UNCLASSIFIED/ /f^R O rrtC iA L U S E nN I Y 03 January 2011 Defense Intelligence Reference Document D efense Futures ICO D 30 A ugust 2010 D IA -08-1101-023 Negative Mass Propulsion UNCLASSIFIED//FOR OITICIAL USE ONLY UNCLASSIFIED//-FOR OFFICIAL USE QMhY Negative Mass Propulsion The Defense Intelligence Reference Document provides non-substantive but authoritative reference information related to intelligence topics or methodologies. Prepared by: Technology Warning Division (DWO-4) Defense Warning Office Directorate for Analysis Defense Intelligence Agency A uthor? AAP Person 72 Administrative Notes: (U) COPYRIGHT WARNING: Further dissemination of the photographs in this publication is not authorized. This product is one in a series of advanced technology reports produced in FY 2010 under the Defense Intelligence Agency, Defense Warning Office's Advanced Aerospace Weapon System Applications CAAWSAl Program. Comments or questions pertaining to this document should be addressed to | |AAP Person |AAP Person 1 ^AWSA Program Manager, Defense Intelligence Agency, ATTN: JUIAF - DI/DWO-3, i Bldg 6000, Washington, DC 20340-5100. il UNCLASSIFIED/ /FOR OFFICIAL U6i ONEY UN CLASSI FI ED//rOR OrriCIAL USE ONLY Contents 1. Introduction......................................................................................................2 2. The Theory by Bondi..........................................................................................4 3. Hund's Nonlinear Newtonian Theory of Gravity.................................................... 6 4. The Theory of Bondi Revisited.......................... 10 5. The Zitterbewegung Phenomenon as a Manifestation of Negative Masses.............10 6. Planck Aether Hypothesis................................................................................. 14 7. Dynamic Interpretation of Lorentz Invariance.............. ......................................18 8. Negative Mass Interpretation of the Aharonov-Bohm Effect.................................23 9. Negative Masses in Cosmology.........................................................................29 10. The Cusp/Core Problem in Galatic Halos..........................................................31 11. Searching for Negative Matter in the Gravitational Potential Well of the Moon.....32 12. Making a Tunnel through the Moon................................................................. 33 13. Conclusion..................................................................................................... 38 Figures Figure 1. Forces.....................................................................................................2 Figure 2. Translation of Mass Dipole.......................................................................11 Figure 3. Circular Motion of a Pole-Dipole Particle.................................................... 12 Tables Table 1. Interactions.............................................................................................. 2 iii UNCLASSI FIED//EQB OEEirTAI IISEfiNIY UNCLASSI FIED/ /fOR OmCIAL USE ONLY Negative Mass Propulsion Summary It is easy to prove that there are negative masses all around us, albeit hidden behind positive masses. But their use for propulsion by reducing the inertia of matter, for example in the limit of macroscopic bodies with zero rest mass, depends on a technical solution to free them from their imprisonment by positive masses. It appears that there are basically two ways this might be achieved: 1. By the application of strong electromagnetic or gravitational fields or by high particle energies; 2. By searching for places in the universe where nature has already done this separation, and from which the negative masses can be mined. The first of these two possibilities is for all practical means excluded, because if possible at all, it would depend on electromagnetic or gravitational fields with strengths beyond what is technically attainable, or on extremely large particle energies likewise not attainable. With regard to the 2nd possibility, it has been observed that non- baryonic cold dark matter tends to accumulate near the center of galaxies, or places in the universe which have a large gravitational potential well. Because of the equivalence principle of general relativity, the attraction towards the center of a gravitational potential well, produced by a positive mass, is