The Myth of Gravity

Interesting sequence, Ray. What do zeroth and minus zeroth powers of /phi/ mean?

Tom

Hi Tom,

Any number raised to the zeroth power (or equivalently minus zeroth power) is equal to one. So, phi^0=1 and (-phi)^(-0)=1, and the sum equals 2 - the "zeroth" term in the Lucas sequence. I wrote it that way to tie in with this pattern of weird fractal combinations that produce exact integers.

Have Fun!

Ray

Dear Tom,

Perhaps I am being too literal. The lattice vertices/ spheres appear to be discrete. However, the struts that connect these vertices should build smooth and continuous strings. Perhaps we are simply looking at different sides of the same problem, and Supersymmetry/ Scale Invariance/ Frame Independence/ Reciprocal Lattices bring us full-circle to the same problem.

Have Fun!

Golden ratio numbers have a musical interpretation, which leads to physics. The old diatonic scale for tuning notes is 1 9/8 81/64 4/3 3/2 27/16 243/128 2, which might correspond to the C-major scale CDEFGABC, where from C to high C the frequency of the sound doubles. The A note has the ratio 27/16 = 1.6875, and the golden ratio is φ = (1 sqrt{5})/2 = 1.618034 ... , is in many ways a preferable tuning ratio for A/C and the corresponding ABCDEFGA scale is the C-minor scale tuned according to partitions thereof. So the resolution of the two diatonic scales according to their respective pentatonic relationships involves the golden ratio. So a φ^2 will now take us to another scale entirely, which is the F-scale, and one can cycle through this. This has a bearing on physics, so bear with this.

Now we don't use old tuning system. The problem is that if you tune the instrument to the C-major scale this way and it sounds great. In fact if you have a compositional software package, say Sibelius, you can tune to a golden ratio system --- it sounds interesting. This is not a very convenient way to tune scales, and has a slight dissonant quality to it. So the above old version was used, which fits better in the western notion of musical tuning. A use of the golden ratio is more in line with Indian and Islamic music. The problem with the old diatonic tuning system is that if you change scales it sounds like donkey crap. So Johan Sebastian Bach wrote a book of compositions called "Das Wohltemperierte Klavier" (The Well Tempered Clavier (harpsichord)) and devised a tuning compromise with the ratios 1 9/8 5/4 4/3 3/2 5/3 15/8 2, where the ratio for the A is 1.666... , and this works pretty darn well, and one can tune all scales this way without problems.

The golden ratio is what determines the roots of the E_8 group. Further, for a string on an extremal black hole the ratio of masses of string is determined by the (8,1) portion of the E_8 irreducible representation with these roots. There are then 8 masses for the supergravity multiplet in this massive broken phase which corresponds to the tuning ratios from major and minor scales. This is an interesting example of how maybe Pythagoras might have had some sort of insight when he talked about the music of the spheres as being related to the exponential maps. Tymencho, as I recall the spelling, wrote a couple of articles on how musical dyads and triads in musical composition obey certain orbifold relationships, or the discrete subgroups of compactified manifolds in string theory.

Cheers LC

Hi Lawrence,

Your posts are very interestings.

The music is a beautiful road.

Bach was the best mathematic musician.

His partitions are difficults and are quicks.

A good allurement is necessary for playing Bach.

The sequences are relevants about the harmonization and superimposings.

I don't know the idea of pythagore about the music of spheres, it's interesting , what is this exponetial maps ?

Regards

Steve

Hi Ray,

Okay, I get it. Although minus zero could be problematic, because it suggests that zero has a successor (or predecessor, as it were) on the real line, which screws up our arithmetic, because it suggests that zero succeeds itself, in which case all numbers are zero.

Such examples that destroy natural well ordering of the integers led me some time ago to the complex analytical model. I reasoned that if there is a natural well order of quantum (i.e., integral)successors, it is necessarily hyperspatial; there isn't enough room on the 1 dimension line to transform quantities -- if we want a natural well order independent of axioms (Zorn's lemma/axiom of choice) 2 dimensions is minimal -- because we need a point outside that line -- and because we get 4 dimensions for 2 by complex analysis, as I explained in a previous post, hyperspace well ordering is minimal. (This is formally detailed in my ICCS 2006 paper.)

