### Could the value of fine structure vary in cosmological scales?

There has been claims and counter claims about the possible time variation of the fine structure constant. The effect is extremely small. There is also a rather recent claim about the spatial variation of the finite structure constant (thanks to Ulla for the link). The claimed variation of alpha was along certain direction and about Δ α/α≈ 10

^{-6}for a distance of order of length travelled by light during the age of the Universe if I understood correctly (see this). The claim is based on the study of the atomic spectra of distant galaxies.

The article tells that the spatial variation is along different (how different is not told) directions depending on the method used. This suggests that the reason for observations is not the variation of fine structure constant but something else: most probably a measurement error or with much smaller probability a genuine new physics effect.

The measurements are extremely difficult. One must compare the frequencies of two spectral lines expressible in terms of alpha. These spectral lines should come from same source to eliminate the effect of red shift, one must eliminate the effects of local motions causing red shift, one must eliminate the effects of local magnetic fields, etc... Therefore it is very easy to make some measurement error.

**Could the possible variation of alpha relate to coupling constant evolution?**

No one claims that the running of gauge coupling could somehow cause the effect and no-one dares to ask why no one does this. Scientists painfully learn to avoid saying anything stupid: when a friendly looking colleague encourages to make stupid questions, the worst thing to do is to really make a stupid question! Shame is an excellent teacher. As a crackpot I can however unashamedly break this rule;-).

The assumption seems in my crackpottish eyes to boil down to the assumption that the natural length scale assignable to electron as its Compton length -and therefore its mass- determines the length scale used in atomic physics. Therefore electron mass would determine the value of the fine structure constant used in atomic physics calculations. Electron mass is simply assumed to have the same value everywhere in the Universe. Therefore also the fine structure constant used by all atomic physicists of the Whole Big Universe would be the same. I might be wrong and miss something important. I would be really happy if I understood this aspect better.

In any case, it is good to try gain some quantitative understanding about the situation.

- Fine structure constant runs roughly from 1/137 to 1/125 in the mass scale range defined by electron mass and weak boson mass scale. This makes Δα/α∼ 10/137: this makes roughly 5 orders of magnitude giving in linear approximation : Δ α/α (m)= k Δ m
_{e}/m_{e}with k ≈ 6× 10^{-3}. - If Δ α/α ≈ 10
^{-6}were due to the running fine structure constant, it would require Δ m_{e}/m_{e}∼ 2× 10^{-4}. The change of electron mass by about 50 eV to be compared with .5 MeV mass of electron and to the ionization energy about 13 eV of hydrogen atom. This is clearly an atomic energy scale. It seems that the relative variation of electron mass of order Δ m_{e}/m_{e}∼ 2× 10^{-4}is definitely excluded as too large. Why?

[Note that in TGD framework gauge coupling evolution is replaced with p-adic coupling constant evolution which occurs as jumps at half octaves of the basic mass scale so that this explanation is excluded].

**Could the possible variation of alpha be "environmental" effect?**

What about the environment of atoms? This is a question that an innocent layman who knows nothing about the rules of the academic theatre might ask.

- I must confess that I do not understand how the "environment" of atoms could be same at distances of order light age of the Universe in so incredible accuracy. The basic idea behind atomic hypothesis is that the effects of environment on atomic energy levels can be neglected (forgetting of course strong local electric and magnetic fields). But can one be so sure about absence of delicate "environmental" effects not reducing to strong electric and magnetic fields? What one means with "environment"?
- The absence of "environmental" effects seems to be in a sharp contrast with the observations of Shnoll and others that nuclear decay rates, rates of chemical reactions, etc.. vary with astrophysical periods assignable to solar system. If nuclei, why not atoms? Why also the energy levels could not vary with astrophysical periods and therefore depend on astrophysical environment?
[For the TGD based model of Shnoll effect see this. For the implications of the model for understanding of real-p-adic correspondence and p-adic length scale hypothesis see this].

Theoreticians, those lucky ones who need not perform the experiments;-), can of course imagine endlessly mechanisms for the variation of fine structure constant. In many-sheeted space-time this exercise is not terribly difficult.

- For instance, one could ask whether charged particles could leak some of their electric flux to some large space-time sheets so that fine structure constant could be reduced. I indeed did so for few years ago when the news about possible time variation of fine structure constant emerged. Charge quantization does not encourage this idea. Whether the leakage can happen is impossible to tell at this moment.
- Or could the analog of Shnoll effect predicted to be very general in TGD Universe and reflect real physics- p-adic physics duality (see this) be involved, and cause extremely tiny small spatial and temporal variations on energy levels due to "environment" in cosmic scales?

## 11 Comments:

Matti,

This sort of claim is hardly recent. For one thing my recent posts do discuss the fine structure constant and other issues that now seems your area of interest.

For another thing it is a general axiom of Einsteins. Can gravity vary itself over time or across the universe? I recall that question in the sci mags of 1960. Is there some sort of pressure underneath things that explains it all as the one commenter pointed out about Weyl?