for negative masses the same as for positive masses. Large amounts of negative masses might have over billions of years been trapped in these gravitational potential wells. Now it just happens that the center of the moon is a potential well, not too deep that it cannot be reached by making a tunnel through the moon, not possible for the deeper potential well of the earth, where the temperature and pressure are too high. Making a tunnel through the moon, provided there is a good supply of negative mass, could revolutionize interstellar space flight. A sequence of thermonuclear shape charges would be required to make such a tunnel technically feasible. 1 UNCLASSIFIED//FOR OFFICIAL USE ONLY UNCLASSI FIED/ /fOR OmCIAL USE ONLY 1. Introduction If we extend the law of gravity to negative masses, but hold onto the equivalence of inertial and gravitational masses, we have to distinguish between the following four cases, if a test particle is placed near a gravitational field producing mass (Table 1): Table 1. Interactions Case Gravitational field producing mass Mass of test particle Motion of test particle 1 + + attraction 2 + — attraction 3 — + repulsion 4 - — repulsion Under the principle of equivalence if a negative test mass particle would be placed in the gravitational field of earth, it would not fall upwards, as happens in science-fiction antigravity machines. A test particle, regardless of whether it has positive or negative mass, would there always fall down. It would fall upwards only if placed in the field of a large negative mass. A somewhat different situation arises if both masses, the field producing mass and the mass of the test particle, have the same absolute value but are permitted to have different signs. There we have to distinguish between the cases shown in Figure 1. 2 UNCLASSI FI ED//FOR OFFICIAL USE ONLY U N CLASSI FI E D//WR OFFICIAL USE ONLY If both masses are positive, we have the usual Newtonian attraction. For negative masses, the force has the same magnitude but is repulsive. A quite different situation exists if one mass is positive and the other one is negative. With both forming a mass dipole, the system becomes self-accelerating, because one mass is repelled and the other one attracted. With the two masses having opposite sign, the total energy and momentum of the combined system remains zero for all times, leaving intact the conservation laws of energy and momentum. Under its self-acceleration, the mass dipole would eventually reach the velocity of light. It is this property of self-acceleration without expenditure of energy that has intrigued many researchers and raised the prospect of a propulsion system without limits. We remark that even without an appreciable gravitational interaction, a mass dipole with zero, or close to zero inertial mass, could be accelerated to very high velocities with negligible jet power and energy. No matter how strange the properties associated with negative masses appear to be, there can be little doubt that they can be incorporated into Einstein's gravitational field theory as long as they do not violate the principle of equivalence. In particular, the well known Schwarzschild solution for a positive mass M dr2 ds2 =------------— + r2(d02 + sin2 0d< p2)-(1-2/M / c2r)c2dt2 (1) \-2yM I c‘r can be extended to a negative mass, simply by replacing M with -M : dr2ds2 =------ ------- + r2(dO 2 + sin2 0d(p2)-(l + 2yM /c2r)c2dt2, (2) 1 + 2yM / c r where y is Newton's constant. One therefore has to raise the question if nature has not made use of negative masses somewhere. Over and over again we have found that what is possible, within the framework of the fundamental laws of physics, exists. Only one important physical set of laws, Einstein's special theory of relativity appears to forbid the existence of negative masses. This is because in a relativistic quantum field theory the particle number is not a conserved quantity, and the existence of negative masses would make all matter unstable against decay into negative masses. 