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Unusual gyroscope MGEF (Module Generator of Entropic Forces). The real model unusual gyroscope occupies a domain in between classical and quantum mechanics, a domain often thought to be empty.

Bob: «What’s in the optical hologram is a real: film or a three-dimensional image?».

Alice: «Yes, film, but external source of coherent oscillations is required».

Bob: «if we assume that coherent oscillations are inherent not only in the film but to the surface of the universe, we can do without an external source. Then all Physics on the surface is simpler and passes the test of the *Ockham*».

** Unusual gyroscope in the Theory of Everything**

** Alex Isakov**

Today, the Holographic Principle — is hundreds of theoretical works by famous world-class physicists: G. ‘t Hooft, L. Susskind, J.D. Bekenstein, E. Verlinde, J.M. Maldacena, R. Bousso …. It is a theory that unites incompatible, but in fact, it is the most accurate reflection of the current state of science when scientific discoveries and their practical applications are so incredible in terms of ordinary human perception, that in them hard to believe. Already there are experimental studies confirming the operation of the Holographic Principle [30], [32]. Since 1997, more than 10,000 works have been published supporting this idea.

Understanding of the emergent nature of space-time and gravity comes from the laws of black hole thermodynamics and the Holographic Principle was born after the discovery of the laws thermodynamics on their surface. Bekenstein [7] have suggested a deep connection between gravity and thermodynamics. Through several decades of research and experimentation, physicists have brought forth a unified theory of the Universe that is based on information theoretic principles. The Holographic Principle states that the entropy of ordinary mass (not just black holes) is also proportional to surface area and not volume; that volume itself is illusory and the Universe is really a hologram which is isomorphic to the information «inscribed» on the surface of its boundary — this holographic screen.

The complexity of physical theories based on a holographic principle, for example, research at the level of quantum particles of the atomic nucleus and electronic shells, requires the creation of an effective spatial model of a computer simulator for testing, example, Theory Of Everything (TOE) but even this is not enough. Because the relevant distance scale at which fundamental modifications of our present theoretical views are expected to be needed is the so-called Planck Length, some 10‾³³ cm, which is more than a billion billion times smaller than anything that can be studied directly with laboratory experiments. However, for a tandem approach — experimental of measurements as a cooperative quantum phenomenon and visualize quantum processes on the basis of an electro-mechatronic device — unusual gyroscope and computer simulator of the dynamics of the projections of quantum particles «IsAN» this in some cases may be possible.

Modern researchers consider the line as one-dimensional space. As soon as the zero point is placed on the line, as the origin, this means in engineering language the binding of this line to the real space. However, in this case, eliminating the point 0 from the set, to call a line «the one-dimensional space» means to violate the law of preservation of information of the holographic principle.

The development of Euclidean geometry has shown that its main element is not a point, but a vector, that is, a pair of points. Therefore, if it is required to consider a transition along a line from -∞ to a point 0 and to + ∞, then it is necessary to turn around the point 0 along the arc ε and make a rotation through the angle Ѳ = ± π.

If we ignore this fact, calling the line a one-dimensional space, then it means breaking the law of preserving the information of the holographic principle and, consequently, making a mistake in the foundation of physics. If we accept the impossibility of losing information as the basis for describing the world around, then it is necessary to accept the fact that the line has a discontinuity at the origin, regardless of the minimum radius of the arc ε → 0, but now this can not be called a one-dimensional space.

Next, we consider the steady-state concept of a two-dimensional (flat) space. If the plane is drawn without the origin, then this concept does not bear physical meaning. If the plane is tied to real space, then the origin of coordinates is fixed in it. In this case, the logic of the previous reasoning takes effect. The neighborhood of zero does not belong to this two-dimensional world. The neighborhood of zero is a punctured point on a two-dimensional space. Definition, zero physically means that the plane is punctured by a ray emanating from another emergent dimension. The letter also asserts that the plane carries an element of the emergence of space within itself, and this is confirmed by the holographic principle itself, and this statement is its basic content. In this process, the transition to other large-scale measurements ends, because according to the holographic principle, really there is only one surface with information — the holographic screen of the universe. Thus, continuing the transition to the plane from -∞ through the point 0 to + ∞, we must again circle 0 along the arc ε in order to make a rotation through the angle Ѳ = ± π. Likewise, as we circled the point 0 on the line, on the plane we can additionally rotate the coordinates around the point 0, therefore each arc ε will describe the hemisphere.

If we now fix the arc radius to zero (ε → 0), then on the quantum level there will be a rotation through the angle Ѳ = + π or Ѳ = -π, and on the pole of the emergent sphere there will be the interaction of the particle with the measuring device (and/or with temperature gradient), which fixes the value of classical physical values and the distribution of their probabilities. In our universe, this is determined by the fact that two diametrical pairs of points on a spherical screen project one point in the emerging three-dimensional space with the Euclidean distance definition. This formalism demonstrates the inextricable connection between particles — waves and particles — points.

Holographic principle, based on the law of information preservation, allows the projection of any phenomenon onto the holographic screen of the universe and roundtrip without loss of information. Therefore, naturally, the sphere we have obtained is considered on the holographic screen of the universe.

With such a geometric and physical interpretation of the abstract concept of a point is are detailed: each point of emerging three-dimensional space is a sphere. Thus, the particle is a point, and the statistical trajectories projections of the particle in a natural way (from a simple formula of coherent oscillations) arise on two hemispheres have different temperature and belonging to one sphere of the holographic screen (in the experiment, proved the temperature anisotropy of the universe [5]). Now dualism becomes understandable from the position of classical physics, the particle is localized at a point, and the wave occupies the entire surface of the holographic screen.

In quantum mechanics, particles have internal degrees of freedom, which, under thermodynamic isolation, are not related to the motion of the particle as a whole. The statistic dynamics of the particle projections may be demonstrated of trajectories. The evolution of such a thermodynamic system is represented by classical trajectories that «survive» on the screen as a result of the interaction of the particle projections between themselves and the global temperature gradient and this process we can visualize in the simulator «IsAN».

In the simulator «IsAN» fragments of computer calculations of angular displacements are shown — a geometrical representation of the probability density of some projections of particles constructed by combinations of coherent oscillations from one parametric formula or a coherent evolution law:

The angular displacement of the vector around the corresponding axes: θx, θy, θz and parameters θ= πt and -1 ≤ t ≤ 1; where is geometrical angle admeasured by arbitrary clockwise and/or anticlockwise direction, starting from the relevant semiaxis, and t sets the needed accuracy of angular rotations. The formula is given parametrically, and it is applicable for any radius. When Δt → 0. the coordinates of the center and ε → 0.