But is seems to me, as in Lubos last two posts, this is all about our concepts of probability. Perhaps the misapplication of them in social or political matters really. I shall post on that today (The Physics of Events and Coincidence) which came from my mapping the primes in different regions of space in a quasic framework. Sorry if that sort of arithmetic did not match up to t your interest and help.

7000 years from now they two might look back and wonder if our great edifaces of mountains were just burial grounds in the hope of some space flight, or just holy ground where we feel the old ancestor spirits come back to life- (to reverse that null hypothesis Lubos before Biblical time.)

The PeSla

http://kea-monad.blogspot.com/2008/07/varying-alpha.html

electron spin-time

Maybe I did the mistake and really did ask all those stupid questions :)

PeSla,

The quasic grid is coming from the primes, but only secondary? First there are octonions as modelled by Bott periodicity, as instance?

If I know this right?

God is a quasic structure in metaphysics. Also here it is secondary? First are the trinities? The elements, Platonic solides.

A neo-Ptolemaic system of navigation, attested by radial markings on old maps, used a projection of the sphere within unit circle and logarithmic metric. To the Orthodox divine this transpired within the eye of the soul, with the reasoned distances as cognitions p for 1/p.

In Orthodox theology the eye of the soul is Nous, which one may take back to Anaxagoras for the sense of the elements sorted in the turnings or vortex. Here lie reefs on which Socrates and Descartes faltered and foundered.

In the Tetrabiblos of Ptolemey all transpires in the play of Aristotelian or common elements by polarities of temperature and humidity, and Hypatia then took a lock of her naturally curly hair to make the psychrometer or hygrometer. Her spirit-children are the Ninas, rulers of our weather-chaos, and Feigenbaum's now classic period-doubling cascade resolves in the complex square root into half-octave (in the harmonoic sense) materiality.

My question is still, is this rest mass or relativistic mass or potential energy, as in diphotons? Here the mainstream relies on Big Bang to dynamize the material process, lacking which theoreticians look to path integrals, Hamiltonian constraints or combinatorics.

Orwin,

I am familiar with the integral program and the depth of Wilbur's philosophy- I used his words depth and span for my take on things.

The difference you ask of the rest mass or relativistic mass can be asked on a much higher level which I suspect Matti is talking about.

Ulla,

I hope I am not confusing you. I might speculate on the structure of the soul but none of this can impose its concepts on the idea of God including number anymore than path integrals, Hamiltonian s, and combintorics and so on describe and reduce things to enough depth in span of the universe(s).

While the world remains simple- perhaps we share with the Deity the asking of stupid questions as we design our logic and universe. But the embellishments are fun where they go beyond a theory. The primes are beyond these frameworks I imagine- all is poetry in a sense... I am looking more into the 16 dimension spaces now way beyond the octonions and well complex square roots and octaves- all part of the picture.

The PeSla

PeSla, no, you are not confusing me. It was this I thought was a bit odd;

which came from my mapping the primes in different regions of space in a quasic framework.I would want to ask of Volovich again. A different frame, but how different? Can he be used as reference?

http://arxiv.org/PS_cache/arxiv/pdf/0904/0904.4205v1.pdf

One can argue that at the very small (Planck) scale the geometry of the spacetime should be non-Archimedean [2, 3, 7]. There should be quantum fluctuations not only of metrics and geometry but even of the number field. Therefore, it was suggested [2] the following number field invariance principle:

Fundamental physical laws should be invariant under the change of the number field.

Ulla, if I can take may historical review a step further, the confusion already swirled around George Cantor, who expected great things of number theory for the life sciences, and was said to be mad. He came in after Weierstrass' Approximation Theorem founded statistical mechanics on route to the weird results in measure theory, like absolutely any set can be well-ordered due to fractal organization.

Then Levi-Cittiva showed that general relativity freezes in 3-D dynamics due to Bianchi Identity and has to be transposed into sympletic manifold. Here's now a dynamics and potential theory(!) of non-Archimedean points:

Matthew H Baker, Robert Rumley, 2005, Equidistribution of small points, rational dynamics, and potential theory. arXiv:math/0407426v2

GR treats any connected mass, even large organic molecule, as a component of the energy-momentum tensor, so gravity within the monad remains to be addressed, with self-repulsion in charged particles. Weyl found not gravity but electromagnetism to be measure of space-time, not in a sympletic treatment, which is why I'm interested to see Baker and Rumley extending Green's functions. But equidistribution is just basic stat. mech., nothing non-linear, still less fractal.

To Ulla:

Volovich is one of the pioneers of p-adic physics.

Unfortunately, most proponents of p-adic physics relate p-adic physics to exotics in Planck length scale. I see this as a fatal mistake explaining why this approach has not developed much and remained just a passive repetition of what has been done in real context.

I believe that just the opposite is true. p-Adic physics relates to long scales since p-adically infinitesimal is infinite in real sense! p-Adic physics constrains physics at long distances: this resolves the landscape problem of string theories due to the fact that almost unique short distance physics is not able to say anything interesting about long distance physics (the physics at LHC!). The complete failure of superstring inspired guesses about new physics at LHC concretely demonstrates this.

