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Giorgio Piacenza Giorgio Piacenza is a sociologist student in the Certificate program leading to a Master's degree in Integral Theory at JFK University.


and the New Physics

Can a Possible Disparity between the Inertial and Gravitational Masses in Einstein's Formulas lead to the Possibility of Self-Propulsion and Substantiate the Interpenetration of Quadrants?

Giorgio Piacenza Cabrera

We arrive at the conclusion that nobody has demonstrated the "constant" of the gravitational law is really a constant of Nature.

Are two equal masses completely equivalent if one is at rest and the other is accelerating or perhaps in a rotational movement? Is the Gravitational Constant really a true constant and unchanging? In this article, I inform that by correcting the Gravitational Constant and then introducing it to Lagrange's equations for planetary motion Jose Alvarez Lopez PhD, apparently came up with Einstein's correct equations for planetary motion. Thus, G at motion or changing position (applicable to inertial mass) would not be equivalent to G at rest (as gravitational mass).This would allow the possibility of self-propulsion which, in turn, might be linked to the Subtle Realm relational logic that would allow characteristics of opposite quadrants to interpenetrate. In this case the intelligence of the left quadrants in Ken Wilber's “Integral Theory” might be able to organize objective, physical structures under what is known as “autopoiesis.”

Professor Jose Alvarez Lopez

Professor Jose Alvarez Lopez (1914-2007) held PhD's in mathematics, Physics and Chemistry from the University of La Plata, Argentina. In 1956 he personally published in Cordoba, Argentina “The Time Concept in Special Relativity,” “The Concept of Mass in General Relativity,” “The Principle of Variational Homogeneity” and “The Meaning of the Clock Paradox.” In 1961 he published “Relativistic Dimensional Analysis.” Then in 1968, Alvarez Lopez published “Gravitational Interference in the Einstein Effect” and “La Thesis Electromagnetique de Poincaré-Cremieux” (with the Faculty of Sciences at the University of Röen). In 1972 was published “Relativistic Space Propulsion” (also in Cordoba, Argentina) and in 1976 “About the Non Existence of Electronic Inertia in Metallic Conductors” (with the Real Academia de las Ciencias, Madrid, Spain).

This Professor was keenly aware of the epistemological issues raised by modern physics and didn't hesitate to tackle them as an experimentalist, a deductive physicist, a mathematician and even by adventuring into less scientifically orthodox areas of knowledge. For instance, besides orthodox works in physics, he also wrote about more speculative matters such as Yoga, Cybernetics, Archeology, and about the profound but unappreciated mathematical, engineering and astronomical knowledge apparently possessed by the ancient Hebrews and Egyptians. As expected in a scientifist world, this got him in trouble with many of his colleagues.

Many years ago, during a series of interviews I enjoyed with Professor Alvarez Lopez in Miami, Florida in Icho Cruz, Cordoba, Argentina, Professor Alvarez Lopez told me that he had conducted research under the direction of Professor Giorgio Piccardi at the Laboratory of the Institute of Chemistry and Physics in Florence, Italy. He also told me that he had conducted research at the Electrophysical Technical Institute under the direction of professor Köning in Munich, Germany; at the Institute for Advanced Studies, directed by professor James Mc Connell in Dublin, Ireland; and in the Lawrence Berkeley Laboratory, in Berkeley, California, where he had been invited by professor Luis W. Alvarez in 1975 to research the “Behavior of Joule's Law in Electrical Coronas.” He also informed me that he had received positive commentaries from Albert Einstein (shortly before his death) and met in Paris with Count Louis de Broglie. There also were favorable personal or letter exchanges with scientists like Alexander Wilkens, Burnington Brown, David Bohm, William R. Corliss, Kiril Stanjukovich, J.L. Synge and Dr. de Puymorin, former director of France's Space Commission.

I'm not an accredited physicist but, basically possess a well-informed layman's concern and -in reporting on some of my conversations with Professor Jose Alvarez Lopez- I'm trying to bring up ideas which may still be important to the physics community and, subsequently, to science, metaphysics and philosophy in general. Perhaps the ideas were too controversial during the Professor Alvarez Lopez's lifetime but nowadays a paradigm like the “Equivalence Principle” is being questioned. Professor Alvarez Lopez did manage to publish some of his ideas in Argentina and non-English speaking countries but, while recognized by some, was (perhaps due to his metaphysical and epistemological interests) also considered to be too extravagant by others who didn't have the time or the inclination to carefully read his work and review it. However, perhaps the Professor's work could still nowadays add to our knowledge of the possibility of manipulating how objects respond to gravity or exert gravitational forces. For instance, I ask (hoping not to venture into the nonsensical) whether the General Relativity formulas (under a modified Gravitational Constant) allow for an asymmetry between inertial and gravitational masses so that now a Coulomb Effect in rotational masses might become a self-propulsive distortion of space-time. Perhaps some kind of directional space-time torsion field producing an effective vector force could be generated.

