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NASA Technical Reports Server (NTRS) - Anomalous Thrust Production from an RF Test Device Measured o

BRETT

Paranormal Novice
NASA Technical Reports Server (NTRS) - Anomalous Thrust Production from an RF Test Device Measured on a Low-Thrust Torsion Pendulum
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Anomalous Thrust Production from an RF Test Device Measured on a
Low-Thrust Torsion Pendulum
NTRS Full-Text: Click to View [PDF Size: 11 KB]
Author and Affiliation:Brady, David(NASA Johnson Space Center,
Houston, TX, United States);
White, Harold G.(NASA Johnson Space Center, Houston, TX, United
States);
March, Paul(NASA Johnson Space Center, Houston, TX, United States);
Lawrence, James T.(NASA Johnson Space Center, Houston, TX, United
States);
Davies, Frank J.(NASA Johnson Space Center, Houston, TX, United
States)
Abstract:This paper describes the eight-day August 2013 test campaign
designed to investigate and demonstrate viability of using classical
magnetoplasmadynamics to obtain a propulsive momentum transfer via the
quantum vacuum virtual plasma. This paper will not address the physics of
the quantum vacuum plasma thruster, but instead will describe the test
integration, test operations, and the results obtained from the test
campaign. Approximately 30-50 micro-Newtons of thrust were recorded from
an electric propulsion test article consisting primarily of a radio
frequency (RF) resonant cavity excited at approximately 935 megahertz.
Testing was performed on a low-thrust torsion pendulum that is capable of
detecting force at a single-digit micronewton level, within a stainless
steel vacuum chamber with the door closed but at ambient atmospheric
pressure. Several different test configurations were used, including two
different test articles as well as a reversal of the test article
orientation. In addition, the test article was replaced by an RF load to
verify that the force was not being generated by effects not associated
with the test article. The two test articles were designed by Cannae LLC
of Doylestown, Pennsylvania. The torsion pendulum was designed, built, and
operated by Eagleworks Laboratories at the NASA Johnson Space Center of
Houston, Texas. Approximately six days of test integration were required,
followed by two days of test operations, during which, technical issues
were discovered and resolved. Integration of the two test articles and
their supporting equipment was performed in an iterative fashion between
the test bench and the vacuum chamber. In other words, the test article
was tested on the bench, then moved to the chamber, then moved back as
needed to resolve issues. Manual frequency control was required throughout
the test. Thrust was observed on both test articles, even though one of
the test articles was designed with the expectation that it would not
produce thrust. Specifically, one test article contained internal physical
modifications that were designed to produce thrust, while the other did
not (with the latter being referred to as the "null" test article). Test
data gathered includes torsion pendulum displacement measurements which
are used to calculate generated force, still imagery in the visible
spectrum to document the physical configuration, still imagery in the
infrared spectrum to characterize the thermal environment, and video
imagery. Post-test data includes static and animated graphics produced
during RF resonant cavity characterization using the COMSOL Multiphysics®
software application. Excerpts from all of the above are included and
discussed in this paper. Lessons learned from test integration and
operations include identification of the need to replace manual control of
the resonant cavity target frequency with an automated frequency control
capability. Future test plans include the development of an automatic
frequency control circuit. Test results indicate that the RF resonant
cavity thruster design, which is unique as an electric propulsion device,
is producing a force that is not attributable to any classical
electromagnetic phenomenon and therefore is potentially demonstrating an
interaction with the quantum vacuum virtual plasma. Future test plans
include independent verification and validation at other test facilities.
Publication Date:Jul 28, 2014
Document ID:20140006052 (Acquired Jun 03, 2014)
Subject Category:MECHANICAL ENGINEERING
Report/Patent Number:JSC-CN-30345
Document Type:Conference Paper
Meeting Information:AIAA/ASME/SAE/ASEE Joint Propulsion Conference; 50th;
28-30 Jul. 2014; Cleveland, OH; United States
Meeting Sponsor:American Inst. of Aeronautics and Astronautics;
Washington, DC, United States
American Society of Mechanical Engineers; Naperville, IL, United States
Society of Automotive Engineers, Inc.; Warrendale, PA, United States
American Society for Electrical Engineers; United States
Financial Sponsor:NASA Johnson Space Center; Houston, TX, United States
Description:1p; In English
Distribution Limits:Unclassified; Publicly available; Unlimited
Rights:No Copyright
NASA Terms:ANOMALIES; CAVITY RESONATORS; LESSONS LEARNED; LOADS (FORCES);
LOW THRUST; MAGNETOPLASMADYNAMICS; MOMENTUM TRANSFER; PENDULUMS;
PROPULSIVE EFFICIENCY; RADIO FREQUENCIES; THRUST AUGMENTATION; TORSION;
VACUUM CHAMBERS; VACUUM TESTS
Availability Notes:Abstract Only
 

