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DISCOVERING THE NATURE OF THE DARK MATTER Vu Huy Toan - Vietnam Academy of science and technology - Construction Machinery and Industrial Works CONINCO Joint Stock Company (CONINCO-MI) No.4 Ton That Tung, Hanoi, Vietnam. Email: vuhuytoan@conincomi.vnvuhuytoan@conincomi.vn

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CONTENTS I - INTRODUCTION 1- What is the dark matter? 2- The accepted postulates 3- The total energy of physical objects in the potential force field II - NATURE OF THE DARK MATTER 1- What is the photon? 2- Photon is the reason for the fast rotary of a galaxy III - CONCLUSIONS V - ACKNOWLEDGMENTS

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I- INTRODUCTION

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I-1. WHAT IS THE DARK MATTER? When observing the movement of the stars in the galaxy, Mr. Jan Oort [1] discovered that the stars are far from the centre of galaxy do not rotate slowdown as the calculation of Newton’s mechanics but nearly do not change, and this phenomenon is observed in all galaxies. See the Fig. 1 and Fig. 2 A - The calculation without dark matter B – The observation Figure 2 Figure 1 A - B - Distance Rotary speed

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I-1. WHAT IS THE DARK MATTER? Figure 3. Some body assume that galaxies Abell 222 and Abell 223 are connected by the dark matter fibre. However, it is wrong! In own report, the author would like to proof that the existance of the abnormal rotate of galaxies are not caused by any “dark” matter but only the “visible” matter in the universe, it is just photons.

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I-2. THE ACCEPTED POSTULATES Postulate 1: All physical objects interdependently exist. Until now, the physics only consider every thing according to the opposite concept that "existence itself" accordingly, allowing the existence of a physical object (PO) isolating completely, unique in the universe, with mass m and then from there to consider its movement under action of a force by the laws of dynamics. m F = m a X Z Y 0 m – isolated body Figure 7. Free space IT IS WRONG m

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I-2. THE ACCEPTED POSTULATIONS r ∞ R Field Body “Physical object” = “Body” + “Field” Field 1a. Aspect of a form: Formally, every PO consists of 2 parts: - A “body” part with the limited size (r) which we can “see” and The “field” part with the unlimited size (R ∞ ) which we cannot “see”. “The interdependent existence” is shown for 3 aspects: Field Figure 8. Thus, it can be said that the universe "within every PO" is not wrong and that is also true for any other object and for this reason, they are interdependent. Both the two the “body” and “field” parts related to each other dialectical: The more the energy of this part increases, the more the energy of other one reduces and vice versa

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I-2. THE ACCEPTED POSTULATES - Every PO can mutual interact with other PO – it is simple because “You are in me and I am also in you”. -This interdependent existence” has the internal cause, it is the “interaction”; M1M1 Interaction of Physical object M4M4 M3M3 M2M2 1b. Aspect of the content: “Interaction” Figure 9.

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I-2. THE ACCEPTED POSTULATES 1c. Aspect of a manifestation mode: Both the above form and contents lead to a most common manifestation mode for every PO that, by our subjective awareness, we call a “mass” with two types: - “Gravitational mass” (we will symbol by M i ) characterize for an interaction ability of each PO and - “Inertial mass” (we will symbol by m ik ) characterize for an inertia of movement of a PO having a gravitational mass M i in a potential force field of other PO having the gravitational mass M k. For example, if we only pay attention to two PO with the gravitational masses M 1 and M 2, their inertial mass m concerns to that gravitational mass as per the formula which have been proofed by the author in the book “The New way For Physics” [3]:

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I-2. THE ACCEPTED POSTULATES In here, F 12 and F 21 – are the gravitational forces of M 1 and M 2 acting on each other correspondingly; a 12 and a 21 – are the relative movement accelerations of M 2 and M 1 with respect to each other correspondingly. Shortly: (1)