3 UNCLASSIFIED//FOR OFFICIAL USE ONLY UNCLASSI FI ED//WR OFFICIAL USE ONLY Apart from Einstein's purely kinematic interpretation of special relativity, being the expression of a Minkowskian space-time structure, there is an older alternative dynamic interpretation by Lorentz and Poincare. In it space and time are absolute, but it can explain all relativistic effects as well. It assumes the existence of an aether, with all objects in absolute motion through the aether suffering a Lorentz contraction and time dilation. If this aether has a grainy structure, characterized by some smallest length (e.g., the Planck length ~ IO-33 cm), then according to Heisenberg's uncertainty principle special relativity would ultimately break down at a high energy. If the length is very small, this energy can be so high as to be far beyond the capabilities of any existing particle accelerator or even beyond the high energy of cosmic ray particles, making both interpretations of special relativity experimentally indistinguishable at the energies presently available. 2. The Theory of Bondi The first attempt to introduce negative masses into general relativity to describe a mass dipole was made by H. Bondi [1]. For a uniformly accelerating mass dipole Bondi uses the axially symmetric metric by Weyl and Levi-Civita [2]: ^ 2 - e2< pdt\ela{dr + dz2) + r2d^J, (3) where (p = (p{r,z) and +V -^Pll = "^' = ^ = ^fe = ^^ d(pd(p da k T^ = 2 ——-r— 12 d% d% 5^0 (10) In solving these equations Bondi assumes that

— > c): = m + rcra) = m + rc Comparing (40) with (37) shows that 2m + rc = h and m /m + =r/rc. (41) (42) (43) 13 UNCLASSIFIED//FOR OFFICIAL USE ONLY UNCLASSI FI ED//WR OFFICIAL USE ONLY Experimentally, the electron is indistinguishable from a point. This would make r = 0. In reality its size must be finite but in principle can be very small. This means that m + (and|w”|) are likely to be very much larger than m . t has been conjectured by Hbnl and Papapetrou [5] that the electron is a pole-dipole particle where the surplus positive energy comes from the positive gravitational interaction energy of a very large positive m+mass with a likewise very large negative ffl'=-|ffl+ | mass. According to this hypothesis one would have for the electron rest mass energy 2 /Ki2 m c‘= — --- -. (44) r Combining (44) with (42) one can compute m + . The result is [5]: + I m eh m ~ 6 X i0^ § ' <45) larger by a factor 3.6x10“ times the mass of the proton. We therefore see that there are huge amounts of negative masses bound to positive masses in Dirac spinors. It shows that it cannot be a simple matter to free the negative masses from the positive masses. And it explains why the masses of the elementary particles are so much smaller than the Planck mass, m p ~ 10-5 g. 6. Planck Aether Hypothesis [7,8] We make here the proposition that the fundamental group is SU2, and that by Planck's conjecture the fundamental equations of physics contain as free parameters only the Planck length rPl the Planck mass m P and Planck time tp (y Newton's constant, h Planck's constant, c the velocity of light): UNCLASSI FI ED//FOR OFFICIAL USE ONLY 14 U N CLASSI FI E D//WR OFFICIAL USE ONLY The assumption that SU2 is the fundamental group means that nature works like a computer with a binary number system. Since SU2 is isomorphic to SO3, the rotation group in R3, this explains why natural space is three-dimensional. The Planck's aether conjecture is the assumption that the vacuum of space is densely filled with an equal number of positive and negative Planck mass particles, with each Planck length volume on the average occupied by one Planck mass, with the Planck mass particles interacting with each other by the Planck force over a Planck length, and with Planck mass particles of equal sign repelling and those of opposite sign attracting each other. The particular choice made for the sign of the Planck force is the only one that keeps the Planck aether stable. While Newton's action-reaction remains valid for the interaction of equal Planck mass particles, it is violated for the interaction of a positive with a negative Planck mass particle, even though globally the total linear momentum of the Planck mass plasma is conserved, with the recoil absorbed by the Planck aether as a whole. It is the local violation of Newton's action-reaction which leads to quantum mechanics at the most fundamental level, as can be seen as follows: Under the Planck force F^ =m c2 / rp, the velocity fluctuation of a Planck mass particle interacting with a Planck mass particle of opposite sign is &v = {^ plm p^ tp=(c2lrp^ (rp/c} = c, and hence yields the momentum fluctuation Ap = m pc. But since Aq = rp and because m prpc = h, one obtains Heisenberg's uncertainty relation ^ p^ q = h for a Planck-mass particle. Accordingly, the quantum fluctuations are explained by the interaction with hidden negative masses, with energy borrowed from the sea of hidden negative masses. 