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Thrust Measurements and Evaluation of Asymmetric Infrared Laser Resonators for Space Propulsion

Authors:

Abstract

Since modern propulsion systems are insufficient for large-scale space exploration, a breakthrough in propulsion physics is required. Amongst different concepts, the EMDrive is a proposed device claiming to be more efficient in converting energy into propulsive forces than classical photon momentum exchange. It is based on a microwave resonator inside a tapered cavity. Recently, Taylor suggested using a laser instead of microwaves to boost thrust by many orders of magnitude due to the higher quality factor of optical resonators. His analysis was based on the theory of quantised inertia by McCulloch, who predicted that an asymmetry in mass surrounding the device and/or geometry is responsible for EMDrive-like forces. We put this concept to the test in a number of different configurations using various asymmetrical laser resonators, reflective cavities of different materials and size as well as fiber-optic loops, which were symmetrically and asymmetrically shaped. A dedicated high precision thrust balance was developed to test all these concepts with a sensitivity better than pure photon thrust, which is the force equivalent to the radiation pressure of a laser for the same power that is used to operate each individual devices. In summary, all devices showed no net thrust within our resolution at the Nanonewton range, meaning that any anomalous thrust must be below state-of-the-art propellantless propulsion. This puts strong limits on all proposed theories like quantised inertia by at least 4 orders of magnitude for the laboratory-scale geometries and power levels used with worst care assumptions for the theoretical predictions.
SP2020_104
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THRUST MEASUREMENTS AND EVALUATION OF ASYMMETRIC INFRARED LASER RESONATORS
FOR SPACE PROPULSION
SPACE PROPULSION 2020+1
17 18 19 MARCH 2021
O. Neunzig (1), M. Weikert (2) and M. Tajmar (3)
Institute of Aerospace Engineering, Technische Universität Dresden, Marschnerstrasse 32, 01307
Dresden, Germany
(1) Research Associate, Email: oliver.neunzig@tu-dresden.de
(2) Research Associate, Email: marcel.weikert @tu-dresden.de
(3) Institute Director and Head of Space Systems Chair, Email: martin.tajmar@tu-dresden.de
KEYWORDS: Laser resonators, EMDrive,
Propellantless Propulsion, Thrust balance
ABSTRACT:
Since modern propulsion systems are insufficient
for large-scale space exploration, a breakthrough
in propulsion physics is required. Amongst different
concepts, the EMDrive is a proposed device
claiming to be more efficient in converting energy
into propulsive forces than classical photon
momentum exchange. It is based on a microwave
resonator inside a tapered cavity. Recently, Taylor
suggested using a laser instead of microwaves to
boost thrust by many orders of magnitude due to
the higher quality factor of optical resonators. His
analysis was based on the theory of quantised
inertia by McCulloch, who predicted that an
asymmetry in mass surrounding the device and/or
geometry is responsible for EMDrive-like forces.
We put this concept to the test in a number of
different configurations using various asymmetrical
laser resonators, reflective cavities of different
materials and size as well as fiber-optic loops,
which were symmetrically and asymmetrically
shaped. A dedicated high precision thrust balance
was developed to test all these concepts with a
sensitivity better than pure photon thrust, which is
the force equivalent to the radiation pressure of a
laser for the same power that is used to operate
each individual devices. In summary, all devices
showed no net thrust within our resolution at the
Nanonewton range, meaning that any anomalous
thrust must be below state-of-the-art propellantless
propulsion. This puts strong limits on all proposed
theories like quantised inertia by at least 4 orders
of magnitude for the laboratory-scale geometries
and power levels used with worst care assumptions
for the theoretical predictions.
1. INTRODUCTION
Space propulsion encounters seemingly
unattainable boundaries in their ability to fulfil
humankind’s ceaseless desire to explore the
universe beyond our solar system. To lay the
foundation for large-scale space exploration within
our lifetime, a breakthrough in propulsion physics
is required. Despite continuous advancements,
modern propulsion technologies are limited in
performance due to exponentially scaling
propellant requirements according to the famous
Tsiolkowsky rocket-equation, when facing
enormous distances of interstellar missions.
Solutions may hide in yet unknown interactions and
origins of fundamental properties like mass and
inertia themselves.
One proposed concept is the so-called EMDrive,
which postulates to produce thrust using a
microwave resonator inside a tapered cavity.
Shawyer originally proposed that a difference in the
radiation pressure between both ends of the cavity
amplified by the cavity’s quality factor Q is
responsible for the effect [1]. The claimed force-to-
power ratio of 1-100 µN/W is many orders of
magnitude above classical radiation pressure with
0.033 µN/W, if we consider a laser producing thrust
instead. This has been met with high scepticism, as
it would violate basic conservation laws.
Nevertheless, a number of theories as well as
experiments have been proposed to support the
EMDrive claim. A review of experiments and
theories as well as a recent high-precision test can
be found in our companion paper [2].
Taylor [3] suggested that the use of a laser
resonator instead of microwaves may boost the
produced thrust by orders of magnitude. Such a
laser-EMDrive could also be much more compact
and even simpler to build, which would be very
interesting for potential applications. His analysis is
based on the theory of quantised inertia by
McCulloch, who claimed to explain the EMDrive as
well as a number of other anomalies including dark
matter [4], [5].
In order to test laser-EMDrives and related
concepts, we developed a high-accuracy inverted
counterbalanced double pendulum thrust balance,
which allows operating laser devices with minimum
2
drifts to reach a sensitivity in the sub-Nanonewton
regime. This ensures that we have a resolution
comparable to the photon thrust limit, which serves
as the benchmark for propellantless propulsion.
We tested a number of different concepts including
configurations close to the idea of Taylor with a
laser resonator of asymmetrical shape, reflective
cavities as well as photon-loops with different
geometries.
The paper starts with a summary of the theoretical
predictions and gives an overview of our different
experimental concepts. After an introduction of our
thrust balance, we present the test results for all
devices.
2. THEORETICAL PREDICTIONS
Properties or the cause of inertia within our
universe has never been understood in its entirety.
Despite numerous efforts, neither its origin nor
means to modify its properties were witnessed thus
far. A new model to describe its underlying effects
was proposed by McCulloch [6] within the theory of
quantised inertia (QI) due to a Modified inertia
Hubble-scale Casimir effect (MiHsC). In his model,
inertia of an object emerges from dampening of
Unruh radiation while it experiences acceleration.
To explain the origin of inertia he assumes the
formation of a relativistic Rindler horizon,
appearing in the opposite direction to its
acceleration that damps the Unruh waves thus
creating an inhomogeneous distribution of
radiation pressure. This process results in the
effect we perceive as inertia with a modified inertial
mass (mi), including the standard inertial mass m,
the speed of light c, the diameter of the observable
universe and the magnitude of the acceleration
of the object compared to the surrounding matter
, and is given by

Eq. 1
With his theory, McCulloch provides alternative
explanations for numerous physical topics
including dark matter as well as the force
generation of the EMDrive. In the laboratory,
accelerations of regular masses are so low that this
effect only appears at cosmic scales. However, this
may change for radiation. His key assumption is
that photons at the speed of light bounce back and
forth in the cavity so fast, that  with s being
a representative length. This reduces the distance
to the horizon and the Unruh waves will be short
enough to interact with the cavity walls. For a
tapered cavity of length L and diameters d and D at
the smaller and larger end respectively, he
expresses the force for the EMDrive [4] as

Eq. 2
where P is the power into the cavity and Q the
quality factor. Taylor [3] expanded this concept and
expressed Q as a function of the wavelength
,
which leads to (correcting a wrong sign in his
derivation)
 

Eq. 3
with
as the cavity loss per oscillation or the energy
lost divided by the energy initially stored. It
immediately becomes clear that a short
wavelength, e.g. of a laser compared to a
microwave, should therefore lead to a larger force.
His assumptions for an infrared laser with
=0.1
and centimetre lengths give a force of 0.1 N for 1 W
of input power [3], which is huge considering the
force of just a few Nanonewtons for the same
power as the classical radiation pressure force. He
proposed a laser resonator with a dual-mirrored
crystal, having a tapered cone shape like the
EMDrive and being pumped by an array of laser
diodes.