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Constance

Paranormal Adept
"Test results indicate that the RF resonant cavity thruster design, which is unique as an electric propulsion device, is producing a force that is not attributable to any classical electromagnetic phenomenon and therefore is potentially demonstrating an interaction with the quantum vacuum virtual plasma. Future test plans include independent verification and validation at other test facilities."
Please update us on any further developments, and thank you for posting this.
 

Charlie Prime

Paranormal Adept
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Might as well go big...

Eagleworks Laboratories: Advanced Propulsion Physics Research
Dr. Harold “Sonny” White, Paul March, Nehemiah Williams, William O’Neill
NASA Johnson Space Center
Houston, TX
ABSTRACT
NASA/JSC is implementing an advanced propulsion physics laboratory, informally known as
"Eagleworks", to pursue propulsion technologies necessary to enable human exploration of the solar
system over the next 50 years, and enabling interstellar spaceflight by the end of the century. This work
directly supports the "Breakthrough Propulsion" objectives detailed in the NASA OCT TA02 In-space
Propulsion Roadmap, and aligns with the #10 Top Technical Challenge identified in the report. Since the
work being pursued by this laboratory is applied scientific research in the areas of the quantum vacuum,
gravitation, nature of space-time, and other fundamental physical phenomenon, high fidelity testing
facilities are needed. The lab will first implement a low-thrust torsion pendulum (<1 uN), and commission
the facility with an existing Quantum Vacuum Plasma Thruster. To date, the QVPT line of research has
produced data suggesting very high specific impulse coupled with high specific force. If the physics and
engineering models can be explored and understood in the lab to allow scaling to power levels pertinent
for human spaceflight, 400kW SEP human missions to Mars may become a possibility, and at power
levels of 2MW, 1-year transit to Neptune may also be possible. Additionally, the lab is implementing a
warp field interferometer that will be able to measure spacetime disturbances down to 150nm. Recent
work published by White [1] [2] [3] suggests that it may be possible to engineer spacetime creating
conditions similar to what drives the expansion of the cosmos. Although the expected magnitude of the
effect would be tiny, it may be a “Chicago pile” moment for this area of physics.
INTRODUCTION
NASA/JSC is implementing an advanced propulsion physics laboratory, informally known as
Eagleworks", to pursue propulsion technologies necessary to enable human exploration of the solar
system over the next 50 years, and enabling interstellar spaceflight by the end of the century. This work
directly supports the "Breakthrough Propulsion" objectives detailed in the NASA OCT TA02 In-space
Propulsion Roadmap(2.3.7), and aligns with the #10 Top Technical Challenge identified in the report:
Pursue investigation and development of advanced in-space propulsion technologies (TRL < 3). Since the
work being pursued by this laboratory is applied scientific research in the areas of the quantum vacuum,
gravitation, nature of space-time, and other fundamental physical phenomenon, high fidelity testing
facilities are needed. The lab will first implement a low-thrust torsion pendulum (<1 uN), and commission
the facility with an existing Quantum Vacuum Plasma Thruster. The lab will eventually incorporate an
interferometer to be used to measure York Time effects of test devices (expansion/contraction of space)
This effort was performed under internal funding at the Johnson Space Center, Houston, TX.RESULTS AND DISCUSSION
TORSION PENDULUM
Construction of the torsion pendulum is progressing. The framework for the torsion pendulum is
complete, and the custom low-torsion linear flexure bearings manufactured by Riverhawk have been
installed in the rig. A custom electrostatic paddle system [4] is used to provide a non-contact calibration
force, and calibration of the system has been completed. The paddle system consists of two aluminum
cylinders, with a minor diameter of 0.5 inches. The theoretical equation for the force is:
F =
1
V 2
ε 0 � � A
2
L
F is the force, V is the charge voltage, L is the separation gap, and A is the area of the cylindrical
paddle. The empirical data results versus theoretical is shown in Figure 1. The calibration of the paddles
indicates an approximate 5% as-manufactured deviation from the theoretical equation. The calibration of
the paddles was done using a Fluke 343A DC Voltage Calibrator (0-1000V), and the force was measured
using a Scientech SA210 scientific balance. For each calibration run, the positively charged paddle is
placed on the balance, isolated by an acrylic mounting block, and the grounded paddle is accurately
positioned over the positive paddle using optic bench micro-positioning stages capable of all the
necessary degrees of freedom.
Figure 1 Calibration Data for Electrostatic Paddle System