Hyperspatial order, then, results in 1, 2 and 3 dimensional symmetries, because these symmetries are embedded in n-dimensional (n >= 4) self organized spacetime which is symmetric about the real and complex axes and a subset of 0 1 dimension spacetime. Also, though, when one introduces an entropic form of gravity, every occurrence of order in d =< 4 is an increase in disorder in d > 4. So the evolution of novel forms in our familiar world is a measure, not a cause, of cosmic evolution. Supersymmetry is both sufficient and necessary to fix the boundaries of the measure within hyperspace length 1. I find a limit of 10 dimension non-lattice sphere packing identical to the 4 dimension horizon, implying that structures of 3 dimensions and less embedded in 4 dimension space are identical to those embedded in 10 dimension space.

Tom

The music of the spheres is a logical result of the Pythagorean obsession with rational numbers. That is, if the counting numbers are orderly, the interval should be orderly as well. Between musical beats on a scale, between points on a line, between planets in the heavens.

Because musical harmony is a sophisticated and artistic form of counting, only rational numbers conform to beat combinations.

A similar idea is being investigated today by Michael Berry in the UK, in connection with the Riemann Hypothesis (RH) and the distribution of prime integers. The RH is a conjecture in the complex plane, extending harmonic analysis (the sum of the harmonic series using real integer exponents) to prime integers with complex exponents, with the consequence that the real part of the summed result appears to always lie on the singular line 1/2. Because the RH appears to indicate a deeper and perhaps more exact order to distirbution of the primes than can be estimated by the prime number theorem, one wonders if a counting order (and thus, orderly intervals as well) can be derived from these "atoms" of the counting numbers (fundamental theorem of arithmetic).

Sir Michael is using advanced computer techniques to derive a "music of the primes."

Tom

Thanks dear Tom.

It seems very relevant all that.

My knowledge of the Riemann zeta function is young,it's here on FQXi I knew it .

I think that the secret is still in the sphere and the correct distribution of numbers with their pure harmonious series and superimposings.

at my knowledge

we have

sum (infinity and n=1)(-1)exp n-1/n²=pi²/12...and we substitute for obtain the series as fourier like f(x)=Sum (inf. n=0) a(n) cos nxconsidering f(x)= x² for example and x between - pi and pi .....the value of pi takes all its sense ...the distribution of primes inside a sphere shows us the harmonization .

But the real universal distribution is difficult to perceive like it's difficult to see the Planck scale.Like it's difficult to check the universal energy.In fact we are youngs at the universal scale , thus we understand our young knowledges.

I think strongly that the sphere helps in all centers of interest, like a gauge .The distribution inside a closed evolutive system permits to see more clear about the real series .A real puzzle all that .....the universal partition and its secrets ....

Regards

Steve

The Pythagorean tuning is the "old" diatonic scale system, which tunes one scale well, but not others. One can play with tuning a bit and use the golden ratio, but it is not convenient. Pythogora's sytem is a close approximation to this, as is the Bach "Well Tempered Clavier" compromise. There are other cultures which tune in different ratios for notes. For the diatonic scale it is interesting that the C to A ratio is close to the golden ratio, to within about 4%.

Of course rhythm has to be integral or rational.

Cheers LC

Dear Friends,

My E-Infinity Friend, Dr. Scott Olsen of the College of Central Florida in nearby (for me anyway) Ocala, Florida has a short book on "The Golden Section - Nature's Greatest Secret". He covers these and other applications of the Golden Ratio. The best piece of information that I got out of his book was the Lucas number sequence. I think this is the critical link for two reasons:

1) There is a relationship between powers of phi and exact integers, and

2) Exact expressions relating powers of phi and its inverse automatically admit Scales and Scale Invariance.