However, there may be a major error in both Eqs. 2
and 3 as we believe that this Q is not the same
quality-factor as the one used by Shawyer for his
EMDrive predictions [1]. The quality factor of a
microwave resonator is a dimensionless parameter
and describes the stored energy divided by energy
lost per cycle. It characterizes the damping
properties of the oscillator with low-energy loss in
high-Q resonators and high energy-loss in low Q-
resonators. But McCulloch understands Q as the
equivalent number of times that the photons
bounce back and forth within the cavity, “…the Q
factor quantifies how many trips there are before
the power dissipates [4]. For optical cavities, the
number of trips is the finesse divided by pi (2 for
the number of round-trips) or the photon force
amplification factor S. For two reflectivities R1 and
R2 on each side of the cavity, this can be expressed
as
Eq. 4
which is used to describes the force that pushes
the mirrors apart from each other [7], [8]. That
3
doubts Taylor’s derivation and reduces the actual
thrust predictions from quantised inertia in Eq. 2
(and invalidates Taylor’s Eq. 3) if we set Q=S as we
believe McCulloch assumed. Using typical values
for high-reflective mirrors, S can be in the range of
several hundreds, while the actual optical quality
factor may be in the order of millions. Assuming
that the length is at the same order of magnitude
as the diameters of the cavity, this reduces the
predicted forces to be 2-3 orders of magnitude
above the photon thrust limit, which is still of major
interest.
Assuming that we use photons that can produce
the high accelerations necessary to interact with
their environment, the theory then suggests two
types of asymmetries, which can be tested: Mass
asymmetries around the photons or different
accelerations e.g. by putting photons in a loop with
different radii as a geometrical asymmetry on one
side compared to the other one, as suggested by
McCulloch and Diaz [9]. Both types can be mixed
as well. We decided to test the following
configurations:
Laser guiding into metal cavities with highly
reflective surfaces: This closely resembles the
original EMDrive concept. The cavities feature
different radii as well as mass asymmetries
around both ends. Copper and silver were
used to test different force amplification values.
LED light inside a silver cavity with
asymmetrical shape (called BART drive [9]).
Various laser resonators targeting Taylor’s
concept: We tested configurations with
different mirror radii, crystals closer to one
mirror as well as different wavelengths.
Because the laser was present at one end only,
it also features a mass asymmetry.
Photon-loops: We started with a classical
symmetric photon loop and tested if a force
appeared if we put a metal shield close to one
end as suggested by McCulloch [10]. Then an
asymmetrical loop was tested to directly obtain
different photon accelerations on both ends.
Again, a mass shield was put on both ends to
see if that has an influence too.
Every theory described was subject of thorough
investigations in our laboratory with a high
accuracy thrust balance. The following chapters
summarize the developed setups we used to
account for the variety of theoretical predictions
with laser resonators for space propulsion
applications.
3. EXPERIMENTAL SETUP
Our main benchmark was to develop a test setup
that has the sensitivity of the equivalent photon
thrust for a given input power into the devices. In
order to achieve this, we had to limit thermal drifts
as much as possible as this is known to create
balance deflections from center of gravity shifts or
changes in the spring constants that can easily be
misinterpreted as a real thrust. We therefore
decided to limit the maximum laser power to one
Watt, which translates into an equivalent photon
thrust of F=P/c=3.3 nN. Following the work from
Taylor and the availability of commercial off-the-
shelve components, we decided to target the near-
infrared range.
The laser source of choice was a modular diode-
pumped solid-state laser-kit by Leybold with a
variety of optical components extended with highly
reflective mirrors from Laser Components. The
laser emits a fixed wavelength of 808 nm with
adjustable power-levels between 0.01 W and
0.65 W with laser injection currents of up to 0.7 A
supported by Peltier elements for temperature-
controlled wavelength stabilization even in a
vacuum environment. A collimator and converging
focussing lenses handle parallelization of the bar-
shaped beam. For high finesse resonator
applications, especially the setups mentioned by
Taylor, we utilized a Nd:YAG crystal with an
attached coupling mirror to gain access to
asymmetrically shaped beam patterns while
converting the 808 nm into a wavelength of
1064 nm within the crystal. To confirm the active
resonator by visualizing the 1064 mm only, a filter
for the 808 nm wavelength was positioned within
the setups. Concave and convex mirrors with
reflectivities above 99.8% achieved the highest
number of reflections.
Accurate predictions of the produced thrust
required precise knowledge of the generated laser
power in the test setup. For this purpose, we used
a Coherent LaserCheck power-meter a handheld
measurement device for laser-power based on a
calibrated silicon cell. With a maximum
detectable power of 1 W and a minimum resolution
of 0.01 µW for wavelengths between 400 nm and
1064 nm, it is well-suited to ensure and inspect the
laser power at different stages within each
resonator. In addition, knowledge of the force
amplification factor is required, which we computed
using the reflection coefficients according to Eq. 4.
For the photon-loop, this will be simply the number
of turns of the fiber-optic cable.
4
3.1 Testing Environment and Thrust Balance
Thrust measurements of the proposed setups in
the vicinity of sub-micronewtons is a crucial
objective when it comes to investigating and
characterizing the underlying concept. Reliable
measurement principles have to withstand doubts
of any kind towards either the principle itself, the
setup or most importantly measurement errors due
to interactions with the test-environment.
Especially newly developed thrust balances
require enormous efforts to initially detect and
minimize any undesired influences. Historically the
single most popular measurement principle for
electric propulsion systems is a torsion balance
[11]. By measuring the deflection of a rigid spring-
mounted beam onto which a thruster applies a
torque, forces in the range of sub-micronewton can
be detected. The simplicity of such devices is very
appealing for high accuracy thrust measurements
for space propulsion. Although this measurement
principle is sophisticated and offers possibly the
highest resolution amongst previously utilized
balances, it inherits very specific disadvantages,
like any measurement principle so far, that
constrain measurements depending on thruster
mass and power consumption on the balance. The
main difficulties in detecting forces with the
required accuracy are center of mass shifts due to
thermal expansion of mechanical components and
magnetic interactions of power lines on the balance
with external magnetic fields. Both of which lead to
undesired deflections of the main beam and cause
pseudo forces in measurements, which cannot be
distinguished from real thrust.
We developed a new thrust balance with another
measurement principle to counteract the
disadvantages of torsional balances. The system of
choice is presented in Fig. 1 with an inverted
counterbalanced double pendulum. This
measurement principle is based upon a deflecting
frame onto which thrusters apply a force that
linearly deflects a spring-mounted parallelogram,
which is measured with an attocube laser
interferometer. The device consists of two
horizontal planes that rest on three aluminium
beams for static determinateness. A total of nine
torsional springs withhold relative motion between
the components and ensure linear deflective
behaviour. Thrust measurements rely on precise
characterizations and calibration of the
dependency between deflection and exerted force.
Besides deflecting in another orientation, the
center of mass-dependant deflective behaviour is
the biggest difference between torsional balances
and the double pendulum principle. The deliberate
center of mass manipulation in the double
pendulum balance enables an adjustability of
measurement range and time for the balance to
react on applied forces (reaction time). High
resolution is acquired at the cost of high reaction
time and vice versa. This property only counts for
centre of mass shifts on the main beams
connecting the upper and lower planes. Center of
mass shifts on the planes itself do not interfere with
measurements to a certain limit which leads to
advantageous properties in measurements of high
power/high weight thrusters.
Figure 1 Thrust Balance Schematic (Left: CAD-Model of the Inverted Counterbalanced Double Pendulum
with the Taylor-Classic Setup, Right: Schematic Sketch of the Measurement Principle)
SP2020_104
5
Measuring small deflections of the balance as a
result of applied thrust is very sensible towards any
kind of stiff connections and wires to the deflecting
frames. Every wire disturbs measurements by
preventing deflections due to the stiffness of wire
materials. To counteract this problem, the balance
features electrical feedthroughs utilizing a metal
alloy called Galinstan, which is liquid at room
temperature and exhibits very low vapour pressure
to operate in a vacuum environment.
Considering the prominent measurement errors
due to magnetic interactions of power lines with
external magnetic fields, especially Earths’
magnetic field, the balance features twisted-pair as
well as coaxial cables. Undesired vibrational
excitation of the balance is decreased by
Sorbothane sheets. Measurements with devices
that produce excess heat on the balance at
atmospheric pressure lead to buoyancy effects in
close vicinity of the balance components that
deflect the frame. Therefore, measurements take
place in a cylindrical stainless-steel vacuum
chamber to disable buoyant influences. We
operated at a pressure of 10-2 mbar using an
Edwards scroll pump which was sufficient for our
purposes.
During initial measurements, a variety of additional
influences were detected, caused by the laboratory
environment and the balance components among
each other. The predominant measurement error
was caused by a magnetic interaction between
wires on the balance and the permanent magnet of
the pressure gauge, which was resolved by
replacing and relocating the gauge. Additionally,
the permanent magnets of the initially utilized
passive eddy-current damping system repelled
power-lines from the laser while operating.
Replacing the passive system with an active
damping system eliminated this influence. Still
another error source was surface tension between
the pin contacts and the liquid metal feedthroughs,
which depended on the applied current. This was
mostly taken care of by either powering the laser
from a separate structure off the balance, or by
using a battery powered laser. Some setups
required a laser on the balance and power through
the Galinstan contacts, which then had to be
characterized before the actual thrust
measurements.
