The Lorentz Factor and the Probability Density by Boris S

Global Journal of Science Frontier Research: A

Physics and Space Science

Volume 17 Issue 3 Version 1.0 Year 2017 Type : Double Blind Peer Reviewed International Research Journal

Publisher: Global Journals Inc. (USA)

Online ISSN: 2249-4626 & Print ISSN: 0975-5896

The Lorentz Factor and the Probability Density By Boris S. Dizhechko Abstract- New Cartesian physics based on the identity of space and matter and makes the principle of uncertainty Heisenberg by a principle of physical irrationality of points of space- matter from which naturally follows a probabilistic way of describing the developments in quantum mechanics. New Cartesian physics relates the probability of an event in quantum mechanics with the factor of Lorentz of the special theory of relativity, which turns idle geometric space in the physical, in which space moves.

GJSFR-A Classification: FOR Code: 020399p

TheLorentzFact orandtheProbabilityDensity

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© 2017. Boris S. Dizhechko. This is a research/review paper, distributed under the terms of the Creative Commons Attribution- Noncommercial 3.0 Unported License http://creativecommons.org/licenses/by-nc/3.0/), permitting all non commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. The Lorentz Factor and the Probability Density

Boris S. Dizhechko

Abstract - New Cartesian physics based on the identity of New Cartesian physics, based on identity of space and matter and makes the principle of uncertainty space and matter, argues that space is moving and

Heisenberg by a principle of physical irrationality of points of movement is the main vortex, i.e. the circumference. In spac e-matter from which naturally follows a probabilistic way this case the linear motion is movement on a curved of describing the developments in quantum mechanics. New path with an infinitely large radius of curvature. The Cartesian physics relates the probability of an event in cause of vortex motion space new Cartesian physics quantum mechanics with the factor of Lorentz of the special 201 sees that the impact of the factor of Lorentz for the

theory of relativity, which turns idle geometric space in the r

physical, in which space moves. motion trajectory reduces the length of segments and ea speed on her because of the law of conservation of Y 1. Introduction momentum increases and reaches the rotation center of 691 the speed of light. We can assume that the space- he factor of Lorentz in physical formulas appeared after physicists began to consider the limitation of matter moving in such a way to neutralize the paradoxes speed of movement of bodies the speed of light. of relativity theory. T At the heart of quantum mechanics lies

Obviously, this limitation occurs as a result of changes V Heisenberg's uncertainty principle, which implies a

in the parameters of the interaction of bodies that were III probabilistic method for determining the state of the found during their movement with the speed close to ue ersion I

electron. In new Cartesian physics ethe principle in the s zero. It was necessary to find an operator whose effect s physical space turns into its opposite, i.e., becomes a on the existing formula limited of speed of movement of I principle of definiteness of points. To show this is to take bodies the speed of light. This operator was found by the most known attitude of uncertainty Heisenberg — XVII Lorentz and named after him. between coordinate and momentum of a particle in 1 space:[2] = 2

