It seems, after several comments I've received, that the way MiHsC (may) work on the emdrive is easily misunderstood (including by me, so I've just rewritten this blog again!). Anyway, here is an attempt to clarify it and explain why I think you get a push consistently towards the narrow end from MiHsC and why, although new physics, it is at least perfectly self-consistent. This is based on the maths in my published paper (see the reference below).
Imagine a microwave photon bouncing from end to end of the emdrive cavity (see the diagram below). As the photon goes from the narrow end to the wide end (see the lower arrows) the number of allowed Unruh waves increases because of MiHsC (more are allowed on the right because the cavity is wider) so the photon's inertial mass increases (so the right hand arrow is thicker). This means that MiHsC has disturbed momentum conservation, which can only be satisfied by applying a leftwards force to slow the photon down (its speed is represented by the arrows' length).
As the photon bounces off the right end plate and goes leftward again (upper arrows) it looses inertial mass by MiHsC (the upper left hand arrow is thinner) so the only way to satisfy momentum conservation is again to apply a leftward force to speed the photon up (the left hand arrow is longer). In both cases, to satisfy both MiHsC-induced mass changes and the conservation of momentum, a new force must appear towards the narrow end. Since the momentum at both ends is the same, the photon pressure on the end walls cancels (see this previous post). This new thrust predicted by MiHsC agrees quite well with the emdrive data (see the reference below).
McCulloch, M.E., 2015. Can the emdrive be explained by quantised inertia? Progress in Physics, 11, 1, 78-80. Link
EM waves inside a circular microwave waveguide do not travel at c, they travel much slower at a fixed Group Velocity.
The Group Velocity is fixed per the circular waveguide diameter, excitation mode, external frequency, Guide Wavelength and Cutoff Wavelength.
Any theory that is based on the EM waves inside the EMDrive moving at c, is against all known microwave waveguide physics.
This might be a difficult request but can you draw the UnRuh waves in that diagram? Thanks.
What happens when the rightward-moving photons (which have a higher inertial mass) hit the big end of the cavity? It looks like they would impart more momentum than leftward-moving photons, and so the cavity should move to the right.
I think you have it backwards. The Xmm resonant frequency at the small end is larger than the Xmm resonant frequency at the big end. Therefore, there is a loss of "potential energy" as the energy moves from the small end to the big end. To compensate for this, the frustum loses potential energy relative to this stored energy, by moving "forward" toward the small end.
One could look at this such that the relative energy of the Xmm mode, relative to the Unruh energy in the cavity goes down, as the mode energy moves from the small end to the big end, where the Unruh energy is larger. In doing so, the frustum must move the other way to conserve energy and momentum.
I have a paper coming out soon, that will show this explicitly, using the rocket equation.
Traveller: I'll look at the effect of a change of speed on the derivation.
Jim: I'll get some time this evening to redraw.
Eirinn: You're right about the momentum at the ends: I'd misrepresented my original derivation and was trying to conserve c and momentum. I have rewritten, in haste, but I think the new version makes more sense, since the momentum is now conserved (same at both ends) so there's no net force on the walls. Thanks.
If the force is generated as the photons gain inertial mass when travelling the length of the cavity, could this continue indefinitely? What if the cone was hundreds of meters long?
TheTraveller: That link is about group and phase velocity not the speed of light itself changing. I am just an engineer, not a physicist but I was taught c was constant in a vacuum whether it is in a waveguide or not.
Eirinn: It wouldn't work if the cavity was much longer than it was wide, because you need a short trip back-and-forth to make accelerations high enough that the Unruh waves become short enough to fit within the width of the cavity (subject to the uncertainties we discussed before about what the acceleration is).
I'm also an engineer. ;)
Inside a waveguide, EM waves are constrained and travel slower than c. Waveguide physics shows the internal Guide Wavelength of the EM wave is not the same wavelength as external. Likewise the internal Group Velocity is not the external c.