Prior and after each individual thrust measurement,
a calibration of the thrust balance is essential to
ensure unaltered behaviour of the testbed. By
applying forces of different magnitude with a
voicecoil, we characterized the resulting
deflections of the balance in the desired
measurement range with statistical significance.
Figure 2 illustrates an exemplary calibration
process in two different measurement ranges. The
graphs presented are consecutive measurements
with different forces layered on top of each other.
The voicecoil was activated for 50 s to determine
the reaction time of the balance and resulting
displacement that is monitored by the laser
interferometer. An initial coarse calibration with
forces of -0.9 µN to +0.9 µN in steps of 0.1 µN
(Fig. 2, Left) is followed by a fine calibration near
the desired measurement range with forces
between -0.08 µN and +0.08 µN in steps of
0.01 µN (Fig. 2, Right). With a reaction time of 8 s,
an operational time of 30 s for each laser-
resonator-setup is sufficient to detect anomalous
forces. Subsequently each data point is transferred
into a linear fit of commanded force against
measured displacement to verify linear deflective
behaviour of the torsional springs in the
measurement device (Fig. 3, left). Outcome of this
process is the so-called calibration factor of
0.9682 µN/µm with a standard deviation of
±0.0013 µN/µm. This value was used to convert
the measured displacement into corresponding
thrust forces.
Figure 2 Balance Calibration (Left: Rough Calibration through Commanded Forces with a Voicecoil, Right:
Fine Calibration for the Desired Measurement Range)
010 20 30 40 50 60 70 80 90 100 110
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
Displacement [µm]
Measured Displacement
Commanded Force
Time [s]
Force [µN]
Identification of the Calibration-Factor (± 900nN)
6
Figure 3 Balance Characterisation (Left: Identification of the Calibration-Factor by a Linear Fit of
Consecutive Data Points from the Commanded Forces, Right: Example for Software-Based Thermal Drift
Removal)
Figure 4 Verification of the Voicecoil Calibration by Averaging 40 Consecutive Profiles with Commanded
Forces of +1 nN (Left) and -1nN (Right)
As mentioned before, thermal effects may cause
anomalies in measurement data that can be easily
misinterpreted as real forces since they produce
convincing thrust signatures. Thermal drift in thrust
measurements, especially in the range of
Nanonewtons, is always present and
superimposed on actual force-plateaus. As long as
the drift is within a tolerable magnitude, we used
software tools with LabView to automatically detect
and remove them. To illustrate this process,
consider the measurement in Fig. 3 (Right). The
data shown is an average of 50 consecutive
measurements from the effects of a laser beam fed
into a beam trap. Each profile is divided into five
sectors with fixed durations. Sector I and V
characterize the balance behaviour prior and after
feeding power into the resonator. Sector II and IV
are ramping-periods that take the reaction time of
the balance into account. Lastly, sector III contains
the most meaningful information whether thrust is
present. With linear fits of each sector, real thrust
can be distilled from the raw measurement data
that inherited a thermal drift of 9 nN for the
measurement time of 150 s.
Using our voicecoil calibration technique, Fig. 4
shows an example to illustrate that the balance is
sensitive enough to detect a Nanonewton of force
as required. The data was averaged with several
profiles to reduce noise and gain statistical
significance. This was used throughout all
measurements.
3.2 Beam Trap
To confirm the sensitivity and thrust noise level of
the balance, we utilized a device that absorbs the
laser power to a negligible amount. This process
simulates a thrust device with S=1 by absorbing the
photons on the measurement device and detecting
the resulting force generation due to photon
pressure. The beam trap BTC30 by Thorlabs
served for this purpose as it absorbs up to 5 W of
laser power with wavelengths between 200 nm and
3 µm and has a backscatter of 0.005 as a fraction
of entrance beam power. The opening aperture of
-1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Consecutive Measurements
Linear Regression
Commanded Force [µN]
Displacement [µm]
Linear Fit y=a+b*x
Calibration-Factor 0. 9682 ± 0.0013
Unit µN/µm
Correlation Coeff. R² 0.99995
Identification of the Calibration-Factor
020 40 60 80 100 120 140
-10
-8
-6
-4
-2
0
2
4
6
8
10 I
Thrust-Balance Drift
Thermal Drift Removed
Time [s]
Thrust [nN]
Thermal Drift Removal
IVII III V
7
8 mm diameter ensures that the beam from our
laser source with an estimated beam diameter of
2 mm is absorbed almost entirely. The absorbed
energy generates heat within the beam trap that is
transmitted to the thrust balance via thermal
conduction and radiation. As mentioned before,
thermal power generation on the balance may
cause undesired measurement artefacts. We
therefore stalled any heat transfer to the balance
by adding thermal mass to the beam trap with pure
copper blocks and a thermal radiation shield made
from aluminium that is positioned around the beam
trap except the beam entrance.
3.3 Metal Cavities CC/CX CC/CC Circle,
BART
Following the ideas of a geometrically and mass-
asymmetric laser resonator, our first setup to be
measured was a series of three different
geometries made from solid copper. This material
is well suited for reflective applications due to its
theoretical maximum reflectivity of approximately
96% for wavelengths of 808 nm as well as its
intrinsic property to serve as a heat sink for
absorbed laser power preventing thrust balance
heating. Our own measurements with the Coherent
powermeter resulted in a reflectivity of 89%,
probably due to the milled curved surface. Despite
the high heat capacity, every copper cavity was
encapsuled in an aluminium case, similar to the
beam trap mentioned previously, to minimize heat
radiation to the balance components. The
geometries were chosen carefully to provide first
insights into quantised inertia theory in a laboratory
environment. Every cavity possesses a beam
entrance with a diameter of 3 mm to ensure that the
laser power enters unaffected. The cavities were
polished prior to and in between thrust
measurements to prevent a degradation in
reflectivity. Detachable copper lids make sure that
scattered laser beams are redirected into the
resonator rather than expelled from the setup. All
cavities are shown in Fig. 5.
The cavity described with CC/CX is characterized
by two reflective surfaces with concave (CC) and
convex (CX) shapes. The curved surfaces are
arranged in such a way that a laser is fed parallel
to the axis of the entrance, where it is then reflected
between the inner surfaces until being absorbed
entirely. A sketch of the theoretical beam pattern is
provided in Fig. 5 (D) with the geometric
dimensions of d=26 mm, D=37 mm and L=22 mm.
Here the geometric asymmetry is similar to an
EMDrive tapered cavity but in 2D and the mass-
asymmetry originates from the unequal copper
mass distribution in front and behind the machine-
milled resonator boundaries. These properties
should lead to locally uneven damping of Unruh
radiation of the reflecting photons and produce
thrust according to quantised inertia.
In a similar manner, we manufactured the cavity
described as CC/CC for both reflective surfaces
characterized by concave shapes. The surfaces
include a slight difference in radii to focus the beam
and prevent it from escaping the resonator through
the same pattern it entered the cavity. A difference
to the cavity CC/CX is an increase of mass
asymmetry while changing the beam pattern as
shown in Fig. 5 (E).
The last approach with copper resonators,
described as Circle, involves a drastic change in
beam pattern by guiding the laser along a circular
trajectory while maintaining the mass asymmetry.
Instead of back and forth reflections, the photons
perform roundtrips with a defined radius R of
20 mm. This is actually similar to our later photon
loop setups but with the Unruh shield as close as
possible.
In order to directly test quantised inertia theory, we
tried to increase the force amplification factor while
maintaining the features, properties and even
impurities due to the manufacturing process of
each geometry. This was done by electroplating
the copper cavities with a thin layer (<1 µm) of pure
silver to increase reflectivity of every surface to a
theoretical maximum of 97.7% for infrared lasers at
our 808 nm wavelength. Indeed, our own
measurements gave a reflectivity of 97.5% close to
the datasheet value. Simultaneously the number of
reflections increases proportionally enabling a
direct comparison between the same cavities and
investigating the predicted linear dependency
between thrust and number of reflections.
8
Figure 5 Metal Cavities (A-C: Machine-Milled Solid Copper Cavities with Distinct Resonator Geometries. D-
E: Schematic Sketch of Beam Patterns within the Cavities. G-I: Silver Plated Cavities).
A very simple setup was suggested by Lucio and
McCulloch and initial positive tests were reported
by Komala [12] on a related metal cavity called the
BART drive. Here, a 3 W LED diode was placed
inside a closed silver cavity with a flat surface at
one end and a zig-zag shape on the other, which
leads to a significant increase in surface area and
hence geometrical asymmetry. He claimed a
thrust-to-power ratio of 1.75 µN/W. We decided to
include this in our series of tests and developed a
similar device as shown in Fig. 6 with an LED at a
wavelength of 660 nm in the visible spectrum of
light. We operated the LED at 0.77 W and 1.5 W
optical power, which required currents that were
similar to the one used for the photon-loops. The
dimensions of the cavity were a diameter of 75 mm
and a length of 100 mm. The zig-zag pattern had 4
spikes on the outside and 3 spikes on the inside
over a height of 25 mm. We can express an
equivalent diameter for the larger inner surface
area on the right side, which is approximately
106 mm for our design. This can be viewed as a
geometric asymmetry of 75 mm versus 106 mm for
the cavity, which again resembles an EMDrive-like
setup that can be computed by using the
theoretical prediction in Eq. 2.
