From finite to infinity 2/2

From renormalization to fractals



« Quantum field theo­ry, to date, [eli­mi­nates] through a pro­cess of renor­ma­li­za­tion, (…) an ener­gy den­si­ty that would be for­mal­ly infi­nite if it were not exclu­ded from cal­cu­la­tions through renor­ma­li­za­tion. » [1]


At the cos­mo­lo­gi­cal level as well as at the quan­tum level, the equa­tions pre­dict infi­ni­ty. Yet our stan­dard theo­ries of phy­sics do not reflect these pre­dic­tions. Either they ignore infi­ni­ty if it comes from the sin­gu­la­ri­ties of the cos­mo­lo­gi­cal level. Or, at the quan­tum level, they try to eli­mi­nate it by renor­ma­li­za­tion, i.e. to make it finite, acces­sible, mea­su­rable. This is what I pro­pose to dis­co­ver in this article.


Zero point

Zero-point ener­gy, or quan­tum vacuum ener­gy, is the ener­gy that remains when all other forms of ener­gy have been remo­ved. The cal­cu­la­tion shows that this ener­gy – the lowest of the quan­tum field – is infi­nite. Therefore, it can­not be dif­fe­ren­tia­ted from higher ener­gy. Unless renor­ma­li­zed to zero at the lowest level, allo­wing for the obser­va­tion and mea­su­re­ment of ener­gy varia­tions with res­pect to this floor.

This renor­ma­li­za­tion is not incom­pa­tible with an esti­ma­tion of the value of the vacuum ener­gy. To make this esti­mate, phy­si­cists use Planck dis­tance : 1.616 x 10-33 cm. Far from being the smal­lest thing that exists in the uni­verse, this value is the fun­da­men­tal boun­da­ry condi­tion that defines our rela­tion­ship to it. Planck dis­tance is used to cal­cu­late the den­si­ty of 1 cm3 of vacuum, which is equi­va­lent to 1093 g/cm3 (article Unity from ether to space). Thus infi­ni­ty is arti­fi­cial­ly made finite.


Zero pointing

If it belongs to the field of phy­sics, renor­ma­li­za­tion, in prin­ciple, finds a cer­tain echo in the medi­cal field and in the way fields of conscious­ness are consi­de­red. In this way, conscious­ness is renor­ma­li­zed in order to enter into boxes that cor­res­pond to cer­tain men­tal pro­cesses, beyond which it has almost no more rea­li­ty.

This is not the way of thin­king of Nassim Haramein. Neither in terms of phy­sics, nor in terms of conscious­ness. For him :


« For more than 100 years – ever since we dis­co­ve­red that there is an infi­nite amount of ener­gy at eve­ry point – ins­tead of saying « we found the source of crea­tion », we’ve been loo­king for a way to stop the infi­nite.… Planck dis­tance became the end of the equa­tion. » [2]


One could say that infi­ni­ty does not scare him, and consi­der his approach much more objec­tive. In fact, it is just much more conscious. But how does he take infi­ni­ty into account in his uni­fied field theo­ry ? To find out, we have to be inter­es­ted in fractals !





Fractal and aneurysm

On a human scale, an aneu­rysm, for example, makes it pos­sible to observe what frac­tal dyna­mics are. It contains a tur­bu­lent blood flow which, while at first glance it gives an impres­sion of disor­der and com­plexi­ty, is on the contra­ry very struc­tu­red when you look at it more clo­se­ly. The « vor­tices » that make it up fol­low a frac­tal pro­cess. The divi­sion of large eddies into smal­ler ones allows ener­gy trans­fer from large to small scales, such as ener­gy cascades.

As an inter­de­pendent part of the human body, the aneu­rysm is also in a frac­tal rela­tion­ship with it. More gene­ral­ly, at the bio­lo­gi­cal level, there is an inter­de­pen­dence bet­ween the parts and the todd­lers, the todd­lers them­selves always being parts of a lar­ger whole. Thus, in order to exist, the human body depends on organs, which depend on cells, which depend on DNA and so on. Each higher level takes over the cha­rac­te­ris­tics of the pre­vious one while adding addi­tio­nal functions.


The strong link

This is cal­led holar­chy, after Arthur Koestler’s term [3]. A holar­chy contains ele­ments – holons (here DNA, cells, organs…) – that func­tion both as a self-regulating whole and as part of a lar­ger whole (the human body). The holons are connec­ted to the whole, which depends on them. Thus, a holar­chy implies a hie­rar­chi­cal rela­tion­ship in which each level func­tions auto­no­mous­ly, and where the smal­lest level is the most impor­tant because it condi­tions all the higher levels. All levels are invol­ved in a dyna­mic of infor­ma­tion feed­back, thus influen­cing each other.

This point of view is close to that of Nassim Haramein, for whom loo­king at infi­ni­ty and finite sys­tems as oppo­sites leads our phy­sics into an impasse. It would be bet­ter, in his opi­nion, to consi­der them as com­ple­men­ta­ry, and to do so, use fractals.


An order behind the mess

fractales-autosimilariteThe term « frac­tal », deri­ved from the epo­ny­mous adjec­tive, was coi­ned by the French-American mathe­ma­ti­cian Benoît Mandelbrot in 1974. This term comes from the Latin frac­tus, which means « bro­ken, irre­gu­lar ». Irregularity or frag­men­ta­tion cha­rac­te­rizes frac­tal shapes and pre­vents their des­crip­tion in tra­di­tio­nal geo­me­tric terms.

