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#2100 by JohnFornaro on 15 Oct, 2014 00:57
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From this it is clear that L is the Unruh wave length and that the cavity walls are assumed to act like a Hubble horizon.
Fixed that for ya. This is an assumption or a speculation, not a proven fact.
Correct me if I'm wrong. -
#2101 by Rodal on 15 Oct, 2014 01:25
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From this it is clear that L is the Unruh wave length and that the cavity walls are assumed to act like a Hubble horizon.
Fixed that for ya. This is an assumption or a speculation, not a proven fact.
Correct me if I'm wrong.
These are the critical assumptions:
1) the microwaves-photons bouncing around within the EM Drive cavity have inertia (due to their momentum), which is determined by McCulloch's quantised inertia.
2) the microwaves-photons within the EM Drive cavity undergo momentum change ("acceleration") large enough to produce McCulloch inertial changes due to Unruh radiation . The momentum change ("acceleration") must be greater than 8 c^2 / (DiameterOfBaseOfCone).
3) In McCulloch's quantised inertia the Unruh waves are allowed only if they fit exactly within the Hubble horizon (or within a local Rindler horizon). For the formula to apply the EM Drive cavity walls must act like a horizon.
Photons exhibit inertia by resisting a change in momentum. (Conservation of momentum is one of the most fundamental laws of Physics, in General Relativity, Quantum Mechanics and in Continuum Mechanics). As Aerospace Scientists and Aerospace Engineers know, conservation of momentum is more general than Newton's 2nd Law for rigid bodies (for example as in the rocket equation, where the mass of the rocket changes as it ejects propellant).
The momentum of a photon is given by p =hk = (h /(2*Pi) )* k, where k is the wave vector, which has magnitude 2*Pi*frequency/c and points in the same direction as the propagation direction of the photon. Therefore the magnitude of the photon's momentum is h*frequency/c .
The momentum of a photon can change in two possible ways:
A) its direction can change. For example as in gravitational lensing, where the path of a photon changes due to gravitation.
B) its frequency can change. For example as in gravitational redshift. As it moves away from a much more massive body it loses energy and momentum. As it loses momentum, it becomes redshifted. -
#2102 by ThinkerX on 15 Oct, 2014 05:09
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Ok...if I am understanding the more recent posts correctly, then the thrust produced by this device is very frequency dependent?Quote
1) the microwaves-photons bouncing around within the EM Drive cavity have inertia (due to their momentum), which is determined by McCulloch's quantised inertia.
2) the microwaves-photons within the EM Drive cavity undergo momentum change ("acceleration") large enough to produce McCulloch inertial changes due to Unruh radiation . The momentum change ("acceleration") must be greater than 8 c^2 / (DiameterOfBaseOfCone).
3) In McCulloch's quantized inertia the Unruh waves are allowed only if they fit exactly within the Hubble horizon (or within a local Rindler horizon). For the formula to apply the EM Drive cavity walls must act like a horizon.
So the idea would be to make certain points 2 and 3 above are 'in sync?' Which, if I follow the previous posts right, means the size of this device and angle of the cone are also crucial?
Or, in other words, 'tuning' this thing to work correctly - or at all - is as important as the mechanism design itself. I wonder if this could account for some of the past experimental flops? -
#2103 by Rodal on 15 Oct, 2014 12:01
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Whether the experimental response is an experimental artifact or whether it is thrust that may or may not be useful eventually for space propulsion, it is a fact that it is very dependent on tuning the device to reach maximum amplitude resonance. As the amplitude of resonance is in general a very nonlinear response of frequency, and as in this case the researchers are purposely seeking high Q (low damping), the bandwidth of the response is very small and hence it is difficult to produce a consistent response. This has been brought up by Ludwick in his excellent post above. The uncertainty in the results has to do with resonance, high Q (low damping), small bandwidth, knowing at what precise frequency the maximum amplitude of resonance takes place and keeping the frequency at that critical frequency.
for high Q, Q ~ (ResonantFrequency) / (half-power bandwidth); so
(half-power bandwidth) ~ (ResonantFrequency) / Q
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#2104 by JohnFornaro on 15 Oct, 2014 13:14
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This is understood by any structural engineer using beam equations instead of fully 3-D equations that are unsolvable without numerical analysis.
