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Building on the various manifestations of the forces latent in the quantum vacuum of spacetime such as Hawking’s radiation and Unruh temperature, we resolve a major paradox connected to an immensely important proposal by NASA scientists for constructing a practically fuelless spacecraft. In a nutshell, preliminary laboratory work shows that NASA’s electromagnetic drive project is viable and several experiments and measurements show it is real. Yet the proposal violates a fundamental principle of classical mechanics, namely Newton’s third law. The resolution of this paradox is quite straight forward in principle. It is simply the case that although the proposal seems to be based on classical mechanics and classical thinking it is only superficially so. Deep at the roots, the EM drive proposal of NASA is not classical physics but rather based on the vacuum forces of quantum cosmology and the theory of dark energy density of the universe. In fact the proposal is deeply linked to Hawking’s radiation and Unruh temperature, which is explained in some detail in the main body of the present short paper within the frame work of E-infinity Cantorian spacetime theory and D. Gross’ Heterotic superstring theory. In short the quintessence of our explanation is to regard the EM drive as a quasi electromagnetic cavity with an effective event horizon akin to that of a Hawking black hole emitting radiation causing ultimately the needed thrust to push the spacecraft forwards. In addition and by invoking fractal spacetime self similarity we show that a spacecraft will be subject to another cosmic thrust on the large scale of the entire cosmos.

Newtonian mechanics as well as classical elasticity are the main analytical tools in constructing stable spacecrafts and determining its flight trajectory [

In what follows we hope to prove that NASA’s proposal for an EM drive is in principle possible [

In this section we would like to show quantitatively how a back reaction in empty spacetime can never the less create a thrust, pushing a spaceship forwards without violating conservation of momentum enshrined in Newton’s third law [

γ = 1 + ( 5 − Δ ) + ( 16 + k + Δ ) 22 + k (1)

we see that our exact ordinary cosmic energy density is given by the first term of Equation (1) [

γ ( O ) = 1 22 + k = 0.04508497187 ≃ 4.5 % (2)

The second term in Equation (1) is clearly connected to a Kaluza-Klein quantity, namely a five dimensional object or a topological mass equal 5 so the density is approximately equal 5/22. However we notice an interesting coupling term D that will play a fundamental role in our theory and the present analysis as will shortly transpire [

γ ( D M ) = [ 0.2218033989 − ( 1 / 22 + k ) ] ( 22 + k ) 22 + k = ( 0.17618427 ) ( 22 + k ) 22 + k = 3.919674776 22 + k = 5 − 0.08032522476 22 + k = 5 − Δ 22 + k (3)

exactly as it should be [

γ ( P D ) = 16 + k + Δ 22 + k (4)

Applying the above to the balance of forces acting on our “fuel-less” spaceship, we see that ± Δ , interpreted as quasi quantum particles, can solve the problems of creating a vacuum thrust pushing the spaceship “forward” without violating fundamental conservation laws of physics [

The preceding interpretation could also be formulated using a lower dimensionality theory, namely that of a fractal Kaluza-Klein D = 5 + ϕ 3 [

γ ( O ) = ϕ 3 5 + ϕ 3 γ ( D M ) = 1 + Δ 5 + ϕ 3 (5)

and

γ ( P D ) = 4 − Δ 5 + ϕ 3 (6)

However the coupling D changes to Δ = k − [ ( 8 + k 2 ) / 100 ] / ( 4 + ϕ 3 ) and the plus and minus are exchanged. This exchange of signs is harmless because in an infinite spacetime manifold plus and minus as well as up and down or left and right are all conventions and nothing more than that. At the end all what matters is that + Δ − Δ = 0 and we have the vacuum thrust, which does not violate conservation of momentum [

From the preceding analysis and discussion we come to the following general conclusion: when a classical mechanics design seems to violate Newtonian principles and yet we can see clearly from the experimental set up that it works, then it is surely not a classical mechanics problem and a deeper look is required to see quantum mechanical roots to it or at a minimum to realize that some nonlinear dynamics, chaos and fractals are probably involved on a fundamental level [

Our present conclusion and resolution is the following: The quantum topology of our universe dictates that it is made up of two parts, a) a low density interior with 4.5% energy density and b) a high energy density surface with 95.5% of the total energy. This gradient is in the large what makes fuelless interstellar journeys possible so that we can state without any doubt that in principle EM drive is science and not science fiction any more. On the other hand any ordinary EM engine can be used because it is needed for navigation only. However to enhance the local cosmic thrust it may be possible by invoking self similarity [

El Naschie, M.S. (2018) NASA’s EM Drive Thrust from the Forces of the Quantum Vacuum of Spacetime. Advances in Aerospace Science and Technology, 3, 1-9. https://doi.org/10.4236/aast.2018.31001

We give in this appendix in a very condensed form an account of the Cantorian interpretation of quantum vacuum fluctuation as well as the generalization of Hawking radiation [_{1} and P_{2} when it is dissected to ϕ 2 multiplied with ϕ where ϕ 2 is the empty set quantum wave and ϕ is the zero set quantum particle [_{1} and P_{2} intersect and give us Unruh temperature ϕ 2 ϕ 2 = ϕ 4 while the two zero sets ϕ and ϕ intersect and give us the empty set Aether [