That's conflating relativistic mass with rest mass. I know the conclusion that potential energy raises a system's mass is commonly accepted as an inevitable implication of GR, but it's one frought with pitfalls:
For instance, i dig a 1 meter-deep hole next to a 1 kg mass, at 1 G the system now has 9.81 J of PE. But is there a relativistic mass increase (i don't care how small it'd be - multiply the scale if you wish)? What if the mass never falls into the hole? Similarly, a vertical wheel is balanced on a hilltop, with an unequal drop on either side, so the system's PE is indeterminate - could relativistic mass also be indeterminate? The clue is in the name "potential energy" - which can depend on chance, or even conscious agency. Certainly, KE has relativistic mass, but PE is something notional, arbitrary, and frame dependent (in a word, subjective). Thin ice, here. But assuming our EM craft was battery powered, and that relativistic mass does apply to chemical PE, it is still the chemical PE that has been converted to work (acceleration of the craft, relative to its point of origin), not its relativistic mass energy equivalency, which itself is incidental, aside from a minute reduction in the craft's net inertia. In a conventional rocket, the momentum of the exhaust ejecta is precisely equal to the momentum gain of the remaining vehicle (per Newton's 3rd), but because the ship is big and the gas molecules small, their KE per unit of momentum is much higher. So, most of the rocket's chemical PE has been spent accelerating gas, a little has been creamed off by the vehicle that PE's mass equivalency has disappeared (because mass constancy only applies to rest mass). A nuclear power plant would match your description though - the gain in net KE (vehicle plus ejecta, where applicable) would be equal to the mass deficit. On Mon, Mar 14, 2016 at 6:44 PM, David Roberson <[email protected]> wrote: > Good argument. I just wanted to add one thought. > > From the EM drive's point of view the CoE must be violated because as it > accelerates in space a portion of it's mass must be converted into energy > that is used to power the drive. When it ceases to use the drive it begins > to remain motionless in space from its point of view. Where did that mass > go which was converted into energy that powered the drive? Did it simply > vanish? > > This problem does not exist for normal rocket engines that expel a > reaction mass. In that case, the energy is accounted for by the mass that > is speeding rapidly away from the rocket. > > Dave > > > > -----Original Message----- > From: Vibrator ! <[email protected]> > To: vortex-l <[email protected]> > Sent: Mon, Mar 14, 2016 7:03 am > Subject: Re: [Vo]:Re: EM Drive(s) > > Yes, and this is why KE = 1/2 MV^2 - ie., why the acceleration unit cost > escalates; a given force has to be applied over an ever-greater distance as > velocity (time rate of change of position) increases. Alternatively, we > could hold displacement constant and progressively raise the force > magnitude. > > Yet Craig still seems to have a point - without some kind of corporeal > reaction mass, what is an EM drive's velocity actually relative to? What's > its reference frame, if not the thing it's pushing against? > > To illustrate the conundrum, suppose i have an EM drive aboard a train, > and you the observer are standing on the platform as the train passes > through the station: I fire the engine, and it accelerates by 1 meter / > sec. > > Suppose the engine weighs 10 kg. From my perspective, its KE has > increased by 5 Joules - ie. it's perrformed 5 J of mechanical work, > regardless of how much more energy may have been wasted to heat. > > But if the train was already travelling at 10 m/s, and the drive > accelerated in the same direction, then from your stationary perspective > the drive has accelerated up from 10 to 11 m/s - and for a 10 kg mass > that's a workload of 105 J - bringing its KE up from 500 J to 605 J. > > So, has the drive burned 5 J or 105 J? > > > If i cheated - the drive doesn't really work, and i just gave it a > surreptitious shove - this same paradox is resolved by a corresponding > deceleration of the train - ie. if i accelerate a small mass against the > inertia of a larger mass, the latter is decelerated and net momentum is > conserved. > > Except here, the drive ISN'T pushing against the train. Yet it still > benefits from its ambient velocity. Net momentum is NOT conserved, and > neither is energy. > > > And so the question arises, how does the EM drive "know" what its > reference frame is? Shawyer claims (or seems to imply) that the unit cost > of acceleration increases as we would normally expect (distance over which > a given force is applied keeps rising) - but how does it measure > "distance"? Relative to what, exactly? Without physical reaction mass, > such a system has its own unique reference frame - from within which, > energy may be conserved, but which from without, cannot be. > > I mean this not as a crtitique against the plausibility of such systems, > and share the prevailing cautious optimism. But if they do work, then we > also have an energy anomaly. > > In the many years i've been researching classical symmetry breaks, one > thing has become clear - the only way to explain away a real symmetry break > is to invoke another somewhere else up or downstream (it's a standard > recourse for pseudoskeptics). As much as i'd welcome free energy, momentum > and FTL travel, and despite Shawyer's assurances everything's classically > consistent, these enigmatic implications remain.. for me, at least. > > On Mon, Mar 14, 2016 at 4:17 AM, <[email protected]> wrote: > >> In reply to Craig Haynie's message of Sun, 13 Mar 2016 21:08:43 -0400: >> Hi, >> [snip] >> >> Note the use of the word "acceleration". >> >> Acceleration produces a force. Force times distance = energy. >> >> >This doesn't make any sense: >> > >> >"For a given acceleration period, the higher the mean velocity, the >> >longer the distance travelled, hence the higher the energy lost by the >> >engine." >> > >> >Since we're not talking about relativistic speeds, then the idea that a >> >device will consume more energy, over a given period of time, simply >> >because it's moving, would violate Einstein's Special Relativity which >> >says there's no preferred frame of reference. The moving object cannot >> >be said to be moving at all. >> > >> >Craig >> Regards, >> >> Robin van Spaandonk >> >> http://rvanspaa.freehostia.com/project.html >> >> >