9
Figure 6 Schematic Sketch of BART Drive in Sectional View (Rotationally Symmetric around Middle Axis)
illustrating the Difference in Area A1 < A2
3.4 Taylor Setups
Following the ideas of Taylor [3], we designed four
different laser-setups to test quantised inertia
theory against high-finesse optical resonators in
addition to the metal cavities. These particular
setups utilized the modular components of the
Leybold diode-pumped solid-state laser-source on
a rigid rail with optomechanical mounts for quick
and precise adjustments. The mirror mounts
include adjustment screws to achieve a stable
resonator by manual alignment and variation of its
arrangement. The manufacturer ensured vacuum
compatibility of the components as well as the laser
source. Taylor’s idea was to use a crystal in a
tapered cone shape similar to an EMDrive, with
reflective end surfaces that will create laser beam
reflections inside that closely resemble the same
shape. Such a crystal geometry is not commercially
available, limiting us to a standard cylindrical
shape. However, we were able to create laser
resonators, where the beams indeed formed a
tapered cone shape. In addition, we were able to
introduce a variety of geometry and mass
asymmetries, which we believe are even more
asymmetrical compared to Taylor’s design.
It is important to note, that the component holders
and the rail provided a U-shaped cavity mass
around all resonators. This does not represent a
complete metallic enclosure as for the EMDrive,
but at least a partial one. Although this was not part
of Taylor’s design and it is unclear if this is even
necessary, our high sensitivity being 2-3 orders of
magnitude better than any prediction should cover
this aspect. In any case, the vacuum chamber acts
as a full metallic enclosure too.
Accomplishing a resonator was difficult due to the
fact, that infrared light is not visible to the naked
eye. Three different approaches verified the
desired operational mode during resonator setups
and prior to measurements. The handheld
powermeter mentioned previously monitored the
laser power at different stages in between
resonator components. In addition, optical
confirmation was utilized too by using an infrared-
laser detection card, whose constituents are
excited by the laser beam allowing visibility to the
naked eye, and a camera that is sensitive to the
infrared spectrum to confirm the operational
modes. By operating the laser in pulsed mode, we
could determine the typical decay time of the
resonator using a Leybold photo diode and an
oscilloscope, which is a measure of the quality of
the resonator and the time the photons spent within
the cavity.
This was done in the following way: The laser with
a wavelength of 808 nm enters the cavity where a
Nd:YAG crystal converts it into 1064 nm. The
mirrors in the cavity are reflective for 1064 nm and
let the 808 nm pass through. Only a tiny amount of
power from the 1064 nm, which is the resonating
part, is passing through. After the cavity, a filter for
the 808 nm is located such that only the 1064 nm
part can be measured by the photo diode behind.
By pulsing the laser, the decay time was measured
by an oscilloscope. Our decay times for all setups
were at a similar order of magnitude as the one
given as an example in the manufacturer’s
handbook of 250 ns, which indicates the high
quality of our resonator modes (equivalent to a Q
of millions). In addition, the filter acted as a beam
trap as most of the laser power was not allowed to
pass through.
The following setups were implemented as
illustrated in Fig. 7.
10
3.4.1 Taylor-Light
In order to obtain the best thrust noise, we mounted
the laser and collimator-lense assembly just next to
the thrust balance on a separate platform
eliminating potential electrical feedthrough
problems. A Nd:YAG crystal with a diameter of
3 mm and a length of 5 mm was used as an
entrance into the asymmetrical resonator. It
converts the 808 nm into 1064 nm and has a flat
mirror on its left end that is transparent for the
incoming and reflective for the outgoing beam. At a
distance of 75 mm, a concave mirror with a
reflectivity of >99.8% for 1064 nm, a diameter of
25 mm and a curvature with a radius of 100 mm is
located. Widening of the beam by the crystal and
the concave shape of the mirror ensures the
tapered cone shape of the laser beam inside the
resonator. This setup features a number of mass
asymmetries:
Dielectric only on one side (5 mm out of 75 mm
length). That’s similar to what is claimed to be
important for EMDrives [2]. In addition to
different propagation speeds, this is also a
strong mass asymmetry along the beam path.
Setup Asymmetry: With the laser and
collimator-lense assembly on one side only,
the setup itself provides a strong mass
asymmetry. In addition, the inserts for the
crystal and the mirror on both ends are also
dissimilar adding another asymmetry
component.
3.4.2 Taylor Halfway Crystal
Here, the entrance is similar to Taylor-Light with the
addition of another Nd:YAG crystal of diameter
10 mm and length 25 mm at a distance of 1 mm
away from the first crystal. It features anti-reflective
coatings on the end surfaces to ensure that the
laser beam can pass through with minimal losses.
The mirror on the right side has a 10 mm diameter
with the same 100 mm curvature radius as in the
setup above but with a higher reflectivity of
>99.98%. The main goal of this setup was to
increase the path length through a dielectric to
roughly half the length of the resonator of length
50 mm, to investigate if this has any influence. In
addition to the asymmetries listed above, the
crystal and holder component now adds another
important mass asymmetry along the laser path.
3.4.3 Taylor Dual Crystal
This setup is a combination of the two above. It is
based on Taylor-Light, but with the larger Nd:YAG
crystal included as well. This modifies again the
path length of the laser through the dielectric
(5+25 mm along a total length of 75 mm) with the
larger diameter mirror at the right side that leads to
a more pronounced conical beam shape.
3.4.4 Taylor Classic
This configuration is as close as possible to
Taylor’s idea. It consists of a convex-concave
mirror configuration with a resonator length of
65 mm to ensure the tapered cone shape laser
beam with the large Nd:YAG crystal (10 mm
diameter, 25 mm length) in between. The convex
mirror was 25 mm in diameter with a curvature of
50 mm, a reflectivity of 99.7% and high
transmissivity for the 808 nm wavelength to allow
the laser beam to enter the resonator. The opposite
side is occupied by a concave mirror with the same
25 mm in diameter but a curvature of 100 mm and
a reflectivity of 99.8%. The conversion crystal was
placed close to the entrance mirror to enhance
asymmetry. Only in this setup, the laser was
mounted together with all other optical components
on the same rail as the correct alignment and
tuning was very difficult and could not be achieved
otherwise. This introduced artefacts from the
currents passing through the feedthroughs that had
to be taken into account.
11
Taylor Light:
Taylor Halfway Crystal:
Taylor Dual Crystal
Taylor Classic:
Figure 7 Illustrations of Taylor-Setup Configurations (Light, Halfway Crystal and Dual Crystal have Laser
mounted Externally, Classic has Laser Mounted on Balance)
SP2020_104
12
3.5 Fiber-optic Loop/Photon-loop
Following the predictions of QI-Theory, we tested
another setup that, in contrast to the metal-
resonators described above, possesses an
accurately defined number for the force
amplification factor. By feeding a laser into a fiber-
optic loop, the travelling photons should perceive a
change in acceleration relative to their surrounding
matter. Furthermore, the emerging Rindler horizon
of an accelerated object may be substituted with an
artificial horizon in the shape of an electrically
conductive metal plate as illustrated Fig. 8. The
plate was situated on one side of the fiber-optic
loop, leading to an asymmetric dampening of the
emerging Unruh radiation of the accelerated
photons. To convert this idea into a physical test
setup we utilized 2.2 km of multimode fiber-optic
cable for a coil diameter of 160 mm. We calculated
the number of windings from its geometry resulting
in at least 4330 although a value of 4000 was used
for force predictions to account for uncertainties
due to the coil thickness and to do a conservative
estimate.
The same fiber-optic cable was reused on an
asymmetric coil, which has two different radii. The
support structure was 3D printed out of
Polyetheretherketone (PEEK) with a radius of
70 mm on the big end and 40 mm on the small end.
The center points of the radii are 150 mm apart
from each other, resulting in an EMDrive-like cross
sectional shape. With an accumulated number of at
least 3300 windings for the same length, significant
amounts of thrust should be generated. In addition,
also in this asymmetric coil setup, an Unruh shield
can be placed close to either radii.