I'm partly new, but mostly older, ergo am rusty with structural engineering. But structural engineering is actually doable at my level; here's a simple beam program I wrote nearly twenty years ago.
Point being, I fully appreciate the value of the 1D analysis, as it would have pragmatic value in the schematic design of starships, just as the simple equztions of beam stiffness, yada yada are completely sufficient for structural engineering.Quote from: BonesThe usefulness of closed-form solutions ... is certainly understood by Aerospace Engineers.
It was never a question of whether or not AE's could "understand" these complex equations. I continue to point out that the Unruh Effect is hypothetical. If it is real, then it appears to predict some of the "anomalous thrusts", but by no means all of them. If the Hubble constant is not known, and the theory depends on this knowledge to derive the Unruh wavelenth and the sweet frequency spot, it causes me emotional struggle:Quote from: AeroAnd just in case you are unaware of it, the best estimate of the value of the Hubble constant has changed several times during the past 10 years. Current best estimate seems to be 2.19725E-18/s with uncertainty of about 5%.
It seems to be the bane of the theorist, shifting constants.
As an aside, I'm guessing that it isn't a "constant", it is a "habit".Just for fun, let's say the prediction curve is absolutely accurate and based on 70 years of experience w/ copper waveguides and resonators. Then the difference w/ these tapered chambers represent a loss of power which is going somewhere
The copper waveguide is full of compressed hummingbird wings (CHBW), which are absorbing the heat. There is no evidence presented regarding the interior of the copper device. If not full of CHBW, it is full of air. Which should get warm, if the 34% chart is accurate. Right?The uncertainty experimental bars are very large and they overwhelm the very small frequency range that was explored.
A guitar is either in tune, or it is not. I wonder if the theorists here believe that there is a special sauce quality about the frequency ranges investigated?Quote from: AeroWhat can we say about the nature of the acceleration coupling to the Unruh wave?
Well, yeah.
I gotta run to the store and get some more peanuts.
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#2105 by JohnFornaro on 15 Oct, 2014 13:20
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In McCulloch's quantised inertia the Unruh waves are allowed only if they fit exactly within the Hubble horizon (or within a local Rindler horizon). For the formula to apply the EM Drive cavity walls must act like a horizon.
So, you have to assume that the copper walls "must" act like a horizon. Which suggests an experiment to determine if they do or not, before erecting the thoretical house of cards too high. -
#2106 by Rodal on 15 Oct, 2014 14:32
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Overdue emphasis on physical explanations rather than mathematical examination of the data is misplaced, particularly with anomalous results of early experimental results with high uncertainty bars.In McCulloch's quantised inertia the Unruh waves are allowed only if they fit exactly within the Hubble horizon (or within a local Rindler horizon). For the formula to apply the EM Drive cavity walls must act like a horizon.
So, you have to assume that the copper walls "must" act like a horizon. Which suggests an experiment to determine if they do or not, before erecting the thoretical house of cards too high.
An objective, cool, mathematical viewpoint (rather than passionate subjective beliefs) is called for.
A great example of this is Maxwell's book on Electromagnetism. Maxwell's equations are still correct. However, the physical reasons for electromagnetic waves are different. A reading of Maxwell's book is very revealing on the need for a mathematical language rather than words. Another example is the arguments concerning corpuscular vs. the wave explanations for light (it turns out that light is both: both a particle and a wave).
This is why mathematics, rather than words, is the language of Physics.
At this point, the emphasis should be on the mathematical formula presented by McCulloch. McCulloch's simple formula, without any fudge factors, and with a minimum of parameters, does a much better job at predicting the experimental results than anything else presented so far:
Force = ( PowerInput * Q / frequency ) * (1/DiameterSmallBase - 1/DiameterBigBase)
Ink spent arguing about unwarranted extrapolations to pointy cones, unexamined geometries, unexamined frequencies, unexamined Q, unexamined power inputs, are the responsibility of those who engage on those extrapolations.