The paddle system has been mounted to the torsion pendulum by adapting a NRC FP-2 Fiber
Optic Positioner (5-axis). The grounded paddle is mounted to the torsion balance arm, and continuity is
accomplished by passing the ground through the linear flexure bearings, eliminating an extra wire that
can be a source of spurious torque across the interface. Force produced by a test article will beaccomplished by using an accurate optical displacement sensor system, the Philtec muDMS-
D63Bv1C1ET1, and converting the measured displacement of the far end of the torsion balance arm to a
force by using the calibration system just discussed. Figure 2 shows both systems being roughed in on
the torsion pendulum prior to being installed in the vacuum chamber. The relative placement of the optical
displacement sensor relative to the paddle system will be accomplished by using the axial stage on the
positive paddle to initiate contact between the positive and negative paddles (power supply off!), and use
the optical displacement sensor to establish the moment of contact deduced by steady increase in
distance. This will provide as-installed relative positioning of the optical displacement sensor and paddle,
so the optical displacement sensor can be used to determine the paddle separation when a calibration
pulse is initiated prior to testing a test article. Passive magnetic dampers will be added to the torsion
balance arm as well. Two approaches are being considered to pass power and data across the interface
to a test article. JPL has provided guidance an inputs on wire selection and mounting to establish an
effective interface without sacrificing fidelity (< 1 micro Newton). Some additional discussion is taking
place about using a liquid metal interface approach to eliminate all systematic torque. The torsion
pendulum will be used to evaluate performance of several quantum vacuum plasma thruster test articles.
Figure 2: Electrostatic Paddle Force Calibration System
and Philtec Optical Displacement Sensor mounting
QUANTUM VACUUM PLASMA THRUSTERS (Q-THRUSTERS)
Can the properties of the quantum vacuum be used to propel a spacecraft? The idea of pushing
off the vacuum is not new, in fact the idea of a “quantum ramjet drive” was proposed by Arthur C. Clark(proposer of geosynchronous communications satellites in 1945) in the book Songs of Distant Earth in
1985: “If vacuum fluctuations can be harnessed for propulsion by anyone besides science-fiction writers,
the purely engineering problems of interstellar flight would be solved.” [5]. When this question is viewed
strictly classically, the answer is clearly no, as there is no reaction mass to be used to conserve
momentum. However, QED, which has made predictions verified to 1 part in 10 billion, also predicts that
the quantum vacuum (lowest state of the electrodynamic field) is not empty, but rather a sea of virtual
particles and photons that pop into and out of existence stemming from the Heisenberg uncertainty
principle. The Dirac vacuum, an early vacuum model, predicted the existence of the electron’s
antiparticle, the positron in 1928, which was later confirmed in the lab by Carl Anderson in 1932.
Confirmation that the QV would directly impact lab observations came inadvertently in 1948 while Willis
Lamb was measuring the 2s and 2p energy levels in the hydrogen atom. Willis discovered that the energy
levels were slightly different, contrary to prediction, but detailed analysis performed within weeks of the
discovery by Bethe at Cornell predicted the observed difference only when factoring in contributions from
the QV field. The Casimir force, derived in 1948 by Casimir in response to disagreements between
experiment and model for precipitation of phosphors used with fluorescent light bulbs, predicts that there
will be a force between two nearby surfaces due to fluctuations of the QV. This force has been measured
and found to agree with predictions numerous times in multiple laboratories since its derivation.
What is the Casimir force? The Casimir force is a QV phenomenon such that two flat plates
placed in close proximity in the vacuum preclude the appearance of particles, whose wavelength is larger
than the separation gap, and the resultant negative pressure between the two surfaces is more negative
than the pressure outside the two surfaces, hence they experience an attractive force. A historical,
classical analog to the idea behind the Casimir Force can be drawn considering training given to sailors of
the tall-ship era who were instructed to not allow two ships to get too close to one another in choppy seas
lest they be forced together by the surrounding waves requiring assistance to be pulled apart. Although
the forces have typically been small, from a practical perspective, micro-electromechanical systems
(MEMS) are already utilizing this phenomenon in design application.
How much energy is in the Quantum Vacuum? The theoretical calculation for the absolute zero
ground state of the ZPF can be calculated using the following equation[6]:
ω cutoff
E 0 =

