ABOVE — the GBAR experiment, Gravitational Behaviour of Antihydrogen at Rest.
One of the fundamental questions of today’s physics concerns the action of gravity upon antimatter. No experimental direct measurement has ever been successfully performed with antimatter particles. CERN has thus launched a research program with the Antiproton Decelerator (AD) allowing to prepare a measurement of the effect of gravity on antihydrogen atoms. The primary aim of this experiment is to determine how antimatter reacts to gravity. A first test will be to verify the sign of the gravitational acceleration for antimatter, which would translate as an elevation rather than a fall of an antimatter atom only submitted to the gravity force of the Earth. Other theories predicting less spectacular deviations with respect to standard gravitation will also be tested. The GBAR experiment started its installation at CERN in December 2016. GBAR is highly multidisciplinary, a collaboration of 19 institutes in 9 countries. The goal, ambitious and complex, is fundamental for physics, because any difference between matter and antimatter in respect to gravity would necessitate radical revision of current models at the most fundamental level.
Sunday, 23 September 2018
This is an open access scientific research paper distributed under the terms and conditions of the Creative Commons Attribution License ( CC BY 4.0 )
ABSTRACT
Based on the massenergy equivalence from special theory of relativity, we conjecture simple and clear framework for the purpose of conceptualizing atomic mass generation mechanism for a single hydrogen atom. We then apply it to see if it would offer conclusive clarification of the issue of the sign of gravitational interaction between the Earth and antihydrogen atoms at CERN. Our testable prediction is that the interaction will be conclusively repulsive, i.e. of equal and opposite magnitude as compared to the attractive one. We are confident that, if experimentally verified, our conjecture has sufficient potential to result in a theoretical basis of the first experimentally testable quantum gravity hypothesis.
1. INTRODUCTION
The principle of universality of free fall, or Weak Equivalence Principle (WEP) states that all bodies fall with the same acceleration, independent of mass and composition. The WEP has been tested with very high precision for matter but never directly for antimatter. The principal goal of ALPHAg, AEgIS, and GBAR experiments is to test the Weak Equivalence Principle with antihydrogen atoms at the European laboratory for particle physics (CERN), using the antiproton decelerator (AD) to provide antiprotons and a source to provide antielectrons, which we combine to form antihydrogen atoms. Tests with charged antiparticles are hopeless, given the extreme weakness of gravity in comparison with the other forces, while tests with electrically neutral antihydrogen atoms are merely extremely difficult.
Atoms of ordinary matter fall down due to the pull of gravity, but the same might not be true of antimatter. Particle physicists wonder whether antimatter atoms would instead fall up when subjected to Earth’s gravity, and whether antigravity exists. “In the unlikely event that antimatter falls upward, we’d have to fundamentally revise our view of physics, and rethink how the Universe works”, said Joel Fajans, a Professor of Physics at the University of California, Berkeley.
Magnetism is not electricity, however, there isn’t any such magnetism to be found in hydrogen atom that would be independent of electric charge and its behavior. And vice versa, there isn’t any such electric charge to be found in hydrogen atom that would exist in the absence of magnetic field.
Hydrogen atom happens to be a piece of matter. Matter has mass, and mass is considered to result in gravity. There isn’t any such gravity to be found in hydrogen atom that would be independent of atom’s mass, and there isn’t any such mass to be found in hydrogen atom that would exist in the absence of atom’s gravity.
As we just established, in hydrogen atom there isn’t any magnetism to be found independent of electricity, and there isn’t any electricity to be found there in the absence of magnetism. In general, electricity gives rise to magnetism, and mass gives rise to gravity.
Mass and gravity are neither electricity, magnetism, nor electromagnetism, however,
CONJECTURE 1.
we conjecture that there aren’t any such mass and gravity to be found in hydrogen atom that would be independent of atom’s electricity, magnetism, associated angular momenta (and whatever other forms of energy we could possibly find in the atom), and such that could exist in their absence, because any one of energies present in hydrogen atom is, in principle, equivalent of some portion of its mass.
2. THE MASSENERGY EQUIVALENCE
Albert Einstein explains his famous formula, as recorded in the soundtrack of the 1948 film, Atomic Physics:
It followed from the special theory of relativity that mass and energy are both but different manifestations of the same thing — a somewhat unfamiliar conception for the average mind. Furthermore, the equation E is equal to m csquared, in which energy is put equal to mass, multiplied by the square of the velocity of light, showed that very small amounts of mass may be converted into a very large amount of energy and vice versa. The mass and energy were in fact equivalent, according to the formula mentioned above. This was demonstrated by Cockcroft and Walton in 1932, experimentally.
