NEW TYPE OF THE RED SHIFT

Ivan Ľ. Baják

Abstract: The note presents an elementary consideration saying that a red shift can be caused as a consequence of interference of two waves with slightly diverging wave vectors.

 

The picture of the universe so called the standard model which has been developing during past decades is of an expanding swarm of galaxies that started as “big bang” about 20 000 millions years ago. The belief in expansion of the universe is supported by the observation of   red shift in light coming from the remote stellar objects and is interpreted as a consequence of Dopper effect. The standard model is receiving a great respect and therefore it is rather audacious to assert that the red shift in light coming from universe may not be the result of Dopper effect.

 Now we shall show that the red shift can be originated also through interference of two waves which have angular frequency ω and wave vectors k₁   and    k₂   forming a small angel 2α.

Let us assume that waves

                            u₁  = u₀ e^{(iωt – k}₁^r)    and     u₂ = u₀ e^{(iωt – k}₂^r)                                             (1)

                                                                    

propagate    in (x,y)  plane  so that k₁  = (k_x , k_y ) and   k₂  = (k_x ,− k_y ) ,  | k₁ | = | k₂  | = k       where    k_y = k sin α  ,  k_x = k cos α.  Then

                                 u  = u₁  + u₂ = u₀ 2cosk_yy   e^{i(ωt – k}_x^r)                                                                                    (2)

is the plane wave propagating along k_x   i.e. in x- direction. ( The symbols in above relations have their common meaning)

            Thus according to (2) the resulting wave field of plane waves has wavelength

                                                    λ_x=λ ⁄cosα                                                                            (3)

 As λ_x ≥ λ it can be  considered as a red shift due to Doppler effect and thus it can be judged as wave generated from moving object. The amplitude of wave (2) is modulated. Since α is very small the length of modulation       λ_y=λ ⁄sinα  is large enough to not influence the results of the measurement of  λ_x.

            This elementary consideration should be taken into account when light of any remote galaxy is examined. There is a high probability that such light does not propagate as plane waves with strictly parallel rays. The light wave field can have slightly diverging wave vectors and may fulfil conditions for creation of wave showing the red shift. Experimental verification of the above described idea should not  be complicated and can bring surprising results supporting further development in cosmology.