Redshift is the wavelength enlargement that causes the error in time as wavelength dilation.

Authored by Soumendra Nath Thakur. 

Author ORCID: 0000-0003-1871-7803

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. 

#PhaseShift #RedShift #GravitationalRedShift #CosmicRedshift #DopplerRedshift #relativisticeffects #wavelengthdilation #eventtime #TimeDilation

Redshift (Z) can be calculated as 1/360 for each 1° phase shift of Gravitational or Cosmic waves.

To calculate redshift using the values of phase shift in frequencies, follow the derivations. Here's a step-by-step explanation for each case:

Gravitational or Cosmic Redshift: 

Start with the formula for 1° phase shift: Z = (λ₀/360) / λ₀, where λ₀ is the wavelength at the source.

Rearrange the equation to express λ₀ in terms of frequency: λ₀ = 1/f₀, where f₀ is the frequency at the source.

Substitute the expression for λ₀ into the redshift formula: Z = ((1/f₀)/360) / (1/f₀).

Simplify the equation to obtain the final formula for gravitational or cosmic redshift: Z = (1/360f₀) / (1/f₀) = 1/360.

Therefore, for gravitational or cosmic waves, the redshift (Z) can be calculated as 1/360 for each 1° phase shift.

Refer the derivation: How to calculate redshift using values of phase shift in frequency of wave equation?

#PhaseShift #RedShift #GravitationalRedShift #CosmicRedshift

Derivation: How to calculate redshift using values of phase shift in frequency of wave equation?

Derived by Soumendra Nath Thakur. (ORCID: 0000-0003-1871-7803)

Summary

To calculate redshift using the values of phase shift in frequencies, follow the derivations. Here's a step-by-step explanation for each case:

Gravitational or Cosmic Redshift:

Start with the formula for 1° phase shift: Z = (λ₀/360) / λ₀, where λ₀ is the wavelength at the source.

Rearrange the equation to express λ₀ in terms of frequency: λ₀ = 1/f₀, where f₀ is the frequency at the source.

Substitute the expression for λ₀ into the redshift formula: Z = ((1/f₀)/360) / (1/f₀).

Simplify the equation to obtain the final formula for gravitational or cosmic redshift:

• Z = (1/360f₀) / (1/f₀) = 1/360.

Therefore, for gravitational or cosmic waves, the redshift (Z) can be calculated as 1/360 for each 1° phase shift.

Doppler Redshift:

Begin with the formula for 1° phase shift: Z = (λ(rest)/360 - λ(rest)) / λ(rest), where λ(rest) is the wavelength at rest.

Similarly to the previous derivation, express λ(rest) in terms of frequency: λ(rest) = 1/f(rest), where f(rest) is the frequency at rest.

Substitute the expression for λ(rest) into the redshift formula: Z = ((1/f(rest))/360 - (1/f(rest))) / (1/f(rest)).

Simplify the equation to obtain the final formula for Doppler redshift: 

• Z = (1/360f(rest) - 1/f(rest)) / (1/f(rest)).

Therefore, for Doppler redshift, the redshift (Z) can be calculated based on the given phase shift and the frequencies (or wavelengths) at rest.

In both cases, you'll need to know the frequency (or wavelength) at the source/rest and apply the appropriate formula to calculate the redshift. Additionally, keep in mind the specific velocities of the waves involved, whether it's the speed of sound (343 m/s) for acoustic waves or the speed of light (299,792,458 m/s) for electromagnetic waves.

Description:

The value of a redshift is denoted by the letter Z, corresponding to the fractional change in wavelength, positive for redshifts, negative for blueshifts, and by the wavelength ratio 1 + z, which is >1 for redshifts, <1 for blueshifts. And so, red-shift (z,>1) is the displacement of spectral lines towards longer wavelengths (Δλ+λ₀) > λ₀ i.e. the red end of the electromagnetic spectrum.

Where, velocity of the wave v = fλ, where acoustics waves speed 343 m/s and electromagnetic waves speed 299792458 m/s. 
                                   
For gravitational or cosmic waves, wavelength at the source is λ₀ and observed change in wavelength is Δλ.

The time interval T(deg) for 1° of phase is inversely proportional to the frequency (f). We get a wave corresponding to the time shift.

1° phase shift = T/360.

Since, T = 1/f,

1. Derivation of formula for gravitational and cosmic waves:

For 1° phase shift, T(1°) = T/360 = (1/f)/360 = ΔT. 

Since, λ = T = 1/f.

λ₀ = T₀ = 1/f₀. Where, T₀ is the period and f₀ frequency at the source.

Δλ = T₀/360 = (1/f₀)/360 for gravitational or cosmic waves.

Or, Δλ = λ₀/360 = (1/f₀)/360 

Since, Z = Δλ/λ₀ 

For 1° phase shift, Z = {(1/f₀)/360}/(1/f₀) or, (λ₀/360)/λ₀. formula for gravitational and cosmic redshift... (1).

2. Derivation of formula for Dopplar redshift:

For 1° phase shift, T(1°) = T/360 = (1/f)/360 = ΔT. 

Since, λ = T = 1/f.

λ(rest) = T(rest) = 1/f(rest). Where, T(rest) is the period and f(rest) frequency at the source.

λ(obs) = T(rest)/360 = {1/f(rest)}/360 for Doppler redshift.

Or, λ(obs) = {1/f(rest)}/360 = λ(rest)/360.

And since, Z = λ(obs)-λ(rest)}/λ(rest)

For 1° phase shift, Z = {1/f(rest)}/360 -1/f(rest)} / 1/f(rest) or λ(rest)/360 - λ(rest)}/λ(rest) formula for Dopplar redshift ... (2).

Therefore, depending upon acoustic or, electromagnetic wave, we can calculate respective values of f₀ or f(rest), to obtain respective values of redshift (Z), using vales of respective phase shift in frequencies f₀ or f(rest) for gravitational and cosmic redshifts, or Doppler shift respectively, applying respective velocities of the waves, whether acoustics wave or electromagnetis wave.

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#superheterodyne #Heterodyne

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