Feeding the Leybold diode-laser beam into the
fiber-optic cable was not possible as this would
require a dedicated fiber-optic coupler which is
difficult to tune. Instead, we replaced the diode-
laser with a semiconducting laser that had a direct
fiber-coupler attached for easy integration. It was
supplied by LUMILOOP and featured a wavelength
of 830 nm with up to 1 W of laser power starting
from 50 mW. To prevent overheating in a vacuum
environment, the laser was attached to an
aluminium radiator with sufficient thermal mass. A
FTAPC1 beam trap from Thorlabs prevents
photons at the end of the fiber from escaping the
measurement-setup terminating a maximum power
of 1 W.
The compactness of the semiconductor laser,
which did not need separate control electronics like
the Leybold laser, enabled to operate the whole
assembly using a battery with six 18650 Lithium-
ion cells and a small power supply that was
commanded via Bluetooth wireless
communication. This eliminated all electrical
feedthrough problems. Unfortunately, this battery
solution was developed rather late in our program
such that only the asymmetrical loop tests were
done in this optimum configuration. The
symmetrical loop used the same semiconductor
laser but powered through the liquid metal
feedthroughs, which resulted in some current-
dependent offsets that had to be taken into
account.
A picture of the actual setups is shown in Fig. 9.
Figure 8 Photon-loop Configurations (A: Symmetric Fiber-optic Loop with Unruh Shield, B: Asymmetric
Fiber-optic Loop with Unruh Shield Close to its Bigger Radius)
13
Figure 9 Photon-loop Setup during Tests (Left: Symmetric Fiber-optic Loop with a Semiconducting Laser-
Diode, Right: Asymmetric Fiber-optic Loop with Electrical Components)
4. THRUST MEASUREMENTS
A summary of all measurements can be found in
Tables 1-5 including a comparison to predictions by
QI-theory where applicable. We used the simple
equation

Eq. 5
without geometry factors, as in most cases it’s not
exactly clear which length should be used. In any
case, this gives the right order of magnitude and
should provide a worst case thrust as geometric
asymmetry and dielectric inserts should actually
increase this value [4]. Simply put, we expect a
force equivalent to photon thrust times the force
amplification factor, calculated from the cavity
reflectivities or the number of turns for photon-
loops.
4.1 Beam Trap
Our first measurements were used to get an
independent verification of the thrust balance
performance by using a known force, the photon
thrust from our laser, which was fired from a
separate structure to avoid electrical feedthrough
problems into the BTC30 beam trap that was
mounted on the balance. Each measurement was
performed with at least two different power-levels
to assess the power-scaling behaviour.
The acquired data resulted in thrust values of
(0.32±0.23) nN, (0.94±0.31) nN and
(1.64±0.26) nN for measured laser power-levels of
109 mW, 292 mW and 497 mW respectively. The
values exactly match the calculated photon thrust
of 0.36 mN, 0.97 nN and 1.66 nN based on their
input power with total absorption (Table 1). Thrust
measurement examples are shown in Fig. 10. This
verified our ability of detecting forces with the
fundamental physical mechanism of momentum
exchange with photons (S=1).
Figure 10 Thrust Measurement of the Beam Trap BTC30
14
Figure 11 Thrust Measurement of the Silver Cavity Circle
4.2 Metal Cavities CC/CX CC/CC Circle,
BART
As we are shooting with the externally mounted
laser into the metal cavities mounted on the
balance, we expected to see a force amplification
factor with respect to classical photon thrust of 9
and 39 for the copper and silver cavities
respectively. All force measurements for the
CC/CX, CC/CC and Circle setups are summarized
in Table 2 for three different power levels. They
show an excellent agreement with classical photon
thrust and no anomalous force as predicted by QI.
However, during our test campaign we
encountered an interesting problem that produced
a false-positive thrust effect, which is important to
note for possible replication efforts. After finishing
measurements with copper resonators, we
electroplated the same cavities with pure silver to
increase their reflectivity. First measurements of
the silver-coated cavity CC/CX indeed showed a
force that was 50% higher compared to the
equivalent photon thrust. Due to suspicious on- and
off-delays in the occurred force plateaus compared
to the fast reaction time of the balance, we
suspected a measurement error of unknown origin
at that time. Taking all ideas into account, we
identified, that the manufacturer responsible for the
silver coating did not mention a transparent film on
top of the silver layer to protect it against
degradation. It turned out that the laser locally
heated and vaporized the non-vacuum compatible
layer that increased the measured thrust and was
responsible for the spurious delays of the signal.
We detected this error by noticing a pressure
increase within the chamber during and after laser
operation, monitored by the pressure gauge. The
solution to this problem was heating the cavity in
an oven at 200° for several hours to destroy the
protective layer. The resulting thrust
measurements showed no anomalous forces
above the equivalent photon pressure. Thrust
measurements of the silver cavity for two power
levels are shown in Fig. 11, where the laser current
indicates when the laser was on. No anomaly
beyond classical photon thrust and excellent
balance response can be seen in this case.
The BART silver cavity measurements are
summarized in Table 3. As the LED was mounted
inside the cavity, classically one would not expect
any thrust at all, which is indeed what we
measured. At 1.54 W of optical LED power, the
expected thrust from the claimed measurement
would have been 2700 nN [12], however we
measured (0.22±4.13) nN, ruling out any
anomalous thrust by 4 orders of magnitude.
4.3 Taylor-Setups
Thrust measurements of the Taylor-setups
required increased effort due to their vulnerability
against misalignments of the optical axis. A precise
parallelisation of both optical axes was achieved by
varying the adjustment screws while monitoring the
infrared beam with a camera. A resilient resonator
mode was achieved when an indicator occurred on
the infrared detection card (Fig. 12).
A summary for all configurations is given in
Table 4. The first three Taylor setups (Light, Dual
Crystal and Halfway Crystal) were straightforward
as the laser was mounted externally from the
balance. As the laser power was mostly absorbed
within the resonator and the filter at the end of the
rail, the classical prediction would be again to
measure pure photon thrust. The much higher
reflectivities of the commercial mirrors with respect
to our own polished metal surfaces resulted in an
order of magnitude higher force amplification
15
factors, which was varying between 500 and 908
for the setups. These values are equivalent to
actual measurements with similar mirrors [7], [8].
Again, our data showed only classical photon thrust
ruling out theoretical predictions by three orders of
magnitude. An example for Taylor-Light is shown
in Fig. 13.
For the Taylor-Classic configuration, the laser was
mounted on the main balance rail. Therefore, we
had to take the influence from the current passing
through the liquid metal contacts into account. This
was done by first blocking the laser to have a zero-
thrust reference, and second without the laser
block. Our results in Table 4 show that the
feedthrough influence is very small at around 6-
7 nN for 500 mW. Still this was above our photon
thrust threshold. By taking the difference between
both measurements we get a null result below
photon thrust as expected. No anomaly was seen
also in this configuration, which is as close as
possible to Taylor’s original idea. The thrust
measurements with blocked, unblocked and
differential configurations are shown in Fig. 14.
Figure 12 Taylor-Light Setup with an Active Resonator Configuration indicated by the Infrared Detection
Card (Note: Laser is Mounted on a Separate Rail external to the Balance)
Figure 13 Thrust Measurements of the Taylor-Light Setup
Figure 14 Thrust Measurements of the Taylor-Classic Setup
SP2020_104
16
4.6 Symmetric- and Asymmetric Fiber-Optic
Loops
The fiber-optic loops finalized our efforts of
investigating force generation in photon-based
resonators. Specifically, the known number of
windings is important for a correct thrust prediction
using QI-theory.
First, the symmetrical circular fiber-optic coil was
tested. We used the coil as shipped by the
manufacturer to ensure that the fiber was intact
with low losses. However, we noticed some elastic
plastic material on which the coil was spun. The
manufacturer could not tell us if this was vacuum
compatible and there was the risk that this elastic
material could rupture during evaporation, which
could damage the fiber. We therefore decided to do
this test at ambient pressure. The laser was
powered by using the liquid metal contacts and
therefore we expected an influence in the
Nanonewton range as with the Taylor-Classic
setup. However, as the number of windings were
at least 4000, thrusts in the µN range were
expected according to QI. The coil had a radius of
80 mm, and we placed an aluminium metal plate of
dimensions 400x140x10 mm³ at a distance of the
radius away from the coil. By performing
measurements with and without this Unruh-shield,
a net QI thrust was expected. This differential
measurement also eliminated our constant offset
from the liquid metal feedthroughs.
Fig. 15 (Left) shows the actual setup of the coil on
the balance. Table 5 gives a summary of all our
measurements, where we used the average power
between input and output for the actual force
prediction. Indeed, for the no-shield configuration,
we measured again a few Nanonewtons offset, as
this semiconductor laser used similar currents
compared to the diode laser in the Taylor-Classic
setup. However, this value was independent of the
fact if a metal Unruh-shield was present or not.
Taking the difference gives a null result as shown
in Fig. 16 for two power levels.