The small-angle approximation is a useful simplification of the basic trigonometric functions which is approximately true in the limit where the angle approaches zero. They are truncations of the Taylor series for the basic trigonometric functions to a second-order approximation.

**sin(θ)≅ θ**

“In the limit of a very large region, the bonding surface can be taken to be a flat plane at infinity». Then рrojections on holographic screen H = A=∞, S — Arc length — the path of the projected point and O — Line segment on a holographic screen. Then S = O and

**sin(θ)= θ.**

Thus, the number of directions of coherent oscillations (Number trajectories of apex) can be calculated:

**4³- 4=60,** (±cosθ,±sinθ→4 for 3 coordinates).

The table does not show four variants from all (64) that do not fall under the definition of coherent oscillations (there is no phase shift).

We identify one bit of information with one of the phases of orthogonal coherent oscillations as the fundamental bit of natural coding of information in one area of the bar of a spherical holographic screen. But already two areas of the bar carry information from three bits, because according to thermodynamics on the holographic screen, the entropy of the expanding holographic screen naturally measures and encodes the information. The hologram is represented by temperature and entropy gradients that are stored and moved across the screen. Thus, only sixteen bytes of information encode all possible trajectories of simple particles and antiparticles.

In the simulator, the arrow indicates the projection of the particle onto the holographic screen of the universe. In the physical sense, the arrow on the spherical holographic screen is the direction of the local temperature gradient, the vector between the centers of two, once arbitrarily chosen, diametrically located areas of the bar. A pair or more projections of particles in the center of the projections form a simple particle.

Thus, the total number of simple particles in the simulator is exactly 60. The Standart Model of elementary particles describes 61 particles (the last discovered was the Higgs boson).

On the simulator, you can see a picture in which there are pairs of diametrically located projections of particles, which in themselves do not have mass. We give these particle projections the names «Is» and «AN». Being massless projections, they move along diametrically opposite sections of the holographic screen without limiting speed of light, but instead it can be observed on the simulator that they «rock» back and forth on it, and the forward motion of the particle «Is» continuously turns into a backward motion of the particle » AN «, and vice versa. In fact, this is the realization on the holographic screen of a phenomenon called «zitterbewegung» in quantum physics and consists in the fact that the instantaneous movement of an electron, for example, because of participation in such vibrations, always occurs without the speed limit of light, although the full the average motion of an electron is characterized by a velocity less than the speed of light. Therefore for the projection center (electron), the locality principle does not break. Each of these ingredients has a spin of 1 / 2ℏ in the direction of motion corresponding to the left rotation in the case of the projection of the particle «Is» and the right for the projection of the particle «AN». The real motion of the projections of the electron «Is» and «AN» is composed of a large number of such separate processes so that the observed motion of the electron can be regarded as the result of some «averaging» (although, strictly speaking, quantum superposition takes place here).

After running the simulator on a spherical screen, you see special points — the poles of the sphere and the cluster points, the discrepancies between the projections of the particles. They can be identified as specific interaction points for particles and as nodes for the formation of complex composite particles. For composite particles, some of the projections consist of more complex sets of their trajectories. More complex composite particles, in physical terms, have more «windings» of projections on the surface of the sphere of the holographic screen.

To each fundamental fermion, there corresponds an antiparticle with the same mass. All the charges of the antifermion are opposite. Projections of antiparticles moving «backward in time» are also important for research, but they are still excluded from consideration in the simulator.

One of the arguments in favor of the reliability of computer simulation of the dynamics of the projection of particles is its natural appearance from one concise parametric formula of coherent oscillations. The first thing that is observed in the simulator after its launch is the dynamics of the projections of particles of three generations on a holographic screen.

All reasoning and conclusions obtained as a result of observation on the computer simulator for the dynamics of particle projections require verification on the operating model of an unusual gyroscope.

The fundamental bricks from which matter is built are not limited to electrons and two quarks. In addition to the charged electron, it is necessary to add neutrinos — as a copy of the electron, only without charge and almost without mass. «Almost» must be taken into account, since the global temperature gradient has a flat relief on the holographic screen.

The global temperature gradient of the Universe projected onto a holographic screen without loss of information.

The relief of the global temperature gradient on the everybody two hemispheres screen interacts differently with moved projections of the particles «Is» and «AN» on the holographic screen, which gives the particles different properties (mass, for example). This mechanism for many different particles of matter, according to thermodynamics on the holographic screen, is responsible for the appearance of the entropic force, which acquires the appearance of all known fundamental forces and interactions.

On the screen of your computer after loading into the simulator the parametric formula «coherent evolution law» «IsAN», we can have:

1. The appearance of a spherical screen, which can be viewed from any pre-selected position.

2. The appearance of two hemispheres screen and move projections of the particles «Is» and «AN» at different speeds.

3. Projections of 60 particles of the Standard Model, their dynamics and characteristic intersection points of their statistic trajectories.

4. The characteristic trajectories of particle projections, which we have associated with three generations particles of the Standard Model.

5. The trajectories projections of particles are uniquely determined on a spherical screen per cycle. At every instant, the rules lead to one single, unambiguous prescription as to what will happen next. The cycle time can be varied.

6. According to thermodynamics on the holographic screen described below, against the background of the fact that entropy does not decrease (information about past is preserved), the interaction of particle projections with global and local temperature gradients on a holographic screen determines the cause of the events that occur. «We have causality: every event must have a cause, and these causes all must lie in the past, not in the future. A demand of this sort is mandatory. What it really means is that, what is supposed to happen next, we should never be confronted with a circular situation, or in other words, we should always know in which order the rules must be applied. Whatever that order is, can be used to define time. So now we can distinguish future from past. Only the past events are relevant for what happens next, and whatever they dictate, will only affect the future»[1] [Page 5. 31].

7. The visualization of the interaction with the global temperature gradient (the events in the past) and with other particle projections on the screen demonstrates the effectiveness of the coherent evolution law. «Efficiency. Not all events in the past, but only a few of them should dictate an event in the presence. This suggests that there is a power limitation in we can’t have that every particle in the past, instantly determines the behavior of every particle in the future. If for computing the behavior of one particle, we only need the data concerning a few particles in its immediate environment, then the calculation will go a lot quicker. We are simply asking for a maximum of efficiency». [1] [Page 6. 6].