There were interesting reports of alleged discoveries. For instance, during some personal meetings, Professor Alvarez Lopez told me that he and his group of experimentalists in Argentina had developed a micrometer that had shown that electrons didn't possess mass in electrical conductors. He had also apparently found that the atomic constants were coordinated by the non- dimensional 'atomic constant' “alpha,” also known as the “Fine Structure Constant.” Moreover, after learning about a strange experimental effect in Argentina in which (after pumping DC current for several days along an 'antenna' aligned with the local geomagnetic field) the total output of energy seemed greater than the input, and Alvarez Lopez allegedly conducted a partially related experiment at Lawrence Livermore under the auspices of Dr. Luis W. Alvarez.

Certainly, I'm not a physicist but for several decades I've been pondering and gradually learning about a few relevant issues in philosophy of science and have read a broad range of popular books on quantum physics and cosmology. I hope that, in reporting on some of these conversations with Professor Jose Alvarez Lopez, I'll bring to the attention of suitable academics ideas which –if confirmed true- could be fundamentally important to science, metaphysics, ontology, philosophy and humanity in general.

I would like to present some of Professor Alvarez Lopez's alleged findings that also seem to connect Einstein's Special and General Relativity. I'm would like to see knowledgeable physicists review the Professor's works (like “Relativistic Dimensional Analysis”) and verify or discard if he was correct in concluding that Einstein overlooked a certain disparity between Inertial Mass and Gravitational Mass. The 1961 publication titled “Relativistic Dimensional Analysis" explains much better than I many of his ideas in relation to the issues raised. It is a matter of finding this and other works to carefully review them.

Here I also want to make reference to research papers dealing with the possibility that orthodox concepts about gravity and the Equivalence Principle can be modified, complemented or challenged. For instance, an article written by Japanese physicists Hideo Hayasaka and Sakae Takeuchi titled “Anomalous Weight Reduction on a Gyroscope's Right Rotations about the Vertical Axis on the Earth” published in the December 18, 1989 issue of Physical Review Letters. Seems to show that charged rotating masses alter the gravitational field.

I also found that the results reported by Hayasaka and Takeuchi had been questioned in 1990 by Dr. S.H. Salter, a mechanical engineer at the University of Edinburgh who, (while not trying to replicate the original findings with a similar amount of magnetic material also used) proposed that vibrations in the ball bearings of the rotating gyro could explain the effects. Reference: S. H. Salter, Nature, (February 4, 1990).

Nevertheless, a few years later, Hideo Hayasaka et al. wrote an article after conducting experiments that seem to back support the results published in 1989. It is titled “Possibility for the Existence of Antigravity: Evidence from a Free-Fall Experiment Using a Spinning Gyro” and was published in Speculations in Science and Technology, 20 (173-181) (1997).

Moreover, some other experiments seem to corroborate Hayakawa and Takeuchi's basic results, thus bringing to question the Equivalence Principle. For example, “The Phenomenon of Weight Reduction of a Spinning Wheel,” written by R. Waite for Mechanica: An International Journal for Theoretical and Applied Mechanics Volume 42, Number 4, 359-364, presents an alleged general validation of the original results.

Then again (and still related to these issues) another article appearing in Physical Review Letters makes the case that the Equivalence Principle may be violated by the action of the still mysterious “Dark Energy.” The reference is “Dark Energy as a Born-Infeld Gauge Interaction Violating the Equivalence Principle” by A. Füzfa and J.M. Alimi, Phys. Rev. Lett. 97, 061301 (2006).

Then, can information be the source for space, inertia and gravity? Read Erik P. Verlinde's plausible and original work 'On the Origin of Gravity and the Laws of Newton' 6 January 2010, Apparently, the entropy differences among parts in the universe would generate the gravitational force by distributing matter to maximize overall entropy according to the Second Law of Thermodynamics. A stronger force would be related with a higher entropic probability.