ASSUMPTION 1.
We assume that when hydrogen atom absorbs, or emits, a lowenergy photon (thermal radiation), then it respectively gains, or loses, a tiny bit of its mass equivalent of photon’s energy.
This assumption is, in principle, in agreement with Einstein’s massenergy equivalence. The massenergy equivalence is unconditional in a sense of being valid for photons of any energy, and not for highenergy ones only.
Direct implication of this assumption is that atomic mass could undergo limited fluctuations. This implication receives theoretical support from the peerreviewed, published theoretical research by Woodward J.F. on transient mass fluctuations based on the Mach’s Principle, and from its preliminary experimental verification. Further experimental testing of transient mass fluctuations and their potential application to space propulsion will be conducted by NASA.
 https://www.nasa.gov/directorates/spacetech/niac/2018_Phase_I_Phase_II/Mach_Effect_for_In_Space_Propulsion_Interstellar_Mission
 https://physics.fullerton.edu/~jimw/staif2000.pdf
 http://www.enthea.org/docs/WoodwardMachianMassFluctuationEffect.pdf
Another theoretical, soon to be experimentally testable, possibility of transforming energy of photons into particles of matter is described by the theory of BreitWheeler process that is based on QED theory, and on the massenergy equivalence.
According to Einstein’s special theory of relativity, mass of a material body depends on its velocity. Even though for nonrelativistic velocities this dependence is negligible in practice, it still nonetheless holds true in theory. By analogy, atomic mass fluctuations due to absorption, or emission, of lowenergy photons are also negligible in practice. Similarly, it is only the lowenergy neutron that is absorbed by fissile uranium’s nucleus, and not the highenergy one.
In view of the above, it seems reasonable to conclude that ASSUMPTION 1 is plausible enough.
3. HYDROGEN’S MASS GENERATION MECHANISM
When hydrogen atom absorbs, or emits, a photon, then the distance between electron and proton increases, or decreases, respectively. This change of the distance results in the corresponding change of value of the electric dipole moment between electron and proton.
When absorption of a photon by hydrogen atom results in equivalent increase of its mass, then this mass increase is reflected in the corresponding increase of the electric dipole moment value. Direct implication of it becomes our
CONJECTURE 2.
We conjecture that hydrogen atom’s electric dipole moment, being energy of electric potential, constitutes a measure of its mass. A measure of atomic mass so defined is a vector that represents energy.
In addition to CONJECTURE 2, we recall CONJECTURE 1, which states that, in our view, there aren’t any such mass and gravity to be found in hydrogen atom that would be independent of atom’s electricity, magnetism, associated angular momenta (and whatever other forms of energy we could possibly find in the atom), and such that could exist in their absence, because any one of energies present in hydrogen atom is, in principle, equivalent of some portion of its mass.
4. WILL ANTIHYDROGEN ATOMS BE GRAVITATIONALLY REPELLED BY THE EARTH?
Attractive gravity of the Earth can be conceptualized as lines directed inward, towards the center of its mass. This agrees with hydrogen atom’s inwardly directed vector of electric dipole moment. This, in turn, reflects the natural fact that hydrogen atom’s mass gives rise to attractive gravity. In this sense, it also reflects the fact that two material bodies composed of atoms which have their electric dipole moment vectors directed inward will gravitationally attract each other. On the other hand, antihydrogen atom’s electric dipole moment vector is directed outward.
OUR TESTABLE PREDICTION

The above strongly suggests that antihydrogen atoms at CERN will be conclusively gravitationally repelled by atoms of matter, i.e. with equal and opposite magnitude as compared to hydrogen atoms.
OUR SECONDARY PREDICTION

Furthermore, in view of the above we would expect the gravitational interaction among atoms of antimatter to also be repulsive.
Direct implication of our secondary prediction is that antimatter atoms would not be able to form massive bodies in the Universe that could be easily detected by astronomical observations.
This, in turn, would imply that we could expect vast regions of atomic antimatter dust to be present in the intergalactic space, thus solving the mystery of the missing antimatter. Similar scenario was theorized by Itzhak Bars and Albin James in their paper, Physical Interpretation of Antigravity. Such vast regions of antimatter dust would power not only galactic expansion, but would also power selfexpansion, which increases the galactic expansion even more. Antimatter and its antigravity would naturally eliminate the need for dark matter, and dark energy.