7a. «Zitterbewegung» (the instantaneous movement of a particle), for example, because of participation in such vibrations two projects, without the speed limit of light, although the full the average motion of a particle is characterized by a velocity less than the speed of light. Therefore for the projection center — of a particle, the locality principle does not break. The locality for all particles is that space is three-dimensional and have Euclidean definition of distance. «Locality. All configurations one needs to know to determine the behaviour of an object at a given spot, must be lying in its vicinity. This means that we will have to define distances. Only points at very small distances from a given point are relevant for what happens there. What ‘vicinity’ really means still has to be define»[1] [Page 6. 14].

8. After going through the steps of Verlinde, considering the thermodynamics of the holographic screen, we conclude that the acceleration is associated with the entropy gradient. This is our one of the basic principles: inertia is a consequence of the fact that the resting particle will continue to rest, since it is not subjected to the action of entropy gradients. Principle of equivalence leads us to the conclusion that this is the very law of inertia — the rule that stems from entropy.

«Velocity. Any object for which it has been decided how it behaves when at rest, will behave very similarly when it moves along a straight line in any direction, with any constant velocity (within limits, see the next rule). The rule of its behaviour at this velocity must be derivable in a simple way from what the rules are when it stands still. [1] [Page 6. 30].

To improve visualization of the simulator «IsAN», three generations of particles are identified by three spectra: green, blue and red. In the grand unification theory, particles: quarks (u, d) and leptons are grouped into three generations: quarks (u, d) with an electron (e -) and an electron neutrino (ν_e) form the first generation, quarks (c, s) c muon (μ -) and muonic neutrinos (ν_μ) form the second generation, and the quarks (t, b) together with the tau lepton (τ -) and the tau lepton neutrino (ν_τ) are the third generation:

Based on results of simulator we argue that the fundamental laws of nature appear to be chosen in an extremely efficient way and quantum mechanics is too.

Reproducing realistic quantum models for locally interacting quantum particles along the lines proposed.

**The anisotropy of the Universe **

Commensurate in scale with the Holographic Principle was the discovery of the anisotropy of the Universe in 1992 (anisotropy of cosmic microwave background (CMB) — (this the difference of temperature in different directions on the sky) [5] Experimentally confirmed by the anisotropy of the CMB and the discovery of coherent acoustic waves in the early Universe is of great importance not only for cosmology but for the whole of natural science as a whole. It can be said that large-scale three-dimensional sound coherent oscillations act before recombination period and ended after 379,000 years, but did not disappear completely, and recorded big scale on the sky. As a result, the temperature anisotropy of the Universe, according to the Holographic Principle, may be projected on its holographic screen. It is experimentally confirmed the fact that coherent oscillation of the elements of mass can be projected without any loss of information to the specific locations of the holographic screen. All calculations and experimental data in the modern cosmological model, in particular, explain the observed anisotropy of the Universe are connected with the speed of sound three-dimensional coherent oscillations of the primary plasma. the discovery of CMB confirmed the theory of the hot Universe and is now one of the most important facts supporting the theory of the Big Bang and the expanding Universe. We can say that experimentally is not confirmed equipartition of temperature on the cosmological horizon of the inflationary Universe. Investigating thermodynamics on the holographic screen, we must take into account the impact of it’s of global temperature anisotropy on the dynamics the projections of phenomena. The dominance of gravity, on a large scale, in particular, and existence all four known forces a whole can be explained by the influence of a large-scale thermal anisotropy Universe.

The CMB dipole anisotropy. The color scale shows a spread of ±3.5 mK.

For experimental verification of the Holographic Principle is offered unusual gyroscope MGEF. It is assumed that MGEF can generate and control the direction of gravitational forces, can be used as a propulsion system and can easily be reprogrammed to work as a device for measuring the geometry and dynamics of the Universe in the real-time (without limiting the speed of light). Let us consider in detail how it works.

To demonstrate the possibilities of generating artificial gravity forces we define that is very important: Although the bits of information are encoded on a two-dimensional (2D) screen the observed images appear three-dimensional (3D) since their nature is holographic.

«Usually, holography is studied in relativistic contexts. However, the gravitational force is also present in our daily non-relativistic world» [25] [page 3. 5].

«we will argue that the central notion needed to derive gravity is information» [25] [page 2. 23].

Motivated by Bekenstein’s argument, let us postulate that the change of entropy associated with the information.

The relationship between entropy and information is that the change in information * ΔI* is represented by a negative change in the entropy

*.*

**ΔS***ΔI = — ΔS*.

*ΔI = — ΔS*.

On the other hand, gradients of temperature, entropy, and force are associated with acceleration and the resulting mass:

«We can express the entropy change in terms of the acceleration» [25] [page 11. 14]. «Thus, we conclude that acceleration is related to an entropy gradient. This will be one of our main principles». [25] [page 11. 22].

**ΔS ∼ α**

**ΔS ∼ α**

To shorten the text, we mean that the temperature, entropy, and entropic forces are on the holographic screen — the cosmological horizon of the Universe.

Let’s start with the postulate of Holographic Principle:

1. «In the limit of a very large region, the bounding surface can be taken to be a flat plane at infinity. In some way, the phenomena taking place in three-dimensional space can be projected onto a distant «viewing screen» with no loss of information» [3] [page. 3. 18]. This means that all the information, the receiver, the transmitter, and the observer is on the holographic surface the cosmological horizon of the Universe. For us, it is very important not to forget and this greatly simplifies the exchange and processing of information for the observer.

2. Unusual gyroscope MGEF is that the cycle of its spherical rotor makes one complete revolution around the three axes. The movement of the rotor in a vacuum is controlled by a computer control system.

3. Since the spherical motion (forced coherent oscillations) of the spherical rotor is made around the three orthogonal axes, then there we have are six areas (groups) of angular accelerations elements of mass. All elements mass of the rotor moves over the surfaces of concentric spheres around a fixed point — the center of mass. Nodes and anti-nodes of angular accelerations create a stationary interference pattern. Thus, we are dealing with the cooperative a quantum phenomenon.

4. According to the Holographic Principle, we can make this projection the six groups of angular accelerations (αCi) elements of mass (gradient entropy) on a holographic screen — the cosmological horizon of the Universe without losing information. Actually, the projection and is not required, if you understand the essence of the Holographic Principle. In the presence of horizons, it is natural to define on the horizon global gradient temperature ΔTgl.