The asymmetric loop used the battery-powered
laser with Bluetooth control without any
feedthrough issues. As we made the coil ourselves
with known materials, the test could be done again
in vacuum. The complete setup is shown in Fig. 15
(Right). As summarized in Table 5, also here, no
thrust was seen at all independent of the
configuration with the asymmetric coil alone or with
the Unruh shield next to the smaller or larger
radius. We even decreased the metal shield
distance to 10 mm away from the coil without
seeing any difference. An example of the thrust
measurement with or without the Unruh shield at
the big radius is shown in Fig. 17.
These measurements rule out anomalous thrust
predictions by 4 orders of magnitude for the
average power levels used.
Figure 15 Fiber-Optic Loops (Left: Symmetrical Loop positioned on the Thrust Balance with an Artificial
Unruh-Shield, Right: Asymmetrical Loop with an Artificial Unruh-shield facing its Larger Diameter)
17
Figure 16 Difference in Measured Thrust Values in the Presence and Absence of an Unruh-Shield for the
Symmetric Loop at Ambient Pressure (Influence of Liquid Metal Contacts).
015 30 45 60 75 90 105 120 135 150
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
Force
Laser Injection Current
Time [s]
Thrust [nN]
Asymmetric Loop (Big Radius Shield): PAverage= 203mW (49 profiles)
-800
-600
-400
-200
0
200
400
600
800
Current [mA]
Figure 17 Thrust Measurements of the Asymmetric Loop in Vacuum without and with Unruh Shield facing
the Big Radius of the Loop
5. CONCLUSION
We performed an extensive investigation of
detecting any anomalous thrust from laser
resonators and photon-loops that were motivated
by McCulloch’s QI theory, which suggests that
photons are fast enough to interact with their
environment. In order to produce thrust, either
mass asymmetry such that the environment-
interaction on either side are not equal, or a
geometric asymmetry for different photon
accelerations on both ends is believed to be
necessary.
Key to our search was the development of a thrust
balance, that eliminated all known thermal and
electromagnetic interactions to such an extent, that
a resolution was possible below the photon thrust
limit. This is equivalent to the classical radiation
pressure force emitted in one direction using the
input power of the device under test. Usually, this
can be demonstrated with a laser as the state-of-
the-art in propellantless propulsion. Any
anomalous thrust must be larger than this limit in
order to be of interest for applications.
Many different configurations were tested including
metal cavities with different shapes, laser
resonators as recently suggested by Taylor or
symmetric and asymmetric fiber-optic coils, which
were tested with and without metal shields that
should have affected the photon’s environment
significantly. No such effect was seen in any of our
setups within our resolution of photon thrust.
Comparing to predictions from QI theory,
anomalous forces should have been detected at
least 4 orders of magnitude above. In our
comparison, we always used worst-case
assumptions like a minimum number of wounds for
our coils or no specific geometrical modifications of
the thrust prediction formula, which would increase
the predicted anomalous thrust even more. We
used the force amplification instead of the quality
factor for the resonator predictions, as we believe
that this is the correct interpretation, which would
otherwise add another 4 orders of magnitude or
discrepancy.
Of course, one has to take into account that our
simple application of QI thrust prediction must be
18
only an assumption as in reality the actual
geometry must play an important role. However,
McCulloch claimed to exactly match claimed
thrusts for the EMDrive and other devices with his
simple equations [4], [5], which should then apply
to our configurations with similar dimensions too. In
any case, at least 4 orders of magnitude are a lot
to take some non-ideal geometrical parameters
into account. It should be no surprise that our
recent measurement on the EMDrive question the
good EMDrive-QI correlation as well [2]. Our setup
implementation with a proper vacuum chamber,
balance, laser source and typical resonators or
fiber-optic coils is representative for an actual
implementation as it was suggested that such
devices may compete with electric propulsion
thrusters on satellites.
Our results rule out anomalous laser-based
propellantless thrusters above classical photon
thrust that were inspired by McCulloch and Taylor
within our laboratory-scale geometries and power
levels up to approximately one Watt. This puts
strong limits also on other theories and designs that
are based on these concepts.
6. ACKNOWLEDGEMENTS
We gratefully acknowledge the support from
DARPA DSO under award number
HR001118C0125 and discussions with M.
McCulloch. The quick supply of the semiconductor
laser by LUMILOOP was greatly appreciated.
7. REFERENCES
[1] R. Shawyer, “Second generation EmDrive
propulsion applied to SSTO launcher and
interstellar probe,” Acta Astronaut., vol.
116, no. October, pp. 166174, 2015.
[2] M. Tajmar, O. Neunzig, and M. Weiker,
“High-Accuracy Thrust Measurements of
the EMDrive and Elimination of False-
Positive Effects,” in Proceedings of the
Space Propulsion Conference, 2021, p.
SP2020_268.
[3] T. S. Taylor, “Propulsive Forces using High-
Q Asymmetric High Energy Laser
Resonators,” J. Br. Interplanet. Soc., vol.
70, no. 7, pp. 238243, 2017.
[4] M. E. Mcculloch, “Can the Emdrive Be
Explained by Quantised Inertia?,” Prog.
Phys., vol. 11, no. 1, pp. 7880, 2015.
[5] M. E. McCulloch, “Testing quantised inertia
on emdrives with dielectrics,” Europhys.
Lett., vol. 118, no. 3, p. 34003, May 2017.
[6] M. E. McCulloch, “Inertia from an
asymmetric Casimir effect,” Epl, vol. 101,
no. 5, 2013.
[7] Y. K. Bae, “Photonic laser propulsion:
Proof-of-concept demonstration,” J.
Spacecr. Rockets, vol. 45, no. 1, pp. 153
155, 2008.
[8] Y. K. Bae, “Photonic Laser Thruster: 100
Times Scaling-Up and Propulsion
Demonstration,” J. Propuls. Power, vol. in
press, pp. 18, Dec. 2020.
[9] D. Hambling, “The EmDrive Just Won’t
Die,” Popular Mechanics. [Online].
Available:
https://www.popularmechanics.com/space/
rockets/a33917439/emdrive-wont-die/.
[Accessed: 29-Jan-2021].
[10] M. McCulloch, “LEMdrive?” [Online].
Available:
http://physicsfromtheedge.blogspot.com/20
16/07/lemdrive.html. [Accessed: 29-Jan-
2021].
[11] J. E. Polk et al., “Recommended Practice
for Thrust Measurement in Electric
Propulsion Testing,” J. Propuls. Power, vol.
33, no. 3, pp. 539555, 2017.
[12] M. McCulloch, “Physics from the Edge Blog
(25th July 2020).” [Online]. Available:
http://physicsfromtheedge.blogspot.com/.
