Download all in a zip file (21,773,048 bytes) and check out readme.html or readme.pdf (9 pages) inside, pp. 103-161 in gravity.pdf (15.02.2018, 19:43 GMT), FRAUD.pdf (30.12.2017, 19:32 GMT), and my forthcoming video lecture on 21 September 2018 'About Space and Time': God (Luke 17:21) does exist, both as purely mathematical object (pp. 21-26 in Hyperimaginary Numbers) and as The Holy Trinity, in line with the doctrine of trialism (Slide 14 in Quantum Spacetime).

Please be aware that I am interested only and exclusively only in hyperimaginary numbers (p. 20 in Hyperimaginary Numbers), which may offer unique solutions to various problems in point-set topology, set theory, and number theory. Therefore, I cannot address any issue, which is not directly related to hyperimaginary numbers, and will have to ignore it due to the lack of time.

D. Chakalov

Easter 2018, 21:40 GMT

About Space and Time

D. Chakalov


Commemorating 110 years of Hermann Minkowski's lecture RAUM UND ZEIT, given at the 80th Meeting of the Natural Scientists in Cologne on 21 September 1908 and based on the crucial contributions to the theory of Special Relativity by Hendrik Lorentz, Albert Einstein and Henri Poincaré, I am happy to announce my video lecture, entitled: About Space and Time. It will be posted at my YouTube channel on Friday, 21 September 2018, at 10 GMT. Here is a brief introduction (draft version), which will be amended with the final text version of the lecture by the end of September 2018.

about_spacetime.pdf, 16 pages

Easter 2018, 21:40:02 GMT

Also viXra:1802.0397vA, 16 pages, 2018-04-06

Gravity-Matter Duality

D. Chakalov


Gravity-matter duality is suggested as the first step toward quantum gravity, ensuing from the idea that the phenomenon dubbed ‘gravitational field’ is a new form of reality, known as Res potentia — “just in the middle between possibility and reality” (Heisenberg, Slide 7). The essential similarities and differences between gravity-matter duality and wave-particle duality are briefly examined, with emphasis on the proposed joint solution to exact localization of gravity and “quantum waves” at spacetime points. The latter are endowed with brand new structure and topology due to the fundamental flow of events suggested by Heraclitus — Panta rei conditio sine qua non est.

gm_duality.pdf, 9 pages

November 1, 2017, 17:40:13 GMT

Also viXra:1707.0400vE, 2017-11-01

My objections to EU-funded Einstein Telescope and LISA can be downloaded from this http URL.

According to the proponents of GW astronomy, the wave pattern (shown above) of binary black hole (BBH) merger dubbed GW150914 1:1 matches the wave pattern of very strong GWs at the immediate vicinity of the same BBH merger over one billion years ago, because the latter was absolutely not altered due to non-linear interactions of very strong GWs with matter and fields in the cosmos for over one billion years, before being detected by LIGO on 14 September 2015.

No. We do not accept "ghosts" that would "act" without being acted upon for over one billion years, even if they are backed by Nobel Prize:

The 2017 Nobel Prize for physics was awarded to a FRAUD.

D. Chakalov


After a brief recall of the widely known, and still unsolved problems of the coupling of gravity to matter and the non-linear transport of mass-energy (equivalent to "200 solar masses per second") by gravitational waves (GWs), it is concluded (p. 19) that the alleged "detection" of GWs and black holes on 14 September 2015, dubbed GW150914, is impossible, and therefore is FRAUD. I also provide various conditions under which the conclusion can be proven false and refuted. For example, regarding the origin of GW energy, if the so-called "mixed procedure" (Jose Pereira) can be derived from non-linear GW effects (MTW p. 968) due to arbitrary GW amplitude (Michele Maggiore) inducing stresses in matter (Robert Wald), say, in a plastic bottle (p. 21) at distance 1 AU from GW150914, the conclusion by Hermann Weyl on the linearized approximation of GR (p. 19) will be refuted. Then all projects in GW astronomy, including Laser Interferometer Space Antenna (LISA), will be duly vindicated, and I'll eat my hat.