5. We have the stationary interference pattern of the six groups of angular accelerations (gradient entropy) is on diametrical sections of the holographic screen. rotor control system produces shifts of the rotor (any the pairs (4 of 6) projections, reverses the rotation of the half-line). Gradients entropy of αEi — angular accelerations (they emerge at displacement elements of mass) by moving on the screen part of the projections are experiencing the different entropic force as they interact with a certain dipole global gradient temperature. Thus we are able to control the position of the on-screen projections of two angular accelerations αCi and αEi. The center of projections angular accelerations is displaced under the action of the forces of entropy associated with a temperature gradient. therefore, the center of accelerations of the rotor is attached to the entropic force «F» — this is a long-range gravitational force.

6. Let us consider.

** The thermodynamics on the holographic screen (hs) with the dimension of «2 + 1» (2D).**

Let us leave only the physical body outside the center (inside) of the spherical holographic screen (screen) of the Universe with area A, and place the observer in the center of the screen. Then the screen can be presented as a memory device for storing information related only to our physical body. Consider the experimentally established temperature of the Universe, projected without losing information on its screen:

**(1)**

where *Tpr*— temperature on the screen, ΔT — positive or negative temperature difference at two points per unit distance between them a vector quantity — * Δx*. The minimum limit Δx is Planck length. The max limit

*is the distance between the two central points of petals of global temperature dipole anisotropy of the Universe. T is the projected temperature on the holographic screen without loss of information (therefore, further as the temperature T on the screen),*

**Δx***is the vector value (according to Conclusions of thermodynamics, the direction of the vector from high to lower temperature).*

**Δx**Considering that the entropy of a system depends on the distance * ∆x*, an entropic force F

*entr*could arise from the thermodynamical conjugate of the distance as [25] [page 7. (3.7)]

**(2)**

The fundamental entropic force may be regarded as an indication that is realized on the screen in the range * ∆x*. Substitute (1) in (2).

**(3)**

where «ΔT» — global gradient temperature, «ΔS» — gradient entropy caused by the acceleration projections of the matter.

Assume that for an entropy force in three-dimensional space as for any of the four forces, it is necessary to supplement it with a vector factor **Δx** perpendicular to the screen, and the screen temperature (in the classical approximation) is assumed constant. Then:

**(4)**

where T temperature of the screen, «ΔS» — gradient entropy caused by the acceleration either projections of the matter.

The product Fentr * Δx* can be considered as the energy that should be applied to the system in order to withdraw it from the equilibrium state. The existence of a vector factor

*(perpendicular to the screen) is the reason that the world seems to us to be three-dimensional. Space occurs on a macroscopic level only after discretization. Consequently, with each configuration of matter, the final entropy is connected. This entropy measures the microscopic amount of information that is invisible to a macroscopic observer. In general, this amount of information will depend on the distribution of matter. This information will be processed by entering the microscopic evolution of the screen, which seems random from a macroscopic point of view. Such an assumption goes back to Bekenstein’s thought experiment in the derivation of his famous formula for entropy. He considered a particle with a mass m that approaches the horizon of a black hole. Directly near the horizon, the particle merges with it. As a consequence of the infinite redshift, the mass of the particle increases the mass and area of the horizon by some small (classical) value. As soon as the particle is at a distance of the Compton wavelength*

**Δx***from the horizon, it can be regarded as part of a black hole. Then it increases the mass and area of the black hole horizon by a small amount that Beckenstein associated with one bit of information, which led him to the law of correspondence between the area of the black hole’s horizon and its entropy.*

**Δx**Verlinde considered the situation, not alongside a black hole, but with a flat non-relativistic space, ie, next to a small plate — a holographic screen, and a particle of mass **m** that approaches it. Eventually, the microscopic degrees of freedom of the particle merge with the screen, but just before that, some amount of information is transmitted to the screen. Thus, a holographic direction appears perpendicular to the screen. Guided by Bekenstein’s considerations, Verlinde wrote down the formula for the entropy increment associated with the mass [25] [page 4] (3.6):

Where **c** is the speed of light in a vacuum,** ħ** is the Planck constant.

**(5)**

How does entropic force arise?

Each cell of the screen by definition contains one bit. Assuming the fulfillment of the holographic principle, let us write down that the information capacity of a spherical screen is proportional to the area of the shell:

**(6)**

Where N is the number of bits on the screen

In our closed system, the energy **E** is equivalent to the mass of the physical body **M**, which is concentrated in the part of the space surrounded by the screen. Since temperature and acceleration are closely related and have a direction in a three-dimensional space perpendicular to the screen, then, in accordance with the holographic principle, we can project them without loss of information. Unruh showed that the observer in the accelerated reference system has a temperature **T**:

**(7)**

Where **α** is the acceleration, **k B **is the Boltzmann constant. As will be shown below, using this formula, we can display the temperature associated with the bits on the screen.

According to the proposed method of projecting the phenomena on the screen, suggested by L. Susskind [3], the memory cells of the screen with the temperature projected on it, connected with the physical body, occupy one hemisphere of the screen, this is what we call the global temperature gradient.

We have chosen the usual position of the center of mass of the physical body when it is displaced relative to the center of the screen. According to the proposed method of projecting the phenomena on the screen, suggested by L. Susskind, the memory cells of the screen with the temperature projected on it, connected with the physical body, occupy one hemisphere of the screen, this is what we call the global temperature gradient. Nevertheless, the energy equivalent to matter and uniformly distributed across the cells of the screen must, subject to the holographic principle, carry information about the mass and coordinates of the physical body in three-dimensional space without loss. Note that these conditions are contradictory. In the classical approximation, the total energy that is associated with the physical body can not be uniformly distributed across the screen, otherwise, information about its coordinates will be lost. To solve this problem, it is required to break up the total energy equal to the mass of the physical body into kinetic and potential and, only then it can be assumed that the total energy tends to be uniformly distributed among the memory cells. Thus, we come to the important conclusion that, for any physical body, there is its own global temperature gradient on the half of the screen, which carries information about its mass and coordinates (potential energy), and the displacement of the global temperature gradient under the action of entropy gradient displacements (Kinetic Energy) complements the associated energy **E** to the full. Then we can assume that the entropic force arises from the movement of the global temperature gradient on the inflation screen, which leads to a shift in the center of the projections of the accelerations of the mass elements or the coordinates of the physical body in the three-dimensional space. In full accordance with the conclusions of Verlinde, the emerging entropic force in the three-dimensional space acquires the appearance of a gravitational force.

