I would feel indebted for getting an introduction at our level :-)

> Could you be more specific about what the difficulty is?

Yes, you presuppose a lot of knowledge from you foregoing writings. A self-
containing exposition would be highly appreciated.

> I am more than willing to walk people through the reasoning involved
> in the Discrete Fractal Paradigm, how it leads to a revised Planck
> scale, and how the revised Planck scale leads to an understanding of
> the fine structure constant. But you have to make some effort too.

Sure

> If you ask specific questions, or pose specific potential problems,
> then we will have something to work with.

First, let us see the outcome of the question asked in another posting,

Thank you,
Peter

Robert

unread,
Jul 26, 2007, 12:24:40 AM7/26/07
to
On Jul 25, 2:23 pm, Peter <end...@dekasges.de> wrote:
>
> I have only a Dr. habil. in Theoretical Physics, thus, am, obviously, far
> below your requirements. However, since I'm not the only layman in this
> group, I would feel indebted for getting an introduction at our level :-)


At www.amherst.edu/~rloldershaw you will find discussion of the
Discrete Fractal Paradigm on many levels of technical difficulty. In
the "Selected Papers" section, there is a description of each paper
and an indication of whether it is a "popular" exposition, or more
technical.

As I recommended to Ray Tomes, Papers #1 and #2 give a fairly
comprehensive introduction that uses a minimum of technically
difficult material.

There is also a "Main Ideas" section that runs through the basic ideas
in about one page. There are also some pictures in "A Remarkable
Example of Stellar-Atomic Self-Similarity".

What more can I say?

Robert L. Oldershaw
www.amherst.edu/~rloldershaw

Peter

unread,
Jul 26, 2007, 5:06:27 AM7/26/07
to
Robert <rlold...@amherst.edu> writes:

> On Jul 25, 2:23 pm, Peter <end...@dekasges.de> wrote:
> >
> > I have only a Dr. habil. in Theoretical Physics, thus, am, obviously, far
> > below your requirements. However, since I'm not the only layman in this
> > group, I would feel indebted for getting an introduction at our level :-)


> At www.amherst.edu/~rloldershaw you will find discussion of the
> Discrete Fractal Paradigm on many levels of technical difficulty. In
> the "Selected Papers" section, there is a description of each paper
> and an indication of whether it is a "popular" exposition, or more
> technical.

> As I recommended to Ray Tomes, Papers #1 and #2 give a fairly
> comprehensive introduction that uses a minimum of technically
> difficult material.

Have read that and plan to read it

> There is also a "Main Ideas" section that runs through the basic ideas
> in about one page. There are also some pictures in "A Remarkable
> Example of Stellar-Atomic Self-Similarity".
>
> What more can I say?

That's fine, thank you,
Peter

Al.R...@gmail.com

unread,
Jul 26, 2007, 4:16:42 PM7/26/07
to

Some people has tried to get the fine structure constant from the
logarithm of the quotient between the mass of the electron and the
mass of Planck. At the end, this is simply the calculation of the self-
energy of a charged particle with a cut-off of the order of the planck
mass and the postulate that this self-energy must be of the same order
that the electron mass. This point was well-known by the forefathers,
but nowadays it is hidden under the cloak of naturalness and
hierarchy.

Note that the quotient between mass of the electron and the mass of
Planck is also the gravity coupling of the electron; people as Nottale
prefer to argue from this point of view and the fractal scaling
instead of using standard QFT.

Robert

unread,
Jul 27, 2007, 1:43:44 AM7/27/07
to


Thanks for the comment.

I think that as long as we labor under the delusion that the
conventional Planck scale makes sense, with its totally bizarre Mpl =
10^-5 g, we will not make progress in understanding the fine structure
constant, atomic physics or HEP.

The scaling transformations for the Discrete Fractal Paradigm show how
to calculate the correct Atomic Scale value of G, let's call it Gn-1.
Then if you use Gn-1 to derive the Planck Scale length, mass, time and
charge, they are all very close to values associated with the proton.

On the other hand the old Planck scale values are are random
assortment of wingnuts that have no connection with nature.

I think my case is quite strong, but not airtight. I would welcome
references to the ideas you mention, but if the fine structure
constant had been explained satisfactorily before, we would be
exceedingly much more aware of it.

Sincere thanks for the response.

Rob
www.amherst.edu/~rloldershaw

Al.R...@gmail.com

unread,
Jul 27, 2007, 7:37:41 PM7/27/07
to
On Jul 27, 7:43 am, Robert <rlolders...@amherst.edu> wrote:
>I would welcome
> references to the ideas you mention, but if the fine structure
> constant had been explained satisfactorily before, we would be
> exceedingly much more aware of it.

Well, if you havent read Nottale and his calculation of the electron
mass, you have not done your homework, because it is exactly about
your topic (and he uses fractal ideas instead of Quantum Field
Theory).

As for the self-energy of the electron, it appears in almost every
old QFT textbook, but they only write ln (m_e/Lambda) telling that
Lamba is "a suitable cutoff" or something so. If you set the "suitable
cutoff" to Planck Mass, then you have the result of a self-energy of
the same order than the mass of the electron.