Inside waveguides, the world changes and nothing (information, energy nor momentum) travels at c. They travel at Group Velocity which alters as the waveguide diameter changes.
Sure the photons travel slower than c? ...
Due to total reflection at the walls, waves are confined to the interior of a waveguide. The propagation inside the waveguide, hence, can be described approximately as a "zigzag" between the walls.
This description is exact for electromagnetic waves in a hollow metal tube with a rectangular or circular cross-section.
I think group velocity is the velocity seen in x axis, that is the true propagation of the energy, information... but the waves in the y axis still travels at c so the Model of MiHsC is correct.
Of course, wavelength must fit in the width of the waveguide
Mike - You should be aware of this by now, but the folks at the NSF site are looking over Tajmar's paper - second time this device has been tested in a vacuum. Results are tiny - about on a par with what Eagleworks reported. So is Tajmar's device - about the same size as the 'baby EM Drive.' Also features a (relatively) huge vertical slit waveguide in the devices side. Tajmar is...lukewarm...about the test, going out of his way to mention side effects. Might be politics involved.
Seems Shawyer was consulted extensively by Tajmar for this project.
One other thing on Tajmar's tests - one NSF member matched his results against your calculations. Dang close.
Oh, a couple other EM Drive items.
First off, Eagleworks has a Facebook page. Last entry (July 3rd) describes an EM Drive theory invoking a sort of 'Doppler Effect,' which a few members of the NSF group saw as more credible than the other theories out there. Notsosureofit seems especially interested.
Other thing is cavitation. (the break the water filled bottle party trick - video on site.) Been put forth as a possible explanation.
Don't know if either of these pertain to your theory.
What leads you to believe that photons have inertial mass? Would this not directly affect other significant, long standing physical theories we have?
What acceleration are you citing for the generation of an Unruh field?
Have you considered trying to derive the effect from Bogoliubov transformations of a photonic field trapped in a cavity?
Photons do have inertial mass in special relativity. It is their rest mass m0 that is zero. A proof of this can be found in D.F. Lawden’s 'Elements of relativity theory', page 69-70. You start from m=m0/sqrt(1-v^2/c^2) where m is the inertial mass and m0 is the rest mass. Use E=mc^2 and momentum, p=mv and you get E=c*sqrt(p^2+m0^2c^2), so even when rest mass m0 is zero, if you have energy E you get momentum p and inertial mass. This is also proven experimentally, by radiation pressure. If photons have inertial mass, MiHsC should apply. A possible application I haven't looked at yet is gravitational lensing.
In the emdrive, the only acceleration I can define clearly is that caused as the photons bounce end to end, see the derivation in my paper. Not ideal. I'm intrigued that there's another way (B' transformations). It might avoid the acceleration ambiguity..?
Mike- The NSF crew has been going over the Tajmar paper and pictures very closely. Seems that the dimensions given in the paper are not correct: what was termed 'diameter' should have been 'radius.' Also serious design issues raised as well; with a number of posters impressed he got any results.
Thank you for the response.
I'm afraid I don't follow your logic for the inertial mass of photons. If m=m0/sqrt(1-v^2/c^2) and m0=0, then by default, m=0. The other fact here is that v=c and therefore the gamma factor is also 0. I do not have access to the book you are referencing, however that is not how I know the energy-momentum relation to be derived. To me E=m0c^2 is a result of equation E=c*sqrt(p^2+m0^2c^2). Photons only have energy through their momentum and not their mass. Photons can never be slowed down (EM waves on the other hand are a different matter) as group velocity, phase velocity etc. cannot be reliably defined for a photon. If a photon cannot be slowed down then it cannot have inertial mass. How does your theory correspond to the measurements that a photon has a mass upper bounded by 7 × 10−17 eV? Do you still get the desired effect?
The other issue I have is that you cannot think of a photon 'bouncing end to end'. A photon is not a macroscopic object and does not bounce off a metallic surface. It is absorbed and re-emitted. That way, we cannot identify a unique photon as bouncing from end to end. As a photon cannot 'accelerate' up to c (to do so would violate SR) it is emitted at c and no acceleration is involved.