Obeying the holographic principle, complete information about the physical body and its coordinates, related to the kinetic and potential energy, tends to spread evenly across the screen. This means that any physical body has inexhaustible energy from the source of kinetic energy necessary to move its global temperature gradient across the screen. Kinetic energy is the result of inflation — the accelerated expansion of the screen itself (the continuation of the Big Bang).

If our assumptions are correct, then thermodynamics on the surface of the screen must inevitably lead to the conclusion of fundamental laws, in particular, to the Law of World Gravitation. Let’s consider more in detail

So, we assert that the potential plus kinetic energy on the screen is equal to the total energy (Ek + Ep = E). Then the total energy equal to the mass of the physical body tends to be evenly distributed between bits of the screen N (by ½kBT for each bit).

**(8)**

Where kBT is the temperature of one cell. We use the well-known formula for energy.

**(9)**

Where **M** is the mass of a physical body enclosed in a part of the space bounded by a spherical screen. The surface area of the spherical screen is **A**.

**(10)**

Where **R** is the radius of the screen.

If we now introduce a second physical body of mass m into consideration, the position of the global temperature gradient on the screen will cease to be the same. In the general case, the temperature gradients will no longer be given by the same rule.

In quantum mechanics, there is that radical idea that particles do not just move along the shortest path, but go all the way possible routes pass, including random zigzag wanderings. From the position of the holographic principle, this process extends over the entire surface of the holographic screen of the universe with a global temperature gradient on it. The quantum mechanism of moving, now the projections of particles of physical bodies around the screen and their interaction with temperature gradients is the source of the entropy force applied to the center of the projections. This is a key postulate for explaining the mechanism of mass generation and entropy force (gravitational force). Each projection of a particle of a physical body has traveled both in the present and in the future, passing through all possible trajectories. The contribution from all trajectories, except for one single, classical, was reduced. Thus, the existence of the Hamiltonian principle in classical physics is a consequence of the displacement of projections of particles along the screen and their interaction with the global dipole temperature gradient of the Universe.

Inflation of screen adds to the gravitational interaction an additional repulsive force between the masses, a kind of anti-gravity that reflects on the gravitational constant **G**. Therefore, in the formula for the entropy force, it is necessary to introduce a constant **G**, which can be equal to Newton’s gravitational constant for our Universe.

Projections of global temperature gradients of two bodies on the holographic screen of the Universe.

The entropic forces tend to minimum the distance R between two bodies. This process occurs because when we introduce a second body into the system, the balance between kinetic and potential energy for each of the two bodies is violated. Accordingly, the balance of the opposing forces moving the projections of particles on the screen, connected with the bodies M and m, and the force of the screen creating inflation, are violated. Projections of particles M and m when moving them along the screen interact with temperature gradients m (circle) and M (ring). As a result of the imbalance, the forces of expansion of the screen entropy increase, which increase the area of the screen with temperature gradients m (circle) and M (ring), for m, respectively, more than M. For the body of a larger mass M and, accordingly, the disbalance of entropic forces and, consequently, the body m approaches M with a large acceleration, which is interpreted in 3D as a result of the action of gravity. The distance R rapidly decreases, and with it the centers of the projections also move rapidly. Eventually, the temperature gradients merge, and, therefore, the bodies collide. In this situation, for two black holes with the maximum information density on the inflation screen, they merge, and the displacement of the particle projections associated with them is identified with «radiation» and leads to a known «evaporation.» Thus, the information is preserved, and black holes are interpreted in 3D only as 2D objects. We conclude that the natural identification of gradient of temperature and information density on the inflationary holographic screen directly leads to the laws of the theory of gravitation.

Using formulas (8) and (9), excluding **E**. we substitute the expression for the number of bits N (6) that determine the temperature **T** (7). To determine the force in (4) we use the expression for entropy change (5), finally substitute (10) and **G**, we get:

**(11)**

Thus, the force of gravitational interaction of two bodies arises as a result of a holographic scenario, which explains its long-range action.

We use formula (4) and replace the temperature by (7), the entropy gradient by (5) and obtain the second Newton law.

**(12)**

Since each bit carries an energy of 1/2 kBT, then their number** N** is determined from the relation:

**(13)**

When we substitute this equation in (5) and use (7), we can express the entropy increments through acceleration:

**(14)**

Combining equations (4), (14) and (13), expressing the temperature through the mass, and the entropy gradient through acceleration, we again arrive at the equation **F = mα** for the entropy force. However, by entering the number of bits associated with the energy on the screen, we demonstrate that the constant **c** and **ħ** fall out of the ratio, which corresponds to expectations. This conclusion means a lot to us, for example, that the entropy (gravitational force) can be artificially created with the help of a hybrid of a classical and quantum device for generating accelerations (an unusual gyroscope) without using exotic masses and energies. The kinetic energy of accelerated screen expansion associated with the mass of the rotor of an unusual gyroscope can be used in the recovery mode and used as an inexhaustible source of clean energy.

Applying the formula for the entropy increment associated with the acceleration (14) and substituting it in (4) for the entropy force, using (7), (10), we obtain the entropy force on the screen surface with radius **R**:

**(15)**

Where 𝒂 are equal accelerations associated with the temperature and entropy on the screen of radius **R**.

The absence of mass in the equation may seem unobvious. But this equation is on the surface of the Universe, and all mass/energy is information on a holographic screen that has no thickness. This equation tells us about two massless one-dimensional vibrating strings and their interaction on the emerging surface, the coding of information by the phases of string vibrations, the appearance of: fractals — the structure of space / time (spatial bundles), all known and not yet discovered particles, and the most entropic (Super) force responsible for the appearance of mass and gravity.

Using (13) and substituting (6), (10), and (7) into it, we obtain an equation for the mass on the screen:

**(16)**

Combining (15) and (16), we again arrive at the equation** F = mα **.

