## ALPHA

Geometrodynamic engineering will enable mastering the fundamental force of gravitational interaction via the ability to technologically shape the geometry of spacetime. Just as technological control of the electromagnetic interaction reshaped human civilization in the 20^{th} century (electromagnetic generators, motors, light bulbs, and wireless communication), gravity control technology will reshape nearly every facet of our current civilization, from limitless engines to energy production, to gravitational-based wireless communications technology. Modulating the spacetime metric to cause a local negative energy density, like in the Casimir effect, causes a negatively curved or “expanding” spacetime geometry resulting in an accelerative force opposite in orientation to positively curved spacetime—if positively curved spacetime geometry causes objects to accelerate “down” then a negatively curved spacetime geometry will cause objects in that field to accelerate “up”. Positively curved spacetime is what we experience under normal conditions like the force holding us to the surface of Earth.

When an expanding region of the vacuum resulting from negatively curved spacetime geometry is set diametrically opposite a region of contracting vacuum from positively curved spacetime, with a flat metric in the intervening space between the expanding and contracting regions, a gravitational dipole or spacetime bubble is generated. An engine capable of inducing a gravitational dipole is called a warp drive, and the resulting spacetime bubble is called a warp drive metric. Conventionally, it is assumed that only some form of exotic matter—presumably with a negative mass-energy—can induce an expanding spacetime and the “repulsive” gravitational interaction associated with such a negatively curved spacetime geometry. There was a small hope that antimatter might behave as “exotic matter” and have a negative mass-energy that would cause such an expanding, negatively curved spacetime geometry. If so, antimatter could be used to generate a gravitational dipole and therefore would have been a plausible route to engineering spacetime with warp field mechanics. Now, that small hope has been dashed with recent experiments that have measured the gravitational interaction of antimatter and have found that it appears to respond to the gravitational field just as “normal” matter does.

In an experiment published in Nature [1], the ALPHA collaboration at CERN’s Antimatter Factory have shown that, within the precision of their experiment, atoms of antihydrogen—a positron orbiting an antiproton—experience the force of the gravitational interaction in the same way as their matter equivalents. A long sought after result, the observation of a gravitational effect on the motion of antimatter finally answers the question “does antimatter ‘fall’ up?” The results of the experiment are significant for furthering our understanding of the nature of gravity and verifying some facets of Einsteinian gravity, like the principle of equivalence. Although some might see the result as a near-terminal strike against any hopes of “antigravity”, the results of the measurement of the gravitational acceleration of the antiproton does not rule out potential non-Newtonian, non-Einsteinian, and/or a large anomalous gravitational response for the antiporoton. Even more importantly, however, is that the results of this remarkable experiment do not dash mankind’s aspirations for a warp drive technology because although initial solutions to warp field metrics imply a necessity for negative energy or repulsive-gravitational action, which it is assumed would require some for of exotic matter, A role that some postulated antimatter may have been able to fulfill, Additionally, there are other novel ways—that we will explore—to generate gravitational dipoles and geometrodynamically engineer warp drive metrics.

## A speculative candidate for warp field engineering

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```Anybody who is not focused on new physics is not taking interplanetary travel seriously.

Eric Weinstein

The Alcubierre warp drive metric, developed by physicist Miguel Alcubierre in 1994, demonstrated that general relativity permits the construction of a gravitational dipole, or warp field, in which solutions of Einstein’s field equations describe a unique spacetime geometric configuration, or metric, that enables arbitrarily fast transit—even superluminal—without locally violating the speed of light. There is a class of spacetime geometries that effectively permit faster-than-light travel without relativistic violations; comprised of wormholes, the Krasnikov tube [2], and the Alcubierre bubble. With the Alcubierre bubble (i.e., warp drive metric), spacetime geometry is engineered around an object—generating the gravitational dipole / warp bubble architecture—so that while the object itself in its own frame of reference can be veritably stationary (not traveling faster than light) it still arrives at its destination more quickly than light would in normal space without breaking any physical laws [3].

While “negative energy” may sound like an exotic or even self-contradictory thing, it is germane to consider that there are known conditions in which the Weak Energy Condition is violated, and negative energy densities are extant. In the laboratory, this can be achieved via the Casimir effect or the quantum energy teleportation protocol, while naturally occurring instances are found in the ergospheres of black holes—resulting in the Penrose process and superradiance, which is one reason why quasars are one of the most luminous objects in the universe. Similar to negative energy that causes an expanding spacetime geometry, there is dark energy that while not being considered as a negative energy does have similar effects. Cosmology’s current Cosmic Energy Inventory list approximately 72% of the Universe as being comprised of dark energy [4] (the more recent Planck spacecraft observations of the cosmic microwave background have given an estimate of 68.3% dark energy, 26.8% dark matter, and 4.9% ordinary matter), a putative energy that is thought to be driving the accelerating expansion of the universe via a negative pressure. It has been proposed that if antimatter had an opposite gravitational interaction (a negative gravitational charge) then virtual gravitational dipoles—of particle-antiparticle pairs of quantum vacuum fluctuations—could account for the cosmological constant and dark energy density [5]. However, when the accelerating expansion is taken to be the result of the quantum vacuum energy density [6, 7] then a cosmological fluid with negative pressure is not required to explain the observed behavior.

