Download page for "Beyond Einstein: non-local physics" 2015, 2019 by Brian Fraser
(Last modified 10-14-2019)

Click this link to download BeyondEinstein_2nd_edition.pdf     (June 28, 2019, TX 8-760-669)  (recommended)

The paper can also be downloaded from:      

1st edition
Click this link to download BeyondEinstein.pdf   (2015; Registration: TX 8-223-345)

The paper can also be downloaded from:    

The document format supports printing of two pages per sheet, and binding on the left long edge.

Intended audience:
1. People who enjoy science, especially physics.
2. People who teach physics, especially at the highschool and college level.
3. People who want our society to progress, and who want to eliminate blindspots and misconceptions.

Errata (2nd ed.):
 A clarification is needed regarding the dimensions of the expansion of a balloon surface. The "dimension" of the spatial surface expansion  is given as s2/t. Note that this is NOT two dimensions of motion.  A "motional dimension", as I often call it, is (s/t)1 or (t/s)1. "Two motional dimensions" would be (s/t)2 or (t/s)2 . I have not found clear, unambiguous, non-confusing terminology here. Example: mass is (t3/s3). That  is, mass is ONE three-dimensional motion, not three (dimensionally separate) one-dimensional motions (t/s)3    Again, this usage is different from what you learned in highschool (page 7).  Be careful, and anticipate some confusion with this terminology (until the dust settles).   Likewise, do not confuse "dimension" with "intensity" or "amount".

Not mentioned in the article (2nd ed.):
This is a comprehensive and important document. Be sure to read it, especially the parts about the effects on gravitation of high voltage DC monopolar pulsed power with asymmetric wave shapes. See also    

"Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this ether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it."

 Physicists say space has properties of magnetic permeability, electric permitivity, and a free space impedance of 377 ohms.  Mathematians  say it is "metrizable"  (supports the common concept of distance; not all "spaces" do this.). Astronomers say it "progresses" or "expands" and has three dimensions. With space having so many properties useful to physics, we may as well say it is a manifestation of an aether,

Does time also have specific properties?  It probably does, but this possibility has not been investigated "physically".  All that is commonly known  is that time progresses and is scalar in the equations of space.

Errata (1st ed.):
 page 2: In the phrase "the Universe really does have non-casual, non-local behaviors",  the words "non-casual" should be deleted. The word "casual" was an unintented mis-spelling of "causal"; Even so, the non-local events described are clearly caused by the experimental conditions imposed by the experimenter.

pages 8 and 22: the words "gravity waves" should be changed to "gravitational waves"

Not mentioned in the article`(1st ed.):

“the source of a substantial fraction of the FUV background radiation remains a mystery. The radiation is remarkably uniform at both far northern and far southern Galactic latitudes…” See “The Mystery of the Cosmic Diffuse Ultraviolet Background Radiation”, Richard Conn Henry, Jayant Murthy, James Overduin, Joshua Tyler (2014)

“What we know as the universe could actually be just one of a pair that exists in the same space but at different times.” (Science News, July 25, 2015, p. 17 “Times Arrow”.)

light speed?
Quasars, certain galaxies, and gamma ray bursters have redshifts above z = 1. Example: the quasar ULAS J1120+0641, is at z = 7.1  The "non-local" interpretation is that this kind of  redshift represents  motion at 7 times the speed of light. The "local"  interpretation is that these redshifts are Hubble shifts (indicative of distance) and should be "corrected" to less than light speed.    (Refs: ;  see note 3  )  

I made some brief comments about the Aether on page 12 ("The static Aether was not detectable").  Most textbooks will state that the fringe shift of the Michelson-Morley experiment was absolutely zero (within experimental error). I believed that the non-directional motion described in my article would affect the perpendicular beams equally, and result in no fringe shift.  But apparently there actually was a small fringe shift. Yet this piece of experimental data got buried by institutional politics because of prevailing views about Relativity. This subject will have to be revisited.

In the meantime enjoy The Aether by Jeremy Fiennes  
"Relativity in the Global Positioning System", Neil Ashby (2003)      

"Although the theories cannot answer what happens at c, the scientists suspect that an object crossing the "light barrier" may have some very interesting consequences. They compare our current understanding of this boundary to that of an object crossing the sound barrier for the first time, an event that was highly disputed before it was achieved in 1947.

"People wondered what would happen," Hill said. "Were we all going to disintegrate? Would the plane fall apart? It turns out passing through the speed of sound led to a big bang. I suspect going through the speed of light will be more interesting. I have a feeling the world will change in some dramatic way as we move through the speed of . All sorts of things could happen. Time and space could interchange."

