Summary:
In various forms of redshift, including Doppler redshift and gravitational and cosmic redshifts, the observed wavelength λ(obs) and Δλ is enlarged compared to the rest wavelength λ(rest) or λ₀ of the source. This wavelength enlargement corresponds to a distortion in time, as wavelength (λ) and period (T) of a wave are inversely related. The enlargement in wavelength λ(rest) and Δλ corresponds to a change in time period (ΔT) of the wave.
In the case of time dilation, relativistic effects such as speed or gravitational potential difference can cause phase shifts in the frequency of a wave, resulting in infinitesimal loss of wave energy and corresponding enlargement in the wavelength of the wave. This wavelength dilation then leads to errors in the reading of clock time.
The relationship between wavelength and time distortion is expressed as Δλ ∝ ΔT. This means that changes in wavelength correspond to changes in time. For example, a phase shift of 1455.50° in the wave of an atomic clock oscillation with a frequency of 9192631770 Hz can result in a time delay (ΔT) of 38 microseconds per day.
Based on this relationship, it can be concluded that redshift, which is the enlargement of wavelength, is also associated with the error in time due to wavelength dilation.
Description:
For electromagnetic waves or light, there is an inverse relationship between the period (T) and frequency (f) of a wave, expressed as T = 1/f. and the wavelength (λ) of a wave is directly proportional to its period, λ ∝ T. The distortions of wavelengths exactly correspond to time distortions; through the relationship is λ ∝ T., where λ denotes wavelength and T denotes period of oscillation of the wave.
The relativistic effects, such as speed or gravitational potential difference, cause phase shift in the frequency due to infinitesimal loss of wave energy, corresponding to the enlargement in the wavelength of the wave or light.
Enlargement of wavelength in various redshifts:
Whereas all forms of redshifts are the wavelength enlargement. Whereas, observed wavelength of light in Doppler redshift, or in Gravitational and Cosmic Redshifts enlarged as λ(obs) or Δλ compared to their respective sources λ(rest) or λ₀. The corresponding formulas for these redshift are –
- Z = {λ(obs)-λ(rest)}/λ(rest); for Doppler redshift.
- Z = Δλ/λ₀ and also
- Z = Δλ/λ₀, for Gravitational and Cosmic redshifts respectively.
Since, the enlargement of wavelength exactly corresponds to time distortions; through the relationship Δλ ∝ ΔT.
Therefore, for Doppler redshift wavelength of observed light is λ(obs) that corresponds to time period T(obs) of the light and for Gravitational and Cosmic redshifts the wavelengths of observed light is Δλ, those correspond to its time period ΔT..
Enlargement of wavelength in time dilation:
The relativistic effects, such as speed or gravitational potential difference, affects the clock mechanism, and causes phase shift in the frequency due to infinitesimal loss in the wave energy, and corresponding enlargement in the wavelength of the clock oscillation, correspondingly results error in the reading of the clock time through the relationship λ ∝ T.
Since distortions of wavelengths exactly correspond to time distortions as in the expression Δλ ∝ ΔT.
Whereas, for 1455.50° phase shift of the wave of atomic clock oscillation having a frequency 9192631770 Hz., the time shifts (time delay) ΔT = 38 microsecond/day.
The relationship is Δλ ∝ ΔT in all causes of electromagnetic waves, either in redshift or in time distortion.
Therefore, the scientific conclusion is that the redshift is the wavelength enlargement that also causes the error in time as is wavelength dilation.
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