It is tempting to think that antimatter would have negative mass and anti-gravitate, such that an anti-apple would fall *up *in Earth’s gravitational field. However, antimatter is perhaps an unfortunate word choice to describe what is just a form of mirror symmetric matter: like how it would not make sense to arbitrarily call a left hand an “anti-hand” and a right hand a “normal hand”, because despite any subjective bias, they are both just hands with mirror symmetry. It could be considered that true “anti-matter” would be as Dirac originally conceptualized it, a “hole” or vacancy in a sea of virtual particles—what today we call the quantum vacuum particle flux—and, indeed, such a condition would have a negative energy density (relative to the ambient vacuum energy density) causing it to have the kind of negative spacetime curvature that results in an opposite gravitational interaction than that of positive energy density with positively curved spacetime.

Now, thanks to the work of the ALPHA team of researchers at CERN’s antimatter factory it is no longer necessary to speculate on the nature of neutral antimatter’s interaction with the gravitational field of matter, as it has been empirically shown that the interaction is not repulsive, or in other word the results indicate that neutral antimatter has an attractive acceleration in Earth’s gravitational field just as matter does. The experiment found that the local gravitational acceleration of antihydrogen is directed toward the Earth and has a magnitude of approximately 0.75*g*, where *g *= 9.81 m*s^{-2}. Although this value appears to indicate that antihydrogen has a *lower *accelerative attractive force—being at 75% of 1*g*—the experimenters assert that within the stated errors of statistical analysis the value is consistent with a downward gravitational acceleration of 1*g *for antihydrogen (since the experiment is based on the behavior of a few hundred anti-atoms there is significant statistical variability). Additional experimentation will be required to obtain more precise results and determine if the seemingly reduced response of 0.75*g *is within statistical variability of the experiment or if it may potentially be indicating some kind of non-Newtonian, non-Einsteinian, and/or a large anomalous gravitational response for the antiporoton, which would point the way to new physics and answer questions like “does the universe prefer ‘right’ to ‘left’?” (as some studies have indicated may be the case).

To obtain these empirical values the research team utilized the ALPHA-g machine, which is a vertically oriented antihydrogen trap designed to study gravitation. With ALPHA-g, the team was able to trap and accumulate (neutral) atoms of antihydrogen and slowly release them by opening the top and bottom “barrier potentials” of the vertical trap. Since the accumulated antihydrogen is a cold gas, there will be some proportion that diffuse out of the top as well as the bottom of the trap. However, any attractive force arising from interaction of the neutral antimatter with the Earth’s gravitational field will bias the antihydrogen atoms to fall through the bottom of the trap. By counting the number of atoms that fall through the bottom versus the top, the researchers could quantify this bias.

Numerical simulations of atom trajectories had indicated that if hydrogen atoms were trapped and gradually released from a vertically symmetric trap then under ALPHA-g conditions about 80% of them would exit through the bottom, the asymmetry being due to the downward force of gravity. When this test was run (repeatedly) with antihydrogen observation matched the numerical simulation of what would be expected for hydrogen and the statistical analysis confirmed that the antihydrogen atoms preferentially fall through the bottom of the trap and, hence, have a positive acceleration in Earth’s gravitational field, as opposed to a putative repulsive “anti-gravitational” acceleration. This result rules out cosmological models that postulate repulsive gravitational interaction between matter and antimatter as well as proposals for utilizing putative negative gravitational mass of antimatter for warp field engineering of superluminal space drives.

_{Figure 1. Empirically derived escape curve (from experimental data) and predicted curves from simulations. The experimental data most closely (though not exactly) matches the curve generated from simulations in which there is a positive gravitational interaction—biasing the escape trajectories to the bottom of the trap over the top of the trap. The experimental data does not match simulations of repulsive gravitational interaction at all. Image from [1]. }

## The Equivalence Principle Holds True

In the general theory of relativity, the equivalence principle, also known as the weak equivalence principle (WEP) requires that all masses react identically to gravity, independent of their internal structure (assuming that all masses are positive). While anti-particles are mirror symmetric to particles, the mirror symmetry is still a positive mass-energy, and hence anti-particles should interact with gravity as per the WEP, i.e., identical to particles. The recent experiment with ALPHA-g seems to confirm this as antihydrogen gas was observed to behave in a way consistent with gravitational attraction to the Earth. As such, speculation about a possible repulsive ‘antigravity’ of antimatter is ruled out in this case and the experiment opens opportunities for precision studies of the magnitude of the gravitational acceleration between anti-atoms and Earth to further test the WEP.