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I-2. THE ACCEPTED POSTULATES From (1), we can see clearly that the interdependent existence has been shown how to quantity: Only one of two gravitational masses equals z ero and that PO is considered as the isolation, i.e, the inertial mass is also equals z ero. Or in the other words, when one PO moves without interaction with other PO, its inertial mass will be zero (m ≡ 0). M 1 X Z Y Figure 10. The interdependent existence Potential force filed M2M2 M1M1 M2M2 M1M1 + M 2 m = m = 0 Free space 0 0. a = F/m = ∞ There is a truth: Non-Interaction ≡ Non-Inertia

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I-2. THE ACCEPTED POSTULATES Postulate 2: The fundamental particles The fundamental particles are the particles cannot be broken further into anything other, so all physical objects are composed of them. The author assumed a following postulate: “Electron and positron are two fundamental particles; they have only electric interaction rather than gravitational interaction”.

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I-3. THE TOTAL ENERGY PHYSICAL OBJECT IN THE POTENTIAL FORCE FIELD As we know, “total energy” of a body is determined by Einstein as per the famous expression [3]: (2) However, people have forgot the important detail the expression (2), is not total energy of the PO, because it only consists of kinetic and internal energies, in which it does not completely contain a potential energy.

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I-3. THE TOTAL ENERGY PHYSICAL OBJECT IN THE POTENTIAL FORCE FIELD In the book “The New Way for Physics” [3], the author has proofed an expression of total energy of the PO corresponding to a most characteristic state – a freely falling state, or resting in a force field: (3) where U k – the critical potential energy of the PO in the force field, i.e, the biggest potential energy that one PO can have in that force field, still maintain its structure; exceeding this value, the “body part” of the PO will be crushed by the force field. Also starting from that critical condition, the formula (3) can be written in the more simple form: (4) Compare (4) with the formula (2) received by Einstein for a body freely moved, we see that when calculating to potential energy in a force field, its total energy is bigger than twice.

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I-3. THE TOTAL ENERGY PHYSICAL OBJECT IN THE POTENTIAL FORCE FIELD On the other hand, according to the postulate “1a”, photon must have its “field” part far ∞ so, according to the postulate “1b”, it must have an interaction with other PO in this “field”, this interaction can be only the gravitational. In other words, photon have the gravitational interaction as any other PO that we know. While, according to the postulate “1c”, it must have gravitational mass M ph and inertial mass m ph in gravitational field. We can approximately determine this minimum gravitational mass of photon based on the total energy of electron and positron to create it as per the expression (4): As per (4), we can write for photon: From here, we can calculate the inertial mass of photon when balancing (5) and (6): (5) (6) (kg) (7)

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II- NATURE OF THE DARK MATTER

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II-1. WHAT IS THE PHOTON? In the "Photon structure" Report published in the Proceedings: “Advances in Optics, Photonics, Spectroscopy & Applications VI, 2011” [4], the author showed that there are some experiments, for example, phenomena of photon decay and photon emission, evidences us the structure of photon, including two fundamental particles: electron and positron; these particles in some way, the combination of two particles with opposite charge may result in the electric neutralization from a certain distance, like atom, molecule. e-e- From certain distance R T, atom become the neutral object p+p+ RTRT + F = 0

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II-1. WHAT IS THE PHOTON? Figure 4. Motion of a photon created the “electromagnetic wave”. “Photon” is the particle which have the structure from electron and positron both turning around the center of the common inertia and moving with the light speed c (see Fig. 4a) In the near distance, this photon creates electromagnetic field with the vector of electric-field intensity E and magnetic-field intensity H putting as per the description of the Maxwell equations. X E H E = 0; H = 0 c) R e-e- e+e+ X Orbit of e - Orbit of e + λ c a) e-e- e+e+ RTRT E H Electromagnetic wave b) X H E At the limited distance R T far from the movement axis X, photon do not interact with other electric charges and from the distance R ≥ R T, it does not have the inertial mass in the electromagnetic field, i.e, its inertial mass must be zero.

