In various forms of redshift, including Doppler redshift and gravitational and cosmic redshifts, the observed wavelength λ(obs) and the change in wavelength Δλ are enlarged compared to the rest wavelength λ(rest) or λ₀ of the source. This wavelength enlargement is directly related to the redshift phenomenon.
The relationship between the rest wavelength and the observed wavelength is expressed as λ(rest) ∝ 1/λ(obs), where λ(rest) is inversely proportional to λ(obs). This inverse relationship between the rest wavelength and the observed wavelength indicates that as the observed wavelength increases redshift, the rest wavelength decreases.
This change in wavelength corresponds to a distortion in time. Since wavelength and frequency are inversely related λ ∝ 1/f, a change in wavelength implies a change in frequency. This change in frequency, in turn, affects the time characteristics of the wave.
Therefore, the enlargement of the observed wavelength and the corresponding decrease in the rest wavelength indirectly relate to the distortion in time. The specific relationship between wavelength dilation and time distortion is governed by the mathematical expressions and principles of the respective forms of redshift.
These relationships have been derived and supported by scientific theories and observations. They provide valuable insights into the behavior of waves and the effects of redshift on wavelength, frequency, and time.
Reference : Relativistic effects on phaseshift in frequencies invalidate time dilation II
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