It just amounts to argumentative noise based on randomness emanating from extrapolations.
Arguments based on such random extrapolations are futile and sterile. -
#2107 by zen-in on 15 Oct, 2014 16:19
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Whether the experimental response is an experimental artifact or whether it is thrust that may or may not be useful eventually for space propulsion, it is a fact that it is very dependent on tuning the device to reach maximum amplitude resonance. As the amplitude of resonance is in general a very nonlinear response of frequency, and as in this case the researchers are purposely seeking high Q (low damping), the bandwidth of the response is very small and hence it is difficult to produce a consistent response. This has been brought up by Ludwick in his excellent post above. The uncertainty in the results has to do with resonance, high Q (low damping), small bandwidth, knowing at what precise frequency the maximum amplitude of resonance takes place and keeping the frequency at that critical frequency.
The resonant frequency of the device in the paper by Brady, White, et al would to be determined by two things: The diameter of the loop antenna inside the device and to a lessor extent the dielectric material near it. Earlier I stated there had to be some kind of ceramic resonator inside. But I know think there isn't one and the concensus is that the dielectric is a large disk of polystyrene in the small end. A small loop will have a natural frequency based on its inductance and parasitic capactance. The Q of a loop antenna inside a shielded and grounded enclosure will be quite high. I think the different experimental runs shown in table E of the paper were done after changing that loop. The resonant frequency and Q were then determined with the network analyzer. Bob Ludwick stated it is very difficult to get a VCO precisely on frequency when the Q is high. A better method is to use the high Q cavity itself as the frequency determining element and to build a free-running high power RF oscillator around it. It will automatically lock to the resonant frequency and track any changes due to temperature. Low phase noise RF generators use tuneable cavities driven at low power. Whether that will produce a propellantless propulsion device is still TBD. I still think there are undiscovered thermal or magnetic errors in these experiments.
for high Q, Q ~ (ResonantFrequency) / (half-power bandwidth); so
(half-power bandwidth) ~ (ResonantFrequency) / Q -
#2108 by Rodal on 15 Oct, 2014 16:36
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Earlier I stated there had to be some kind of ceramic resonator inside. But I know think there isn't one and the concensus is that the dielectric is a large disk of
polystyrenein the small end.
Notpolysterene (PS). The dielectric was Polyethylene (PE), as first found by @notsosureofit. -
#2109 by frobnicat on 15 Oct, 2014 16:40
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@Rodal : science is not only reason but also passion. Hopefully this is a passion for truth and at the end, reason wins. Nevertheless a minimum of stamina, intuition and some amount of randomness and chaos plays its role in discoveries, as AI as shown. So futile maybe, not always sterile, just often. And unless explicitly stated otherwise by admins, can't we have a bit of fun with the words and ideas ? Obviously we are all significant parts of reality, we have some right to have a passionate experimental opinion about what is reality and how it works. I was considering building a random formula generator for seeing best empirical fit, but alas the data are really sparse.
Still struggling to see how the momentum conservation would propagate to rest of cosmos in some "photon Unruh" generated perturbation, like pushing on the walls of its own universe or pushing on one's own acceleration. Surely this costs some energy, how can this energy be less than c*acquired_momentum or else borrowed from some potential, that is, communicated to the outside ? Also I fail to see how the "Unruh effect zone" could act differently when something is entering than leaving, I guess it is a dynamic "potential" but in this case it costs energy to maintain (there is more energy put in a pool wave generator than a surfer can recover). Anyway I enjoy reading both the serious attempts at synthesis and futile extrapolations. Hope we are not thrown from the bar by the keeper for all this noise (jetés du bar par le tenancier à cause de tout ce bruit)
All my best
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#2110 by Notsosureofit on 15 Oct, 2014 16:42
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Whether the experimental response is an experimental artifact or whether it is thrust that may or may not be useful eventually for space propulsion, it is a fact that it is very dependent on tuning the device to reach maximum amplitude resonance. As the amplitude of resonance is in general a very nonlinear response of frequency, and as in this case the researchers are purposely seeking high Q (low damping), the bandwidth of the response is very small and hence it is difficult to produce a consistent response. This has been brought up by Ludwick in his excellent post above. The uncertainty in the results has to do with resonance, high Q (low damping), small bandwidth, knowing at what precise frequency the maximum amplitude of resonance takes place and keeping the frequency at that critical frequency.