Then, at the level of apples, applied to a hybrid of a classical and quantum device (an unusual gyro-controlled accelerator), the mass can be represented by the elements of the rotor mass and artificial accelerations of its coherent oscillations projected without losing information on the holographic screen. Displacements of accelerations associated with an artificial mass relative to the center of mass of the rotor lead to the appearance of a directed gravitational force:

*F**grav**=**ηm**α**²*

*F*

*grav*

*=*

*ηm*

*α*

*²*

**(17)**

where Fgrav — gravitational force. The emergent laws of gravity contain gravitational force describing the ‘elastic’ response due to the entropy displacement of the projection.

η — order parameter (η > 0) (the inverse of the thermodynamic effect of the external environment),

m — the mass of rotor,

**α**² = **α**Ci**α**Ei ⁄ 6 gravity accelerations (when **α**Ci = **α**Ei), 6-the number of projections.

* αCi — angular accelerations *(they emerge at forced a coherent oscillations elements of mass).

* αEi* – angular accelerations — the entropy displacement (they emerge at displacement elements of mass).

This means that to obtain long-range gravitational forces do not require exotic masses and energies.

Holographic Principle concludes that: gravity is explained as an entropic force. The equivalence principle leads us to conclude that it is actually this law of inertia whose origin is entropic. This thermodynamics on 2D, arising from the statistical behavior of microscopic degrees of freedom associated with a global temperature anisotropy and localized on the holographic screen of the Universe. Thus the force of gravity and his long-range is not postulated but derived from a holographic scenario.

In contrast to the entropy change when a particle approaches the screen equidistribution temperature, the entropy change when each of the projections of particles (elements of mass) moving on the screen interacts with the gradient of temperature and carries more information than when artificially introduced the equipartition of temperature on screen. As a result of the interaction of the gradient of the entropy projections particle arising entropic force applied to the geometric center of the particle. Therefore, this mechanism is maybe responsible for the appearance of a mass. A result of the encoding information on the holographic screen appears mass/energy, gravity, and space-time itself. Unusual gyroscope MGEF can be used for a detailed study of this assumption.

The series generated in MGEF directed long-range gravitational forces leads us to be able to control gravity.

MGEF device can answer the question: Does the Holographic Principle is valid, according to which the physics of our 3D n-dimensional space-time is equivalent to the physics of the hypersurface with the dimension of 2D. In addition, we get the information directly from the surface of the cosmological horizon in real time and without limiting the speed of light

Gravity — ordered action entropic forces on the projection of the phenomena on a 2D the holographic screen. As a result, the centers of the projections are changing their position in 3D. Entropic (gravity) force — is the result of the interaction of the entropy gradient on the holographic screen caused by the acceleration of matter and the global temperature gradient, known as anisotropy of the Universe. Thus, the movement of information on the 2D holographic screen leads to the long-range directional gravity force in 3D.

After transformation in 3D away quite easily possible to deduce the fundamental laws of Newton (in particular the Second Law). This means that to obtain long-range gravitational forces do not require exotic masses and energy (see below Formalism Verlinde in the emerging space-time (the physics of 3D on the border of 2D).

Newton’s third law is not violated since the size of a closed system is increased to the cosmological horizon of the Universe. Series directed long-range gravity forces leads us to manipulate gravity. Note that the computer of the rotor motion control system has received information on the situation of the global dipole temperature anisotropy of the Universe without limiting the speed of light.

Global temperature gradient Universe and projection on a holographic screen interference pattern of the six groups of angular accelerations *αCi *(respectively, gradients of entropy). Arrows indicate the possible direction of the angular acceleration displacement * αEi*.

Where F_grav is the gravitational force, y is the order parameter, the value lying between zero and unity, m is the mass of the rotor of the unusual gyroscope, and a is the product of two equal accelerations. One of which is the rotational acceleration caused by artificial coherent oscillations of the rotor and, second, is caused by a controlled displacement (one of 60 variants).

Obtaining a directed gravitational force in an unusual gyroscope does not contradict the law of conservation of momentum since the size of a closed system is the holographic screen of the Universe.

If our assumptions are correct, then the prospects are opened with the use of an unusual gyro MGEF for:

- Artificially creating coherent vibrations of the rotor of an unusual gyro, controlling the direction of the acceleration of the elements of mass, we can create entropy (gravitational) forces on the screen in any chosen direction and, therefore, control gravity.

2. Generating the gravitational force and determining its direction, we can build a hybrid of the classical and quantum device for measuring the parameters of the Universe in real time.

3. There is the possibility of using the inexhaustible energy of the accelerated expansion of the holographic screen.

4. Unusual gyroscope MGEF can be used to transmit and receive information directly from a holographic screen without limiting the speed of light.

If there are intelligent civilizations in the Universe, they will use this communication channel.

**MGEF**

- Base.
- Enclosure.
- The Stator (diameter front section).
- Frame
- Rotor.
- Magnets (100 pcs.).
- Magnetic point.
- Optical point.
- Induced coils (66 pcs.).
- Sensors (magnetic and infrared).
- Slave controllers and drivers of induced coils.
- Computer.
- Accumulators.
- Solar batteries.
- Retaining bolts.

Let us discuss the concept of the MGEF design, ‘a thick-walled sphere with the magnets in a vacuum inside another sphere with induced coils’. The design allows for three-dimensional oscillations of the balanced ceramic rotor 5 (hereinafter, the rotor) with the magnets pressed into it around its center of mass. Such gyroscope without mechanical axes can be obtained by a master electromagnetic suspension that acts based on the principle of the rotor levitation with magnets in the magnetic field. The rotor displacement from a predetermined equilibrium position is measured by the position sensors. The signals from the sensors are processed by a multi-core microprocessor control system which regulates the currents pulse in the induced windings of the stator so that the magnetic forces return the rotor to the predetermined position and can simultaneously produce full angular rotations of the rotor in any direction under computer control. The control program is provided with the possibility of stabilizing the cyclic rotor speed.

Thus, we are able to rotate the balanced ceramic sphere in a vacuum around one fixed point in any direction under computer control.

**Forced coherent fluctuations of a rotor to make angular accelerations (αCi) of each element of mass. On multiple concentric spherical surfaces, angular accelerations take constant positions in space, in a time of a cycle and create an interferential system.**

In full accordance with the Holographic Principle, one of the most important properties of coherent fluctuation of a rotor is to concentrate the gradients entropy displacement by its angular accelerations round each of semiaxis of motionless Cartesian coordinates on a «remote» holographic surface of the Universe and angular accelerations may be projected with no loss of information and travel on it without time delay.