15 UNCLASSIFIED//FOR OFFICIAL USE ONLY U N CLASSI FI E D//WR OFFICIAL USE ONLY According to Newtonian mechanics and Planck's conjecture, the interaction of a positive with a negative Planck-mass particle leads to a velocity fluctuation ^ =a t =c with a displacement of the particle equal to < 5 = (\/2}apP = rp/2 , where ap = Fp/m p . Therefore, a Planck-mass particle immersed in the Planck aether makes a stochastic quivering motion (Zitterbewegung) with the velocity ''o=-(';c/2)W«)- (46) where n = l/rp is the average number density of positive or negative Planck mass particles. The kinetic energy of this diffusion process is given by I 2 J I 8 J P I « J J™ JI«J (47) Putting v = —VS m p (48) where S is the Hamilton action function and v is the velocity of the Planck aether, the Lagrange density for the Planck aether is L-n ,dS h2 h— +---- dt 2m p (vs2)+ u+— (— ' ' 8m„ I n Vn (49) Variation of (49) with regard to S according to 4— a^S/a/ J dt[dS/dr) leads to —+ —V(WS) = 0 dt m „ (50) (51) 16 UNCLASSI FI ED//FOA OFFICIAL USE ONLY U N CLASSI FI E D//WR OFFICIAL USE ONLY or —■ + V(nv) = 0 dt ' (52) which is the continuity equation of the Planck aether. Variation with regard to n according to (dL\ dL drydn^ dr = 0 (53) leads to i 55 rrh — + 1/ + dt h2 2mP h2 4mP If E^ 2 \ n \ V2n = 0 n (54) or ,dS .. h— + U dt h2 2^ P ^^ = 0. n (55) With the Madelung transformation yj=^ ne , y/ -\ine -iS (56) one obtains from (51) and (55) the Schrodinger equation -.5^ - zn — dt h2 2m -V2^/ + [/(// (57) In the Planck aether hypothesis all particles, save and except the Planck mass particles, are quasi-particles of the Planck aether, like the phonons, rotons, excitons, etc., of condensed matter physics, and by the wave structure of the Planck aether are Lorentz invariant. In forming quantized vortices, the Planck aether also has vortex waves, simulating Maxwell's and Einstein's electromagnetic and gravitational waves. Dirac spinors are made possible by the negative masses of the Planck aether. 17 UNCLASSIFIED//FOR OFFICIAL USE ONLY UNCLASSI FI ED//WR OFFICIAL USE ONLY Quantum mechanics predicts for each harmonic oscillator the zero-point energy (l/2)h . (58) Now (58) turns out to be just the only spectrum that is Lorentz invariant. But the spectrum (58) is also the only one which does not lead to a friction force on a charged particle moving through an electromagnetic spectrum with this frequency dependence. This means that special relativity is a consequence of quantum mechanics, leading to the zero point vacuum energy, and can be interpreted by saying that the zero-point vacuum energy "generates" the Minkowski space-time. 7. Dynamic Interpretation of Lorentz Invariance A cut-off at the Planck frequency generates a distinguished reference system in which the zero-point energy spectrum is isotropic and at rest. In this distinguished reference system, the scalar potential from which the forces are to be derived satisfies the inhomogeneous wave equation: 1 52® , —7-7+V-0=4^(r,/), (59) c dr where p(r,t) are the sources of this field. For a body in static equilibrium at rest in the distinguished reference system for which the sources are those of the body itself one has V2O = -4^(r). (60) If set into absolute motion with the velocity v along x-axis, the coordinates of the reference system at rest with the moving body are obtained by the Galilei transformation: 18 UNCLASSI FI ED//FER OFFICIAL USE ONLY U N CLASSI FI E D//WR OFFICIAL USE ONLY x' = x-vt, yf = y, z’ = z, t' = t transforming (59) into 1 gO^ 2v ^G1 f._£W (^ 6^ c2 dt'2 c2 dx'dt' k c2) dx'2 dy'2 dz2 (61) = -4^(r',f). (62) After the body has settled into a new equilibrium in which d/dt' = O , one has instead of (60) L v2Vo' a2®' a2®' . , 1— 7 —t+ — r^ ^ - = -^ p(x ,y,z). , c2Jdx'2 dy2 dz2 (63) Comparison of (63) with (60) shows that the left-hand side of (63) is the same if one sets 0' = ® and dx' = dx^ {^ Jc2. This implies a uniform contraction of the body by the factor ^1 -v2/c2 because the sources are contracted by the factor ^1—v2/c2 as well, whereby the right-hand side of (63) becomes equal to the right-hand side of (60). Since the zero-point energy is invariant under a Lorentz transformation, the