RE: Uncertain About Heisenberg\'s Principle
Space-Time Travel Device
As you may or may not know, Cherenkov radiation is emitted whenever charged particles pass through matter with a velocity v exceeding the velocity of light in the medium. The charged particles polarize the molecules, which then turn back rapidly to their ground state, emitting prompt radiation (in the form of photons). The emitted light forms a coherent wavefront if v]vt; Cherenkov light is emitted under a constant Cherenkov angle with the particle trajectory, and at a given maximum emission angle. Given this information, you can see that traveling faster than the velocity (speed) of light (in a vacuum) already occurs.
The velocity of light is dependent upon the medium you are working within. Potentially a device (or particle) could be built (generated) which incorporates the mathematics of Cherenkov radiation, the Heisenberg principal and Lorentz formulae (as applied to a given medium), and within that medium ‘move' an object through a ‘time dilation'. Working along these unified lines, anything within a given medium and confined energy field (used to polarize the molecules of the medium) exhibiting the above ‘unified mathmatica', could hypothetically travel in time.
Given that we can calculate the velocity of Cherenkov radiation eminations in a given medium, revisiting the wave/particle duality, we can negate the need for ‘finding' its velocity and concentrate on ‘knowing where it is'. We also know that the particle is also in motion (just as you stated). The direction of travel of the particle (and hypothetically a ‘device') would (should) be derived and identified via the ‘unified mathmatica' as described above. This direction should be identical to the Cherenkov angle.
Based upon this ‘unified mathmatica' and the Cherenkov emission angle, the hypothetical field mechanism noted above, entertains the possibility of being incorporated into a study by NASA (Journal of Propulsion and Power (AIAA), Vol. 13, No. 5, pp. 577-682, (Sept.-Oct. 1997)) known as a ‘Pitch Drive'.
This drive uses a localized slope (ie the Cherenkov emission angle) in scalar potential induced across the vehicle which causes forces on the vehicle. It is assumed that such a slope can be created without the presence of a pair of point sources. If V is the gravitational scalar potential for the combined system, which is equal to the superposition of the potentials from the vehicle and the induced pitch effect, the term for the vehicle's gravitational potential is the familiar Newton's gravitational potential where r is the distance from the source mass (r2 = x2 + y2 for the x - y plane). The origin is taken to be at the center of the vehicle. To entertain the possibility of a Pitch Drive, a localized gradient in the scalar gravitational potential is superimposed across the symmetric gravitational potential already present from the vehicle's mass. This induced pitch effect is represented by a magnitude, A (units of acceleration), with a negative slope in the positive x direction, and is localized by a Gaussian distribution, e-r2, over the distance, r, centered at the origin. This localizing equation is illustratrative only.
By taking the gradient of the scalar potential at the location of the vehicle, specifically the derivative of V with respect to r of the induced pitch effect at r=0, the acceleration for the vehicle is determined to be equal to A, and acts in the positive x direction. NOTE that the ‘x direction' denoted above is assumed to be the Cherenkov emission angle and not specifically along a planar geometric x-axis.
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