19
Table 1 Beam Trap Measurements
Setup
Measured Power
Classical Photon
Thrust (S=1)
Measured Thrust
Beam Trap
109 mW
0.36 nN
(0.32±0.23) nN
292 mW
0.97 nN
(0.94±0.31) nN
497 mW
1.66 nN
(1.64±0.26) nN
Table 2 Metal Cavity Measurements
Setup
Surface
Material
Force
Amplification
Factor (S)
Measured
Power (P)
QI Force
Prediction
(F=PS/c)
Classical
Photon
Thrust (S=1)
Measured
Thrust
Concave/
Convex
(CC/CX)
Copper
9
109 mW
3 nN
0.36 nN
(0.39±0.19) nN
292 mW
8 nN
0.97 nN
(1.02±0.15) nN
497 mW
14 nN
1.66 nN
(1.67±0.16) nN
Silver
39
292 mW
38 nN
0.97 nN
(1.08±0.18) nN
497 mW
65 nN
1.66 nN
(1.73±0.24) nN
Concave/
Concave
(CC/CC)
Copper
9
109 mW
3 nN
0.36 nN
(0.40±0.15) nN
292 mW
8 nN
0.97 nN
(1.03±0.14) nN
497 mW
14 nN
1.66 nN
(1.65±0.22) nN
Silver
39
292 mW
38 nN
0.97 nN
(1.28±0.34) nN
497 mW
65 nN
1.66 nN
(1.76±0.28) nN
Circle
Copper
9
109 mW
3 nN
0.36 nN
(0.34±0.28) nN
292 mW
8 nN
0.97 nN
(1.12±0.25) nN
497 mW
14 nN
1.66 nN
(1.71±0.27) nN
Silver
39
292 mW
38 nN
0.97 nN
(1.13±0.27) nN
497 mW
65 nN
1.66 nN
(1.89±0.24) nN
Table 3 LED Cavity (BART Drive) Measurements
Setup
Measurement
Influence
Power (P)
Measured Thrust
BART Drive
None (Differential)
770 mW
(0.13±1.35) nN
1540 mW
(0.22±4.13) nN
Table 4 Taylor-Like Laser Resonator Measurements
Setup
Measurement
Influence
Dielectric
Force
Amplification
Factor (S)
Measured
Power (P)
QI Force
Prediction
(F=PS/c)
Classical
Photon
Thrust (S=1)
Measured
Thrust
Taylor
Light
-
No
500
292 mW
487 nN
0.97 nN
(1.03±0.14) nN
497 mW
828 nN
1.66 nN
(1.78±0.31) nN
Taylor
Dual
Crystal
-
Nd:YAG
Crystal
500
292 mW
487 nN
0.97 nN
(1.14±0.57) nN
497 mW
828 nN
1.66 nN
(1.62±0.15) nN
Taylor
Halfway
Crystal
-
Nd:YAG
Crystal
908
292 mW
885 nN
0.97 nN
(0.97±0.12) nN
497 mW
1505 nN
1.66 nN
(1.75±0.32) nN
Taylor
Classic
Liquid metal
contacts;
Laser Blocked
Nd:YAG
Crystal
0
292 mW
0 nN
0.97 nN
(3.98±0.61) nN
497 mW
0 nN
1.66 nN
(6.82±1.53) nN
Liquid metal
contacts
624
292 mW
608 nN
0.97 nN
(4.41±0.87) nN
497 mW
1035 nN
1.66 nN
(6.64±1.32) nN
None
(Differential)
292 mW
608 nN
0.97 nN
(0.43±0.87) nN
497 mW
1035 nN
1.66 nN
(0.18±1.53) nN
Table 5 Photon-loop Measurements
20
Setup
Measurement
Influence
Windings
(S)
Unruh
Shield
Average
Fiber
Power (P)
QI Force
Prediction
(F=PS/c)
Measured
Thrust
Symmetric
Loop
Liquid metal
contacts
>4000
No
31 mW
0 nN
(2.64±1.42) nN
210 mW
0 nN
(6.41±1.28) nN
Yes
31 mW
420 nN
(2.62±1.27) nN
210 mW
2809 nN
(6.91±1.44) nN
None
(Differential)
>4000
Differential
31 mW
420 nN
(0.02±1.42) nN
210 mW
2809 nN
(0.50±1.44) nN
Asymmetric
loop
-
>3300
No
31 mW
341 nN
(0.02±0.23) nN
203 mW
2234 nN
(0.08±0.26) nN
At Small
Radius
31 mW
>341 nN
(0.09±0.33) nN
203 mW
>2234 nN
(0.02±0.34) nN
At Big
Radius
31 mW
>341 nN
(0.09±0.31) nN
203 mW
>2234 nN
(0.10±0.39) nN
... Last but not least, Taylor predicted that an EMDrive operating at optical frequencies instead of microwaves might be more compact and efficient [28]. This was experimentally investigated by ourselves in a separate paper [29]. The continuous development of the various setups provided us with a good understanding of different experimental artefacts and led to the development of a reliable setup that eliminated spurious interactions and drastically boosted our sensitivity to below the photon pressure force, which is our design benchmark for propellantless propulsion. ...
Conference Paper
Full-text available
The EMDrive is a proposed propellantless propulsion concept claiming to be many orders of magnitude more efficient than classical radiation pressure forces. It is based on microwaves, which are injected into a closed tapered cavity, producing a unidirectional thrust with values of at least one mN/kW. This was met with high scepticism going against basic conservation laws and classical mechanics. However, several tests and theories appeared in the literature supporting this concept. Measuring a thruster with a significant thermal and mechanical load as well as high electric currents, such as those required to operate a microwave amplifier, can create numerous artefacts that produce false-positive thrust values. After many iterations, we developed an inverted counterbalanced double pendulum thrust balance, where the thruster can be mounted on a bearing below its suspension point to eliminate most thermal drift effects. In addition, the EMDrive was self-powered by a battery pack to remove undesired interactions due to feedthroughs. Using a geometry and operating conditions close to the model by White et al that reported positive results published in the peer-reviewed literature, we found no thrust values within a wide frequency band including several resonance frequencies. Our data limits any anomalous thrust to below the force equivalent from classical radiation for a given amount of power. This provides strong limits to all proposed theories and rules out previous test results by more than three orders of magnitude.
... An "Atomic-like" structure at the Planck scale produces a thermodynamic layer that is used to describe superradiant radiation sourced by Unruh radiation. The photon absorption and emission forces (F) are symmetric around the fiberoptic loop and anomalous acceleration is constrained by emdrive IR-laser balance beam experiments [12]. ...
Conference Paper
Full-text available
A theoretical foundation required to measure the effects of quantum statistics on inertia and gravity is presented. Optical pressure in fiberoptic loops, caused by the reflection of electromagnetic radiation, is used to produce spontaneously emitted Unruh photons in the fiberoptic. The Unruh photons stimulate the emission of superradiant photons in the accelerated reference frame, that are observed as photon pairs produced by fiberoptic heat in the laboratory reference frame. An analogy using tidal friction superradiance is presented. Inertia is defined as an entropic force that is emergent from the IKKT matrix model and caused by "mild" UV/IR mixing. Dark energy density is used to define the source of the quantum statistical fluctuations responsible for inertia and the to-be measured quantum statistical effects. Recent analysis of Unruh photons, measured at CERN and produced by accelerating positrons, averages with the superradiant photons produced in the Bosonic fiberoptic to produce IKKT supersymmetric mixed states.
... An "Atomic-like" structure at the Planck scale produces a thermodynamic layer that is used to describe superradiant radiation sourced by Unruh radiation. The photon absorption and emission forces (F) are symmetric around the fiberoptic loop and anomalous acceleration is constrained by emdrive IR-laser balance beam experiments [12]. ...
Preprint
Full-text available
A theoretical foundation required to measure the effects of quantum statistics on inertia and gravity is presented. Optical pressure in fiberoptic loops, caused by the reflection of electromagnetic radiation, is used to produce spontaneously emitted Unruh photons in the fiberoptic. The Unruh photons stimulate the emission of superradiant photons in the accelerated reference frame, that are observed as photon pairs produced by fiberoptic heat in the laboratory reference frame. An analogy using tidal friction superradiance is presented. Inertia is defined as an entropic force that is emergent from the IKKT matrix model and caused by “mild” UV/IR mixing. Dark energy density is used to define the source of the quantum statistical fluctuations responsible for inertia and the to-be measured quantum statistical effects. Recent analysis of Unruh photons, measured at CERN and produced by accelerating positrons, averages with the superradiant photons produced in the Bosonic fiberoptic to produce IKKT supersymmetric mixed states.
Article
Propellantless propulsion concepts based on electromagnetic waves like the EMDrive are claimed to be far superior with respect to the state of spacecraft propulsion systems. Such devices consist of enclosed cavities with different geometric shapes that are injected with electromagnetic waves, producing unidirectional thrust without expelling propellant. Additional concepts emerged from theories like quantised inertia and involve laser-type EMDrives with optical cavity resonators and fiberoptic loops in the infrared spectrum. Claimed forces of these devices in the micronewton range are confronted with growing scepticism when basic conservation laws are applied. With cutting-edge measurement devices, we were able to characterize these concepts in a space-like environment with nanonewton resolution for thruster masses of up to 10 kg. Additionally, we enhanced our inverted double pendulum thrust balance with the ability to perform thrust measurements at cryogenic temperatures (65 K) to operate also a superconducting EMDrive that was claimed have orders of magnitude higher thrust compared to classical resonators. In this paper, we present changes to each setup, based on criticism to our latest results, as well as thrust measurements of each device. Neither the EMDrive cavities nor the infrared laser resonators created a net-thrust above our balance noise. With the exception of the superconducting EMDrive, our data limits anomalous thrust below the threshold of classical propulsion with photon pressure for equivalent power-levels. Despite the enhancements made to each device, we did not detect any evidence in favour of the proposed theories.
Conference Paper
Facing the ever-growing commercialisation of space, particularly within low earth orbit, the academic space sector has reached a pivotal point that will define its role in the upcoming decades. At the same time, space exploration has reached its biggest momentum since the Apollo era. In the Global Exploration Roadmap, the leading space fairing nations defined the way ahead: via cis-lunar space and the moon to Mars. However, 50 years after the Apollo missions, many challenges still remain unsolved, especially for manned missions. This is where academic institutions like universities could play again a key role, as they did when paving the way for the democratisation of low earth orbit. The Chair of Space Systems at the Institute of Aerospace Engineering at TU Dresden conducts comprehensive research, ranging from breakthrough space propulsion over miniaturised systems for satellites to scientific payloads and physico-chemical processes-intensively lab tested and flown in space. In particular, our research for space exploration is focused on novel propulsion systems (e.g. miniaturised ion thrusters and aerospike engines for landers), energy systems (e.g. miniaturised fusion reactors and flexible foil based thermo-electrics) and electrochemical processes (carbon dioxide electrolysis, miniaturised and fast-response gas sensors for extreme applications, in-situ resource utilisation for oxygen and fuel production). This extensive expertise is useful in various areas of space exploration. This paper aims to provide a comprehensive overview of these developments in order to initiate a critical discussion on their application for space exploration, exchange ideas and foster collaborations to accelerate innovations.