Further, we will discuss the holographic dynamics as applied to the spherical rotor in a vacuum. Such closed dynamic system, as we will see below, has central and translational symmetry. It will include (along with the rotor and stator) concentric spherical holographic screens with the entropy associated with the local space occupied by the rotor, its local temperature, and its dynamics.

Let’s receive the parametrical equations of coherent fluctuation from the principle of the smallest action (Hamilton’s principle) for angular displacements of its points.

Let us start with the definition of a coherent oscillation of a classical body (6DoF).

“The motion of a physical body when only one its point *О* remains fixed all the time is called the rigid body motion (rotation) around a fixed point *О*. In this case, all points of the physical body move along the surface of concentric spheres, the centers of which are located in the point *О*. Therefore, such motion is called the spherical motion of the body. Based on the definition of the spherical motion, we obtain parametric equations of the coherent oscillation of the elements of mass from the principle of least action”.

«Coherent oscillations of the elements of mass are the spherical motion of a physical body, the forced full harmonic oscillations of which are successively shifted by 90° or 180° and which are produced in a cycle by angular displacements of its points around the fixed axes of Cartesian coordinates associated with the accelerating observer.»

(10)

Then angles: θx- roll, θy — pitch, θz — yaw and parameters θ= πt and -1 ≤ t ≤ 1; where is geometrical angle admeasured by arbitrary clockwise or anticlockwise direction, starting from the relevant semiaxis, and t sets the needed accuracy of angular rotations. The motion formula (10) is given parametrically, and it is applicable for any rotor radius. When Δt → 0 and the coordinates of the center of mass of the rotor → 0, we have small-angle.

“The small-angle approximation is a useful simplification of the basic trigonometric functions which is approximately true in the limit where the angle approaches zero. They are truncations of the Taylor series for the basic trigonometric functions to a second-order approximation.” [33].

**sin(θ)≅ θ**

“In the limit of a very large region, the bounding surface can be taken to be a flat plane at infinity». [1] [page 3. 18]. Then рrojections on holographic screen H = A=∞, S — Arc length — the path of the projected point and O — Line segment on a holographic screen. Then S = O and

**sin(θ)= θ.**

Thus, the number of directions of coherent oscillations (Number trajectories of apex) can be calculated:

The table shows four variants from all (64) that do not fall under the definition of coherent oscillations (there is no phase shift).

The table shows all (60) variants coherent oscillations of rotor unusual gyroscope MGEF around the fixed axes of the Cartesian coordinates X, Y, Z.

According to the definition of a coherent oscillation, all elements of mass of a physical body move along the surface of concentric spheres around one fixed point. If we compare all the points of the physical body with the elements of its mass, we can conclude that we are dealing with a cooperative quantum phenomenon. The complementary accelerations of the elements of mass that are directedly associated with directed the fixed Cartesian coordinates, nodes and antinodes, make a fixed interference pattern that reflects the known geometric structure. Other ways of describing coherent oscillations (not parametric) can lead to loss of information. For example, the task of finding the final coordinate of point a system can be performed on two legs or one hypotenuse, in the second case it leads to loss of information, although the end result is the same. Recall that the main law of conservation for the Holographic Principle is the law of information preservation. The Holographic Principle, although driven by quantum computation, may be revealed to us the existence of a universal computational mechanism that is capable of representing high dimensional problems using a relatively low number = 60 of model parameters.

** Slow simulation of coherent fluctuations of a spherical rotor on parametrical formulas**

The coherent fluctuations of the rotor occur in a vacuum. Such thermodynamic isolation of the rotor from the nearest external environment is crucial because it eliminates the possible influence of the temperature and entropy changes on the rotor surface. Thus, in a vacuum, the rotor acquires local temperature and entropy when matter (particles) is displaced.

Moreover, such rotor oscillations are characterized by central and translational symmetry, along with mutual orthogonality, as they occur around each of the axis (x¡).

The Graph shows six zero — angular speeds of revolutions of the rotor, when the rotary acceleration (**α**С) becomes zero, for each of the Cartesian coordinate semiaxes.

* αС (x+), αС (x-) — *accelerating along the X-axis,

*Y-axis,*

**α**С (y+),**α**С (y-) —*Z-axis.*

**α**С (z+),**α**С (z-) —It is important to note that, according to the above formula (10), the arising acceleration (**α**Сi) of all points – the electrons (we will treat them as rigidly bound point particles in the atoms, as the elements of the rotor mass) is distributed in space and in cycle time. The phases of the oscillations around each of the axes are a shift in cycle time to 90° and, therefore, the extremes of harmonic functions, due to which the angular shift of the rotor electrons occurs, are distributed in space and in cycle time; see Figure 1. The harmonic functions of the angular movement of the points (the rotor mass elements) are periodic relative to both time t, and to the (x¡). Thus, equipartition of the extremes of harmonic functions of speed (when **α**Сi = 0) in cycle time and in space leads the dynamic system isolated from the external environment to the spatial and temporal coherence.

Relying on the above discussion, let us define the scale gravitational force. Due to the gyroscope property to acquire stability in an effort to save its determined direction relative to the world space and as a result of the rigid connection between all material points (the electrons) of the rotor, they all get the rotary acceleration (**α**Ci).

It doesn’t have an outside or an inside. It just has the rubber surface. You have to learn to think of the surface of the balloon as being all there is. It’s all there is». L. Susskind.

The projections acceleration the surface are possible because: «… have determined that, to high precision, space in our cosmos is flat» [5] [page 1371].

Red and purple are conditionally shown temperature gradients Tu — dipole lobes (on the surface anisotropy) [5]. For a case of coherent fluctuation of a rotor the entropy gradients associated with its angular accelerations: **α**CX+ =0, **α**CX-=0, **α**CY+ =0, **α**CY- =0, **α**CZ+ =0, **α**CZ- =0 concentrate around motionless semiaxis (x¡) on surface of (fig. at the left). For a rotation case (incoherent fluctuation) of a rotor around the main axis, gradients of entropy are making displacement on all surface of (fig. on the right). On two spheres by white color, the arrangement of gradients of entropy on a surface is conditionally shown. For the generation of the directed gravitational force, the program of management of the coherent fluctuation of a rotor makes the displacement of its points round two of three axes of motionless Cartesian coordinates. This results in the acceleration of displacement (αEi). Options are presented in Tab. A, B, C, and D

The scaling and directed gravitational force can be artificially obtained by displacement the position of coherent fluctuations matter relative to two of the three fixed Cartesian coordinate axes, which causes changes in the local entropy on the holographic screen. This can be regarded as a cooperative quantum phenomenon. Thus, the directed scale gravitational force can be generated during the reverse transition of the system to more probable (realized by the greater number of microstates) macro state at the moment of the translational symmetry violation. The fixation of the occurrence of gravitational force can be carried out on a torsion balance. Torsion balance is a compact instrument for measuring the gravitational force and verifying the cooperative quantum effect in unusual gyroscope MGEF based on an elaborately designed Cavendish balance. It uses a reflected laser beam.