The existence of antimatter was first predicted theoretically. Later it was also directly detected experimentally, and even artificially produced. However, the existence of dark matter has neither been directly detected experimentally, nor has dark matter been theoretically predicted. It is even worse. Because the existence of matter is naturally accompanied by antimatter, then shouldn’t we also expect the existence of anti dark matter?
We believe that at this early stage the true beauty and strength of our quantum gravity conjecture is expressed by OUR SECONDARY PREDICTION and its direct implication.
5. COULD ANTIMATTER HAVE NEGATIVE MASS?
Yes, but only in a sense of the letter “m” being preceded by mathematical minus “–” sign in equations.
Otherwise, it is clearly and obviously impossible for physically real negative mass to exist in physical reality, because it is simply illogical. What would the notion of physically real negative mass specifically refer to in physical reality? One of the things it could refer to is “negative wave”, and the other is “wave of negative energy”. What would be the essential difference between a wave of negative energy and a wave of positive energy? How could “negative wave” possibly look like?
The notion of negative energy goes hand in hand with the notion of negative radiation. Therefore, in our opinion, such vague notion as “physically real negative mass” is not sound enough to be taken seriously as an explanation of antihydrogen atoms possibly antigravitating.
However, in view of our conjecture, it can be validly said that antihydrogen atom has “antimass” in virtue of its electric dipole moment vector being directed in the opposite way to that of hydrogen. And that is precisely what the otherwise impossible notion of physically real negative mass refers to in physical reality.
That seems to completely exhaust the pool of possible explanations. There does not seem to be any other clear and convincing explanation left. Therefore, should antihydrogen atoms antigravitate at CERN, we can only hope that our conjecture, surprising as it may be at first, will not be rejected offhand in favor of something else that, like a seductively looking distant mirage, does not exist.
6. THE NOTION OF MASS AND THE GRAVITATIONAL INTERACTION
Let’s recall that our above proposed concept of mass is a vector representing energy. If mass gives rise to gravity, then our mass, as a vector, should give rise to the force of gravity also represented as a vector.
In theoretical physics, a mass generation mechanism is a theory which attempts to explain the origin of mass from the most fundamental laws of physics. To date, a number of different models have been proposed which advocate different views of the origin of mass. The problem is complicated by the fact that the notion of mass is so closely and strongly related to the gravitational interaction, but a theory of the latter has not been reconciled with the Standard Model of particle physics yet.
The concept of mass, with the concept of gravitational mass identified with the concept of inertial mass, is quantified and defined by gravitational phenomenology. Therefore, on purely logical grounds, the concept of mass so defined cannot then be used in the theories of physics as an explanation of the very phenomenology used to define and quantify it, because otherwise it would become a classical instance of meaningless, circular reasoning; meaningless, because not all circular reasonings are created equal.
To address the above issues, let us suppose that hydrogen atom’s electric dipole moment vector can be viewed and interpreted from three closely related perspectives.
The electric dipole moment as a vector representing energy can be understood as validly representing hydrogen atom’s inertial mass, because energy is equivalent of mass, also when hydrogen atom absorbs a single lowenergy photon (thermal radiation).
It could, however, also be understood as validly representing hydrogen atom’s gravitational mass. Which mass, then, it should represent? Inertial or gravitational? Perhaps it should represent the gravitational mass, because the electric dipole moment is a vector, therefore gravitational mass so understood is conceptually compatible with the vector of gravity force that it is supposed to give rise to.
However, if we decide that the electric dipole moment represents gravitational mass, then where is the inertial mass to be found inside the hydrogen atom? Since both masses are considered to be of equal value, then perhaps they are merely two different ways of looking at the same thing, at hydrogen atom’s electric dipole moment?
It seems that mass, inertial or gravitational, should naturally be a scalar value. Yet, we discovered it as a vector. But how could a scalar mass directly give rise to a vector of gravity force? That seems to be a mystery in its own right.
The third way of looking at hydrogen atom’s electric dipole moment vector is to understand it as representing the vector of gravity force. Because the notion of mass is so closely and strongly related to the gravitational interaction, it is impossible to directly experimentally detect the physical existence of inertial or gravitational mass as something different than, and separate from, the gravitational interaction, even in principle. This should give us a serious pause for reflection.
The above could mean that the reason that inertial and gravitational mass are of equal value is that they are one and the same thing viewed from two different perspectives. Similarly, the reason that even in principle we cannot experimentally detect the physical existence of inertial or gravitational mass as something different than, and separate from, the gravitational force, is that they are one and the same thing (the electric dipole moment) viewed from two different perspectives.