Could physical information be modified by human intention interacting with an information field? According to the former Stanford University Professor emeritus in Material Science and Engineering, William A. Tiller PhD, the gauge symmetry of space can be modified like this. Perhaps this would affect information and, if information is the primary source, then –perhaps- space, time, gravity and inertia as emergent phenomena would also be modified. Read the “white papers” and “The Tiller Model” or watch an interesting interview at

The Gravitational Coupling (adimensional) Constant (GCC) comes to mind as it pertains to how charged particles with mass attract. It is the square of the electron mass in Planck units of mass while alpha is the square of the electron charge in Planck units of charge. The parallels with alpha are interesting but GCC links gravity to charge and should be crucial in the more recent investigations on the origin of mass.

These 'constants' (which as 'pure numbers' can be seen as 'stable' and 'prior' in relation to constants using units of measurement)  may be conceived not as 'true constants' but as modulators of those constants. Their change would also modify the Gravitational Constant. Interestingly, Alvarez Lopez also proposed that G could be relativistically corrected dividing it by 1 - v square/c square. If I'm interpreting this correctly, this could mean that the equivalence principle for two objects in relative motion with each other would have to be modified. Professor Alvarez Lopez then placed the corrected G into a Lagrange equation and arrived at Einstein's equation for planetary motion. He then wrote that "this showed that Einstein correction consisted exactly in transforming the Constant of Gravitation into a Lorentzian invariant." Here again we see Alvarez Lopez´s search for the interplay between a 'prior' factor and a 'dependent' factor.

In "Relativistic Dimensional Analysis" there's a claim that by modifying G (dividing it by 1- v2/c2 and placing this modified G in Lagrange equations) we arrive to Einstein's equations for planetary motion. Alvarez Lopez also proposed that Eötvoss' experiments testing the Equivalence Principle focused upon a relation that could qualify as 'masses at rest'. He claimed that Eötvoss' experiments say nothing in regards to the relativistic behavior of masses in relative motion.

Professor Alvarez Lopez told me that Einstein's General Relativity Theory was “a perfect theory based upon two errors: 1. The equivalence between inertial and gravitational mass, which he tacitly assumed and 2. The constancy of the Gravitational Constant, which he also tacitly assumed.” Then he asserted that “the error about the Equivalence Principle corrects the error about the Gravitational Constant.”

G0 (corrected Gravitational Constant) = G/(1-v^2 ?/c?^2 ) Then, according to Alvarez Lopez, if G0 is utilized in Lagrange's formula we obtain Einstein's formula for planetary motion, a formula that took Einstein 20 pages of tensorial calculus to obtain. Professor Alvarez Lopez also said that “this shows that it is easier to arrive to the same results by starting from Electrodynamics and moving to General Relativity because v(1-v^2 c^2 ) is obtained from Special Relativity which pertains to Electrodynamics. Einstein achieved the formulas but not the theory.”

Thus, Professor Alvarez Lopez also discovered that Einstein was using two kinds of masses: The relative mass of Special Relativity, where mass is a function of velocity and the absolute mass of General Relativity, in which the mass is constant and, therefore, independent of velocity.

Regarding Length, if L = length at rest L_0= Length during movement L = L_0 v(1-v^2/c^2 ) L< L_0

Regarding Time (alternative equation) T= T_0 v(1-v^2/c^2 )

Also, if G were constant, the formula for the gravitational force would be equivalent to the formula of the centrifugal force so that F = G (m M)/r^2 = m w^2 r

Jose Alvarez Lopez's work delves into a distinction between universal and empirical constants and goes into a relativistic dimensional method for arriving (through a method and deduction) to a list of values very closely corresponding to the atomic constants. Moreover, by setting the simultaneity of Space or of Time when using Lorentzian transformations, two sets of indeterminate or ambivalent relativistic results for time and for length result. In relation to this ambivalence in relativistic formulas and in a personal conversation with Count L. de Broglie, Professor Alvarez Lopez was told that it was important to distinguish between the "time of waves" and the "time of corpuscles." In my layman's understanding this seems to connect aspects of General Relativity with Quantum Physics.

I think that, since Professor Alvarez Lopez admired Tolman's “Principle of Similitude” and used his own (also quite interesting) “Principle of Variational Homogeneity” and had the courage to delve into some unclearly settled aspects of physics, his work was only privately well-regarded by a few distinguished scientists. For instance Professor Alvarez Lopez was interested in the role of the adimensional 'constant' alpha and of invariant principles connected to the epistemological possibility of carefully developing an a priori, Platonic, rational method that would complement the empirical approach.

