The Gravitational Invisibility Fran de Aquino To cite this version: Fran de Aquino. The Gravitational Invisibility. 2015. hal-01211820v2 HAL Id: hal-01211820 https://hal.archives-ouvertes.fr/hal-01211820v2 Preprint submitted on 13 Oct 2015 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. The Gravitational Invisibility Fran De Aquino Professor Emeritus of Physics, Maranhao State University, UEMA. Titular Researcher (R) of National Institute for Space Research, INPE Copyright © 2015 by Fran De Aquino. All Rights Reserved. The possible obtention of invisibility by means of a gravitational method is shown in this work. This method is based on a gravity control process patented on 2008 (BR Patent Number: PI0805046-5). It goes far beyond the known methods of invisibility and camouflage, which use the principles of light refraction to allow light to pass right through an object (metamaterials). Key words: Invisibility, Gravitational Invisibility, Real and Imaginary Universes. 1. Intr oduction m ⎧ ⎡ 2 ⎤⎫ An object that cannot be seen by the g ⎪ ⎢ ⎛ Δp ⎞ ⎥⎪ human eyes is in called state of invisibility. χ = =⎨1 − 2 1 +⎜ ⎟ −1⎬ () 1 mi0 ⎢ ⎝mi0 c⎠ ⎥ At this state, the object neither reflects, nor ⎩⎪ ⎣ ⎦⎭⎪ absorbs light, i.e., the light passes freely where m is the rest inertial mass of the through it. Under this condition, we can say i0 that the object is 100% transparent. In the particle and Δp is the variation in the Nature, there is no material 100% particle’s kinetic momentum; c is the speed transparent. of light. The concept of invisibility includes In general, the momentum variation Δp others ranges of the electromagnetic is expressed by Δp= FΔ t where F is the spectrum, such as radio, infrared, ultraviolet, etc., since the object can be applied force during a time interval Δt . detected by instruments operating in the Note that there is no restriction concerning ranges of radio, infrared, ultraviolet, etc. the nature of the force F , i.e., it can be Thus, the invisibility depends on the eyes of mechanical, electromagnetic, etc. the observer and/or the instruments used to For example, we can look on the detect the object. momentum variation Δp as due to At the state of total invisibility, an absorption or emission of electromagnetic object cannot be detected by any real energy. In this case, it was shown observer or instrument, even making use of previously that the expression of χ can be detectors, which operate in real ranges of expressed by means of the following radio, infrared, ultraviolet, etc. expression [5]: Here we will show a method to make a real body totally invisibly. This method is ⎧ ⎡ 2 ⎤⎫ based on a gravity control process patented mg ⎪ ⎛ Δp ⎞ ⎪ χ = =1 − 2⎢ 1 +⎜ ⎟ −1⎥ = on 2008 (BR Patent Number: PI0805046-5, ⎨ ⎢ ⎜ ⎟ ⎥⎬ mi0 ⎪ ⎝ mi0 c⎠ ⎪ July 31, 2008[1]). It goes far beyond the ⎩ ⎣⎢ ⎦⎥⎭ known methods of invisibility and camouflage, which use the principles of ⎧ ⎡ 2 ⎤⎫ ⎛ ⎞ light refraction to allow light to pass right ⎪ ⎢ Unr ⎥⎪ =⎨1 − 2 1 +⎜ ⎟ −1 ⎬= through an object (metamaterials) [2, 3]. ⎢ ⎜ 2 ⎟ ⎥ ⎪ ⎢ ⎝mi0c ⎠ ⎥⎪ ⎩ ⎣ ⎦⎭ 2. Theory ⎧ ⎡ 2 ⎤⎫ ⎪ ⎢ ⎛Wn ⎞ ⎥⎪ In a previous paper, I showed that =1 − 2 1 +⎜ r ⎟ −1 ()2 ⎨ ⎢ ⎜ 2 ⎟ ⎥⎬ gravitational mass, mg , and rest inertial ⎪ ⎢ ⎝ ρc ⎠ ⎥⎪ ⎩ ⎣ ⎦⎭ mass, m , are correlated by means of the i0 following expression [4]: where U is the electromagnetic energy absorbed or emitted by the particle; n is r the index of refraction of the particle; W is 2 the density of energy on the particle 4 4 change E by Erms , and the equation 3 3 (J/ m ); ρ is the matter density (kg m ) above can be rewritten as follows and c is the speed of light. ⎧ ⎡ 4 6 2 4 4 4 ⎤⎫ In the particular case of mg ⎪ nr n Sα S mφ m E rms ⎪ * χ = =⎨1 − 2⎢ 1 + −1⎥⎬ () 5 heterogeneous mixture of matter , (powder, 2 2 6 2 mi0 ⎪ ⎢ 4μ0 ρ c f ⎥⎪ dust, clouds, air, smoke, heterogeneous ⎩ ⎣ ⎦⎭ plasmas†, etc), subjected to incident Also, it was shown that our Real radiation or stationary electromagnetic Universe is contained in an Imaginary fields, the expression of χ can be expressed Universe; in such way that the real by means of the following expression, spacetime of the Real Universe is contained in the imaginary spacetime of the Imaginary which is derived from the above equation ‡ [5]: Universe [4]. Thus, each action in the real spacetime corresponds to an equivalent ⎧ ⎡ 2 ⎤⎫ ⎡⎛ 3 2 2 2 ⎞ ⎤ action in the imaginary spacetime. This, mg ⎪ ⎢ nnSrα S mφ m E 1 ⎥⎪ χ= =⎨1 − 2 1 +⎢⎜ ⎟ ⎥ −1⎬= means for example, that any m ⎢ ⎜ 2μρc2 f 2 ⎟ c n f ⎥ i0 ⎪ ⎣⎢⎝ 0 ⎠()r ⎦⎥ ⎪ momentum, pr , generated in the real ⎩ ⎣⎢ ⎦⎥⎭ r spacetime produces simultaneously an r r ⎧ ⎡ 4 6 2 4 4 4 ⎤⎫ equivalent momentum, pim= p r , in the ⎪ nnSrα S mφ m E ⎪ =⎨1 − 2⎢ 1 + −1⎥⎬ ()3 imaginary spacetime and vice-versa. ⎢ 4μ2 ρ 2 6fc 2 ⎥ ⎩⎪ ⎣ 0 ⎦⎭⎪ In the case of a photon, the momentum p is related to its energy E by where Sα is the maximum area of cross- means of the following expression: section of the body; φm is the average diameter of the molecules of the E= pc , where c is the speed of light at the free space. Thus, when a photon is body; S = πφ 2 4 ; E is the instantaneous m m generated in the Real Universe with an electric field applied on the body; μ0 is the energy Er= p r c its correspondent photon magnetic permeability of the free space; in the imaginary spacetime will have energy f is the oscillating frequency of the electric E= p c . As pr = pr we can field and n is the number of atoms per unit im im im r of volume in the body, which is given by conclude that EEr= im . Consequently, the photon generated in the imaginary N 0 ρ n = ()4 spacetime will have equal frequency, and A the same direction of the real photon (due to 26 pr = pr ). Consequently, when an object where N0 =6.02 × 10atoms / kmole is im r the Avogadro’s number and A is the molar is illuminated with real photons, it is also mass (kg/kmole). being illuminated with imaginary photons. Note that E= Esinω t .The Since there is imaginary mass associated to m the real mass [4]§, then, the imaginary 2 1 2 average value for E is equal to 2 Em photons interact with the imaginary mass associated to real mass of the object, and because E varies sinusoidaly ( Em is the can be reflected, absorbed or transmitted, maximum value for E ). On the other such as occurs with the real photons when hand, EErms= m 2. Consequently we can they incide on the real matter. Real photons in turn do not interact with imaginary * ‡ From the macroscopic viewpoint, a heterogeneous The terms imaginary and real are borrowed from mixture is a mixture that can be separated easily Mathematics (real and imaginary numbers) [6]. (sand, powder, dust, smoke, etc.). The opposite of a heterogeneous mixture is a homogeneous mixture § (ferrite, concrete, rock, etc). These new concepts are widely detailed and explained in the ref [4]. It is essential to study the † Heterogeneous plasma is a mixture of different contents of this reference to get a complete ions, while Homogeneous plasma is composed of a understanding of the matter here developed. single ion specie. 3 matter. Consequently, they pass freely through the imaginary mass (See Fig.1 (a)). Note that the photons can be of any range Imaginary Photon of the electromagnetic spectrum, i.e., radio, Real Photon infrared, light, ultraviolet, etc. The real light photons are detected by the retina of our eyes, and thus we see the object. If the gravitational mass, mg, of our Real Body body is reduced to a value between −0.159mi0 and + 0.159 mi0, (mi0 is the rest inertial mass of the body), it becomes an imaginary body and realizes a transition to the Imaginary Universe [4], from where it still will can see objects, because its Imaginary Body imaginary retina can to detect the imaginary (a) light photons reflected from the imaginary mass associated to the real object (See Fig.1 (b)). Window Imagine then an observer inside a 1 (Glass) spacecraft, seeing for an object out of the Light spacecraft, through a glass window of the Source spacecraft. If the spacecraft and the Imaginary observer are turned into imaginary bodies, Observers then, despite the real photons (reflected from the object) no more interact with the Real retina of the observer, he will still continue Observer seeing the object out of the spacecraft by 2 means of the imaginary photons (associated Imaginary Imaginary to the real photons) that are reflected from Spacecraft Observer (b) 3 the object (See Fig.1 (b)). A second imaginary observer inside the spacecraft, Fig.1 – The real-imaginary pairs of photons seeing for the internal wall of the spacecraft interacting with real and imaginary matter, does not see the real object out of the respectively. (a) The imaginary photons interact spacecraft, because the imaginary photons with the imaginary mass associated to the real mass, reflected from the body do not surpass the and can be reflected, absorbed or transmitted, such as wall of the spacecraft (such as occurs in a occurs when real photons incide on the real matter.