Historically, there are actually two kinds of masses that are described, the inertial mass, which relates to how much force is required to change the velocity of an object, and gravitational mass, which corresponds to how a mass responds in a gravitational field. The Equivalence principle holds that these two masses are one-and-the-same, as for example, an acceleration at 1*g* induces the exact same force as the gravitational field of Earth at its surface. If properly masked, a test candidate would be unable to distinguish between a 1*g* force induced by acceleration, say in a ship, or induced by Earth’s gravitational field at the surface. Hence, the inertial and gravitational masses are equivalent. It was already known that antimatter has a positive inertial mass, this was deduced by its response to induced acceleration. However, in the absence of experimental data it was a theoretically open question whether antimatter also had a positive gravitational mass. Now, this has been experimentally probed and it appears that there is a statistically significant indication that the gravitational mass is positive, and indeed the equivalence principle is upheld (and general relativity survives yet another test).

## CPT Symmetry

If it was found that antihydrogen has an anomalous response to Earth’s gravitational field that could have offered insight into the charge, parity, and time reversal symmetry of our universe. According to this CPT symmetry, in a “mirror-image” of our universe — with all objects having their polarity reversed or spins flipped (corresponding to a parity inversion), all momenta reversed (corresponding to a time inversion) and with all matter replaced by antimatter (corresponding to a charge inversion) — it would evolve the same and be otherwise indistinguishable from our “mirror” universe (the CPT transformation turns our universe into its “mirror image” and vice versa). Since CPT symmetry is recognized to be a fundamental property of physical laws, any violation of this principle would be a fundamental deviation from standard theory and point to new physics.

Deviations in CPT symmetry, that may be observed in behaviors of antimatter—but apparently not so in its gravitational interaction as is now known—can answer some primary questions in physics and cosmology, such as: “where is all the antimatter?”. Indeed, the senior researcher of the group at CERN’s ALPHA lab, Prof. Jeffrey Hangst, calls this “question zero”. When energy combines to form matter, like in the Breit-Wheeler process, conservation laws and CPT symmetry stipulate that matter is produced with equal proportions of chirality, that is equal amounts of matter to antimatter. In conventional theory, it is thought that the universe is dominated by matter, but if baryonic matter formed from the energy of big bang, then it should be in equal proportions matter and antimatter, protons and antiprotons, leading many to ask where then is all the antimatter?

While experiments like this latest measurement of the acceleration of antihydrogen in Earth’s gravitational field can potentially reveal asymmetries in the behavior of antimatter as compared to matter, and hence offer insights into problems like “question zero”, we might point out here that even within the standard model the baryon is filled with near-equal amounts of quarks and antiquarks (mostly as pions, which gives the baryon its mass), and even the electron is surrounded by a cloud of virtual electron-positron pairs. So, the antimatter is there, it is a constituent of “normal” matter! Still, it is interesting to consider questions of CPT symmetry because we can address questions like: what happens if time runs backwards? or is right better than left? (in the biological system, “right handed” nucleic acids are preferred to “left handed” ones and vice versa for amino acids, such that chiral molecules are very important to the living system, and seeming to indicate some fundamental preference for “right” versus “left”).

## Unified Science In Perspective

From the results of the paper *The Origin of Mass and the Nature of Gravity* [8], we see that a baryon’s rest mass-energy, like the proton, arises from the decoherence of collective quantum vacuum fluctuations (QVFs) and the pressure exerted by the collective QVFs results in confinement forces as the pressure forces are screened resulting in an energy gradient from the color force to the residual strong force, and gravitational force going beyond the nuclear scale (therefore unifying confining forces with the gravitational force emerging from the curvature of spacetime induced by quantum vacuum fluctuations). Within the conventional model this binding energy is hypothesized to emerge from a quark-antiquark confinement (so that the baryon mass arises from Pion confinement). Since an antiproton will have confinement force generated in the same way, that is via a strong gravitational interaction as demonstrated in *The Origin of Mass and the Nature of Gravity*, except with different polarity of the Planck Plasma flow (resulting in opposite chirality to the alternative proton configuration) it would be expected *a priori* that the antihydrogen atom has the same gravitational interaction as the proton, that is attractive and not repulsive—otherwise the anti-proton would not be internally stable and would explosively disintegrate because the confinement forces (as shown to be unified with gravity) would become anti-binding forces. Logically, this configuration is non-physical, and you cannot get matter from repulsive gravity, leaving again rarefied regions of the quantum vacuum energy density (i.e., “holes”) as the only candidates for a repulsive interaction or negatively-gravitating force.