Also, Professor Alvarez Lopez claimed that by introducing in the practice of Dimensional Analysis his “Principle of Dimensional Homogeneity” the possibility of determining a priori the constants of nature comes up. Due to this recognition of the possibility of an aprioristic, deductive physics based on general principles, some of Professor Alvarez Lopez's work seems adequate to explore the role of an intelligent interiority in Physics, typically limited to be a “hard science” mostly focused on structured, stable, and objective Exteriority. Perhaps aspects related to an intelligent, physical autopoiesis, to information and, eventually, to the fundamental role of consciousness in the physical universe would relate with this exploration. In relation to a more complex phase of Integral Theory, the importance of considering Interior, Intelligent aspects hiding (or existing in potential states) in the obvious Physical, Exterior, Objective aspects of the Kosmos (rather than expressing as correlated but distinct quadratic perspectives) arises.

In Jose Alvarez Lopez's 1961 work titled Relativistic Dimensional Analysis (p.58) we read:

“Tolman proved that with his Principle of Similitude the aprioristic qualitative determination of all the laws of Nature was possible. He also pointed out that this was not the case for Newton's law of gravitation; and the main objection against Tolman's Principle of Similitude was that with its help the aprioristic determination of Newton's law of gravitation was impossible. Owing to this circumstance the Principle of Tolman was rejected as a physical principle. It is surprising to observe that nobody, at that time, considered the other possibility: that the “constant” of the gravitational law were not a real constant of Nature.

The equivalence between gravitational mass and inertial mass, implicit in the Newton law of gravitation, has always appeared as demonstrated by the existing isochronism of penduli formed out of different materials. Later on, Eötvoss confirmed the result of the isochronal experiments with the help of the famous balance, demonstrating that the relationship existing between masses of different substances in regard to the gravitational and inertial actions was invariant at the poles and at the equator. Taking into account that at the equator the action of the gravitational force is somewhat opposed by the centrifugal action due to the rotation of the Earth, this experimental demonstration was considered sufficient proof for the statement of a “Principle of Equivalence” of the gravitational and inertial masses.

All these experiments and analyses have been so amply discussed in the scientific literature that it is surprising that nobody observed that the experiments of Eötvoss –regardless of their extreme accuracy- were performed under conditions we could qualify as static ones: i.e. the relationship between the masses (terrestrial mass and the mass in the balance) is referred to masses at rest. This is the reason why Eötvoss' experiments say nothing in regard to the relativistic behaviour of masses in relative motion (as, for instance, the masses of a planet and the Sun). In face of such facts -I have analyzed at full length in a previous paper (24) – it is hardly dubious that a physicist will not qualify the relativistic applying of such experiments as “illegitimate extrapolations of experimental results.”

We arrive at the conclusion that nobody has demonstrated the “constant” of the gravitational law is really a constant of Nature, and that in spite of this lack of experimental evidence the constancy of such an entity is an accepted fact of modern physics. Let us think of the methodological mistake involved in the rejection of the Principle of Similitude on the basis of its inability for determining a “constant” that nobody has yet shown to be a constant of Nature.”

The English abstract of Jose Alvarez Lopez's 1957 work El Concepto de Masa en Relatividad General reads:

“In trying to transform trajectories of a configuration space into geodetic lines of a Riemannian space-time, the author has been led to the discovery of an essential requirement


(where m represents coordinate mass) which he calls “Principle of Identity.” Its name suggests it to be a generalization of the Newtonian “Principle of Equivalence” that allows the discussion of dynamical conditions hitherto not taken into account in the analysis of the quoted Newtonian principle.

In section c the author shows –with the help of the well-known “Einstein elevator” - that unless we accept a principle of identity it will be possible to distinguish between gravitational and inertial forces.”

Professor Alvarez Lopez was one of the first scientists able to understand Albert Einstein's theories. While he was recognized by some important established scientists, as a Latin American scientist working independently against prevailing dogmas didn't allow him to be recognized in earnest. In Relativistic Dimensional Analysis, El Concepto de Masa en Relatividad General, The Principle of Variational Homogeneity and Self-Propulsion: A New Flying Technique (some of which may be available through Borderland Sciences, Amazon and Google Books) there are carefully detailed, cogent explanations with step by step mathematical demonstrations that serious scientists willing to learn plausible important corrections to Einstein's theories can find.

I'm aware that according to Erik P. Verlinde, Phd, gravity can be thought of as a derived entropic force linked to information and probability as the statistical behavior of 'degrees of freedom' which can be pictured as encoded (minus one spatial dimension) within the concept of a 'holographic screen'. Thus gravity would originate in a difference on how much entropy and information is found in the space between two masses in relation to its surroundings: More entropy, more gravity and the more bits of information are required to unscramble and to explain this entropy (because more bits of information have been 'lost') would be equivalent to a greater 'gravitational pull'. Here inertia, gravity and space would be emergent and information primary.