"Quantum teleportation relies on the strange nature of quantum physics, which finds that the fundamental building blocks of the universe can essentially exist in two or more places at once."  

'How Einstein Revealed the Universe's Strange "Nonlocality" ',  George Musser  (November 1, 2015)   

"The world we experience possesses all the qualities of locality. We have a strong sense of place and of the relations among places. . . . And yet multiple branches of physics now suggest that, at a deeper level, there may be no such thing as place and no such thing as distance. Physics experiments can bind the fate of two particles together so that they behave like a pair of magic coins. . . . They act in a coordinated way even though no force passes through the space between them. Those particles might zip off to opposite sides of the universe, and still they act in unison. The particles violate locality—they transcend space."
"After 11 years, physicists must rethink gravitational waves",  (September 29, 2015)  
"Could the theory which predicted gravitational waves be wrong?"    

"Experimental Confirmation of the Doubts about Authenticity of Event GW150914", Lukanenkov, A.V. (2017).  Journal of Applied Mathematics and Physics, 5, 538-550.  

Search for Gravitational Waves Associated with Gamma-Ray Bursts During the First Advanced LIGO Observing Run and Implications for the Origin of GRB 150906B

"We present the results of the search for gravitational waves (GWs) associated with γ-ray bursts detected during the first observing run of the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO). We find no evidence of a GW signal for any of the 41 γ-ray bursts for which LIGO data are available with sufficient duration."  

 If gravity propagated at the speed of light instead of instantaneously, the effects on orbits of satelites and solar system planets would be very obvious.  However, these are relatively small systems.  Instead of a solar system, consider the effects on something the size of a galaxy:

We know, the solar system and other stars are orbiting around the center of the Milky Way and the radius of the Milky Way is larger than 5☓104 light-year. . . .  But, we know, the Milky Way is moving with a speed on the level of 5☓102km/s.[6] Therefore, the distance between the retarded position and present position of the center of the Milky way is . . . 25 light-year. And, a galaxy is usually older than . . . 1☓1010 years . . . . The distance between the retarded and present positions of this center should become larger than 5 x 106 ly. In this case, a spiral galaxy could not maintain with the form of a disc. Instead, it was a very long strip along the direction of the galaxy moving. However, no galaxy has become such a long strip one.  ("The speed of gravit;y:  An observation on galaxy motions ", Yin Zhu (September 2016)   DOI: 10.13140/RG.2.2.30917.45287   )


Abstract The LIGO Scientific Collaboration and the Virgo Collaboration have announced that on 14 September 2015, LIGO detected an Einstein gravitational wave directly for the first time, with the first observation of a binary black hole merger. The announcement was made with much media attention. Not so long ago similar media excitement surrounded the announcement by the BICEP2 Team of detection of primordial gravitational waves imprinted in Bmode polarisations of a Cosmic Microwave Background, which proved to be naught. . . .The insurmountable problem for the credibility of LIGO's claims is the questionable character of the theoretical assumptions upon which they are based. In this paper various arguments are presented according to which the basic theoretical assumptions, and the consequential claims of detecting gravitational waves, are proven false. The apparent detection by the LIGO-Virgo Collaborations is not related to gravitational waves or to the collision and merger of black holes.

 Appendix A
. . .

However, the crucial point of the foregoing mathematical development is that Einstein's gravitational waves do not have a unique speed of propagation. The speed of the waves is coordinate dependent, as the condition at Eq.(A.6) attests. It is the constraint at Eq.(A.6) that selects a set of coordinates to produce the propagation speed c. A different set of coordinates yields a different speed of propagation, as Eq.(A.3) does not have to be constrained by Eq.(A.6). Einstein deliberately chose a set of coordinates that yields the desired speed of propagation at that of light in vacuum (i.e. c = 2.998x108 m/s) in order to satisfy the presupposition that propagation is at speed c. There is no a priori reason why this particular set of coordinates is better than any other. The sole purpose for the choice is to obtain the desired and presupposed result.