ω = 0
 ω 3
d ω
2 π 2 c 3
Using the Plank frequency as upper cutoff yields a prediction of ~10 114 J/m 3 . Current astronomical
-26
3
observations put the critical density at 1*10 kg/m . The vast difference between QED prediction and
observation is not currently understood.
Is there a way to utilize this sea of virtual particles and photons (radiation pressure) to transfer
momentum from a spacecraft to the vacuum? A number of approaches have been detailed in the
literature: Vacuum sails that develop a net force by having materials on either side with different optical
properties; Inertia control by altering vacuum energy density and reducing total spacecraft mass thus
minimizing kinetic energy and amount of work needed to accelerate a spacecraft; and dynamic systems
that make use of the dynamic Casimir force to generate a net force.
What is the dynamic Casimir force? The dynamic Casimir force arises as a result of Unruh
radiation where an accelerated observer sees the vacuum as a higher temperature photon bath, and is
the mechanism that facilitates Hawking radiation around a black hole where relativistic accelerationseparates a virtual pair such that one particle goes in the horizon, while the other escapes. Recent
findings reported earlier in 2011 show that the dynamic Casimir effect may have been detected in the lab
[7]. The simplest mechanical construct to help visualize using the dynamic Casimir force to generate
thrust is through the use of vibrating mirrors where the mirror trajectory is designed to generate radiation
in a preferred direction. The magnitude of thrust arising from using the dynamic Casimir force derived
numerous times in the literature has been shown to be very small in comparison with conventional
propulsion systems, but has been clearly shown to be theoretically possible. As a classical construct to
help with visualization, consider how a submarine uses a propeller to create a hydrodynamic pressure
gradient that propels the sub forward while the receding water column carries the momentum information
downstream. The sub does not carry a tank of water and then flow that water across the propeller; rather
it uses the propeller to interact with the environment. The corollary is that there has to be a “wake”
(conservation of momentum is required!).
Are there methods to increase net force? As the calculated energy density of the quantum
vacuum versus observation shows, even though QED is one of the most experimentally successful
theories to date, the community’s understanding of the vacuum is only just beginning as this is a new
field, and the study of the quantum vacuum is at the leading edge of science with a wide open horizon to
explore. Recent models developed by White suggests that there are ways to increase the net force, and
these models have been validated against data at both the cosmological scale, the quantum level, and
test devices have been fabricated/tested in the lab and found to agree with model predictions. Figure 3
depicts the principles of q-thruster operation in tabular form.


Local mass concentrations, say in the form of a
conventional capacitor with a ceramic dielectric,
affect vacuum fluctuation density according to
equation 1
Just as relativistic acceleration (Unruh radiation) can
change the apparent relative density of the vacuum,
so too can higher order derivatives according to
equation 2. Noting that a=-D(phi), equation 2 can be
cast into potential energy time varying terms
• These two relationships can be used to predict the
available vacuum fluctuation density within an active
dielectric being excited by an AC field.
• The tools of magnetohydrodynamics (MHD) can be
used to model this modified vacuum fluctuation
density analogous to how conventional forms of
electric propulsion model propellant behavior.
7
ρ v _ local = ρ v
ρ m _ local
=
ρ v
ρ m _ local ρ v
δρ = 1   1  da 
1 d 2 a  
+
− 2 

