A Mathematical Model for Redshift

Abstract

We have used model scaling so that the propagation of light through space could be studied using the well-known nonlinear Schrödinger equation. We have developed a set of numerical procedures to obtain a stable propagating wave so that it could be used to find out how wavelength could increase with distance travelled. We have found that broadening of wavelength, expressed as redshift, is proportional to distance, a fact that is in agreement with many physical observations by astronomers. There are other reasons for redshifts that could be additional to the transmission redshift, resulting in the deviation from the linear relationship as often observed. Our model shows that redshift needs not be the result of an expanding space that is a long standing view held by many astrophysicists. Any theory about the universe, if bases on an expanding space as physical fact, is open to question.

Numerical Solutions of Nonlinear Schrödinger Equation: An Application Example of Nonlinear Analysis

“…Numerical procedures described in the previous sections have been modified and used to study the propagation characteristics of electromagnetic waves in the form of bright, dark, and anti-dark solitons [10,11,20]. The steps needed are to be described below.…”

“…To carter for the nonlinear nature of Eq. (37) that is associating with Q , an iterative algorithm [9,10] is used.…”

“…Using the procedure described in the previous section and a dispersion map with length Z =6,Figure 3 shows how the solutions converged to stable and periodic pulses [10]. The distance, x, shown is the cumulated distance.…”

“…To apply our numerical findings to cosmological redshift, calibration with measured data must be used as described in Ref. [10,19]. If the starting and ending wavelength is λ 1 and λ 2 , and the half pulse width, W 1 and W 2 , and the dimensionless redshift, z, as defined in astronomy, is given by,…”

“…In Section 3, we apply NLSE to electromagnetic wave propagation through space [10,11], together with two simple examples. We show in Section 4 that long distance, and other characteristic nature of space such as anisotropy, inhomogeneity, and gravitational effect, can be effectively included.…”