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II.2 - PHOTON IS THE REASON FOR THE FAST ROTARY OF A GALAXY Up to now, the modern physics still assume that photon do not have the rest mass, its relative mass is too small and calculated as per the formula of Einstein: where h ≈ 6,63x10 -34 Js – Planck constant; c ≈ 3x10 8 m/s – the speed of light in the vacuum; v – frequency of photon. They estimate that there are about 500 microwave photons in each cm 3 in the space among galaxies or N = 5x10 8 photon/m 3 [8]. While, the density of photon as per the mass is only by: (8)

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II.2 - PHOTON IS THE REASON FOR THE FAST ROTARY OF A GALAXY If the frequency of microwave photon is average about 10 10 Hz, in each m 3 have ~4x10 –32 kg photons. While, the average matter density of universe is ~10 –27 kg/m 3 [8], ie, is bigger than thousand times. May be because of that reason, photons have been ignored? However, if we draw m ph from (7) and place it into (9) with the numerical value we obtain a density of photons ρ p0 ~ 10 –22 kg, that means, it is bigger than the matter density of thousand times.

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II.2 - PHOTON IS THE REASON FOR THE FAST ROTARY OF A GALAXY We will evaluate concretely: Assuming that the matter distribution in the galaxy with the simple form is the black hole in the center with the mass of M 0, the stars and interstellar dust with the density ρ s = const up to the radius R s (see the Fig. 3).

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II.2 - PHOTON IS THE REASON FOR THE FAST ROTARY OF A GALAXY Figure 5. The model of matter distribution in a galaxy RsRs r M0M0 X Y Z RiRi R i+1

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II.2 - PHOTON IS THE REASON FOR THE FAST ROTARY OF A GALAXY In the fig. 6, the density distribution of matter and photons in galaxy is demonstrated.

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II.2 - PHOTON IS THE REASON FOR THE FAST ROTARY OF A GALAXY While, the gravitational mass of the matter quantity contain in the globe with the radius r < R s will be: From this radius (R > R s ), assuming that the matter density reduce as per the formula: where a – any constant. (9) (10)

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II.2 - PHOTON IS THE REASON FOR THE FAST ROTARY OF A GALAXY Simply, we can divide the galaxy into the globe thin-layers with the thickness of (R i+1 – R i ) and assuming that the matter density in the scope of each thin-layer ρ si+1 ≈ const, so we can calculate the matter mass contain in each thin-layer as per the normal way but cannot to use a complex integral: Thus, the total mass in the globe with the radius R > R s will be: (11) (12)

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II.2 - PHOTON IS THE REASON FOR THE FAST ROTARY OF A GALAXY On the other hand, we also assume that the density of photon ρ ps = const in the radius R s, and outside this radius it also reduce as per the exponential function rule as per the distance to the center of galaxy from the value ρ ps ≈ 2x10 –22 kg/m 3 as above mentioned: where with – is the density of photons in the space among galaxies; b – constant. (13)

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II.2 - PHOTON IS THE REASON FOR THE FAST ROTARY OF A GALAXY In the scope of galaxy (<R s ) where the stars and interstellar dust concentrate essentially, photon density is higher in comparison with its density in the space among galaxies because photons always produced from the stars and reduce their density as per the distance. While, similar to the matter form as above mentioned, we also have the gravitational mass of photon contain the globe with the r < R s : I (14)

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II.2 - PHOTON IS THE REASON FOR THE FAST ROTARY OF A GALAXY In the scope of outside radius R s, we also do similar to the type of other matter and so the mass of photon in the globe with the radius R will be: While, we can calculate the total matter quantity of matter and photons in the globe with the radius R as well as centripetal force due to that total quantity effects to a star with the mass M. (15)

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II.2 - PHOTON IS THE REASON FOR THE FAST ROTARY OF A GALAXY a) In a distance r < Rs - From (9) and (14), we have the total mass Mr∑: From a balance condition between centripetal and centrifugal forces, we take out a rotary speed Vr of the star in the radius r: (16) (17)