Have Fun!

May 5th 2010

My remark to this FQXi-article on Verlindes Paper on Gravitation as a kind of enntropy:

I published the idea that gravitation is not a 4. fundamental force but a kind of "existential" entropy (or Planck-entropy) and at the same time counterpart to (physical) information (some sort of it) in february 2009 in "Concept and Method of Physimatics" on blog.physimatics.org.

Moreover I made it a little more detailed and I described gravitation as a kind an algebraical misfit in a process of combinatorial shifts in a big group, called the Universal Group "UG" that is roughly representing space and matter in our universe - without events or without irreversibility. Furthermore I put this in context with a hypothetical existence process of our universe itself.

So I put this approach in a bigger context of a weak structured "substrate" (below Planck scales) thats description is completely based on algebra. Due to the local action ("force") caused by gravitation has local effects, we need a local abegraic mapping as well, attached as a sort of a virtual individual environment to elementary particle. The story is much longer ... and you can make yourself a picture.

Already arround November 2008 I sent the paper "Concept and Method of Physimatics" to arxiv.org where it was first announced for publishing under arXiv:0811.3688 than later rejected as "unapropriate" by Don Beyer together with the hint to send it to a conventional journal.

I sent Brendan Foster on monday this weak an exemplar of my latest version with the title "Concept & Method of Physimatics, the Logic of Existence and

the Logical Time Formula" that is listed an http://vixra.org/abs/1005.0009 in PDF form.

with kind regards from Germany

Robert Gallinat

Berlin/Germany

Robert, I am not entirely sure I follow your idea. You seem to have some idea of an algebraic system, and even nonassociative structures. These are called octoniona, but as yet a clear physical idea which motivates them has not been advanced.

Cheers LC

The last sentence of the article asks "Is that crazy enough?". I believe the answer to that should be a loud resounding "Yes". It almost seems that modern physics has collapsed into a game of theoretical one-upmanship, seeing who can pass off their mathematical suppositions of gravity as science, while for centuries a plausible explanation has languished, prematurely dismissed,and even given the "kiss of death" by a prominent physicist possessing the tools to remove the thermodynamic preclusion to it's validity. So, yes, that's crazy enough. It's time to get real.

The holographic principle shows that relation gravity/electromagnetism is a result of a product of the geometrical relations Planck length/Compton length.

(lp / l x ) * (lp / l y ) = -a Fg / Fe

where lp = Planck length, lx, ly = Compton length, a=alfa (fine structure const.)

It suggests that each oscillation of the charge along its Compton length causes a Planck's length contraction (curvature of the space and Planck's time dilation when the non-local information interfere with another non-local information of the another particle.

The holographic interference of the non-local information create the quantum vacuum with its virtual particle-antiparticle pairs.

Verlinde's example shows it.

His idea sounds very much like a leSage ether theory.

Gravity can only ultimately enjoin electromagnetism and quantum mechanics when space is dynamic and yet highly ordered. Randomness, order, potentiality, actuality, visible, and invisible all are included.

"Quantum gravity" and electromagnetism/light require that the structure and form of sensory experience in general MORE CLOSELY resembles thought.

Gravity ultimately pertains to distance in space as a function of balanced attraction and repulsion.

Everyone seems to forget that, in terms of general relativity, gravity is not a fundamental force either. Technically it's a "fictitious" force (to use Tom Moore's terminology). That's part of the reason that there's a disconnect between quantum mechanics and GR.

From what I understand of the article, the new definition of gravity is NOT as a fundamental force in itself but rather as a side-effect of other fundamental forces. Gravity as a force still exists in this model, but it's not a fundamental quantum energy-exchange force like strong, weak, and electromagnetic.

I have a similarly-related theory I'm trying to put on paper that I believe is in sync with this new idea of gravity. I believe my theory may explain the dark matter and dark energy problems as an underestimation of empty space's quantum mass. The most appropriate name I can think of for this is "Spindle Theory". I'll be posting articles soon..

poxix.com

Jacob Munoz