FRAUD.pdf, 25 pages

December 30, 2017, 19:32:15 GMT

viXra:1712.0017vA, 2017-12-30 12:45:17 GMT

Panta Rei: The Evolution Equation

D. Chakalov


It seems possible to suggest the evolution equation in cosmology, which permits unlimited creatio ex nihilo from the quantum vacuum, without leading to catastrophic events. The physicalized presentation of the Universe is interpreted as 'Brain of the Universe', which gives access to 'God's thoughts' (Albert Einstein) with spacetime engineering performed by the human brain embedded in the Brain of the Universe.

CEN.pdf, 22 pages

June 25, 2017, 10:44:09 GMT

Also viXra:1703.0222vL, 22 pages, 2017-06-25

Penrose-Norris Diagram

D. Chakalov


Brief outline of Penrose diagram and related topics.

Penrose_diagram.pdf, 7 pages

June 21, 2017, 13:52:00 GMT

Also viXra:1705.0219v8, 7 pages, 2017-06-21.

The new theory of gravity seeks to reproduce all effects of gravity (p. 3 in holon.pdf) by tweaking the Platonic matrix of rods and clocks: "spacetime has its own rods and clocks built into itself" (MTW p. 396).

Gravitational Holomovement and Rotation

D. Chakalov


We model the physicalized manifestation of the Universe as bootstrapped ‘Brain of the Universe’ and seek evidence for its brain-like functional organization, resulting from the Holon of the Universe facilitated by space-like correlated gravitational holomovement and rotation. The orthodox model of gravity, based on “tangent vectors” and “curvature of spacetime”, is replaced with the proposal that the physicalized clocks and rulers are very flexible ‘jackets’ (cf. John’s jackets parable in CEN.pdf), which can slow down or speed up viz. shrink or expand, leading to perfectly correlated Brain of the Universe living in so-called ‘relative scale’ (RS) spacetime. The question of Universal Mind, complementing the Brain of the Universe, pertains to physical theology and the doctrine of trialism, and was examined in previous publications (Sec. 6 in spacetime.pdf).

holon.pdf, 6 pages

June 25, 2017, 11:20:21 GMT

Old version: viXra:1705.0147v3, 6 pages, 2017-05-12


Ensuing from first principles, the theory of spacetime and its metaphysical axioms are introduced as prerequisites to physical theology and the so-called relative scale spacetime.

Comment: Dedicated to our Lord and Savior Jesus Christ.

December 24, 2016, 1,586,148 bytes, 36 pages, 13:13:13 GMT.

Also viXra 1601.0209[vF], 36 pages, 2016-12-24 13:32:11 GMT.

Notice the new hyperimaginary numbers (see ref. [3] on p. 28). I am interested only and exclusively only in these new numbers, which are expected to provide solutions to various problems in point-set topology, set theory, and number theory. The alleged local differential geometry is false. We need totally new global boundary conditions to define a closed and conserved Universe in the past, which is coupled (Sic!) to an evolving Universe in the future (Fig. 7 on p. 8). The non-linear coupling between the past and the future states of the Universe, corresponding to the phenomenon of transience (Heraclitus), requires hyperimaginary numbers, and also opens the road to spacetime engineering (p. 34) and to the origin of gravity and inertia.

Details in pp. 59-64, p. 67, p. 77, pp. 80-83, p. 85, and pp. 103-161 in

(3,016,431 bytes, 15 February 2018, 19:43:54 GMT)

Check out also gravity_rotation.pdf (3 pages, August 3, 2016).

What are the basic building blocks of the universe? What are the forces by which they interact with one another? Why is the universe larger than a football ?

Dedicated to 138th birthday of Albert Einstein, 14 March 2017

The slides of my talk 'Quantum Spacetime' can be downloaded from this http URL. Regarding Slides 10 and 15, check out Ivo van Vulpen at this http URL: "Why is the universe larger than a football ?"

