Jim's May 10, 2013 weekly e-mail distribution post should shed some light on the Carver Mead "graviton" rocket thrust limit conjecture in regards to the M-E.
"To recap Carver's argument, he noted that both gravity and electromagnetism, as long range fields, have zero rest mass field quanta (assuming that gravitons actually exist of course). As such, one can simply write E = pc for the energy and momentum carried by the field. Now, if a MET produces thrust by completely converting the power applied to it (that is, dE/dt) into the equivalent momentum flux in the field, then the momentum flux will be dp/dt = (1/c)dE/dt and this is the thrust. As an example, if dE/dt = 100 watts, then dp/dt is a third of a uN. I'm going to call this relationship between power and thrust the "Mead limit".
There are a couple of questions here. Can METs beat the Mead limit? If they do, is there supporting plausible physics that underpins such behavior? The first question is one for experiment. The second one for "theory". Tonight's email chiefly addresses the first question. For if the Mead limit is found to apply in fact, then the second question is one for casual speculation at best.
Several weeks ago, I decided to go after the experimental question by building a device designed to run at higher frequency, one that would exceed the Mead limit if it could be made to perform as well as the devices that have been running now seemingly forever. Then, last weekend, it dawned on me that the answer to this question was already present in the data that these devices have been producing for upwards of a year. Indeed, the behavior is present in plots in chapter 5 of the book already. And it is especially obvious in the constant frequency runs that have been featured in the last few email attachments. Talk about feeling foolish. Especially galling is that there is a cheap tourist trick of analysis that makes interpretation of the data, at least in approximation, trivial. But on to the file (that will be attached to a following email).
The first dozen slides are selected from those sent last week. They include some pictures of the apparatus and the results for the 10 second steady power/thrust test. Immediately following are slides (13 through 16) with the results of a 14 second steady power/thrust test done after replacement of the lower flexural bearing in the balance. They are essentially identical to the shorter interval test. That is, after an initial transient thrust pulse lasting a couple of seconds settles, a steady thrust of a micronewton or two ensues. When the device is switched off, there is a prominent thrust pulse of a couple of seconds duration that quickly settles. The steady thrust, the focus of earlier attention, is right about at the Mead limit for this device. So it cannot be used to settle the question of exceeding the Mead limit.
Until last weekend, the obvious thrust switching transients, noted many time in earlier work, were simply noted and ignored. Last weekend, however, I paid attention to the transients. For two reasons. First, Carver's argument has an implicit assumption: the relationship between thrust and power is: thrust = constant X power. Always. This may be intuitively likely. But it is not necessarily so. If it is so, then the thrust transients in the displays MUST be accompanied by transient power surges that produce them. That is, the voltage squared (proportional to the power) traces (dark blue) should show signs of power transients that produce the thrust transients.
The cheap tourist trick observation is that the thrust balance, as far as transients are concerned, behaves as a "ballistic pendulum". A horizontal and damped pendulum -- which complicates careful analysis -- but a ballistic pendulum nonetheless. If your introductory physics text was Sears and Zemanski, you'll remember that they have a chapter on impulse, force and energy, with the ballistic pendulum as an example. Rudimentary analysis requires only elementary algebra. Impulse is force times time = change in momentum. Shoot a bullet into a block of wood suspended on strings, and the bullet plus block acquires kinetic energy equal to that of the bullet before inelastic impact. The block rises on strings until its potential energy in the gravity field equals the initial kinetic energy. You can compute the velocity of the bullet without fancy timing apparatus.
In our case, the two second thrust transients recorded MUST be produced by a force transient that satisfies the force times time condition to be equal to the thrust times 2 seconds. Especially obvious in the case of the outgoing transient, there is no corresponding power transient that the Mead analysis requires to be present. This is less obvious for in incoming transient, but it is also true there. This can be seen by inspection of slides 18 and 19. Depending on the duration of the power transient assumed, the dark blue traces should show VERY pronounced deviations from simple rise to and fall from steady power supporting the steady thrust condition. No, there is nothing in the system that would filter out such power transients. The implicit assumption in Carver's argument is as a matter of fact wrong in this case.
You may be thinking, gee, that's weird. If power transients aren't producing the thrust transients, what is? The Mach effect. Remember, the first Mach effect is NOT proportional to the power. It is proportional to the rate of change of the power (that is, dP/dt). So simply turning the device on and off should produce transients. Everything needs to be tuned to produce the Mach effect of course. But that does not depend on power transients beyond the simple switching of the power. The size of the transient thrusts should depend on how quickly the power is switched. Power switching is effected by the closing/opening of a relay that controls the driving signal to the power amplifier. One may expect the rise time of the power to be a bit slower than the fall time in these circumstance, and accordingly that the outgoing thrust transient will be a bit larger than the incoming transient.
The data acquisition rate for the routinely stored data is 100 Hz, so detailed analysis of fast transients using it isn't possible. But in slides 18 and 19 it is possible to determine that the rise time is at least a few ms and fall time is less than 10 ms. The cheap trick comes in here. The Mach effect thrust pulse that produces the ballistically measured thrust pulse of 2 s duration is just the measured average of the thrust pulses, say, a few uN, times 2 s divided by the rise/fall time, less than 10 ms. That is, the measured thrust transients tell you that the Mach effect switching transients are on the order of at least hundreds of uN. Given that there is no corresponding power transient, the Mead limit is far exceeded -- indicating that Carver's argument does not apply to these devices AS A MATTER OF FACT. Since Mach effects are derived from elementary physics first principles, we see that the assumption that thrust = constant X power always is false. Heidi and I, and others, are working on how this all works in detail. It is not a trivial problem."
In other words how you get around the Mead thrust output limit is by maximizing the M-E equation's first term's time rate of change of input power or dP/dt. That is when you start extracting from or dumping energy into the G/I field.