Moreover, the assertion that a warp drive requires exotic matter or even negative energy densities is erroneous. It has been shown that superluminal motion sourced from purely positive energy densities—like the stress-energy of a conducting plasma and classical electromagnetic fields—are feasible [9], and studies have shown that there are positive energy warp drive solutions that can be derived from hidden geometric structures [10]. Hence superluminal mechanisms are possible even from a conventional physics perspective.

When amendments to Einstein’s general relativity are considered, specifically the inclusion of spin and torsion effects as in the Haramein-Rauscher solution to Einstein field equations [11] and the Einstein-Cartan theory [12], it is evident that within a vortex gravitational field novel spacetime geometries, like a gravitational dipole or even an Einstein-Rosen bridge [13], are possible without negative energy densities (without violation of the weak energy condition or null energy conditions) and without the need for negative mass-energy or a negative gravitational interaction that some hoped would be present in antimatter—before the ALPHA-g experiment demonstrated otherwise.

Weak energy condition violation, like negative mass-energy of exotic matter or negative energy densities of the Casimir effect type, are not absolutely required for a warp field spacetime configuration when spacetime torsion is factored in as in the Haramein-Rauscher solution and Einstein-Cartan theory. Solutions that appear exotic in general relativity are less peculiar when spacetime torsion, or spin, exists as an extra degree of freedom. Spin, therefore, becomes a significant consideration in engineering spacetime for gravity control, and warp drive mechanics—while still seemingly far from practical realization—do not necessarily require exotic mass-energy configurations, which is a hopeful aspect of ultimately developing interstellar travel technological capabilities.

## Addendum

An important note on much needed clarification regarding the physics of interstellar travel and the erroneous necessity of warp drives: it is often stated that some form of warp drive or spacetime “shortcut” technology is absolutely required if there is to be any hope of traveling interstellar distances, which are measured in light-years and parsecs. It is erroneously stated, for example, since our closest neighbor Alpha Centauri is 4.2 light years away that even if we could travel at the speed of light (often denoted as *c*), it would take 4.2 light years to get to our nearest stellar neighbor. This is wrong. The distance to any stellar system can be made arbitrarily short by approaching velocities closer and closer to the speed of light, which under such conditions there is time dilation and space contraction, so clocks in the traveler’s accelerated frame-of-reference “tick” significantly slower and distances are significantly shorter as compared to a frame of reference “at-rest”. So, if there was a technological means to approach the speed of light—which is in no way forbidden or otherwise prevented within orthodox theory—then any distance can be traversed in arbitrarily short time intervals.

The problem, if one wanted to frame it as such, is when that transit time is compared to the proper time for Earth (assuming one is traveling from Earth to another stellar system). Then, while a cosmic voyager traveling close to the speed of light may have experienced only mere moments of transit time to reach a neighboring star system, hundreds to thousands of years may have passed for Earth. This makes a return voyage essentially time-travel into the far future of Earth. For some, this may be problematic, as experiencing the non-linear nature of time is a whole ancillary voyage aside from traveling in “space” for some “distance”, but time-travel is an indelible facet of traveling in *spacetime*, where any transit in space is a transit in time.

This is where the idea of the warp drive comes into play, it is a hypothetical means to enable a spacetime shortcut such that distances can be traveled in arbitrarily short time periods without the “penalty” of extreme time dilation and resulting time travel into the future (from the relative perspective of an observer’s proper time in an inertial, non-accelerated, frame of reference). Essentially, this is achieved because superluminal velocities in general relativity enable travel “backwards” in time. However, the main impetus for developing a warp drive is not for superluminal travel *per se*, but the associated geometrodynamic engineering that is part-and-parcel to warp drive mechanics and hence the technological ability of gravity control. With gravity control, interstellar travel becomes possible not just because of the potential for superluminal warp craft, but because the gravitational dipole is the most feasible method for interstellar travel even if only approaching light speed velocities. Indeed, gravity control devices may be the ultimate form of propulsion mechanism. Chemical-based propulsion and even nuclear-based propulsion are not feasible modalities of generating thrust for interstellar transit unless one accepts transits on the order of a human lifetime to tens-of-thousands of years: At 0.1*c*, an Orion nuclear-powered starship would require 100 years—as measured within Earth’s proper time—to travel 10 light years, and considering actual technological capabilities of mankind the fastest man-made object—the Parker Space Probe—would take approximately 6,500 years to reach Alpha Centauri (~4.2 light years away).

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