D. Chakalov, March 14, 2017, 00:51:23 GMT


The idea of hyperimaginary numbers is suggested as the first step toward the mathematical basis of res potentia (Plato), presented in the right-hand side of the evolution equation |w|2 = |m|2 + |mi|2. The real and imaginary (tachyonic) components in the right-hand side are always balanced, leading to |w|2 = 0 — the physicalized world is made of positive mass-energy only, |m|2, which is always balanced (not "conserved") by equal amount of |mi|2, once-at-a-time, ever since The Beginning (John 1:1). God is interpreted as mathematical (hyperimaginary) object residing “inside” the 4D instant here-and-now (Luke 17:21), and conceptual solutions to fundamental problems in point-set topology, set theory, and number theory are briefly described.

hi_numbers.pdf, 26 pages, 7 February 2018, 16:00:45 GMT

viXra:1611.0084vH, 26 pages, 2018-02-07, 16:15:04 GMT

The full manuscript will be available only on Christmas 2016, upon request. I will elaborate on the main, and certainly not original, statement made on p. 3 in 'Hyperimaginary Numbers' that the physical world (res extensa) offers only the necessary condition for its existence, while the Platonic matrix of res potentia is the sufficient condition: "It's a bundle18." All this is encapsulated in the so-called Arrow of Space (AoS), because what we call 'time' is not just 'change in space', but 'change of space' as well: it's a bundle. Hence I model the entire physical world as the 'Brain of the Universe', and suggest AoS based on Fig. 3 in 'Hyperimaginary Numbers', along with specific applications of the equation |w|2 = |m|2 + |mi|2 for Mathematics, quantum gravity and cosmology, and spacetime engineering.

D. Chakalov

November 12, 2016


The hypothesis of gravitational wave, suggested by Albert Einstein in 1916, still poses outstanding challenges, which have to be resolved by the theoretical physics community as soon as possible.

September 10, 2016, gw_miracles.pdf, 6 pages.

Also viXra:1607.0377v6, 2016-08-31, 4 pages.


I argue that vacuum spacetime with Tab = 0 is highly exaggerated approximation, like the famous 'spherical cow'. If you are a cowboy and wish only to count the number of cows in your herd, you may of course think of them as 'spherical objects'. But imagine the following situation: as you walk in your grassland, you notice that the grass on a loan has been hardly pressed to the ground, as if some heavy object has passed through your grassland. Would you say that some brand new spherical cows have rolled over the grass? That will be just like GW150914, the alleged discovery of gravitational waves and black holes in vacuum spacetime.

GW150914 is a FRAUD supported by at least 1522 fraudsters: "As this event turned out to be a binary black hole merger, there is little expectation of a detectable electromagnetic signature. (...) In classical general relativity, a vacuum BBH merger does not produce any EM or particle emission whatsoever." (LIGO & VIGRO, arXiv:1602.08492v2 [astro-ph.HE], p. 1 and p. 9)

Vacuum spacetime with Tab = 0 is highly exaggerated approximation, like a 'spherical cow'. If 1522people claim to have detected the pattern of perfect spherical cows rolling downhill like a football, don't buy it.

It is like pink unicorns dancing with red herrings. Proof: a "vacuum" with Tab = 0 cannot contain any gravitational energy, so the gravitational field cannot "do work on matter and vice versa". Yet Kip Thorne claims that GW150914was "by far the most powerful explosion humans have ever detected except for the big bang", only it did not produce "any EM or particle emission whatsoever." What a stinky nonsense.

If you disagree, you'll have to explain the "connection between compact binary mergers and short Gamma-Ray Bursts" (Valerie Connaughton et al., arXiv:1602.03920v3 [astro-ph.HE]) and associate GW150914 with the "transient signal at photon energies > 50 keV (Sic! - D.C.) that lasted 1s and appeared 0.4 s after the GW signal" (Avi Loeb, arXiv:1602.04735v2 [astro-ph.HE]), which INTEGRAL did not detect (Vova Savchenko et al., arXiv:1602.04180v2 [astro-ph.HE]). All this in vacuum spacetime, Tab = 0, which means that "the most powerful explosion humans have ever detected except for the big bang" (Kip Thorne) could be produced and manifested only and exclusively only by Weyl curvature that "governs the propagation of gravitational radiation through regions of space devoid of matter", without "any EM or particle emission whatsoever." What a pathetic nonsense.

GW150914 is a FRAUD. Don't ever say that you knew nothing about it.


As an epitaph of the project for so-called GW astronomy, I suggest the famous saying by Confucius: “The hardest thing of all is to find a black cat in a dark room, especially if there is no cat”. Specific examples are drawn from GW150914 and LISA Pathfinder, to explain why GW astronomy was born dead from the outset. Since the issue of energy transport by gravity is crucial to General Relativity, in the second part of the paper I offer a hypothesis about the origin of gravitational radiation in Relative Scale (RS) spacetime, and outline hypothetical applications of spacetime engineering for producing ecologically clean and unlimited energy by polarization of the so-called light vacuum.