The resonant frequency of the device in the paper by Brady, White, et al would to be determined by two things: The diameter of the loop antenna inside the device and to a lessor extent the dielectric material near it. Earlier I stated there had to be some kind of ceramic resonator inside. But I know think there isn't one and the concensus is that the dielectric is a large disk of polystyrene in the small end. A small loop will have a natural frequency based on its inductance and parasitic capactance. The Q of a loop antenna inside a shielded and grounded enclosure will be quite high. I think the different experimental runs shown in table E of the paper were done after changing that loop. The resonant frequency and Q were then determined with the network analyzer. Bob Ludwick stated it is very difficult to get a VCO precisely on frequency when the Q is high. A better method is to use the high Q cavity itself as the frequency determining element and to build a free-running high power RF oscillator around it. It will automatically lock to the resonant frequency and track any changes due to temperature. Low phase noise RF generators use tuneable cavities driven at low power. Whether that will produce a propellantless propulsion device is still TBD. I still think there are undiscovered thermal or magnetic errors in these experiments.
for high Q, Q ~ (ResonantFrequency) / (half-power bandwidth); so
(half-power bandwidth) ~ (ResonantFrequency) / Q
Used to do this w/ re-entrant cavities where it worked well. Not sure about which mode it might lock to in a tapered cavity, but I'm sure that could be worked out. -
#2111 by Rodal on 15 Oct, 2014 16:51
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science is not only reason but also passion. ...
All my best
Rule Britannia. Better to keep a stiff upper lip.
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#2112 by Rodal on 15 Oct, 2014 17:07
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We continue our statistical exploration of the experimental data. We now examine the experimental and predicted Power Input, for the EMDrive experiments conducted in the US, UK and China, and reported in my my last post with data (please refer to: http://forum.nasaspaceflight.com/index.php?topic=29276.msg1270264#msg1270264 ).
The horizontal axis shows the experimentally measured Power Input.
The vertical axis shows the predicted Power Input from McCulloch's formula (inverted to express the Power Input as a function of the other variables: the measured force, the measured Q, the measured frequency, and the measured diameter of the small and big bases of the truncated cone), expressed as follows:
PredictedPowerInput = (ExperimentalForce)*Frequency/(Q*(1/Dsmall-1/Dbig))
It is obvious from the plot that:
1) There is a significant experimental dependence on Power Input, the R^2 value is statistically significant: 81% (and this is including the outlier data: the very anomalous test reported by Brady et.al at a frequency of 1.937 GHz). The coefficient of determination (R^2) for the Power Input is identical to the coefficient of determination for Q.
2) The actual Power Input dependence is linear as predicted by McCulloch's formula, as shown by the least squares formula shown in the box. It is certainly linear within the (obvious from plotting the data) experimental uncertainty in the measurements.
3) The fact that the predicted curve (in red) is off by a factor of ~21%, as I have previously addressed in Prof. McCulloch's blog is expected, since McCulloch's formula is a 1 Dimensional simplification of the full 3-D Modified Inertia formulation: as the simplified formula neglects the Unruh wave contribution from the curved sides of the cone (the simplified formula only uses the flat areas into consideration).
4) It is obvious from the plot that the power input used by NASA Eagleworks is completely insignificant, lower by orders of magnitude than the power inputs used by Shawyer in the UK and by Prof. Juan Yang in China.
