Matter-light duality and speed greater than light

Transcription

1 Matter-light duality and speed greater than light Shalender Singh* and Vishnu Priya Singh Parmar Priza Tehnologies In. R&D, 155 MCarthy Blvd, Ste 1111, Milpitas, California, USA Abstrat In this paper we demonstrate duality between matter and light. Through mathematial derivation we show that every fundamental matter partile with non-zero rest mass an be represented by a pair of photons. The photons in the representation are not normal photons but a speial kind of ontinuously generating and annihilating virtual photons, whose wave funtions super impose to give the wave funtion of the non-zero rest mass partile and the representation is in agreement with the spin of the partile. We use this duality to derive De Broglie wavelength. We show that a moving matter wave has two frequeny omponents, one of it is with De-Broglie wavelength h/p and the other one is with wavelength h/e. We also orret the De- Broglie wavelength for v = 0 where we show that there is only one frequeny omponent for v = 0 with wavelength h/e. Later in the paper we derive that every photon an be represented by a non-zero rest mass partile pair, one going below the speed of light and the other going above the speed of light. Keywords: Matter light duality, Speed greater than light. Classifiation: PACS b 1

2 I. INTRODUCTION Matter and light have been onsidered as omposed of two different kind of partiles; while matter partiles have a non-zero rest mass, the light partiles have zero rest mass. They are assoiated with different speeds; the speed of light is always same in all frames of referene but matter partiles an never be aelerated to the speed of light [1]. Though both of these statements are orret, these do not rule out the possibility of quantum jumping partiles from speeds less than light to speed greater than light [] [3] [4] [5] [6] [7] [8] [9] [10] [11] [1] [1] [13] [14] [15]. It has been very diffiult to break the speed of light barrier beause the model of the fundamental partiles is not omplete. In this paper we propose a simpler and a more fundamental model with a few simple observations about the equations of energy and momentum. Using these observations we propose duality between matter and light and prove that this duality is onsistent with the existing definition of energy and momentum. In the setion II we propose and validate the first part of the matter and light duality, whih is that every non-zero rest mass partile an be represented by a photon pair. The photons in the representation are not normal photons but a speial kind of ontinuously generating and annihilating virtual photons, whose wave funtions super impose to give the wave funtion of the non-zero rest mass partile and the representation is in agreement with the spin of the partile. Using this result in we prove that a matter wave is omposed of two frequeny omponents, one with the wavelength equal to De-Broglie wavelength h/ P [16] and the other omponent with the wavelength h /E. In the setion III we propose and validate the seond part of the duality; representation of a photon as nonzero mass partile pair with one partile with speed less than light and the other partile with speed greater than light. We further derive energy, momentum and γ for the partiles with speed greater than light. II. PARTICLE WITH NON-ZERO REST MASS REPRESENTATION AS A PHOTON PAIR Statement 1: <TODO> Model of a non-zero rest mass partile as photons in Feynman Diagram Let there be a non-zero rest mass partile P, stationary in an inertial frame of referene B and moving with a non-zero veloity V w.r.t. frame of referene A. Then P an be represented by a photon pair; first photon in the V diretion and the seond one in the V diretion in the frame of referene A. In the ase of V 0, diretion beomes singular, whih means the photon pair an be assumed to be going in any diretion with the first photon in exatly opposite diretion of the seond photon. Model: Validation of statement 1 for Energy and Momentum: Let us take a pair of photons with frequeny in referene frame B. If we take n as the unit vetor in the diretion of V then in frame of referene B: Total energy of the photon pair in B is: E (1) b Total momentum of the photon pair in in B is:

3 P n/ n/ 0 () b Now let us onsider the frame of referene A. In A the photons undergo Doppler shift as: Energy of the away going photon in A is: 1 v/ E1 1 v/ Energy of the in-oming photon in A is: E 1 v/ 1 v/ Where V v Thus total energy of the photon pair in A is: 1 v / 1 v / Ea E1 E 1 v / 1 v / 1 v/ 1 v/ 1 v / 1 1 v / From () & (3) E a Eb E 1 v / Similarly momentum in A is: 1 v / 1 v / Pa / n / n 1 v / 1 v / 1 v/ 1 v/ / n 1 v / v/ n 1 v / From (4) & (5) b (3) (4) (5) P E / V E / V (6) a a b Equations (4) and (6) are the equations of mass and momentum transformations for non-zero mass matter partile aross frame of referene. 3

4 The above proves that the representation works well with the relativisti momentum and energy transformations. From the above we an define the relation of the rest mass of the partile and the photon frequenies as: Eb m m / (7) A. Derivation of De-Broglie wavelength As we have shown in the proof of the statement 1 that non-zero mass partile an be represented by photons, let assume the partile P matter wave equation is given by the sum of light waves opposite diretion, whih means: A A A 1 / As the frequeny of A wave is given by v 1 / 1 v / and of A wave is given by v 1 v / of referene A, the sum of them leads to frequenies: in the frame 1 v / 1 v / 1 1 v / 1 v / 1 v / 1 v / v/ 1 v / 1 v / (8) (9) Substitute from equation (7) in equation (13) / mv m v P h / (10) P P (10) is the De-Broglie wavelength. In the above result we get another omponent1 of the frequeny as follows: 4

5 m 1 m 1 E h 1 / 1 (11) E E B. Wavelength at speed 0 At speed = 0 there is a singularity in diretion and there is only one omponent of matter wave with the wavelength h / E <TODO> We need to look at the spin and other QM aspets. III. PHOTON REPRESENTATION AS TWO PARTICLES WITH NON-ZERO REST MASS Statement 3: <TODO> Model of photon as eletron pair in Feynman Diagram Any photon an be represented as a pair of non-zero eletrons, one going below the speed of light and the other going above the speed of light. If u is the speed of the non-zero mass partile below the speed of light in the opposite diretion of photon, / u is the speed of the other non-zero mass partile above the speed of light in the diretion of photon. Validation: As per [17] [18] the energy and momentum of a partile going above the speed of light is given by: E m / v / 1 v P v mv v If we take v = / / 1 / u E m / / u 1 mu / 1 u / / u (1) P ( m / u ) / / u 1 m / 1 u / / u Also (13) E m u u / 1 / (14) P mu u u / 1 / (15) Adding (1) & (14) E m / 1 u / mu / 1 u / p 5

6 1 u/ Ep m 1 u / 1 u/ Ep m 1 u/ Adding (13) & (15) (16) P mu / 1 u / m / 1 u / p 1 u/ Pp m 1 u / 1 u/ Pp m 1 u/ From (16) & (17) (17) E / P p p The above ratio of energy and momentum means that the ombine energy and momentum of the pair of eletrons one going below the speed of light and one going above the speed of light has the same momentum and energy of a photon. <TODO> We will look at the spin and other QM aspets. 6

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