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238Repulsing objects by photons

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  • abelov0927
    Mar 17, 2011
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      http://knol.google.com/k/alex-belov/repulsing-objects-by-photons/1xmqm1l0s4ys/23#view 

      This system shows repulsing two objects by photons.



      Base on radiation pressure or light pressure phenomenon, the the particle photon without stationary mass has a momentum which can be transfered to an object. 
      The light radiation and objects repulsion must be follow by law of momentum conservation. The figure1 shows repulsing two identical objects with mass m. After a period of time the objects are utilizing photons momentums and start conduct a translational motion. If laser system has identical ray intensity in both directions then objects will have translational momentums P with same value. 
      -vec P=vec P
      Other words, the objects with same mass m will have same velocities v1.
      m(-vec v_1)=mvec v_1
      The laser system with identical ray intensity in both directions has zero net momentum.

      However, the objects will utilize less photon momentums when these objects increase it's own velocities relatively to laser. The speed of light is constant. However, base on Doppler effect the photons will increase wavelength which reduce photons momentum
      p=frac{h}{lambda}
      Where: - photon momentum, - Planck constant, lambda - photons wavelength

      Other words, the objects linear velocities will gain in non-linear mode.

      How photons will repulse objects if one of them is rotating?

      The figure2 shows repulsing objects by photons where one of them conducts rotation around it's own center of mass.


      In this case, this objects will utilize photon momentum differently. After some period of time, the non-rotated object will utilize photons momentums on velocity v. However, the rotated object will utilize photons momentums on velocity v+wR. Base on Doppler effect the rotated object will utilize photons momentums less than non-rotated object. Therefore, after some period of time the rotated and non-rotated objects will have different translational velocities v1 and v2.
      The figure 2_2 shows objects repulsing with mirrors. 

      Here's objects reflect photon back to light source. The photons wavelengths will be different on receiver i.e. photons have a different momentums. 



      A few calculations.


      Will it happen relativistic Doppler effect between source and receivers? How big is it? Let's calculate it.

      The figure 3 shows parts what will described in details.


      The part A shows left non-rotated objects R and source S.

      Let's define frames of referces of these objects R ans S.

      frame of reference in physics, may refer to a coordinate system or set of axes within which to measure the position, orientation, and other properties of objects in it, or it may refer to an observational reference frame tied to the state of motion of an observer. It may also refer to both an observational reference frame and an attached coordinate system, as a unit.

      The objects R and S have owns frames of references. Are these frames of references are equal?
      The object R has translational velocity –V1 relatively to observer on object S. However, the object Shas translational velocity V1 relatively to observer on object R. These objects have translational velocity |V1| relatively to each other. Therefore, these objects and S frames of references are not identical and objects R and S are registering wavelength of light of source S differently.
      Base on Doppler effect:
      gamma=frac{1}{sqrt 1-(frac{v_1}{c})^2}
      f_r=frac{f_s}{gamma}\f=frac{c}{lamb}\frac{c}{lamb_r}=frac{c}{lamb_sgam}\lam_r=lam_sfrac{1}{sqrt 1-(frac{v_1}{c})^2}
      Where: Y – Lorentz factor, c – speed of light, V1 – velocity of source S relatively receiver Rfr – light frequency registered on receiver Rfs – light frequency registered on source Slr – light wavelength registered on receiver Rfs – light wavelength registered on source S.

      The part B shows right rotated objects R and source S.

      As it was shown for part A, the receiver R and source S frames of references are not equal. These objects have translational velocity |V2+wR| relatively to each other. Therefore, base on Doppler effect, the objects and S are registering wavelength of light of source S differently.
      gamma=frac{1}{sqrt 1-(frac{v_2+ome R}{c})^2}
      f_r=frac{f_s}{gamma}\f=frac{c}{lamb}\frac{c}{lamb_r}=frac{c}{lamb_sgam}\lam_r=lam_sfrac{1}{sqrt 1-(frac{v_2+ome R}{c})^2}
      Where: Y – Lorentz factor, c – speed of light, V2 – velocity of source S relatively receiver Rfr – light frequency registered on receiver Rfs – light frequency registered on source Slr – light wavelength registered on receiver Rls – light wavelength registered on source S, w - angular velocity of rotated object, R – distance between center of mass of rotated object and point of light receiving of rotated object.

