DOW-UAP-D152, AAWSAP DIRD, Negative Mass Propulsion, January 2011

This document is a Defense Intelligence Reference Document (DIRD), a technical reference format used by the Defense Intelligence Agency (DIA) to capture baseline knowledge on a specific topic for later analytic use. DIRDs are best understood as reference and synthesis products rather than as original research. It is one of 38 DIRDs produced under the Advanced Aerospace Weapon System Applications Program (AAWSAP) between 2009 and 2011. Because AAWSAP’s scope permitted a broad range of supporting topics, not every DIRD in the series directly concerns aerospace systems or future threat assessment. The following summary reflects the DIRD’s scope and framing at the time of writing and should not be read as implying current validation of the concepts discussed. This DIRD examines whether negative mass could exist in a physically meaningful way and whether it could someday reduce the energy cost of spaceflight. The report reviews the unusual dynamics that would follow if positive and negative mass could interact, including self-accelerating mass pairs and matter with very low or nearly zero effective inertia, and treats such ideas as at least formally compatible with certain extensions of gravitational theory. It then considers two broad paths toward practical use: creating or separating negative mass through extreme fields or particle energies, and locating naturally separated negative matter in deep gravitational wells such as galactic centers or possibly the Moon. However, the document also concludes that the first path is effectively beyond technical reach and treats the second as highly uncertain, resting on a long chain of unverified assumptions about the existence, separability, and macroscopic behavior of negative mass. Overall, this DIRD is a far-reaching theoretical exploration of an exotic propulsion concept whose practical application depends on premises that remain unestablished in consensus physics.

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Defense
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Reference
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Defense Futures
03 January 2011
ICOD 30 August 2010
DIA-08-1101-023
Negative Mass Propulsion
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Negative Mass Propulsion
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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
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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.
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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
Gravitational field Mass of test Motion of test
Case
producing mass particle 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 wou ld 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.
Case
-0
1 ttnu:tion
l
-0 -0
2
aellaeceleretlon
0-
3
-0 0--
4 repulsion
Figure 1. Forces
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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
ds2 = dr2 +r2(d02 +sin20dqi)-(l-2yM!c2r)c2dt2 (1)
2
l-2yM le r
can be extended to a negative mass, simply by replacing M with -M:
(2)
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.
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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 10-33 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]:
(3)
where rp =rp(r, z) and a= a(r, z) satisfy
a a a
( 2 1 2
- +--+- ) rp=O (4)
az
ar2 far 2
(5)
8<:Y = 2r arp arp
(6)
az ar az •
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Inserting (3-6) into Einstein's nonlinear gravitational field equations, one obtains four
nonlinear partial differential equations ( K
=S;r
y / c4 ) given by
(7)
(8)
(9)
arp arp aa
- KT.p =2--- r­ . (10)
- awoa% a%
In solving these equations Bondi assumes that <p is small, which then also implies that
because of (5) and (6) cr is small by the second order, reducing the solution of the
problem to the linear Laplace equation of the scalar Newtonian potential in empty space.
Making this assumption, Bondi can reproduce the uniform acceleration of the mass
dipole, as it is expected from an elementary analysis. It is here that we must disagree
with Bondi1, because it can be shown that the nonlinearity of the gravitational field
equation leads to a very different result. The nonlinearity also sheds light on why it is
so difficult to separate negative from positive masses, whereby negative masses are all
around us, but imprisoned by positive masses.
1 The author had the pleasure to meet Prof. Bondi on a common flight from Graz,
Austria in 1993 (we both are members of an academy which had a meeting in that
year in Graz), and ask him how his solution can be correct since it does not include
the field of the positive gravitational field mass of a mass dipole. This problem will
be analyzed in the next section, and its solution has far reaching consequences.
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3. Hund's Nonlinear Newtonian Theory of Gravity
As explained by Hund [3], already Newton's theory of gravity, in conjunction with the
postulates of special relativity, leads to a nonlinear theory of gravity. With this model
theory of gravity the nonlinearity of the gravitational field can be much better explained
than with Einstein's theory.
Hund begins with the force F acting on a mass m in a "merry-go-round":
mv
F=mg+-xG . (11)
C
If g is the gravitational acceleration by real masses with the density p, one has in
Newton's theory
divg =--4.nyp . (12)
In the merry-go-round g has a vertical component from the earth's gravitational field,
but also a radial component by the radial centrifugal acceleration which is not source­
lgl
free. With = alr, where m= 2TC/T, with T the time of revolution, and r the radial
distance from the center of the merry-go-round, one has
=
divg 2m2 . (13)
Comparing (13) with (12) one sees that the centrifugal force corresponds to a
gravitational repulsion of a homogeneous mass density
(14)
For a typical "merry-go-round" one has T = 10 sec, and hence, w =0.6s-1 For this
•
example one obtains from (14), µ = -106 glcm3 , taken as an absolute value about
equal to the mass density of a white dwarf.
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The mass density (14) is not fictitious but represents physical reality. According to
Einstein's E = mc2 one obtains for an electric field Ethe mass density
(15)
Replacing Eo with-(1/y), one obtains the energy density of the gravitational field
g 2
U=--<0. (16)
8ny
It possesses the (negative) mass density
g2
µ= - --, . (17)
8nyc
Besides the field g, we have on a "merry-go-round" the Coriolis force field
=
G 2cro. (18)
By setting G = g and inserting G into (17) with g2 = G2, one obtains the mass density
(14). This means the centrifugal force is the gravitational force associated with the
mass density of the Coriolis field.
But where is this huge negative mass coming from? The obvious answer is by the very
large vacuum energy, making itself felt by going to an accelerated frame of reference.
In Mach's principle the motion of the distant galaxies as seen in an accelerated frame of
reference is responsible for the inertial forces. But this idea is wrong because if by some
miracle the distant galaxies were to be set into motion, it would take a long time before
their fields propagating with the velocity of light would reach the earth.
Adding the mass of the Coriolis field to the right side of the equation (12), we have by
putting it on the left hand side
1
divF - - 2 c- -?G 2 = -41r '"1 I1 Ip . (19)
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In one further step one should have
divF-~(F2 +G2) = -4,ryp (20)
2c
or if G =0 and F = -'v¢, where ¢ is the Newtonian gravitational potential, one obtains
for Poisson's equation:
(21)
According to (21) the positive mass as the source of the Newtonian potential is reduced
by the negative mass of its field. (Einstein's theory leads to almost the same, except
that there the negative gravitational mass density is twice as large.) One can then write
(22)
The earth is therefore embedded in a sea of negative mass. Making the substitution
(23)
trans