4 π G   a  dt 
a dt 2  
δρ = 1   1  d φ 
1 d φ  
 −
2 

4 π G  φ  dt 
φ dt 2  
(1)
2
2
Dr. Harold “Sonny” White
09/21/2011
Figure 3: Principles of Q-thruster Operation
2

a = −∇ φ
(2)How does a Q-thruster work? A Q-thruster uses the same principles and equations of motion that
a conventional plasma thruster would use, namely Magnetohydrodynamics (MHD), to predict propellant
behavior. The virtual plasma is exposed to a crossed E and B-field which induces a plasma drift of the
entire plasma in the ExB direction which is orthogonal to the applied fields. The difference arises in the
fact that a Q-thruster uses quantum vacuum fluctuations as the fuel source eliminating the need to carry
propellant. This suggests much higher specific impulses are available for QVPT systems limited only by
their power supply’s energy storage densities. Historical test results have yielded thrust levels of between
1000-4000 micro-Newtons, specific force performance of 0.1N/kW, and an equivalent specific impulse of
12
~1x10 seconds. Figure 4 shows a test article and the thrust trace from a 500g load cell [8].
Figure 4: 2005 test article construction and results
The near term focus of the laboratory work is focused on gathering performance data to support
development of a Q-thruster engineering prototype targeting Reaction Control System (RCS) applications
with force range of 0.1-1 N with corresponding input power range of 0.3-3 kW. Up first will be testing of a
refurbished test article to duplicate historical performance on the high fidelity torsion pendulum (1-4 mN at
10-40 W). The team is maintaining a dialogue with the ISS national labs office for an on orbit DTO.
How would Q-thrusters revolutionize human exploration of the outer planets? Making minimal
extrapolation of performance, assessments show that delivery of a 50 mT payload to Jovian orbit can be
accomplished in 35 days with a 2 MW power source [specific force of thruster (N/kW) is based on
potential measured thrust performance in lab, propulsion mass (Q-thrusters) would be additional 20 mT
(10 kg/kW), and associate power system would be 20 mT (10 kg/kW)]. Q-thruster performance allows the
use of nuclear reactor technology that would not require MHD conversion or other more complicated
schemes to accomplish single digit specific mass performance usually required for standard electric
propulsion systems to the outer solar system. In 70 days, the same system could reach the orbit of
Saturn. Figure 5 illustrates the performance capabilities of this advanced propulsion concept for
transforming outer solar system exploration (delta-v’s come from [9]).•