Whether –from another perspective- this pull is also accompanied by a distortion of space-time and to a concentration or dispersal of elementary 'information space-time units' this may also be plausible. To me this suggests that the level of reality capable of modifying how much information is required in order to obtain a practical description is more fundamental. Could this be a higher symmetry level which we can tap into through our awareness and perhaps our very capacity to describe a certain space based on information influences how we modify thermodynamically free information? Can our consciousness connected with quantum non locality decrease entropy? Hopefully physicists knowledgeable of these matters will see if Professor Alvarez Lopez's work is still useful to current discussions in physics.

For a stimulating read find Erik P. Verlinde's 'On the Origin of Gravity and the Laws of Newton'.

If Professor Alvarez Lopez's works establish genuine discoveries, they may have many implications. For instance, it may not be possible to adequately define General Relativity in a Riemannian four dimensional space. Perhaps his works agree with the possibility of finding practical ways to increase the disparity between inertial and gravitational masses and therefore of creating unique dynamic effects. Can movement, the Coulomb Effect and vibrational information states be intentionally imprinted/programmed and used to decrease inertia and to tap into zero-point energy potentials in order to manifest controlled self-propulsion? Might the General Relativity formulas (modified by the inclusion of the non-equivalence of the inertial and gravitational masses) now thus relate with Special Relativity and with Quantum Electrodynamics perhaps allowing an asymmetrical Coulomb Effect to become a self-propulsive distortion of space-time? Could Hiley's “information quantum potentials” be modified by a consciousness-actualized information and intention through a psychically-sensitive connection with a physical-negentropic causal influence (allowed by the quantum-relativistic, Klein-Gordon equation)?


Correlated "quadrants" may pertain to a domain which is itself derived from one which is much more relational, non-local, responsive to consciousness and also information-based. Its higher symmetry may translate in an equal causal relation between its subjective and objective aspects subsuming the physical categories we experience as “space” and “time.” Stable physical laws and patterns could be a result of regulations in this more fundamental domain. The new information physics and consciousness studies may relate more directly with this -often denigrated- domain, which has been normally called "The Subtle Realm" and has, in recent times been discarded as unscientific and visionary. However, in order to keep abreast of scientific advances gradually moving into the recognition of this realm, Integral Theory could consider how may "Quadrants" be understood within this "Subtle" level which perhaps is quite active (and yet directly undetectable and, in this sense, "potential") in the insides of Exterior, objective quadrants, under the phenomena of "autopoiesis."

When Professor Jose Alvarez Lopez found a possible disparity between inertial and gravitational masses through an a priori, rational procedure prevailing over classically-prejudiced physical observations, the possibility of self-propulsion based on more relational entities such as De Broglie's "time of waves," information regulation of potentials and space-distorting, charged motion originates (along with a greater possibility of connecting Physics with a more inclusive, relational, “Subtle” realm).

Some relevant formulas:

Alvarez Lopez's Corrected Gravitational Constant G/√(1-v^2 /c^2 )

G= √(1-v^2-c^2 )

L = length at rest L_0= Length during movement

L = L_0 √(1-v^2/c^2 ), L< L_0,L = f (v) and dL/dt?0

Alvarez Lopez's alternative equation L=L_(0 )/ √1-v^2/c^2 ) L>L_0

M=M_0/√(1-v^2/c^2 ) dM/dt?0


T = T_0/√(1-v^2/c^2 ) T >T_0

Alvarez Lopez's alternative equation T= T_0 √(1-v^2/c^2 ) T< T_0

F= G(m M)/r^2 F= m w^2 r F= G(m M)/r^2 = m w^2 r

Dimensions of the Equivalence principle = (Gravitational Mass)/(Inertial Mass) = 0

Coulomb's Formula F= (Q_(1 ) Q_2)/(r^2 )


Alvarez Lopez, Jose (1957). El Concepto de Masa en Relatividad General. Cordoba: Imprenta de la Universidad de Cordoba.

Alvarez Lopez, Jose (1961 ). Relativistic Dimensional Analysis. Cordoba: Instituto de Estudios Avanzados.

Vaninni, Antonella (2009). “A Syntropic Model of Consciousness.”

Wilber, Ken (2006). Integral Spirituality. Boston: Integral Books.

Wikipedia. “Quantum Potential”

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