I also have concern that you have taken a cosmological notion of the Unruh effect (which is questionable) and confined it to a cavity. I think the better notion is to derive the Unruh effect in the asymmetrical cavity we are considering. i.e. work out the Bogoliubov transformations of the bosonic field modes trapped in the cavity. However there would be no acceleration here as the cavity is at rest in all experiments. And therefore no Unruh effect.
@Matt : isn't EM wave photon?
Unfortunately it's a bit more complicated than that. You can think of an EM wave as the collective behaviour of many photons if you like.
A bit long to read but worth the effort imo.
Mike- No idea if you are still watching this, but thought I'd let you know the gang at NSF went and recalculated the Yang EM Drive Design yet again. New slope angle is assumed to be 15.4 degrees, length 24 cm.
Also, there is a fierce dispute between Traveler, Rodal, and rfmguy about the proper way to measure Q. Traveler favors using single port S11, which gives very high numbers, the others a two port system with far lower Q's. Might want to look over the Q values in your data base, see how they were determined. Very possibly you have Q from both methods.
Czeko: This will take some time to absorb, but it's intriguing. They mention a lot of anomalies I haven't heard of before. I just wish they could include more detailed references so I can dig a bit deeper.
I've read the section on LeSage gravity. I've tried to get gravity this way, using Unruh waves to provide the 'low frequency' waves needed. Haven't succeeded, mainly because there's no solid data on how Unruh waves might be blocked by matter.
Tim: Thanks, I'm still dipping into the NSF when I can, but it moves so fast! I'll wait till the dust settles, since I have enough on my plate trying to convince the reviewer of my next MiHsC-emdrive paper that I haven't fallen out of my tree. I'm hoping to go back to testing MiHsC on globular clusters after that.
Mike- As to the globular cluster bit:
Now an international group of researchers has proposed a theory that dark matter is very similar to pions, which are responsible for binding atomic nuclei together. Their findings appear in the latest Physical Review Letters, published on July 10.
"We have seen this kind of particle before. It has the same properties -- same type of mass, the same type of interactions, in the same type of theory of strong interactions that gave forth the ordinary pions. It is incredibly exciting that we may finally understand why we came to exist," says Hitoshi Murayama, Professor of Physics at the University of California, Berkeley, and Director of the Kavli Institute for the Physics and Mathematics of the Universe at the University of Tokyo.
The new theory predicts dark matter is likely to interact with itself within galaxies or clusters of galaxies, possibly modifying the predicted mass distributions. "It can resolve outstanding discrepancies between data and computer simulations," says Eric Kuflik, a postdoctoral researcher at Cornell University. University of California, Berkeley postdoctoral researcher Yonit Hochberg adds, "The key differences in these properties between this new class of dark matter theories and previous ideas have profound implications on how dark matter can be discovered in upcoming experimental searches
Not what you want to hear, but something you might want to take a look at anyhow.
Not-Fritz at the Astronomy Forums seems impressed, anyhow:
>>>>Actually, no! The LHC may be way too little horsepower for this.
What is going on here is that the authors have proposed a "dark side" to the theory of the strong interaction. It's not a supersymmetric extension of the Standard Model but rather an explicitly dark extension of SM. So unlike the press release that talks about it as though this is just the pion we all know and love from the 1930s, this is the lightest particle available from the proposed "dark side" of the Standard Model.
The mass could be as high as 15-30 Tev, way beyond the capabilities of the LHC. That's the bad news.
The good news is that there is a single definite composition for the particle. It isn't "elementary" but composite. The self interactions and annihilation rates are calculable and agree with observational constraints from the Bullet cluster and the astrophysically observed dark matter halo shapes.
So this proposal can solve all the alleged challenges to the astrophysics of dark matter in a single stroke. WIMPs are not needed, not excluded.