Another departure from the views of pure mathematicians. It is cognition which p-adic physics describes at the fundamental level. The successes of p-adic physics in real physics (consider only p-adic mass calculations) reflects the strong interaction between p-adic and real physics (or to say it in manner irritating maximally the materialist colleague: interaction between cognition and matter).

Number theoretical universality is a basic principle of TGD and states that the form of physics laws is form invariant under change of number field, about which Volovich talks about. This leads to many generalizations including the fusion of various number fields to a larger structure.

Most that I have been talking for one and half decade about physics as generalized number theory relates to a detailed realization of this principle.

The posting Quantum Arithmetics and relationship between real and p-adic physics discusses briefly one particular important step forward in this program. Amusingly, the crucial impulse came from Shnoll effect, a russian biologist!

From TGD point of view the work of Russian scientists has turned out to be much more interesting than the work of colleagues speaking native American English and advocated through every possible communication channel. Big fishes live in silent waters;-).

To Pesla:

assigning (p-adic) prime to space-region is what p-adic mass calculations indeed do. The question about how this correspondence emerges from the basic theory, is far from trivial and has been one of basic problems of TGD approach.

This space-time region could correspond to Euclidian space-time region representing line of generalized Feynman graph. The minimal (minimalism is realism in mathematics;-) assumption is that p-adic prime is assigned with 2-D partonic surface.

At the fundamental level p-adic space-time sheets are those characterized by p-adic prime. The question reduces how p-adic/cognitive space-time sheet/partonic 2-surface with a particular p is assigned to a particular real space-time sheet/partonic 2-surface.

One can argue is that p-adic space-time sheet and real space-time sheet must have many common points so that cognition and matter have a large number of common points (life in the intersection of real and p-adic worlds!). This does not however select any particular p since rationals are common to all number fields in question. Something more is needed. Where could this information about preferred prime come from?

The article discussed in the posting Quantum Arithmetics and the Relationship between Real and p-Adic Physics suggests an answer to this question.

* Particular quantum arithmetics is parametrized by quantum phase exp(i2*pi/p), p the p-adic prime! Rationals are replaced with quantum rationals and one can speak about common *quantum rational* points of the real and p-adic space-time surface.

*The generalization of the canonical identification

sum x_np^n--> sum x_np^(-n)

would map the quantum rational points of the p-adic partonic 2-surface to those of real partonic 2- surface for the preferred p-adic prime defining quantum rationality and vice versa.

Cognitive representation would be mapped to its real world counterpart. Thought bubble to what it represents - in some accuracy of course in the set that the mapping would hold true only for the set of common quantum rational points.

All my talk about life in the rational intersection of realities and p-adicities would be replaced by simple replacement "rational--> quantum rational";-)! In can congratulate myself that I have avoided the pressure of acting like guru demanding that his teachings should be carved in stone!;-) Simple find-and-replace in all .tex files is enough! ;-)

I would like feedback on this. Is this the right form? Does it makes things easier? And especially - is there anything wrong?

http://tgdlessons.blogspot.com/2011/10/tgd-lesson-1.html

Sorry for the delay. Happy Birtday!

This was no good? I was asked for the brick stones, the math. It must come later. This will be no easy thing for someone like me.

Matti,

Thank you for the in depth reply.

Our interest in arithmetic, the nature of numbers and the role of primes in particular seems to me to have deep connection between your framework, Kea's approach, and my ideas on space and structures.

So, without discussion outside the blogs I name this the Triality. I did not post as the idea yesterday was a little speculative even for me, but next day some powerful new ideas on space and information came out I think worthwhile or promising.

By quantum it seems you ask the philosophic and mathematical question- one that is really the seeming unreasonable fact that numbers as well as other mathematics seem to describe our reality. It is almost as if I can understand why the ancients thought so highly of integers as to suggest a separate reality of their own.

But numbers are a little vague- in a sense a class, a quantum uncertainty as well as concrete fact. What I am still further amazed by a simple arrangement in a plane- that in the primes and in higher spaces and generations, that we can find the same numerical patterns hidden in the primes and and composite numbers.

I see Kea's system as containing the first 31 primes in 2^7 space, and yours I get in reading involves the 2^9 space.

It is interesting that both systems involve 8n as in octonions, and beyond. Do we imagine this relating to consciousness? Perhaps if we can extend the interpretations that way which as vague structure sounds well grounded in intuition(ism)- but until we go beyond the quantum uncertainty as an overriding concept we can say little for sure of our ideas of (super-)symmetries. We could for example speculate as Leo, that the neutral or non-existent Higgs is a particle of creation beyond the scope of standard theory. Or we are talking about nothing indeed.

If God made the Integers and all else is the work of man- it is deep within us, our number theory and even our numerology answering things too soon- that we might think of an idea like Higgs as a God particle metaphorically at least. Or perhaps the higher coherence of being or the universe in relation to this surprising pattern in higher dimensions, generations, and symmetry.

ThePeSla

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