quantum potential changes in the same way as O . The body therefore sustains its static equilibrium under a contraction by the factor ^1—v2/c2 if set into absolute motion, explaining the Lorentz contraction dynamically. The clock retardation effect can be derived from the contraction effect, and from there the Lorentz transformation. Following Builder [9] this original interpretation of Lorentz invariance by Lorentz and Poincare has been worked out in every detail by Prokhovnik [10]. To derive the clock retardation effect from the contraction effect one considers a light clock, which is a rod with mirrors attached to its two ends in between which a light signal is sent forth and back. If the length of the rod is I, and if the rod rests in the distinguished reference system, the time needed for the light signal to be sent forth and back is 19 U NCLASSI FIE D//FOR OFFICIAL USE ONLY U N CLASSI FI E D//WR OFFICIAL USE ONLY ?o = 2//c. (64) If prior to being set into motion the rod is inclined against the x-axis by the angle (p, it appears to be inclined against the x-axis by the different angle y after set into motion, with y expressed through

(65) / = (1 —v/c") . The absolute motion then contracts the rod from / to /': /' = / Jl -(v2 / c2)cos2 (p = — . . (66) /^l-(v2 /c^sin2^ Relative to the moving rod the velocity of light is anisotropic, and for the to and fro directions given by c^ -^ c -v sin jy-vcos^ n — < 67> c_=^c -v sin i/+vcosj/ with the time t' for a to and fro signal given by f = r/c+ + r/c_=yt0. (68) Therefore, as seen from an observer at rest in the distinguished reference system the clock goes slower by the factor/ = l/Vl-v2 /c2, independent of the inclination of the rod making up the clock. With solid bodies held together by electromagnetic forces, clocks made from solid matter should behave like light clocks. As it was claimed by Poincare, it should for this reason be possible to obtain the Lorentz transformations solely from the contraction effect with a proper convention about the synchronization of clocks. According to Einstein, two clocks, A and B, are synchronized if 20 UNCLASSI FI ED//FOR OFFICIAL USE ONLY U N CLASSI FI E D//WR OFFICIAL USE ONLY fS=^+^- (69) where t\ is the time a light signal is emitted from A to B, reflected at B back to A, arriving at A at the time tA, and where it is assumed that the time fBat which the reflection at B takes place is equal to the arithmetic average of tA and tA. Only by making this assumption does the velocity of light turn out always to be isotropic and equal to c. From an absolute point of view, the following rather is true. If tR is the absolute reflection time of the light signal at clock B, one has for the out and return journeys of the light signal from A to B and back to A, if measured by an observer in an absolute system at rest in the distinguished reference system: y(tR~ tA) = d/c+ z 2 x n ' (70’ y(t~ A-tR)=d/c_ where d is the distance between both clocks, and where c+and c_are given by (67). Adding the equations (70) one obtains c(d “ ^) = 2yd^l-(v2/c2)sin V ■ (71) If an observer at rest with the clock wants to measure the distance from A to B, he can measure the time it takes a light signal to go from A to B and back to A, If he assumes that the velocity of the light is constant and isotropic in all inertial reference systems, including the one he is in, moving together with A and B with the absolute velocity v, the distance is d' = (c/2)(t2A-t\y (72) And because of (71) d' = yd^l-(v2/c2)sin2^ . (73) 21 UNCLASSIFIED//FOR OFFICIAL USE ONLY UNCLASSI FI ED//WR OFFICIAL USE ONLY Comparing this result with (66), one sees that he would obtain the same distance d', if he uses a contracted rod as a measuring stick, or Einsteins's constant light velocity postulate. The velocity of light between A and B by using a rod to measure the distance and the time it takes a light signal in going from A to B and back to A, of course, will turn out to be equal to c, because according to (72) Id' = f74’ lA ‘A Rather than using a reflected light signal to measure the distance d', the observer at A may try to measure the one-way velocity of light by first synchronizing the clock B with A and then measure the time for a light signal to go from A to B. However, since this synchronization procedure also uses reflected light signals, the result is the same. For the velocity he finds cT _ 2