Therefore, it would seem that notions of inertial mass, gravitational mass, and gravitational force are one and the same thing (the electric dipole moment) viewed, understood and interpreted from three different perspectives, in three different contexts. Let us give a simple example.
One way of looking at electron is that it is subject to waveparticle duality. Second way of looking at electron is that it is a carrierparticle of negative charge. Third way of looking at electron is that it spins. Fourth way of looking at electron is that it is always accompanied by magnetic field.
When we look at the fact that electron spins, we can merely see it as electron having angular momentum, or we can see its spin as the cause of magnetic field. We could say that there are two different phenomena, one is electron’s angular momentum, and the other is the cause of electron’s magnetic field. The problem, as we see it, is that in our minds we almost can’t separate these two facts, because they look to us so well integrated. The flip side of this problem is that in our minds we almost can’t integrate the three notions of inertial mass, gravitational mass, and gravity force as referring to the same fundamental physical phenomenon in three different contexts.
With every new context there will be new notion of mass, like for example, passive mass, or active mass. How many more kinds of masses are there to be discovered?
It is completely natural that depending on a context, we refer to the same person by variety of terms designating its various aspects and functions, like for example “President”, “CEO”, and “husband”. In principle, they could be three different people, but if these terms happen to designate one person, then the “President” and the “CEO” can’t cast two opposite votes at the same time at work, while the “husband” is at home playing with children.
We can’t reasonably expect to be able to physically separate electron from its electric charge, spin, and magnetic field, so why would we expect that inertial mass, gravitational mass, and gravity force must be three physically different phenomena? Where is the proof, or sufficient evidence, or logical argument, which would clearly indicate that inertial mass, gravitational mass, and gravity force must be three physically different phenomena? Could we physically separate spinning electron from its magnetic field? Spinning electron and its magnetic field are two different sides of the same coin.
7. WHAT, SPECIFICALLY, DOES THE NOTION OF MASS REFER TO IN SUBATOMIC PHYSICAL REALITY?
Gravitomagnetism is produced by stars and planets when they spin. It’s similar in form to the magnetic field produced by a spinning ball of charge. Replace charge with mass, and magnetism becomes gravitomagnetism. Written out in full glory, the equations of general theory of relativity are complex. Indeed, they have been solved in only a few special cases. One of them is the case of weak gravity, like we experience on Earth. In the weak field limit, Einstein’s equations reduce to a form remarkably like Maxwell’s equations of electromagnetism. Terms appear that are analogous to electric field, and to magnetic field. The electric terms correspond to the gravity that keeps our feet on the ground. The magnetic terms are wholly unfamiliar; we don’t sense them in everyday life.
It needs to be emphasized that our conjecture of hydrogen atom’s electric dipole moment being a measure of its mass should not be misunderstood as if it were to exist in absence of everything else. In so far as we conjecture hydrogen atom’s electric dipole moment to be a measure of its mass, it is only on condition of being encapsulated in everything else that hydrogen atom provides, like magnetic fields, all associated angular momenta, and whatever other forms of energy we could possibly find in the atom, forms of energy that, in principle, are equivalent of some portion of its mass.
Our hydrogen atom’s mass generation mechanism is a dynamic process. Good analogy would be hydrogen’s electron and proton producing magnetic fields due to their respective spins. Likewise, hydrogen atom’s mass is produced by a fluctuating electric dipole moment, due to combination of electric charges, their magnetic fields, and all associated angular momenta. All energies in the atom combine to produce its mass, because each energy present in hydrogen atom is, in principle, equivalent of some portion of its mass.
This resembles gravitomagnetism in a sense that when we use GTR’s equations in the weak field limit to describe gravity of spinning stars and planets, terms appear that are analogous to electric field, and to magnetic field. The electric terms correspond to the gravity that keeps our feet on the ground. The magnetic terms are wholly unfamiliar; we don’t sense them in everyday life.
If the electric terms correspond to the gravity that keeps our feet on the ground, then it could be due to hydrogen atom’s electric dipole moment being a measure of its mass as the cause of gravity.
In regards to the magnetic terms being wholly unfamiliar because we don’t sense them in everyday life, we think that this is due to magnetic fields being gravity’s propagation medium. We imagine gravity interactions making use of magnetic vortex tubes. It implies that gravity is a very complex phenomenon, much more so than magnetism, and not a fundamental force.