      Since source has two identical rays with opposite direction it's net momentum is zero
      -vec P_l_1=vec P_l_2
      Where: Pl1,Pl2 - momentums of rays of source

      If calculate for one photon then:
      P=frac{h}{lam}\lam_s_1=lam_s_1\frac{h}{lam_s_1}= frac{h}{lam_s_2}
      Where: lamda_s1,lambda_s2 - wavelength of light of source, h - constant Planck, P - momentum

      The left non-rotated object has momentum for one photon equal to:
      P_l=frac{h}{lam_r}\P_l=frac{hsqrt(1-(frac{v_1}{c})^2)}{lam_s}
      Where: Pl - photon momentum, c – speed of light, V1 – velocity of source S relatively receiver R,  lr – light wavelength registered on receiver Rls – light wavelength registered on source S

      The right rotated object has momentum for one photon equal to:
      P_r=frac{h}{lam_r}\P_r=frac{hsqrt(1-(frac{v_2+ome R}{c})^2)}{lam_s}
      Where: Pr - photon momentum, c – speed of light, V2 – velocity of source S relatively receiver R,  lr – light wavelength registered on receiver Rls – light wavelength registered on source S, w - angular velocity of rotated object, R – distance between center of mass of rotated object and point of light receiving of rotated object.

      The photons momentums of left and right receivers are no equal to each other.
      The difference of these momentums will be equal to:
      P_r-P_l=frac{hsqrt(1-(frac{v_1}{c})^2)}{lam_s}-frac{hsqrt(1-(frac{v_2+ome R}{c})^2)}{lam_s}\
      Del P=frac{h}{lam_s}(sqrt(1-(frac{v_1}{c})^2)}-sqrt(1-(frac{v_2+ome R}{c})^2))
      Where: Pr - photon momentum for right receiver, Pl - photon momentum for left receiver, c – speed of light, V1 – velocity of source S relatively to left receiver RV2 – velocity of source S relatively to right receiver R ls – light wavelength registered on source S, w - angular velocity of rotated object, R – distance between center of mass of rotated object and point of light receiving of rotated object.



      The light propulsion system


      As it was shown before, the receivers may register light with different wavelengths relatively to light source. The photon is particle without mass rest. However this particle has a momentum. This propulsion system use this Doppler effect.
      This figure 1_1 show this light propulsion system.
      The receivers have particles which conduct round trip. The Ray of source rich these particle where they have velocity V relatively to light source.
      As it was shown before, these particles frames of references are not equal to light source frame of reference. Therefore, these particles will receive the source light with difference wavelength for each receiver. The particles of left receiver are moving forward to light source. The particles of this receiver are getting light wavelength difference as blueshift. 
      The momentum for one photon of source light for this receiver is:
      P_r=frac{h}{lam_r}\P_r=frac{h}{lam_ssqrt(1-(frac{v}{c})^2)}
      Where: lambda_r,lambda_s - wavelength of light of source on receiver and source, c - speed of light,h - constant Planck, Pr - photon momentum registered on right receiver.

      Otherwise, the particles of left receiver are moving forward to light source. The particles of left receiver are moving away from light source. The particles of this receiver are getting light wavelength difference as redshift.
      The momentum for one photon of source light for this receiver is:
      P_l=frac{h}{lam_r}\P_l=frac{hsqrt(1-(frac{v}{c})^2)}{lam_s}
      Where: lambda_r,lambda_s - wavelength of light of source on receiver and source, c - speed of light,h - constant Planck, Pl - photon momentum registered on right receiver.

      The difference photon momentum for left and right receivers equal to:
      P_r-P_l=frac{h}{lam_ssqrt(1-(frac{v}{c})^2)}-frac{hsqrt(1-(frac{v}{c})^2)}{lam_s}


      Delta P=frac{h}{lam_s}(frac{v^2}{c^2sqrt(1-(frac{v}{c})^2)})
      Where: lambda_s - wavelength of light of source on source, c - speed of light, h - constant Planck, Pr - photon momentum registered on right receiver, Pl - photon momentum registered on left receiver, dP- difference between photon momentums,V - velocity of particles relatively to source of light


      Conclusion

      Base on Doppler effect and particles(photons) with zero rest mass, the repulsed objects may have different translational velocities by value inside isolated system.


      Reference:

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