Neptune trajectory

Using 4000 micro-Newton
for 10W effective power
input, graphic uses Dr.
McNutt’s outer planet
human mission delta-v’s
to establish
approximations for trip
time.
Power and propulsion
specific mass are static at
10 kg/kW.
Full analysis should be
done to improve fidelity
of results, but this
provides early insight into
capability.
14
Figure 5: Q-thruster performance for outer solar system exploration
WARP FIELD INTERFEROMETER
Recent work published by White [1][2][3] suggests that it may be possible to engineer spacetime
creating conditions similar to what drives the expansion of the cosmos. The canonical form of the
Alcubierre metric as derived in [2] provides new insight into how a test device could be constructed to
generate say a spherical region of perturbation of ~1 cm diameter. Figure 5 depicts the graphical layout of
a warp field interferometer experiment capable of measuring possible York Time perturbations within a
small (~1cm) spherical region. Across 1cm, the experimental rig should be able to measure space
perturbations down to ~1 part in 10,000,000. As previously discussed, the canonical form of the metric
suggests that boost may be the driving phenomenon in the process of physically establishing the
phenomenon in a lab. Further, the energy density character over a number of shell thicknesses suggests
that a toroidal donut of boost can establish the spherical region. Based on the expected sensitivity of the
rig, a 1cm diameter toroidal test article (something as simple as a very high-voltage capacitor ring) with a
boost on the order of 1.0000001 is necessary to generate an effect that can be effectively detected by the
apparatus. The intensity and spatial distribution of the phenomenon can be quantified using 2D analytic
signal techniques comparing the detected interferometer fringe plot with the test device off with the
detected plot with the device energized. Figure 5 also has a numerical example of what the before and
after fringe plots may look like with the presence of a spherical disturbance of the strength just discussed.While this would be a very modest instantiation of the phenomenon, it would likely be Chicago pile
moment for this area of research.
Figure 5: Warp Field Interferometer layout (here, φ is the phase angle).
SUMMARY AND CONCLUSIONS
This paper has chronicled the latest developments in the process of establishing an advanced
propulsion physics lab and identified two main lines of research. The one line associated with quantum
vacuum plasma thrusters is a near term effort that is in the middle of shifting out of a pure physics focus
and on to engineering, while the other is very much a fundamental physics pursuit. The benefits of the
near term effort was discussed and some objectives for the next few test articles were discussed to help
establish a roadmap of sorts to develop a test article for on-orbit use, and near term systems applications
(RCS first, then possibly main propulsion). As the OCT TA02 roadmap indicated, one of the important
challenges for the Agency in the pursuit of developing bold exploration missions is to ensure that there is
a sustained level of modest funding for the “seed corn” advanced propulsion and power technologies that
must be explored to identify greatly enabling technologies. The Advanced Propulsion Physics Laboratory,
Eagleworks at JSC is a step back into this tradition of the Agency and should be pursued by other centers
and other Agencies. Godspeed!REFERENCES
[1] Available at: http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20110015936_2011016932.pdf
[2] White, H., “A Discussion on space-time metric engineering,” Gen. Rel. Grav. 35, 2025-2033 (2003).
[3] White, H., Davis, E., “The Alcubierre Warp Drive in Higher Dimensional Space-time,” in proceedings of
Space Technology and Applications International Forum (STAIF 2006), edited by M. S. El-Genk,
American Institute of Physics, Melville, New York, (2006).
[4] Gamero-Castano, M. et. al., “A Torsional Balance that Resolves Sub-micro-Newton Forces,” 27
International Electric Propulsion Conference, Pasadena, California, Paper IEPC-01-235 (2001).
th
[5] Millis, M., Davis, E., editors, Frontiers of Propulsion Science, Volume 227 of Progress in Astronautics
and Aeronautics, American Institute of Aeronautics & Astronautics (2009).
[6] Puthoff, H., "Ground State of Hydrogen as a Zero-Point-Fluctuation-Determined State," Phys. Rev. D
35, 3266 (1987).
[7] Available at: First Observation of the Dynamical Casimir Effect | MIT Technology Review
[8] March, P., Palfreyman, A., “The Woodward Effect: Math Modeling and Continued Experimental
Verifications at 2 to 4 MHz,” in proceedings of Space Technology and Applications International Forum
(STAIF 2006), edited by M. S. El-Genk, American Institute of Physics, Melville, New York, (2006).
[9] McNutt, R., et. al., “Human Missions Throughout the Outer Solar System: Requirements and
Implementations”, Johns Hopkins APL Technical Digest, Volume 28, Number 4 (2010).
 

Erno86

Paranormal Maven
Exciting read...I look forward too more quantum plasma/photon thruster experimentation.
 

BRETT

Paranormal Novice
Is NASA Moving Toward a Hyperspace Drive?

May 2, 2015 08:08 AM ET

Interesting news out of NASA’s Johnson Space Center this week: A group of
researchers has reportedly tested an electromagnetic (EM) propulsion drive that
could potentially facilitate practical space travel in and around the solar
system.
According to a report from industry watcher NASASpaceFlight.com, the EM drive
could take a spacecraft to the moon in a matter of hours, and a trip to Mars in
70 days. It’s not exactly a hyperspace drive, but it’s surely a step in the
right direction.

The idea of an EM drive isn’t new — scientists in the American, British and
Chinese space programs have been investigating the concept for a while.
DNews: What’s Space Exploration Good For? Plenty!
The basic gist — it gets complicated — is to create a form of propulsion that
doesn’t require the use of propellant. Instead, electromagnetic microwaves are
bounced around a conical cavity in such a way that electrical energy is
converted directly into thrust.
The technology is largely theoretical, but initial test results have been
officially presented, by both NASA and Chinese space agencies. The idea is also
quite controversial, since it seems to violate certain Newtonian law of physics.
According to the report, the significance of the new research is that NASA has
successfully tested EM propulsion in a hard vacuum for the first time. Previous
tests were conducted in atmospheric conditions.
‘Impossible’ Space Engine May Actually Work: NASA
Bear in mind that none of this information is coming from NASA directly, and the
numbers regarding solar system travel come from the extremely busy forums at
NASASpaceFlight.com.
But it’s clear that EM drive research is ongoing at several different agencies,
those forums are legit, and hey, sometimes news does leak out through unofficial
channels. Just ask — oh, I don’t know — every single government agency on the
planet.
 

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