Conference Paper
Full-text available
The EMDrive is a proposed propellantless propulsion concept claiming to be many orders of magnitude more efficient than classical radiation pressure forces. It is based on microwaves, which are injected into a closed tapered cavity, producing a unidirectional thrust with values of at least one mN/kW. This was met with high scepticism going against basic conservation laws and classical mechanics. However, several tests and theories appeared in the literature supporting this concept. Measuring a thruster with a significant thermal and mechanical load as well as high electric currents, such as those required to operate a microwave amplifier, can create numerous artefacts that produce false-positive thrust values. After many iterations, we developed an inverted counterbalanced double pendulum thrust balance, where the thruster can be mounted on a bearing below its suspension point to eliminate most thermal drift effects. In addition, the EMDrive was self-powered by a battery pack to remove undesired interactions due to feedthroughs. Using a geometry and operating conditions close to the model by White et al that reported positive results published in the peer-reviewed literature, we found no thrust values within a wide frequency band including several resonance frequencies. Our data limits any anomalous thrust to below the force equivalent from classical radiation for a given amount of power. This provides strong limits to all proposed theories and rules out previous test results by more than three orders of magnitude.
Article
Full-text available
Truncated cone-shaped cavities with microwaves resonating within them (emdrives) move slightly towards their narrow ends, in contradiction to standard physics. This eect can be predicted by a model called quantised inertia (MiHsC) which assumes that the inertia of the microwaves is caused by Unruh radiation, more of which is allowed at the wide end. Therefore, photons going towards the wide end gain inertia, and to conserve momentum the cavity must move towards its narrow end, as observed. A previous analysis with quantised inertia predicted a controversial photon acceleration, which is shown here to be unnecessary. The previous analysis also mis-predicted the thrust in those emdrives with dielectrics. It is shown here that having a dielectric at one end of the cavity is equivalent to widening the cavity at that end, and when dielectrics are considered then quantised inertia predicts these results as well as the others. As a test, quantised inertia predicts that an emdrive's thrust can be enhanced by using a dielectric at the wide end.
Article
Full-text available
The accurate, direct measurement of thrust or impulse is one of the most critical elements of electric thruster characterization, and it is one of the most difficult measurements to make. This paper summarizes recommended practices for the design, calibration, and operation of pendulum thrust stands, which are widely recognized as the best approach for measuring micronewton- to millinewton-level thrust and micronewton-per-second-level impulse bits. The fundamentals of pendulum thrust stand operation are reviewed, along with the implementation of hanging pendulum, inverted pendulum, and torsional balance configurations. The methods of calibration and recommendations for calibration processes are presented. Sources of error are identified, and methods for data processing and uncertainty analysis are discussed. This review is intended to be the first step toward a recommended practices document to help the community produce high-quality thrust measurements. © 2016 by the American Institute of Aeronautics and Astronautics, Inc.
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Full-text available
It has been shown that cone-shaped cavities with microwaves resonating within them move slightly towards their narrow ends (the emdrive). There is no accepted explanation for this. Here it is shown that this effect can be predicted by assuming that the inertial mass of the photons in the cavity is caused by Unruh radiation whose wavelengths must fit exactly within the cavity, using a theory already applied with some success to astrophysical anomalies where the cavity is the Hubble volume. For the emdrive this means that more Unruh waves are “allowed” at the wide end, lea ding to a greater inertial mass for the photons there. The gain of inertia of the photons when they move from the narrow to the wide end, and the conservation of momentum, predicts that the cavity must then move towards the narrow end, as observed. This mode l predicts the available observations quite well, although the observational uncertainties are not well known.
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Photonic Laser Propulsion: Proof-of Concept Demonstration Young K. Bae∗ Bae Institute, Tustin, California 92780 DOI: 10.2514/1.32284 Results of the first demonstration of a subscale Photonic Laser Propulsion engine, Photonic Laser Thruster, PLT, are reported in this Note. Significant thrust was produced by a small laboratory-scale PLT and measured in a laboratory environment. Originally, it was assumed that the operational principle of PLT would be similar to that of the passive resonant optical cavity, which is highly sensitive to the change in the cavity length. Thus, PLT was assumed to be useful only for static applications, such as PTFF. However, during the test prototype operation, it was discovered that PLT is highly stable against perturbations in optical cavity parameters. This discovery enables the expansion of PLT applications to wide ranges of dynamic propulsion applications, including PLP, as mentioned previously. In this demonstration setup, the extracavity laser power, P, was maximized with R ~ 0.8, and P obtained with R ~ 0.99967 was about a factor of 10 smaller than that with R ~ 0.8. Therefore, if there was no effect of the absorption and scattering, the maximum obtainable thrust in the current PLT with R ~ 0:99967 is estimated to be ~350 micro-N. The maximum photon thrust, 35 micro~N, observed in the present PLT was obtained at a pump diode laser power a factor of 2 smaller than that of the maximum pump diode laser power limited by the crystal heating. If there was no heating effect, it was estimated that the current PLT with R ~ 0.99967 is estimated to generate ~70 micro-N, and additionally, if there was no effect from the absorption and scattering, its maximum obtainable thrust is estimated to be ~700 micro-N.
Article
Full-text available
The property of inertia has never been fully explained. A model for inertia (MiHsC or quantised inertia) has been suggested that assumes that 1) inertia is due to Unruh radiation and 2) this radiation is subject to a Hubble-scale Casimir effect. This model has no adjustable parameters and predicts the cosmic acceleration, and galaxy rotation without dark matter, suggesting that Unruh radiation indeed causes inertia, but the exact mechanism by which it does this has not been specified. The mechanism suggested here is that when an object accelerates, for example to the right, a dynamical (Rindler) event horizon forms to its left, reducing the Unruh radiation on that side by a Rindler-scale Casimir effect whereas the radiation on the other side is only slightly reduced by a Hubble-scale Casimir effect. This produces an imbalance in the radiation pressure on the object, and a net force that always opposes acceleration, like inertia. A formula for inertia is derived, and an experimental test is suggested.
Article
The Photonic Laser Thruster (PLT) efficiently uses photons as propellant and thus promises to enable innovative space endeavors beyond the reach of propellant-based conventional thrusters. Previously, the proof-of-principle demonstration of PLT used a neodymium-doped yttrium aluminum garnet (Nd:YAG) rod gain medium and resulted in the maximum thrust of 35 μN. This Paper reports 100 times scaling up of PLT using a ytterbium-doped yttrium aluminum garnet (Yb:YAG) thin-disk gain medium and the first demonstration of propelling and stopping a 0.75 kg mock cube satellite over 2 m in a Class-1000 cleanroom. A thrust stand for PLT was established with a radiation pressure sensor that reduced the thermal convection effect and the configuration complexity. The maximum achieved thrust and specific thrust were 3.36+-0.18 mN and 7.1+- 0.6 mN∕kW, respectively. Further development of PLT using existing high-power laser technologies is projected to increase its specific thrust to 68+-10 mN∕kW, on a par with electric thrusters. The present results conclude that innovative PLT applications, such as propellant-free orbit maneuvering and stationkeeping, are within the reach of existing spacecraft and high-power laser technologies. In addition, the feasibility of PLT-based launchers and landers is discussed.
Article
Recent analyses of spacecraft flyby, Galileo, NEAR, Cassini, and Rosetta spacecraft suggest unusual short-lived changes in their inertia and, likewise, unexplained accelerations. One theory which possibly explains these anomalies assumes the inertial changes are due to Unruh radiation modified by a Hubble-scale Casimir effect. Laboratory scale experiments to demonstrate and verify this theory turn out to be in the form of an asymmetric microwave resonator, also known as, the EmDrive. Various experiments have been performed and are ongoing to verify the validity of the EmDrive using microwaves, but none have been reported in the optical regime. According to the physics of the Unruh radiation and modified inertia due to Hubble-scale Casimir effect theory the net propulsive force generated is a function of the cavity Q and input power. It is proposed in this paper that a high-Q asymmetric, but stable, Fabry-Perot laser resonator should produce very large propulsive forces if the theory is correct. Experiment design to demonstrate the concept is given.
Article
In an IAC13 paper the dynamic operation of a second generation superconducting EmDrive thruster was described. A mathematical model was developed and, in this paper, that model is used to extend the performance envelope of the technology. Three engine designs are evaluated. One is used as a lift engine for a launch vehicle, another as an orbital engine for the launcher and a third as the main engine for an interstellar probe.
The EmDrive Just Won't Die
  • D Hambling
D. Hambling, "The EmDrive Just Won't Die," Popular Mechanics.