1 ) 𝛾𝛾 2 2 A 𝑣𝑣 ℏ ( � − 𝑖𝑖 𝑖𝑖 With increasing speed 𝑐𝑐fro m 0 to c the Lorentz where " " is Planck's constant∆𝑥𝑥 ∆𝑝𝑝 ≥ (h) divided by 2π; factor γ increases from 1 to ∞. - Increment of the momentum. When the impact of this operator statement ℏNote that here the right and left are the 𝑖𝑖 when increasing speed to the speed of light occurs: e∆𝑝𝑝xpression of the angular momentum and therefore Research Volume 2 2 = 0 determines the standard deviation of Time dilation: The time (∆t' ) between two ticks as the radius-vector of rotation from the radius-vector measured in the frame in which the clock is moving, is 𝑖𝑖 𝑖𝑖 0 ∆𝑥𝑥 �𝑅𝑅 − 𝑅𝑅 Frontier longer than the time ∆( t) between these ticks as The principle of uncertainty Heisenberg 𝑅𝑅 𝑅𝑅 measured in the rest frame of the clock ∆ t' = ɣ∆t; between coordinate and momentum of a particle can be Length contrac- tion: The length (∆ x') of an object as written as: measured in the frame in which it is moving, is shorter Science than its length (∆x) in its own rest frame ∆x' = ∆x/ ɣ ; of 2 2 2 And so more [1] 0ℏ ∆𝑝𝑝𝑖𝑖 ≥ The impact of this statement when increasing This inequality shows�𝑅𝑅 that− 𝑅𝑅 reducing the interval speed to the speed of light converts idle space in a containing points with coordinates 0 that Journal moving space. Figuratively speaking a world in which correspond to the radius-vectors and 0, it is 𝑖𝑖 𝑖𝑖 there is no movement in a world in which everything is necessary to increase the increment𝑥𝑥 pulse≤ 𝑥𝑥 for ≤ 𝑥𝑥 the moving. selection of this point of space-matter 𝑅𝑅from other𝑅𝑅 points. Global

The famous Cartesian identity "space ≡ matter" In the infinitely small interval containing the point, this makes a point of the geometric space a material and increment of the momentum becomes infinitely large, therefore capable of movement. Unlike geometric which is almost impossible to create. For this reason, to space, it should be called physical, i.e. able to move. highlight this point as an independent object impossible. It stands out only in the interval. Thus, the uncertainty principle of Heisenberg in new Cartesian physics Author: City of Sterlitamak, Bashkortostan, Russia. e-mail: [email protected] becomes a principle of physical irrationality of points of Report on the project “New Cartesian Physics” space-matter.[6]

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Figure 1 From this it follows that the space-matter moves Write a system of equations consisting of the Research Volume relative to itself overlapping each other by intervals formulas of wave-particle duality and the formulas lower (fragments), the size of which is determined by the limit of the Heisenberg inequality when the speed limit is principle of certainty of the irrational points of the the speed of light

Frontier Heisenberg- Dizhechko Representation of irrational points of space- = 0 2 matter in the form of intervals is the basis of a ℏ

Science probabilistic description of events of moving space- ( 𝑚𝑚)𝑚𝑚𝑅𝑅 = matter, as intervals are involved simultaneously in many � 2 of ℏ spins and variations, and the size determines their Dividing the second eq∆u𝑚𝑚al𝑚𝑚ity∆ i𝑅𝑅n the first, get spacing depend on the magnitude of the impulse. 2 2 Journal Application of the theory of probabilities of 0 events in space-matter is based on a geometric = 0 definition of probability. The geometric probability of an �𝑅𝑅 − 𝑅𝑅 𝑣𝑣

Global event A is the ratio of the measure of area g, conducive After conversion you will𝑅𝑅 get: 𝑐𝑐 to the emergence of an event A to the measure of whole

area G, i.e. Р(А)=mes g / mes G. 2 Consider the simultaneous motion of space- 0 = 0 1 2 matter in an oscillatory motion and in rotation. In this 𝑣𝑣 case, event A is the part of the points of the wave 𝑅𝑅 𝑅𝑅 � − 𝑐𝑐 space-matter at the quantum rotational motion. This formula is analogous to the formula for the Lorentz transformation; it shows a reduction of radius at Therefore, the probability of an event A is equal to the aspiration of speed of rotation to the speed of light. ratio mes g participating in the rotation measure across 2 1 0 the region mes G, which is the oscillation. Multiplication on 2π the formula is to mind: = 1 2, 𝑆𝑆0 𝑣𝑣 © 2017 Global Journals Inc. (US) 𝑆𝑆 − 𝑐𝑐 The Lorentz Factor and the Probability Density where the attitude 1 shows probability of that the density of physical space. When moving space-matter 𝑆𝑆0 at the speed of light, it is on the verge of disappearance particle on the area will be in . 𝑆𝑆0 1 and formation on its place the so-called "black hole." Oscillation and rotation of space-matter can be The motion of the waves, the formation of black holes is displayed on a complex𝑆𝑆 plane by𝑆𝑆 the formulas: prevented by the movement of space-matter, which = and = manages to fill them with the speed of light. At creation 1 1 𝑖𝑖 2 2 𝑖𝑖 ℎ𝐸𝐸𝐸𝐸 ℎ𝑝𝑝𝑝𝑝 of conditions preventing their filling, for example, when a Dividing𝜓𝜓 ψ𝑅𝑅2 for𝑒𝑒 ψ1, obtain𝜓𝜓 the𝑅𝑅 wave𝑒𝑒 function for three-dimensional whirling motion of a physical space the wave of space-matter: formed independent physical objects, which are called material particles. = 2 = ( ) 𝑖𝑖 1 − 𝐸𝐸𝐸𝐸−𝑝𝑝𝑝𝑝 References Références Referencias 𝜓𝜓 ℎ 𝜓𝜓 𝐴𝐴𝑒𝑒 201 Where module A=R2/R1 is a dimensionless 1. https://en.wikipedia.org/wiki/Lorentz_factor