 All the coordinate-systems differ from Galilean coordinates by small quantities of the first order. The potentials gμν pertain not only to the gravitational influence which has objective reality, but also to the coordinate-system which we select arbitrarily. We can ‘propagate’ coordinate-changes with the speed of thought, and these may be mixed up at will with the more dilatory propagation discussed above. There does not seem to be any way of distinguishing a physical and a conventional part in the changes of gμν. “The statement that in the relativity theory gravitational waves are propagated with the speed of light has, I believe, been based entirely upon the foregoing investigation; but it will be seen that it is only true in a very conventional sense. If coordinates are chosen so as to satisfy a certain condition which has no very clear geometrical importance, the speed is that of light; if the coordinates are slightly different the speed is altogether different from that of light. The result stands or falls by the choice of coordinates and, so far as can be judged, the coordinates here used were purposely introduced in order to obtain the simplification which results from representing the propagation as occurring with the speed of light. The argument thus follows a vicious circle.Eddington [38 57]

[38] Eddington, A.S., The Mathematical Theory of Relativity, Cambridge University Press, Cambridge, (1963, reproduction of 1923 publication; the paperback edition is from Forgotten Press and the quote is on  p. 130-131)   (If you search the reprint of this book using Amazon's Look Inside feature, use "vicious circle" for the search text.) 

"Relativity and wavy motions",  Angelo Loinger  (April 2006)  

7.– There is a widespread and erroneous conviction (see e.g. Fock [3], p.194) according to which in GR gravitation is propagated with the speed of light in vacuo, i.e. with the speed of light in empty space of SR. The supporters of this false opinion claim that it follows, e.g., from eqs.(4) and (5), when interpreted as differential equations of wave fronts and rays of GW’s. Now, this is trivially wrong even from the viewpoint of the believers in the physical existence of GW’s, because eqs. (4) and (5) – quite independently of their interpretation– affirm in reality that the concerned wave fronts and rays have a propagation velocity that depends on the metric tensor gjk(x), even if this tensor has the form of a mathematical undulation. The non-existence of physical GW’s has the following consequence: if we displace a mass, its gravitational field and the related curvature of the interested manifold displace themselves along  with  the  mass:  under this respect Einstein field and Newton field behave in an identical way [11].

. . . It is regrettable that various physicists insist on publishing useless considerations and computations on hjk–waves [13]. It is time that astrophysical community desist from beating the air – and from squandering the money of the taxpayers.

"Experimental Repeal of the Speed Limit for Gravitational, Electrodynamic, and Quantum Field Interactions", Foundations of Physics,Tom Van Flandern, Jean-Pierre Vigier,  July 2002, Volume 32, Issue 7, pp 1031–1068

Abstract  )
General relativity has a geometric and a field interpretation. If angular momentum conservation is invoked in the geometric interpretation to explain experiments, the causality principle is violated. The field interpretation avoids this problem by allowing faster-than-light propagation of gravity in forward time. All existing experiments are in agreement with that interpretation. This implies the existence of real superluminal propagation and communication of particles and fields, free of causality problems. The introduction of real physical faster-than-light propagation into gravitation, electrodynamics and quantum theory has important consequences for physics.

Einstein, Relativity and Absolute Simultaneity, edited by William Lane Craig and Quentin Smith (2008)  "Global Positioning System and the twins’ paradox", Tom Van Flandern
. . . it is entirely possible that reality is Lorentzian, not Einsteinian, with respect to the relativity of motion. In that case, physics may have no speed limit when the driving forces are gravitational or electrodynamic rather than electromagnetic in nature. And that may be the most important thing that the GPS has helped us to appreciate.

"On the Signal Processing Operations in LIGO signals", Akhila Raman  (Nov 2017)  

Abstract. This article analyzes the data for the five gravitational wave (GW) events detected in Hanford(H1), Livingston(L1) and Virgo(V1) detectors by the LIGO1 collaboration. It is shown that GW170814, GW170817, GW151226 and GW170104 are very weak signals whose amplitude does not rise significantly during the GW event, and they are indistinguishable from non-stationary detector noise.  

"Contemplation on a Black Spot", research note by W. W. Engelhard   '

"On April 10, 2019, the first image –to be precise –the first “shadow” of a Black Hole was presented to the public in a press conference at Brussels."  

Was this an "image" of a Black Hole ("shadow") or was it something else?  The giant Black Hole is in the center of Messier 87--a famous gigantic spherodial galaxy that is about 55 million light-years from Earth. The Black Hole is about 7.5 microarcseconds in diameter. The Event Horizon (radio) Telescope has a resolution of about 42 microarcseconds. For comparison, the Hubble space telescope has a resolution of about 50,000 microarcseconds and a backyard optical telescope has a resolution of about 1 arc second.  Obviously, the Black Hole cannot be seen optically, and is even below the resolution of the Event Horizon (radio) Telescope. The pictorial representation of the data cannot show any features smaller than 42 microarcseconds, but can show larger features around it. This is a problem because at this distance and this wavelength, and this resolution, the radio waves are coherent. They cannot form an image based on interferometer techniques. The result will be a black spot at the center of the image. So this "Black Hole" could just be nothing more than a diffraction limited picture of an infinitely remote source.