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II.2 - PHOTON IS THE REASON FOR THE FAST ROTARY OF A GALAXY b) At Rs - From (4) and (10), we have the total mass M s ∑ : - From a balance condition between centripetal and centrifugal forces, we take out a rotary speed Vs of star in the radius Rs: (18) (19)

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II.2 - PHOTON IS THE REASON FOR THE FAST ROTARY OF A GALAXY c) In a distance R > Rs: - From (7) and (11), we have the total mass M s∑ : And the rotary speed: The calculation of rotary speed of galaxy is realized by Excel program on a computer for the cases which count not mass of photons (V A ) out and count that mass but with a different density distribution level of matter and photons, we have V B corresponded to the case when a = 3; b = 0,038 and V C corresponded to the case when a = 1,5 ; b = 0,02 while all other parameters are the same. (20) (21)

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II.2 - PHOTON IS THE REASON FOR THE FAST ROTARY OF A GALAXY I one case, We have Vb (correspondence to the case when a = 7; b = 0,05) and in other case, it is Vc (correspondence to the case when a = 1,5 ; b = 0,035) while the other dimensions are the same. From here, we know that the calculation of gravitational mass of photon as per this new way is completely suitable to the observation result of astronomy: The shape of Vb is coincided with the shape of B on the Fig. 1a, the shape of Vc coincided with the shape of B on the Fig. 1b. Figue 1a Figue 1b

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CONCLUSIONS

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IV - CONCLUSIONS 1- It is necessary to accept the postulates: - Every physical object interdependently exist and that existence is shown through the form “body – field”, the content “interaction” and the dynamic characteristics “mass” with two different types, but it has the causality relation together: “gravitational mass” (M), or “interaction mass”, and “inertial mass” (m). - Electron and positron are the fundamental particles and only appear in the electric interaction but without the gravitational interaction…

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IV - CONCLUSIONS 2- It is clear that, the so-called “dark matter” has been shown one’s face: It is just the photons flooding in the Universe made the galaxies rotating much more extraordinarily with the different modes depend to the distribution characteristic of matter as well as photons in that galaxies.

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V - ACKNOWLEDGMENT The author is grateful to Professor Nguyen Dai Hung, Director of Institute of Physics (Academy of Sciences and Technology of Vietnam) for his highly valuable assistance and honest encouragement to finish this work.

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REFERENCES [1] Goddard universe flight center (NASA). Hidden mass. http://imagine.gsfc.nasa.gov/docs/teachers/galaxies/imagine/hidden_mass.html [2] Discovering the dark matter fibre. Khoahoc.com online. http://www.khoahoc.com.vn/khampha/vu-tru/40433_Phat-hien-soi-vat-chat- toi.aspxhttp://www.khoahoc.com.vn/khampha/vu-tru/40433_Phat-hien-soi-vat-chat- toi.aspx [3] Vũ Huy Toàn. Con đường mới của vật lý học. NXB Khoa học và Kỹ thuật. Hà Nội, 2007. [4] Vu Huy Toan. Structure of photon. Proceedings: “Advances in Optics, Photonics, Spectroscopy & Applications VI, 2011”. http://vuhuytoan.wordpress.com/2010/12/25/c%E1%BA%A5u-truc- c%E1%BB%A7a-photon/cau_truc_photon_bc_hnvl_en_18-6_final/http://vuhuytoan.wordpress.com/2010/12/25/c%E1%BA%A5u-truc- c%E1%BB%A7a-photon/cau_truc_photon_bc_hnvl_en_18-6_final/ [5] Vũ Huy Toàn. Khối lượng của photon. 2012. http://vuhuytoan.files.wordpress.com/2012/09/27_khoi-luong-cua-photon.pdf [6] Новиков И.Д. Эволюция вселенной. Москва. “Науки”. 1990.

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