𝜓𝜓 r number. Multiplying ψ in the adjoint function ψ*, will 2. “Atomik Physics” by Max Born, London – Glasgow, ea 2 2 2 receive a square module [ψ] =R2 /R1 , which in quantum 1963 Y mechanics has the meaning of probability density. 3. Descartes, René. The World and Other Writings. 711 Thus, the wave function of quantum mechanics: Trans. Stephen Gaukroger. New York: Cambridge = ( / )( ) University Press, 1998. − 𝑖𝑖 ħ 𝐸𝐸𝐸𝐸−𝑝𝑝𝑝𝑝 4. https://en.wikipedia.org/wiki/Compton_wavelength you can write as a 𝛹𝛹ratio:𝐴𝐴𝑒𝑒 5. Bousso R (2000) Positive vacuum energy and the n- bound. J High Energy Phys 11: Zlatev, Wang L, V 1 III = 𝑝𝑝𝑝𝑝 Steinhardt PJ (1998) Quintessence, cosmic

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coincidence and the cosmological constant. Phys s 2 𝐴𝐴 𝑒𝑒 𝐸𝐸𝐸𝐸

𝑖𝑖 Rev Lett 82: 896. I 𝛹𝛹 ℎ Here A, A1 and A𝐴𝐴2 𝑒𝑒– modules of complex 6. http://gsjournal.net/Science-Journals-Papers/Author numbers, geometrical representation they are radius- /180/Boris%20S.,%20Dizhechko XVII vectors. In quantum mechanics the square modulus of the wave function is the probability density of the event of finding particles at time t+Δt in region with

coordinates x+Δx. ) A

| |2 ( | |2 | |2 1 = = 2 | 2| 𝐴𝐴 𝛹𝛹 𝐴𝐴 By multiplying the numerator𝐴𝐴 and denominator of fraction to 2π formulas should be converted to the Research Volume form: | |2 2 2 2π 1 1 | | | | Frontier = = 2 = 2π| 2| 2 𝐴𝐴 𝑆𝑆 Where, the attitude𝛹𝛹 1 𝐴𝐴shows probability density that a 2 𝐴𝐴 𝑆𝑆 𝑆𝑆 Science particle on the area. 𝑆𝑆 of 2 will be in the 1. Thus detected identity of probability of event in quantum mechanics with the formula of L𝑆𝑆orentz transformation.𝑆𝑆 Journal 2 1 | |2 0 2 = ( 1 2 ) = 2 𝑣𝑣 Global 𝛹𝛹 � − According to this expression𝑐𝑐 𝛾𝛾 the probability density of detecting a particle of physical space inversely proportional to the Lorentz factor and is a function of speed. If it is at rest in some reference frame, the probability of detecting it is equal to 1 if it is moving relative to some frame of reference with a speed close to the speed of light, the probability of finding it decreases to zero, which is equivalent to reducing the