This is pertinent because gravitational waves are theoretically created by colliding black holes.  ( ) But so far there is no solid, undisputed physical evidence that gravitational waves or black holes actually exist.

"A mandatory project proposal for ESA and NASA" , Ahmet Yalcin  (12-11-17)

The second problem is the speed of the gravitational waves. Einstein states that the speed of these waves is the same as the speed of light. Unfortunately, there is no consensus on this issue too. This also has very justified reasons. Firstly, there is a fundamental difference between the propagation of light and the gravitational waves. Light propagates in a form of quanta called photon. A photon emitted from its source, which is probably millions of light years away, is the same as the one reaching our eyes. It is photon entity energy that brings it to us from millions of light years away. The photon is still the same photon because it keeps total entity energy along its route. However, the quantum structure of the gravitational field has not yet been observed. It is likely that the space fabric is the one to allow the emission of the gravitational energy. It is the most important evidence that the gravitational field does not lead to the loss of mass, while radiation does. Propagation of the gravitational energy by the space texture also reduces its probability of propagation at a constant speed, i.e., as the gravitational waves propagate, the speed will decrease. Why?
  . . .
 How can this controversy regarding the gravitational waves end? It is important to end because it leads to unnecessary time and resource loss. This is the reason I suggest a project to ESA and NASA. It is not necessary only but obligatory. The project is a different and simpler renewal of what these organizations have done before.

 . . . Now, with remote sensing, the gravity acceleration can be measured more sensitively than ever. Therefore this is certainly an achievable proposal.

Mass has the dimensions of t3/s3 .  Momentum has the dimensions of  t2/s2 .  Energy is t1/s1 .   Logically then, mass has enough dimensional freedom to absorb (or store) a massless particle (having only momentum) and it could also absorb a photon of energy. But the reverse is not true. Photons cannot store mass, nor can massless particles store mass.  Massless particles, like the neutrino, however, can acquire more energy (as in Beta decay).  And if a massless particle becomes part of a massive system (like an atom) it may contribute to an increase in the mass of that system, even though it has no mass by itself.

The common nuclear model of the atom is based on the concept of locality ("touching is space"), not non-locality.

Go back to Rutherford's original experiment (circa 1911) . He discovered that a material aggregate (gold foil) has an array of tiny massive objects ("kernels") in it, each containing most of the mass of the atom, and each separated by plenty of "space" (or some kind of emptiness) . What were these massive objects?  The previously existing model was based on spatial contract, viz. atoms in an aggregate are pictured as touching each other, like billiard balls in a shoe box. The volume of a ball could be estimated by calculations from soap film experiments and by known molar volumes of metals.  Rutherford found something that was 10,000 times smaller in diameter than that implied by this volume.  Both picutures had factual support and so the tiny massive objects became "nuclei". Hence, the atom "has" a nucleus.

But that is not what his picture really showed. The tiny massive objects, which contain virtually all the mass of the atom, and ultimately account for all the properties of the atom, could be the atoms themselves! The "emptiness" is simply between the atoms, not within the atoms. Physicists could have developed a whole new different form of atomic physics if they had accepted this realization! But historically, they were neither fluent nor comfortable with the concept of non-locality.

Some years later, quantum mechanics began to be developed.  It had features that clearly pointed to a non-locality model. Originally, electron orbits were thought to be clearly defined (like the orbits of planets around the Sun), but later the orbits turned into a fuzzy "electron cloud"; it was not that the electron orbits could not be found and measured, but it was that they did not have any sort of actual spatial trajectory in the first place. Later, more and more conceptual problems developed with the atomic electrons.  It now seems that this model should be discarded and a new one created based on the concept of non-locality.  Atoms exist and they can have various energy levels based on different types of intrinsic spin systems (see links above). Electrons can be an agent to express those energy levels without actually being "parts" of an atom (any more than a gamma ray is a "part" of the atom). A conceptually "cleaner" model of the atom could lead to additional useful insights that are not readily apparent in the current model.

