Houston Examiner 4/20/16 on-line article:
http://www.examiner.com/article/has-the-impossible-em-drive-being-tested-by-nasa-finally-been-explained
IBT 4/21/16 on-line article:
http://tinyurl.com/j4jkfmq
Just propagating incorrect conclusions it seems going from the criticism I've seen online of the original article.
Always good to give our kind readership any links to rebuttals, etc.,
I am going off the comments under the original article & on the EM Reddit.
The latter is not worth linking to IMHO. Those of us with first-hand experience communicating with the anonymous posters there found they're mostly off-topic, unsubstantiated opinions from dubious individuals, some claiming credentials they do not posses. That's a mouth-full for basically a lack of professional communications skills.
p.s. Quoting one of their more prolific users today "You're a charlatan, a dedicated crackpot, or both." I think this gives you the general idea on the level of discourse there...and it is permitted.
Intrigued by your posts about that forum, in which I have never posted, I spent time to look for myself and I found (*) a remarkable high-quality post there (author: iorgfeflkd),
under their PHYSICS thread, not the EM Drive thread, that makes a number of good technical points regarding McCulloch's theory.
Anybody interested in the EM Drive and attracted by this theory should address these points:
The suspicion begins on the first equation when they define conservation of momentum for a photon using the Newtonian formulation, which is not at all appropriate because it's classical, non-relativistic, and depends on mass. For the photon mass they invoke "MiHsC" which means "Modified Inertia due to a Hubble-scale Casimir effect," except it's not due to Hubble-scale confinement in this case, it's due to the walls of the cavity...ok fine...just say "the photon gains an effective mass due to confinement in the cavity." Anyway, they claim an accelerating object gains a proportional increase in mass due to the Unruh effect and also a cosmological factor. Ok, but the photon has zero mass anyway so this won't increase it, according to his own equation.
This is possible because the photons involved are travelling at the speed of light and are bouncing very fast between the two ends of seperation s and their acceleration (a ∼ v^2 /s) is so large that the Unruh waves that are assumed to produce their inertial mass are about the same size as the cavity, so they can be affected by it, unlike the Unruh waves for a terrestrial acceleration which would be far to long to be affected by the cavity
Ok, what? I guess it's some sort of effective "expectation" acceleration for light in the cavity...plugging in some values we get about 1017 m/s^2 for acceleration and applying Wien's law to the Unruh temperature (is that what they're saying?) gives a peak wavelength of 1.5 meters. Ok, 10 times the size of the cavity...where does the inertial mass come from? This is not made clear. Nowhere in this derivation does it say where the inertial mass comes from for the photons, and then it continues to use this mass in the rest of its derivations so I can't really follow it. He uses the relation E=mc^2 to get rid of the photon mass (again, this does not apply to photons) and handwaves this energy into the time-integrated power. Comparing his equation 9 with his equation 7, he is claiming that photons in this cavity have a rest mass of 832 times that of a proton. Experimental bounds on photon mass are thirty orders of magnitude smaller. I thiiiiink that's where he's getting this force from. This also predicts the photons are propagating at roughly 1 m/s. A rough calculation puts the excess mass due to all these photons at about .4 grams, which is proportional to the square of power. Because the force is linear with power, and the excess mass due to photons increases with the square of power, this predicts that acceleration will actually decrease with enough power
In my opinion if they are going to invoke the Unruh effect which comes from quantum field theory, they should work in a formalism that is consistent with quantum field theory and not use Newtonian mechanics with combined massive/massless particles.
The final result is that they derive a force/power ratio for the system of 216 millinewtons/kilowatt (4.6 km/s). If we compare this to what is expected from radiation pressure, which actually exists, that is just the speed of light so 0.003 mN/kW.
tl;dr [too long; didn’t read] the photon gains mass proportional to the microwave power in the cavity, and then gains more mass due to the Unruh radiation from accelerating between the cavity walls.
Why did I spend so much time on this.
edit: I was out for a jog and realized another crucial flaw: it invokes the Unruh effect to explain why the "cone-ness" causes thrust. It uses the acceleration c^2 / d to get the Unruh radiation. However, the photon mass imposed by the cavity (which is a different effect, in this paper) reduces the velocity to 1 m/s, bringing the acceleration down by a factor of 9x10^16 . I think if this were to be propagated through, it would bring the expected force down by the same amount.
It is an excellent post, because rather than make vague qualitative remarks, it actually does what physicists and engineers do: it calculates, using numbers, to ascertain the validity of what is being proposed.
There are a number of important points here questioning the theory (importantly, for example that the rest mass of the photons inside the cavity would exceed by orders of magnitude the rest mass of a proton).
On the other hand, the following point
Because the force is linear with power, and the excess mass due to photons increases with the square of power, this predicts that acceleration will actually decrease with enough power
is a very interesting possible way out of the energy paradox (as the acceleration will actually decrease with enough input power): recall that because according to these EM Drive theories (Shawyer and McCulloch) the force is proportional to the input power, and this exceeds by orders of magnitude the force/PowerInput of a photon rocket, eventually (at high enough speed) the kinetic energy exceeds the input energy. However, since according to McCulloch's theory the excess mass of the photon increases with the square of the power, the acceleration will reach a plateau and will actually eventually decrease, and so will the increase in speed and hence the kinetic energy may be limited,
posing the question whether energy, after all, may be conserved under the assumptions of McCulloch's theory.Has this way out of the energy paradox been previously explored?---------
(*) Hat tip to NSF member WhatAFeynDay