In modert QFT textbook, they prefer to "run up" the fine structure
constant and show that it meets the other coupling constants within a
couple orders of magnitude of the Planck Energy, so they do no study
exactly when the running coupling constant becomes exactly 1 but it is
evident it happens in a near scale.

So the point is that the fine structure is satisfactory within one
order of magnitude when you consider Planck mass, and it can be even
better depending of particular model building. Thus you must be not
surprised than good physicists are not interested for alternate
results (it could be argued that mediocre physicists, and physics fan
mobs, just follow suit without doing further enquiry).

Robert

unread,
Jul 28, 2007, 12:06:17 AM7/28/07
to
On Jul 27, 7:37 pm, "Al.Riv...@gmail.com" <Al.Riv...@gmail.com> wrote:
>
> Well, if you havent read Nottale and his calculation of the electron
> mass, you have not done your homework, because it is exactly about
> your topic (and he uses fractal ideas instead of Quantum Field
> Theory).

I have made at least three attempts to study Nottale's theory.
I have made at least three attempts to contact Nottale in order to
discuss our respective paradigms and the potential for mutually
beneficial collaboration. He chose to ignore my efforts. I can be
accused of several things, but not of shirking my "homework".


> So the point is that the fine structure is satisfactory within one
> order of magnitude when you consider Planck mass, and it can be even
> better depending of particular model building. Thus you must be not
> surprised than good physicists are not interested for alternate
> results (it could be argued that mediocre physicists, and physics fan
> mobs, just follow suit without doing further enquiry).

With all due respect for the grand panjandrums of theoretical particle
physics, the fact that they got the Planck length and mass wrong by 20
orders of magnitude, virtually assures that theoretical HEP is going
to have to be rebuilt from scratch, and this time without "making it
up as you go", but rather by developing a "theory of principle", i.e.,
General Relativity + EM + discrete scale invariance.

You will see that I know (or don't know) what I am talking about when
the Dark Matter is discovered to be vast populations of stellar mass
black holes (or CDM mythicles).

Over and out,

Rob

Al.R...@gmail.com

unread,
Jul 28, 2007, 2:33:06 PM7/28/07
to
On Jul 28, 6:06 am, Robert <rlolders...@amherst.edu> wrote:
> On Jul 27, 7:37 pm, "Al.Riv...@gmail.com" <Al.Riv...@gmail.com> wrote:
> > Well, if you havent read Nottale and his calculation of the electron
> > mass, you have not done your homework, because it is exactly about
> > your topic (and he uses fractal ideas instead of Quantum Field
> > Theory).
>
> I have made at least three attempts to study Nottale's theory.
> I have made at least three attempts to contact Nottale in order to
> discuss our respective paradigms and the potential for mutually
> beneficial collaboration. He chose to ignore my efforts.
> I can be accused of several things, but not of shirking my "homework".

Well, in this case Nottale has more points to be accused of not doing
the "homework", because he had a lot more of opportunities to contact
and collaborate with particle/field physicists and he just choose to
ignore current QFT and go ahead.

> > So the point is that the fine structure is satisfactory within one
> > order of magnitude when you consider Planck mass, and it can be even
> > better depending of particular model building. Thus you must be not
> > surprised than good physicists are not interested for alternate
> > results (it could be argued that mediocre physicists, and physics fan
> > mobs, just follow suit without doing further enquiry).
>
> With all due respect for the grand panjandrums of theoretical particle
> physics, the fact that they got the Planck length and mass wrong by 20

> orders of magnitude.

Er, what I was telling is that it is not wrong. First of all, Planck
mass is a concept defined before quantum theory, in 1899, directly
from Newton and Planck constants. About 25 years before of the
definition of the fine structure constant. It is a perfectly well
defined object, so you go nowhere telling it is "wrong". You can argue
about how useful the concept is.

As for "homework" in this case, all I was telling is that you should
be aware of the logarithms usually appearing in QFT and then to notice
that when one puts the Planck mass as actual cutoff for these
logarithms, then 20 orders of magnitude become nothing, and you can
get predictions very similar to the ones of other "scaling"
approaches, such as yours or Nottale's.

Compare for instance the value of ln (m/M), with m the electron mass
and M the Planck mass, with the value of fine structure constant. If
you multiply both, you get a number of order unity. Actually it is
still of order unity for a long range of the values of the cutoff M,
so it is not a prediction of anything, but a mere indication of the
naturalness of the electron mass. Nottale points out the number is
near 3/8 so it could come from EW mixing, but it is just another
conjecture as the ones appearing in the newsgroups.

Now, there is another hint that the magnitude of the Planck mass can
have a role, and it is the point of unification of coupling constants
in GUT QFTs, which is only a couple orders of magnitude beyond Planck
mass. While this argument is based also in Renormalisation group, It
is a separate argument because the former uses "mass renormalisation"
and the later uses "charge renormalisation" (well, coupling constant
renormalisation).

Reply all
Reply to author
Forward
0 new messages