"Milgrom noted that this discrepancy could be resolved if the gravitational force . . .  came to vary inversely with radius (as opposed to the inverse square of the radius, as in Newton's Law of Gravity).    

"Milgrom’s  correction allows gravitational attraction to fall off with distance more slowly than expected (rather than falling off with the square of distance as per Newton) when the local gravitational acceleration falls below an extremely low threshold. This threshold could be linked to other cosmological properties such as the ‘dark energy’ that accounts for the accelerating expansion of the Universe. "
"Has dogma derailed the scientific search for dark-matter?" Corey S. Powell, ed.  

"MOND, however, proposes that, at very large radii and small accelerations, gravity decays with distance more slowly than Newton’s inverse square law. This removes the need for dark matter, providing a clear explanation for the tight non-Newtonian correlation between visible matter and radial acceleration."   "Galaxy rotation study rules out modified gravity, or does it?"  21 Jun 2018    
A partial answer:  the speed of light equates to the value of 1/1. It is what the speed of light actually is.  And this is a number with special properties.  
1.  Only 1 is equal to its reciprocal
2.  Only 1 has the property of 10 = 11 = 12 = 13
The real question:  why do humans equate this to 186,000 miles per second?

Related: TOP Secret Things about Mathematics you didn't Know - Full Documentary  

I walk across a carpet and then touch a doorknob. A big fat spark leaps from my hand to the doorknob. The doorknob is now charged. It is also being accelerated at 9.8 m/sec^2 (like everything else on this planet). We are told that "accelerated charges radiate eletromagnetic radiation".  Hence the questions:

1. Does the doorknob radiate as long as it retains the charge? Why or why not?

2. Is it possible to accelerate an object without having it change speed, position, or direction in space? (this is related to the "motionless motion" discussed in Beyond Einstein)

3. Suppose the doorknob remains stationary, but the remainder of the room moves or oscillates. Is radiation present? Does this relate to the question of absolute motion?

4. Does this question relate to a "change of direction of motion" or a "change of dimension of motion"?   See "Origin of Intrinsic Spin" for some insights.
  (unit quantity mathematics)

The Periodic Table displayed in chemistry and physics classrooms has only one row based on 12 . The others based on  22, 32, and 42 each have two rows.  The reason for the missing row was not given in the article. The missing row represents massless particles. These do not have sufficient intrinsic spin systems to qualify as mass. They therefore cannot come to rest in a gravitational reference system and do not have "chemical" properties.

Symmetry considerations suggest that antimatter would be just as likely to exist and matter. So where is it? It is actually here with us in our everyday living space. It is not really "anti" matter, but "inverted" matter. That is, it has space/time relationships that are inverted (time/space) from our perspective.  It is represented by an "inverted Periodic table" (and the masses, as seen from our perspective, can be worked out in terms of natural quantities as explained elsewhere in the article). These are all "non-local" to our gravitational reference system and fly through our system atom-by-atom at the speed of light much like the massless particles of our own system. And instead of low energies, they may have extremely high energies. Their distribution in our space is essentially homogeneous and isotropic. We call them "cosmic rays".

An appeal to my readers

 The paper "Beyond Einstein: non-local physics" indicates that approximately half of our potential physics knowledge, the non-local portion, is missing. So far, we have only the non-local physics of quantum mechanics ("physics of unit space") which has a limited (but important) scope. The non-local "physics of unit speed" has been completely ignored, as has the important role played by other unit quantity boundaries. It now seems possible to combine the local and non-local descriptions into ONE seamless physical theory based on nothing more than space and time relationships (mass and charge would be derived concepts). 

This would be a huge undertaking. Currently there is nothing in mainstream science or mainstream publications that even hints of serious interest in this direction. Engineerable technology has been admirably well developed but the science--the basic understanding of how the Universe truly works--is still way off in the weeds. After 100 years we are still arguing about Special and General Relativity, and even something as simple and basic as gravity is still enigmatic at its roots.  