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#2113 by Rodal on 15 Oct, 2014 17:39
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We finalize our statistical exploration of the experimental data. We now examine the experimental and predicted Geometrical Information, for the EMDrive experiments conducted in the US, UK and China, and reported in my my last post with data (please refer to: http://forum.nasaspaceflight.com/index.php?topic=29276.msg1270264#msg1270264 ).
The horizontal axis shows the experimentally measured quantity: (1/DiameterOfSmallBase-1/DiameterOfBigBase).
The vertical axis shows the predicted (1/DiameterOfSmallBase-1/DiameterOfBigBase) from McCulloch's formula (inverted to express (1/DiameterOfSmallBase-1/DiameterOfBigBase) as a function of the other variables: the measured force, the measured Q, the measured frequency, and the measured power input), expressed as follows:
Predicted(1/DiameterOfSmallBase-1/DiameterOfBigBase) = (ExperimentalForce)*Frequency/(Q*PowerInput)
It is obvious from the plot that:
1) There is a significant experimental dependence on (1/DiameterOfSmallBase-1/DiameterOfBigBase) , the R^2 value is very statistically significant: 90% (and this is including the outlier data: the very anomalous test reported by Brady et.al at a frequency of 1.937 GHz). It is a surprising find (at least to me) that the most statistically significant coefficient of determination (R^2) is this geometrical information. It is even more significant than the Power Input and the Q. This represents a big challenge for those attempting to explain the experimental data as an experimental artifact, either due to magnetic, thermal or any other reason not evidently related to the dimensions of the bases of the truncated cone.
2) The dependence on (1/DiameterOfSmallBase-1/DiameterOfBigBase) is linear as predicted by McCulloch's formula, as shown by the least squares formula shown in the box. It is certainly linear within the (obvious from plotting the data) experimental uncertainty in the measurements.
3) The fact that the predicted curve (in red) is off by a factor of ~30%, as I have previously addressed in Prof. McCulloch's blog is expected, since McCulloch's formula is a 1 Dimensional simplification of the full 3-D Modified Inertia formulation: as the simplified formula neglects the Unruh wave contribution from the curved sides of the cone (the simplified formula only uses the flat areas into consideration).
4) It is apparent from this data that Shawyer in the UK and Prof. Juan Yang in China had a better handle on the importance of (1/DiameterOfSmallBase-1/DiameterOfBigBase) as compared to NASA Eagleworks. NASA Eagleworks tested drives that had the least amount of (1/DiameterOfSmallBase-1/DiameterOfBigBase). The Cannae device is practically symmetric and the truncated cone tested by NASA Eagleworks has a significantly smaller difference between the inverse of the base diameters (1/DiameterOfSmallBase-1/DiameterOfBigBase) than Shawyer's and China's drives. This unnecessarily limited the thrust output of the NASA Eagleworks measurements. NASA Eagleworks should learn from Shawyer and China regarding the importance of this geometrical parameter
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#2114 by Rodal on 15 Oct, 2014 18:52
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We summarize our statistical exploration of the experimental data. We have examined the experimental and predicted Power Input, Q, Frequency and Geometrical Information, for the EMDrive experiments conducted in the US, UK and China, and reported in my my last post with data (please refer to: http://forum.nasaspaceflight.com/index.php?topic=29276.msg1270264#msg1270264 ).
The horizontal axis shows the experimentally measured quantity.
The vertical axis shows the prediction from McCulloch's formula (inverted to express the predicted variable as a function of the other variables: the measured force, and the remaining variables). For example, when presenting the difference between the inverted diameters of the bases of the truncated cone, the expression is as follows:
Predicted(1/DiameterOfSmallBase-1/DiameterOfBigBase) = (ExperimentalForce)*Frequency/(Q*PowerInput)
McCulloch's simple formula, without any fudge factors, and with a minimum of parameters, does a much better job at predicting the experimental results than anything else presented so far:
Force = ( PowerInput * Q / frequency ) * (1/DiameterSmallBase - 1/DiameterBigBase)
STATISTICAL ANALYSIS OF EMDrive EXPERIMENTAL DATA
1) The results of this statistical data exploration should be (perhaps) very surprising to those, like me, that started their analysis of the EM Drives experimental data thinking that they must be an experimental artifact.
