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We now remark that the phase difference in the mass fluctuations of the L and C circuit elements compensates for the fact that their accelerations induced by the force transducer are in opposite directions. Accordingly, the stationary forces produced by accelerating L and C as their masses fluctuate are both in the same direction; the L/C/PZT system -- an impulse engine -- experiences a steady, unidirectional accelerating force [which can be estimated with Equation (3.5)]. Should we now attach the power sources to our device, they too will be carried along by our impulse engine, even if they contain fluctuating masses.

It seems that we have constructed a device that blatantly violates the conservation of momentum. Perhaps we have ignored something important. For example, consider an object (a capacitor, inductor, magic brick, whatever), moving with some velocity v with respect to us, whose mass can be made to fluctuate. When the mass changes, does the velocity change too? Ostensibly no external force acts to change the momentum. So conservation of momentum seems to suggest that the velocity must change. If the local momentum conservation implicit in this inference is true, then we can solve our problem. Local momentum conservation guarantees that momentum must be conserved somehow point-by-point throughout our impulse engine. Thus it may wiggle a lot, but it goes nowhere. The assumption of point-by-point momentum conservation in this case, however, violates the principle of relativity, so it must be wrong.

Let us suppose that, viewed in our inertial frame of reference moving with respect to the brick, when the mass of the brick changes, its velocity changes too so that its momentum remains unchanged. (The cause of the velocity change is mysterious. After all, driving a power fluctuation in the brick to excite a mass fluctuation need not itself exert any net force on the brick. But we'll let that pass.) We see the brick accelerate. Now we ask what we see when we are located in the rest frame of the brick. The mass fluctuates, but in this frame the brick doesn't accelerate since its momentum was initially, and remains, zero. This, by the principle of relativity, is physically impossible. If the brick is observed to accelerate in any inertial frame of reference, then it must accelerate in all inertial frames. We thus conclude that mass fluctuations result in violations of local momentum conservation if the principle of relativity is right.

The appearance of momentum conservation violation in our impulse engine doesn't mean that momentum isn't conserved. It means that we can't treat the impulse engine as an isolated system. Since the effect responsible for the apparent violation of the conservation principle is inertial/gravitational, this should come as no surprise at all. As Mach's principle makes plain, anytime a process involves gravity/inertia, the only meaningful isolated system is the entire universe. Since inertial reaction forces appear instantaneous [see Woodward, 1996a and Cramer, 1997 in this connection], evidently our impulse engine is engaging in some "non-local" momentum transfer with the distant matter in the universe. With suitable choice of gauge, this momentum transfer can be envisaged as transpiring via retarded and advanced disturbances in the gravitational field that propagate with speed c.

Gauge freedom muddies up discussions of inertial reaction effects [Woodward, 1996a]. Choosing a gauge where all physical influences propagate at speeds has the advantage that lightcones in space-time have an invariant meaning, whereas the surfaces of simultaneity that appear in other gauges (e.g., the Coulomb gauge) do not. As just mentioned, in the Lorentz [or Einstein-Hilbert] gauge the inertial reaction effect, and thus our impulse engine, consists of a retarded/advanced coupling between the engine and the distant matter in the universe that lies along the future light cone. The introduction of the force transducer in the engine allows us to extract a net momentum flux here and now from the potentially largely thermalized matter in the far future. The net momentum flux is accompanied by a net energy flux, so although our impulse engine, considered locally, appears to violate energy conservation, that need not necessarily be the case. The extraction of useful work from matter that may be completely thermalized raises interesting questions. Boosting, rather than borrowing, from the future, however, seems to be the nature of the process involved.

Is any of this really right? Well, one way to get a fix on this is to run the experimental apparatus described above when it is rotated by 90 degrees -- that is, oriented horizontally rather than vertically. If the observed effect is some spurious local effect or couples to local gravity fields, the observed effect should change when the local orientation of the apparatus is altered. But if the effect is caused by the proposed non-local interaction with cosmological matter, it should be independent of the local orientation of the apparatus. Results obtained with the apparatus oriented horizontally are displayed in Fig. 7. At the level of experimental accuracy there is no significant difference in the magnitude of the effect for the two orientations.


5. CONCLUSION
It seems that at least one part of the physics of Star Trek -- impulse engines -- may lie within our grasp. Indeed, the transient Machian inertial reaction effect that makes impulse engines possible may also make "stargates" and time machines based on traversable wormholes feasible [Woodward, 1997]. This is a consequence of the strong nonlinearity of the total proper matter density as it approaches zero and negative values. (Negative mass has interesting properties. See: Forward [1989] and Price [1993].) The feasibility of such schemes, however, also depends on the magnitude of the bare masses of elementary particles and the nature of the vacuum. These matters are, at the very best, conjectural. Accordingly, the schemes are a good deal more speculative than impulse engines. But they, along with impulse engines, can be explored experimentally with present technology at reasonable cost.

ACKNOWLEDGEMENT
Arguments and questions posed by Thomas Mahood and James van Meter, and John Cramer's recent Analog [1997] article have been most helpful in developing the ideas relating to impulse engines presented here. TM also suggested stylistic improvements (including the suppression of a tasteless remark or two). The experiments described here were supported in part by several CSU Fullerton Foundation grants. The impulse engine method described herein is a specific implementation of the general method of U.S. Patent 5,280,864.

REFERENCES:
Alcubierre, M. (1994), Class. and Quant. Grav. 11, L73-L77.
Cramer, J. (1997), Analog (March), 100-104.
Forward, R.L. (1989), J. Propulsion 6, 28-37.
Morris, M.S. and Thorne, K.S. (1988), Am. J. Phys. 56, 395-412.
Nordtvedt, K. (1988), Int. J. Theor. Phys. 27, 1395-1404.
Price, R.H. (1993), Am. J. Phys. 61, 216-217.
Sciama, D. (1953), Mon. Not. Roy. Astron. Soc. 113, 34-42.
Woodward, J.F. (1990), Found. Phys. Lett. 3, 497-506; (1992), Found. Phys. Lett. 5, 425-442; (1996a), Found. Phys. Lett. 9, 1-23; (1996b), Found. Phys. Lett. 9, 247-293; (1997), Found. Phys. Lett. 10, 153-181.


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Copyright © 1998, James F. Woodward. This work, whole or in part, may not be reproduced by any means for material or financial gain without the written permission of the author.

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Really , what we know about the Newton's first law!?
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