This is one remarkable correspondence, indeed. We believe that it validates our above supposition that notions of inertial mass, gravitational mass, and gravitational force are one and the same thing (the electric dipole moment) viewed, understood and interpreted from three different perspectives, in three different contexts. This finally allows us to always be able to answer the following fundamental question: What, specifically, does the notion of inertial mass, gravitational mass, or gravitational force, refer to in subatomic physical reality? Each of them, depending on its particular context, refers to the electric dipole moment, but only as this moment is embedded in an atom, because all energies in the atom combine to produce its mass and gravity, each energy present in hydrogen atom being, in principle, equivalent of some portion of its mass, which in turn contributes to producing gravity. In other words, it was our CONJECTURE 1, that there aren’t any such mass and gravity to be found in hydrogen atom that would be independent of atom’s electricity, magnetism, associated angular momenta (and whatever other forms of energy we could possibly find in the atom), and such that could exist in their absence, because any one of energies present in hydrogen atom is, in principle, equivalent of some portion of its mass.
The above shows direct correspondence between our concept of mass (vector) as the cause of the force of gravity, and the gravity as gravitomagnetism in the weak field limit equations of Einstein’s general theory of relativity. What a remarkable direct correspondence it is.
Could our quantum gravity conjecture constitute a basis for unifying quantum mechanics with the general theory of relativity?
8. CONCLUDING REMARKS
Quoting Prof. Donald C. Chang from his paper, A New Interpretation on the NonNewtonian Properties of Particle Mass,
As we pointed out above, Einstein’s 1905 paper did not predict the correct velocitydependence of mass. But today, we are taught that STR gave the right prediction. What is the justification for that? After the correct formula for the velocitydependence of mass became known from experiments, physicists gave up Einstein’s original argument from 1905 and used different ways to derive velocitydependence of mass, like for example in a widely used textbook, Special Relativity by A.P. French, which is part of the MIT Introductory Physics Series. The idea that radiation and matter behave similarly was a very interesting assumption. According to the Special Relativity textbook, this assumption was following the spirit of Einstein’s work. Indeed, in many papers written by Einstein, he frequently implied that the energy involved in radiation and the mass of matter are conceptually convertible. One may say that, in Einstein’s mind, mass is some sort of energy. Hence, although Einstein had published many papers on the derivation of nonNewtonian relations of mass, most of his derivations were not based on the principle of relativity. Instead, his theoretical arguments were based on various hypothetical thought experiments which frequently implied that radiation and matter behave similarly. Furthermore, some of these derivations were not free of flaws. One may conclude that the general acceptance of these “nonNewtonian relations” was not based on the soundness of theoretical arguments. Instead, as pointed out by A.P. French, “its real vindication is based on experimentally observed behavior of particles.”
Should the above presented evidence and arguments underlying our quantum gravity conjecture and its two predictions not be considered sound enough, we hope that, before being rejected offhand and forgotten, they would receive the benefit of the doubt until such time when official announcement of results from antihydrogen experiments at CERN is finally made.
Presently, the only experiment that might be in a position to give information on the sign of gravitational interaction between matter and antimatter is the ALPHA experiment, which might carry out such a measurement by the end of 2018.
More likely is the period between 2021 and 2024, when three experiments, ALPHAg, AEgIS, and GBAR should be in a position to carry out the measurement, because CERN’s accelerators are to be shut down in 2019 and 2020 for technical improvements.
We close by quoting 1937 Nobel Prize Laureate, Albert SzentGyorgyi,
Scientific discovery consists of seeing what everybody has seen, and thinking what nobody else has thought. Scientific discovery must be, by definition, at variance with existing knowledge. During my lifetime, I made two. Both were rejected offhand by the Popes of that field of science.
REFERENCES
 Einstein, A. (1905) Zur Elektrodynamik bewegter Körper. Annalen der Physik, 322, 891921. https://doi.org/10.1002/andp.19053221004
 Chang, D.C. (2017) What Is the Physical Meaning of Mass in View of WaveParticleDuality? A Proposed Model. arXiv:physics/0404044 [physics.genph]
 Einstein, A. (1931) Maxwell’s Influence on the Evolution of the Idea of Physical Reality. Published on the 100th anniversary of Maxwell’s birth in James Clerk Maxwell: A Commemoration Volume, Cambridge University Press. http://alberteinstein.info/vufind1/Record/EAR000045810
 Chang, D.C. (2018) A New Interpretation on the NonNewtonian Properties of Particle Mass. Journal of Modern Physics, 9, 215240. https://doi.org/10.4236/jmp.2018.92015