 Another problem is mathematical representation of physical phenomena. It is highly desirable to have seamless mathematics for a seamless physical theory. The mathematical framework must comfortably and naturally handle some rather strange and thoroughly unfamiliar (but still accessible) concepts:

 1. It must accommodate an absolute reference system based on centerless expansion of fundamental discrete unit space/time and time/space (i.e., motion and its inverse) and its relationship to a differential (relative) reference system such as the one in common use. It must comfortably accommodate motion with direction, motion with no direction (scalar motion), direction with no motion (intrinsic rotation), and a fundamentally stationary photon; (See  #DiagramSpeedsInGravBoundRef ;  In Search of the Geometry of Space, Time and Motion ;  )

 2. It must support the derivation of properties of space and time from motion; i.e., what kind of space (or time) comes from what kind of motion? (See   Gravitational Lensing and Deflection of Photons by Gravity ; see nebula photos)

 3. It must clarify a fundamental relationship between intrinsic rotation (spin) and translational motion.  (See  Origin of intrinsic spin  ; Some thoughts about intrinsic spin  ;  Effects of Spin )

 4. It must support mappings of non-local to local reference systems (and vice versa) including representations of fundamentally discrete units, unit quantity boundary inversions, indeterminacy, uncertainty, wave/particle manifestations, quantum interference, probability, effects of unit dimensional equalities  (11 = 12 = 13 ), etc. (See    #UFO Physics ; The Problem of Quantum Reality ; The Problem of Quantum Locality ; The Problem of Quantum Probability ; The Problem of Quantum Uncertainty ;  #PythagoreanProblem  )

 All of this could be handled by the various specialized, piecemeal mathematical systems commonly taught at the college level, but there seems to be a better choice: Geometric algebra:  

"Geometric algebra and its extension to geometric calculus unify, simplify, and generalize vast areas of mathematics involving geometric ideas, including linear algebra, vector calculus, exterior algebra and calculus, tensor algebra and calculus, quaternions, real analysis, complex analysis, and euclidean, noneuclidean, and projective geometries. They provide a common mathematical language for many areas of physics (classical and quantum mechanics, electrodynamics, special and general relativity) computer science . . . and other fields." (Linear and Geometric Algebra, Alan MacDonald  (2010) Preface )


"Scientific knowledge is expressed mathematically, but the importance of the optimal choice of the appropriate mathematical language is often underestimated ... . The geometric algebra (Clifford algebra) formalism, according to Occam’s razor principle, is by far the best choice for modern physics. Clifford algebra provides a simple and unifying mathematical language for coding geometric entities and operations ... . It integrates different mathematical concepts highlighting geometrical meanings that are often hidden in the ordinary algebra. ..." ( Maxwell's Equations and Occam's Razor,  Francesco Celani, Antonino Oscar Di Tommasoy, Giorgio Vassalloz, J. Condensed Matter Nucl. Sci. 25 (2017) 1–29     )


"Even though Gibbs was able to reduce Maxwell’s twelve equations down to four, as mentioned, his formalism for vectors had significant structural limitations. For example, the cross product only applies in three dimensional space, because in four dimensions there is an infinity of perpendicular vectors. However, probably most serious in terms of students learning physics, is that, conventional vectors do not integrate with established algebraic intuitions regarding basic operations. That is, there is no division operation, the cross product does not apply in two dimensions and one cannot freely add vectors to previously known algebraic elements (scalars), so that vector algebra becomes a monolithic structure unto itself. Hence the intuitive understanding of physics concepts, as well as general geometric understanding, which depends on the understanding of vectors, is significantly reduced. Historically, as vectors became more popular in physics and in various other fields, new scientific discoveries such as quantum mechanics and relativity meant that vector analysis needed to be supplemented by a basket of other mathematical techniques such as: tensors, spinors, matrix algebra, Hilbert spaces, differential forms etc. As noted in 7 , ‘The result is a bewildering plethora of mathematical techniques which require much learning and teaching, which tend to fragment the subject and which embody wasteful overlaps and requirements of translation’. "  ( "A simplified approach to electromagnetism using geometric algebra", James M. Chappell, Azhar Iqbal, Derek Abbott  (November 11, 2010)      See also:  Vectors and Beyond: Geometric Algebra and its Philosophical Significance,  Peter Simons, dialectica Vol. 63, N 4 (2010), pp. 381–395 DOI: 10.1111/j.1746-8361.2009.01214.x      )

All of this could keep an army of scientists, mathematicians, and engineers busy for 100 years. It is the scientific equivalent of  "fill the Earth and subdue it" or staffing a newly discovered planet.

These are the things of God, and God will give us assistance just for the asking:

 “Let your cry come to me, and I will give you an answer, and let you see great things and secret things of which you had no knowledge.”  (Bible in Basic English, Jeremiah 33:3)

 Let the asking begin!

 "Though your beginning was insignificant, Yet your end will increase greatly. 
Job 8:7, NASB

"the ant" has "no chief, officer, or ruler" (Proverbs 6:6-7, NASB  
So, get to work!