Comment: Due to the sensitive nature of clean unlimited energy sources from spin-0 gravitational radiation, the full paper is available only upon request (Matthew 7:6).

May 18, 2016, 850,549 bytes, 11 pages + more.


Ensuing from first principles, a new theory of spacetime has been suggested, called ‘relative scale spacetime’. It denounces the absolute size of objects at different length scales, thanks to which the phenomena known as quantum state (“just in the middle between possibility and reality”, Heisenberg) and Einstein’s “total field of as yet unknown structure” are unified as potential reality of quantum-gravitational origin (dubbed causal field), endowed with relative-scale metric. At macroscopic scale, it produces what is known as gravitation, without any dark matter nor dark energy.

Comment: Dedicated to the centenary of Einstein's General Relativity.

Read the final version (8 November 2015, 44 pages, 2,199,898 bytes) in rs_spacetime.pdf.

Notice the interpretation of John 1:1 & Luke 17:21 in physical theology, Case IV in Table 1 on p. 8 in rs_spacetime.pdf. St. Thomas Aquinas raised the question in 13th century (Summa Theologiae, Part I, Question 85, Article 8): "Punctum non ponitur in definitione lineae communiter sumptae." (‘A point is not included in the definition of a line as commonly assumed’). It's all about Mathematics.

Check out also pp. 17-38 in note.pdf and pp. 24-28 in horizon.pdf. I had the impression that have understood the so-called fictitious force in General Relativity only once, in June 1972 at age 20. It was a beautiful feeling, which lasted until the end of 1973 and never came back. How can we understand something that acts like a force and is related to the entire spacetime, but is not a force? Perhaps "inertial effects arise from the gravitational field of a moving universe" (Dennis Sciama, 19 August 1952), provided that its "motion" (the flow of time) and "rotation" are defined with respect to the Universe as ONE.

Download the red herrings known as "event horizon" and "gravitational-wave astronomy" (horizon.pdf, 29 pages and note.pdf, 38 pages), my message to the Human Brain Project (HBP.pdf, 10 pages), the abstract of the first paper introducing the so-called biocausality (January 1990), the final version of Relative Scale Spacetime from viXra:1410.0194 (2015-11- 08 18:34:20, 44 pages) and my comments on it (comments.pdf, 77 pages and censorship.pdf, 27 pages), and the PDF copy of the old (now archived) website plus additional papers,Indefinable.pdf (414 pages, 12,959,446 bytes, 30 December 2017, 20:00 GMT).

Forty-six years ago (January 1972), I started this project with the hope to understand the physics of the human brain and learn to harness its tremendous latent abilities (see ref. [63] inrs_spacetime.pdf). The reason for seeking new physics was explained on 16 July 1997, 16 July 1998, and 20 December 1998, but nobody showed any interest. I created this website on 21 October 2013, to present my project 'Maximal Set Theory' (see Table 1 on p. 14 in spacetime.pdf), but it did not attract any attention and I decided to archive it on pp. 253-351 inIndefinable.pdf. As Upton Sinclair explained, “It is difficult to get a man to understand something, when his salary depends on his not understanding it.”

More in my forthcoming book The Brain of The Universe.

Dimi Chakalov <>

(last name pronounced tcha-KA-lov)

October 21, 2013

Latest update: March 23, 2018, 23:52 GMT

There is no matter as such! All matter originates and exists only by virtue of a force which brings the particles of an atom to vibration and holds this most minute solar system of the atom together. We must assume behind this force the existence of a conscious and intelligent Geist (bewußten intelligenten Geist). This Geist is the matrix of all matter.

Geheimrat Max Planck

Google messed up with my website without my permission ― I never authorized Goggle to replace it with their horrible "new look". I tried very hard to fix their idiotic "improvements", but to no avail, and my website still looks ugly. I wish I could pay Google for their email service and for hosting my website, if only they STOP spying on me and ruining my website.

You can read the original version of this webpage in .pdf format, frontpage.pdf, which is included in below. Unlike Google, I do not spy on you ― never did and never will ― and there is no way to find out whether you have downloaded anything from my website.

D. Chakalov

Easter 2018