2) There is a significant experimental dependence on the following variables, presented here in the following descending order of coefficient of determination (R^2) :
(1/DiameterOfSmallBase-1/DiameterOfBigBase) with R^2 = 90%
Q (resonance quality factor) with R^2 = 81%
Power input with R^2 = 81%
The variable with the highest coefficient of determination (R^2) is the difference of inverse diameters for the bases of the truncated cone, followed by Q and the power input.
NASA Eagleworks tested drives had the least amount of (1/DiameterOfSmallBase-1/DiameterOfBigBase). The Cannae device is practically symmetric and the truncated cone tested by NASA Eagleworks has a significantly smaller difference between the inverse of the base diameters (1/DiameterOfSmallBase-1/DiameterOfBigBase) than Shawyer's and China's drives. This unnecessarily limited the thrust output of the NASA Eagleworks measurements. NASA Eagleworks should learn from Shawyer and China regarding the importance of this geometrical parameter
3) Including all the data (including an obvious outlier) shows practically no statistical dependence on frequency. The coefficient of determination (R^2) for frequency a very poor R^2 = - 12%. There is a clear statistical outlier (Brady et.al. at 1.937 GHz) that I have repeatedly pointed out. The fact that this is a statistical outlier is evident from the plot. Essentially, including the statistical outlier indicates that the uncertainty overwhelms the power to conclude anything concerning frequency dependence. The uncertainty experimental bars are very large and they overwhelm the very small frequency range that was explored. The experiments in the US, UK and China did not peform a satisfactory exploration of frequencies. Basically only two frequency ranges have been explored: ~1.9 GHz in the US and ~2.5 GHz in the UK and China. Considering the data without the outlier gives a still weak statistical dependence: R^2 = 22%. Essentially inversely proportional to the frequency, as predicted by McCulloch, but again there is not enough statistical data to make any statistical conclusion regarding frequency dependence.
A very important issue is the fact that resonance amplitude is a very nonlinear function of frequency. Besides this being expected, such resonance amplitude nonlinear dependence on frequency is shown in the S22 plots. Hence it is not surprising that a formula that is inversely proportional to frequency cannot possibly reflect the huge changes in amplitude resonance emanating from small changes in frequency (for example for Brady et.al. at 1.88, 1.933 and 1.937 GHz), particularly when experimenters deliberately chose to conduct their experiments at frequencies close to resonance.
4) So far, all the experimental data variation in the US (NASA Eagleworks, including the statistical outlier), the UK and China can be explained solely in terms of just three variables:
A) (1/DiameterOfSmallBase-1/DiameterOfBigBase)
B) Q (resonance quality factor)
C) Power Input
5) The uncertainty in the data is due to the very nonlinear relationship between resonance amplitude and frequency, as the researchers seek to test in conditions of highest resonance amplitude with highest Q, with concomitant very narrow power frequency bandwith, which introduces experimental uncertainty particularly when using a voltage-controlled oscillator (VCO). To quote Ludwick:
"If Brady was using a free running VCO, ’tuned’ to the resonant frequency of the thruster, there is next to zero chance that the VCO, and by extension the drive power to the thruster, stayed within the bandwidth of the thruster during the test run OR that, for the high Q thruster, a large percentage of the source power was within the thruster bandwidth, even if the center frequency of the source remained centered on the resonant frequency of the thruster. VCO’s are VERY spectrally dirty and, unless phase locked, very unstable in relation to the spectral purity required by Brady’s thruster."