Very definite calculations exist for how it would self interact and annihilate, though so a definite signal could be calculated for detection by the Alpha Magnetic Spectrometer on the ISS or by the Fermi satellite. Cosmic ray signatures can be calculated.
After not being a fan of SUSY for a long time in my youth, I've come to appreciate SUSY's "charm". It's now "up" at the "top" of my list to get "down" to the serious work of getting to the "bottom" of the dark matter mystery. It is the most "beauty"-ful possible extension of the Standard Model.
But this idea has real legs and a direct purely astrophysical direct detection seems feasible.
An interesting cosmological question arises: there should have been more of this composite non-elementary dark matter in the past. Looking back in time the Dark/Normal matter ratio should have been higher than now. How would this affect the results from Planck? Planck presumably gives us some sort of average Dark/Normal matter ratio as it looks back to the CMB...... Hmmm....<<<<<
Drat! had to leave the link out of the last post:
Ta. I'll take a look, but the main reasons I disbelieve any type of dark matter are that 1) the odd behaviour of galaxies always starts at the radius at which the stellar acceleration decreases to a particular value, which implies that the new effect is a subtle dynamical one, and 2) globular clusters & wide binaries show exactly the same odd behaviour as larger galaxies, but they cannot be governed by dark matter, which must be smooth on those scales.
- I like your previous drawing of the EmDrive better.
- On iPad, iPhone I can't read your website because text is black and background is dark gray.
- Finally, I wanted to ask if MiHsC predicts 'perpetual' motion for the EmDrive. Can microwaves generate a force causing kinetic energy to accumulate to eventually surpass the initial energy input in? What does MiHsC predict? Thanks.
OK Jim. Ironic that I try to make my language as clear as possible, and the system prints it black on dark grey! I'll fix that. I'll get back to you about point 3..
Tim: I've now used the corrected dimensions for the Tajmar expt from NSF and the MiHsC prediction is the same, so no problem there.
Do the wavelengths of the photons affect the thrust? For example, using a 900MHz source instead of 2.45Ghz would result in a 2.7-fold increase in the number of photons bouncing around in the cavity (assuming the same input power). Would that higher rate of flux allow for MiHsC to have a bigger effect on the EmDrive's momentum?
In the MiHsC formulation, the frequency has no direct effect on thrust, but it is necessary to choose it so the microwaves resonate within the cavity. The predicted MiHsC thrust is PQL/c * (1/W1-1/W2) where L and W are the length and widths. You can write this as PQ/f * (1/W1-1/W2) where f is the resonant frequency but of course that is not very adjustable for a given cavity (harmonics?). One way that f might be important is if you changed it slightly to make the Unruh waves resonate better at the narrow end, MiHsC then predicts a thrust reversal.
Hi Mike, is that thrust reversal predicted by the formula? I don't see how changing f would make the whole result become negative.
Correct, this formula is too simple to predict the reversal, since it assumes a spectrum of Unruh waves that are subsampled more or less depending on width. It's not easy to write a formula for the resonance of waves in the cavity but I have derived a simple formula assuming 'one' Unruh wave which does consider whether this wave fits or not at either end, and this predicts the reversal. I've blogged about it here:
Am I correct in saying that the Unruh wavelengths are dependent on the length of the cavity (and C) but not the frequency of the photons? In that case the emdrive will go into "reverse" mode only if L or C changes. So far all the experiments have fixed L to a suitable length to achieve resonance, but if we had a different wavelength (and thus different L) we could see the emdrive reverse.
Presumably, somewhere between "forwards" and "reverse" there is a cavity length where thrust is negligible. The key question is where on that spectrum are the current emdrives? 2.45GHz may not be optimum and we may just be building incredibly inefficient emdrives (aeolipiles). Can you predict a better value for L?
The Unruh wavelengths are just dependent on the cavity length L, since wavelength=8c^2/a=8c^2/(2c/(L/c))=4L (a simplification of acceleration tho, as you know). It should be possible to predict the best value for L given wb and ws. I'll have a go..
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