It may seem para­doxi­cal that a mathe­ma­ti­cian would be inter­es­ted in such forms, which seem by their com­plexi­ty and irre­gu­la­ri­ty to be the very oppo­site of mathe­ma­tics. The fact is that Benoît Mandelbrot did not see an irre­gu­lar shape when he loo­ked at a frac­tal, but a struc­ture, a pat­tern that was repea­ted ad infi­ni­tum through an ite­ra­tive pro­cess. This cha­rac­te­ris­tic is cal­led self-similarity and can be sta­ted as fol­lows : an enlar­ge­ment of a part of the frac­tal struc­ture inva­ria­bly causes the whole struc­ture to reap­pear. A frac­tal is construc­ted by homo­the­ty, i.e. its struc­ture repro­duces itself iden­ti­cal­ly at all scales, and this to infi­ni­ty. In other words, a frac­tal tends towards infi­ni­ty, and yet each of its levels gene­rates a limit, hence the notion of com­ple­men­ta­ri­ty bet­ween finite and infinite.

For Benoît Mandelbrot, many forms present in nature can be des­cri­bed by frac­tals. From then on, mathe­ma­tics no lon­ger applies only to smooth shapes (circles, tri­angles, squares…), but includes rough­ness. This is how mathe­ma­ti­cal laws can be applied to objects or phe­no­me­na that seem to escape them. And there are quite a few of them ! These include : struc­ture of lungs, rocks, light­ning, dis­tri­bu­tion of tree branch struc­tures, dis­tri­bu­tion of galaxies… There is the­re­fore an order behind the appa­rent disorder.


Fractals and golden section


Nassim Haramein talks about high­ly orga­ni­zed sys­tems that gene­rate frac­tal struc­tures eve­ryw­here in nature. Even though each of these struc­tures seems par­ti­cu­lar, they « actual­ly obey [all] the same Phi [gol­den ratio]: 1.618 ». Always 1.618 times smal­ler or lar­ger » [4]. Following this logic, we will never find the « par­ticle of God » that quan­tum phy­sics is loo­king for because there will always be a smal­ler par­ticle. And eli­mi­na­ting infi­ni­ty won’t change that.


A fundamental model of division

It would be bet­ter to look for a fun­da­men­tal model of the divi­sion of space. Fractals offer this pos­si­bi­li­ty because, as he explains, « by means of infi­nite divi­sions we can gene­rate a « sin­gu­la­ri­ty », a connec­tion with eve­ry­thing else » [5]. This fun­da­men­tal model actual­ly gives us the key to unders­tan­ding the crea­tive pro­cess. Therefore, it doesn’t mat­ter on what scale we look at things because :


« Each point contains eve­ry­thing, each point contains all the infor­ma­tion. Each point is connec­ted to the rest of the points in the uni­verse. » [6]


Thus, each frac­tal boun­da­ry is pro­du­ced by divi­ding space and gene­rates a spe­ci­fic struc­ture, spe­ci­fic coor­di­nates in space-time. Each of these limits can the­re­fore be defi­ned as a very spe­ci­fic set of infor­ma­tion. As this pro­cess is ite­ra­tive from one level to ano­ther, it means that an infi­nite amount of infor­ma­tion can be inte­gra­ted at each level into a finite structure.

Want to know some­thing even more inter­es­ting ? Fractals are the pat­terns that emerge when we stu­dy the beha­viour of chao­tic sys­tems, such as an aneu­rysm. To learn more, you can read the articles about the but­ter­fly effect.



Key points


  • Quantum theo­ry eli­mi­nates by renor­ma­li­za­tion the infi­nite value of vacuum ener­gy pre­dic­ted by the equations.

  • The uni­fied field theo­ry rein­tro­duces infi­ni­ty through frac­tals. Thus, finite and infi­nite are not oppo­sed but complementary.

  • Fractals pro­vide a fun­da­men­tal model of the divi­sion of space rather than a fun­da­men­tal particle.




Notes and references

[1] MISNER Charles W., THORNE Kip S., WHEELER John Archibald, Gravitation, London : W.H. Freeman, « Physics Series », 1973, quo­ted by HARAMEIN Nassim, L’univers déco­dé ou la théo­rie de l’u­ni­fi­ca­tion, Québec : Editions Louise Courteau, 2012, p.24, free trans­la­tion
[2] HARAMEIN Nassim. (April 23, 2016). [Video]. L’Univers connec­té : la solu­tion de masse holo­gra­phique et la source de la conscience, free trans­la­tion
[3] The term « holar­chy » was coi­ned by Arthur Koestler in his 1967 book The Ghost in the Machine (Hutchinson ed.). The title of the book refers to an expres­sion of the English phi­lo­so­pher Gilbert Ryle, for whom the mind is no dif­ferent from the acti­vi­ty of the body.
[4] HARAMEIN Nassim. (2003). [Vidéo]. Nassim Haramein at Rogue Valley Metaphysical Library (1)
See also the sca­ling law he wrote.
[5] Ibid.
[6] Ibid.

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