See more: http://isan.com.ua/articles/

**References**

[1] G. ’t Hooft «Free Will in the Theory of Everything» (2017) https://arxiv.org/pdf/1709.02874.pdf

[2] G. ’t Hooft, “Dimensional reduction in quantum gravity” (1993) [arXiv:gr-qc/9310026].

[3] L. Susskind, «The World as a Hologram». J. Math. Phys. 36 (1995) 6377, arXiv:hep-th/9409089.

[4] H. Casini, M. Huerta, J. Hung, A. Sinha, M. Smolkin & A. Yale. «Holographic Entanglmarkent Entropy».

[5] George F. Smoot «Cosmic microwave background radiation anisotropies: Their discovery and utilization» REVIEWS OF MODERN PHYSICS, VOLUME 79, OCTOBER–DECEMBER 2007.

[6] J. Raphael Bousso «The Holographic Principle» http://arxiv.org/abs/hep-th/0203101.

[7] J. D. Bekenstein, “Black holes and entropy,” Phys. Rev. D 7, 2333 (1973).

[8] G. ’t Hooft » The Cellular Automaton Interpretation of Quantum Mechanics» 2014 https://arxiv.org/abs/1405.1548

[9]P. C. W. Davies, ”Scalar particle production in Schwarzschild and Rindler metrics,” J. Phys. A 8, 609 (1975)

[10] W. G. Unruh, «Notes on black hole evaporation» Phys. Rev. D 14, 870 (1976).

[11] A. L. Dmitriev, E. M. Nikushchenko, S. A. Bulgakova «NONZERO RESULT OF MEASUREMENT OF ACCELERATION OF FREE FALLING GYROSCOPE WITH THE HORIZONTAL AXIS» http://arxiv.org/ftp/arxiv/papers/0907/0907.2790.pdf

[12] Aitor Lewkowycz, Juan Maldacena «Generalized gravitational entropy» http://arxiv.org/pdf/1304.4926v2.pdf

[13] E. Santos, Bell’s their mark and the experiments: Increasing vampirical support to local realism: quant-ph/0410193, Studies In History and Philosophy of Modern Physics, 36, 544-565 (2005).

[14] Zurek W. H. «Decoherence, in selection, and the quantum origins of the classical», Rev. Mod. Phys. 75, 715 (2003).

[15] Tittel, 1998: W. Tittel et al., Experimental darkons ration of quantum correlations over more than 10 kilometers, Physical Review A 57, 3229.

[16] Shinsei Ryu, Tadashi Takayanagi «Aspects of Holographic Entanglmarkent Entropy».

[17] Milgrom, M. (1983). «A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis». *Astrophysical Journal*. **270**: 365–370. Bibcode:1983ApJ…270..365M. doi:10.1086/161130..

[18] M. Milgrom, «MOND — Particularly as Modified Inertia», arXiv:1111.1611

[19] Dennis Dieks, Jeroen van Dongen and Sebastian de Haro «Emergence in Holographic Scenarios for Gravity»

[20] Misra B., Sudarshan E.C.G «The Zeno`s paradox in quantum theory».

[21] Tadashi Takayanagi «Entanglmarkent Entropy and AdS/CFT».

[22] Daniel Asenjo, Fabien Paillusson, and Daan Frenkel «Numerical Calculation of Granular Entropy» Phys. Rev. Lett. 112, 098002 – Published 5 March 2014.

[23] Frank Wilczek. «Superfluidity and Space-Time Translation Symmetry Breaking» Phys. Rev. Lett. 111, 250402 – Published 18 Declarer 2013.

[24] (V. N. Samokhvalov “Non-electromagnetic Force Interaction in Presence of Rotating Mass in Vacuum,” [International Journal of Unconventional Science] 1(1), pp. 6-19, 2013 (Article received: 18 Nov 2012; Article accepted for publication: 23 Apr 2013) http://www.unconv-science.org/en/n1/samokhvalov/

[25] [Verlinde, 2010] Erik Verlinde. «On the Origin of Gravity and the Laws of Newton». arXiv:1001.0785v1 [hep-th].

[26] L. Bolotin1, V.V. Yanovsky «HOLOGRAPHIC DYNAMICS». http://fs

[27] A. G. Lisi «An Exceptionally Simple Theory of Everything», 2007, https://arxiv.org/pdf/0711.0770.pdf.

[28] Yi Wang «Towards a Holographic Description of Inflation and Generation of Fluctuations from Thermodynamics» arXiv:1001.4786v2 [hep-th] 31 Jan 2010

[29] [Verlinde, 2016] Erik Verlinde. «Emergent Gravity and the Dark Universe» https://arxiv.org/pdf/1611.02269v1.pdf

[30] Margot M. Brouwer, Manus R. Visser, Andrej Dvornik, Henk Hoekstra, Konrad Kuijken, Edwin A. Valentijn, Maciej Bilicki, Chris Blake, Sarah Brough, Hugo Buddelmeijer, Thomas Erben,Catherine Heymans, Hendrik Hildebrandt, Benne W. Holwerda, Andrew M. Hopkins, Dominik Klaus, Jochen Liske, Jon Loveday, John McFarland, Reiko Nakajima, Cristóbal Sifón,Edward N. Taylor » «First test of Verlinde’s theory of Emergent Gravity using Weak Gravitational Lensing measurements» https://arxiv.org/abs/1612.03034

[31] Yun Soo Myung, Hyung Won Lee, and Yong-Wan Kim «Entropic force versus temperature force» https://arxiv.org/abs/1006.1922v1

[32] Niayesh Afshordi, Claudio Corian, Luigi Delle Rose, Elizabeth Gould, and Kostas Skenderis » Observational Tests of Holographic Cosmology» arxiv.org/pdf/1607.04878v2.pdf

[33] https://en.wikipedia.org/wiki/Small-angle_approximation 0