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#2115 by aero on 15 Oct, 2014 20:30
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I found a relatively new paper (dated 2014) on the Unruh effect that I could almost read mostly because it has more words than equations.
http://www.scholarpedia.org/article/Unruh_effectQuoteThe Unruh effect is a surprising prediction of quantum field theory: From the point of view of an accelerating observer or detector, empty space contains a gas of particles at a temperature proportional to the acceleration. Direct experimental confirmation is difficult because the linear acceleration needed to reach a temperature 1 K is of order 1020 m/s2, but it is believed that an analog under centripetal acceleration is observed in the spin polarization of electrons in circular accelerators. Furthermore, the effect is necessary for consistency of the respective descriptions of observed phenomena, such as particle decay, in inertial and in accelerated reference frames; in this sense the Unruh effect does not require any verification beyond that of relativistic free field theory itself. The Unruh theory has had a major influence on our understanding of the proper relationship between mathematical formalism and (potentially) observable physics in the presence of gravitational fields, especially those near black holes.
The paper goes on to introduce "things" related to the effect which was most interesting. -
#2116 by Rodal on 15 Oct, 2014 20:41
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I found a relatively new paper (dated 2014) on the Unruh effect that I could almost read mostly because it has more words than equations.
http://www.scholarpedia.org/article/Unruh_effect
Yes, I agree, this is an excellent article.
This excellent article should not be used by those that don't like the Unruh radiation explanation to get side-tracked on a discussion of Unruh radiation and lose track of the fact that the experimental data and its analysis show very strong dependence on
A) the difference between the inverse of the diameters of the cone bases,
B) the quality factor Q and
C) the power input.
Instead:
Those thinking that the results are an experimental artifact should seek artifact explanations that are consistent with the experimental data being linearly dependent on just these three variables.
Those uncomfortable with the Unruh radiation explanation (how photons in a microwave cavity can be subjected to inertial changes and the required black-hole-like-accelerations ?) should seek other physical explanations that are consistent with the experimental data being linearly dependent on just these three variables.
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#2117 by frobnicat on 15 Oct, 2014 21:24
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Those thinking that the results are an experimental artifact should seek artifact explanations that are consistent with the experimental data being linearly dependent on just these three variables.
Yes dr Rodal, working on that.
Better to keep a stiff upper lip, hey !
7 data points is sparse to conduct statistical analysis but you do a great job. Though I wonder if it wouldn't be more appropriate to conduct the regressions in log log plane, as the low values dispersions tend to be squashed by the low absolute levels, while their relative dispersion around the (linear) predicted values seem more natural to me : log(experimental/predicted) or equivalently log(experimental)-log(predicted) (then squared as for the least square regression). A linearly scaling formula that predicts 1.0µN for a 1.1µN measure has as much error than predicting 1N instead of actual 1.1N. Maybe this is already the case in your R^2 results ?
Anyway, since you have the tools at hand, can I have a request for log log plots ?
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#2118 by frobnicat on 15 Oct, 2014 21:46
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@dr Rodal, I'm trying to do my homework by having a fancy machine to chew some numbers and symbols, how did you manage the following datapoints ?
- Shawyer (2008) b : 80-214 observed. Is that an apparatus calculated range of error around a single measure or experimental dispersion of many measures ? What do we take, arithmetic mean, geometric mean ?
- Juan (2012) TE011 and TE012 : geometry unknowns, good reasons to believe it's the same as Shawyer ? Considering 9 data points, knowing two are wrong ? Averaging the hypothesis ? (arithmetically or geometrically ?) Discarding those two data points would left us with nothing much...
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#2119 by aero on 15 Oct, 2014 21:58
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Quote
dF = (PQ/c)*((L/w_big)-(L/w_small)) = (PQ/f)*((1/w_big)-(1/w_small)).
Which boils down to dF = (PQ/f)*((1/w_big)-(1/w_small)).
P - Power
Q - Quality factor
f - Drive frequency
w_big - diameter of the big end
W_small - diameter of the small end.
My goodness, where is the Unruh radiation, the Hubble horizon, the Casimir effect or any other strange factors?
The only way MiHsC enters the picture is because it led Prof. M to the above equation.
As it stands the equation can be written as
dF = [ Stored power/w_big - Stored power/w_small ] / f
where stored power = Q * Power.
Does that mean anything helpful?
