Equations of f frequency; T time period; v velocity; λ wavelength; λ₀ source wavelength; Δλ changed wavelength; T(deg) phase shift in degree; z gravitational or cosmic redshift:

Author ORCID: 0000-0003-1871-7803

Given below are the simplified expressions based on the equation and the relationship between the variables. Where, f is the frequency; T time period; v velocity; λ is the wavelength; λ₀ is the source wavelength; Δλ observed change in wavelength; T(deg) phase shift in degree; z gravitational/cosmic redshift. When,  f = 1/T = v/λ = v/λ₀; T(360) => T(deg) = z * 360; For 1° phase shift, T(deg)  = T/360 = (1/f)/360 = z * 360; z = Δλ/λ₀. 

• f is the frequency.

• We are given f = 1/T = v/λ = v/λ₀.
  

• Therefore, frequency f is equal to the reciprocal of the time period T, the velocity v divided by the wavelength λ, and also v divided by the source wavelength λ₀

• The specific velocities of the waves involved (343 m/s) for acoustic waves or (299,792,458 m/s) for electromagnetic waves.

• T time period.

• We are given a complete time period T in 360°, T(360) => T(deg) = z * 360.

• This equation represents the phase shift in degrees T(deg) being equal to the gravitational or cosmic redshift z multiplied by 360.

• For a complete time period T, the phase shift in degrees T(deg) is equal to z * 360, where z represents the gravitational or cosmic redshift.

• v velocity

• We are given v/λ = f = 1/T = v/λ₀.
  

• From these equations, we can see that v is equal to the product of the frequency f and the wavelength λ, and it is also equal to the product of the frequency f and the source wavelength λ₀.

• The specific velocities for acoustic waves (343 m/s) and electromagnetic waves (299,792,458 m/s) indicate the speed at which the waves propagate.

• λ is the wavelength

• We are given v/λ = f = 1/T =  v/λ₀.

• This equation indicates that the wavelength λ is equal to the velocity v divided by the frequency f, and it is also equal to the source wavelength λ₀.

• The wavelength (λ) is related to the velocity (v) and frequency (f) through the equation λ = v/f. Using the specific velocities provided, the wavelength can be calculated by λ = v/f.

• λ₀ is the source wavelength

• We are given v/λ₀ = v/λ = f = 1/T.

• Therefore, the source wavelength λ₀ is equal to the velocity v divided by the frequency f, and it is also equal to the wavelength λ.

• The source wavelength (λ₀) can be obtained by dividing the velocity (v) by the frequency (f), using the specific velocities given. Thus, λ₀ = v/f.

• Δλ observed change in wavelength

• We are given z = Δλ/λ₀.
  

• This equation represents the gravitational or cosmic redshift z being equal to the change in wavelength Δλ divided by the source wavelength λ₀

• T(deg) phase shift in degree

• We are given T(deg) = T/360 = (1/f)/360 = z * 360.

• This equation states that the phase shift in degrees T(deg) is equal to the time period T divided by 360, which is also equal to the reciprocal of the frequency f divided by 360, and it is equal to the gravitational or cosmic redshift z multiplied by 360. For a complete time period T, the phase shift in degrees T(deg) is equal to z * 360, where z represents the gravitational or cosmic redshift

• z gravitational/cosmic redshift.

• We are given z = Δλ/λ₀.

• This equation indicates that the gravitational or cosmic redshift z is equal to the change in wavelength Δλ divided by the source wavelength λ₀.

These are the simplified expressions based on the given equations and the relationships among the variables.

Reference : Relativistic effects on phaseshift in frequencies invalidate time dilation II 

#frequency #timperiod #velocity #wavelength #sourcewavelength #restewavelength #observedwavelength #changedwavelength #Tdeg #phaseshift #degree #gravitationalredshift #cosmicredshift

There is a direct relationship between Phase shift T(deg) and Gravitational/Cosmic Redshift (z):

Authored by Soumendra Nath Thakur. 

 Author ORCID: 0000-0003-1871-7803

Author's Conclusion: T(deg) = z * 360.

The phase shift T(deg) is a measure of the change in phase of a wave, often caused by factors such as motion or gravitational effects. It is typically measured in degrees.

The gravitational/cosmic redshift (z) represents the change in wavelength or frequency of a wave due to gravitational or cosmological effects. It is a dimensionless quantity.

The relationship T(deg) = z * 360 indicates that the phase shift in degrees T(deg) is directly proportional to the gravitational/cosmic redshift (z) multiplied by 360. 

This means that for a given redshift value, the corresponding phase shift will be proportional to that value multiplied by 360.

Phase shift: Phase shift represents the displacement or shift in the phase of a wave. It occurs when a wave encounters a change in its medium or when the observer or source is in motion. Phase shift is related to the relative frequencies of the waves involved.

Redshift: Redshift refers to the phenomenon where the observed wavelength of light or any other wave is larger (shifted towards the red end of the spectrum) compared to the rest wavelength of the source. It indicates the stretching of the wavelength due to various factors such as relative motion or gravitational effects.

Example: T(deg)

Equation given by: ΔΦ = Δω × Δt.  

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; T = 1/f.
• 1° phase shift = T/360 = (1/f)/360.

A wave frequency = 5 Mhz. we get the phase shift (in degree°) corresponding time shift.

1° phase shift on a 5 MHz wave = (1/5000000)/360 = 5.55 x 10ˉ¹º = 555 ps. Corresponds to a time shift of 555 picoseconds.

Therefore, for 1° phase shift for a wave having a frequency 5 MHz. and so wavelength 59.95 m, the time shift Δt is 555 ps. 

In gravitational and cosmological redshifts, the observed wavelength (λ(obs) is compared to the source wavelength (λ₀). The ratio of the change in wavelength, Δλ, to the source wavelength, λ₀, gives the redshift (Z). This redshift implies both a wavelength enlargement and a time distortion. The equation for gravitational redshift and cosmic redshift is Z = Δλ/λ₀.

Reference : Relativistic effects on phaseshift in frequencies invalidate time dilation II 

#PhaseShift #RedShift #GravitationalRedshift #CosmicRedshift

Time dilation (t') is an error and falls outside the time scale:

Authored by Soumendra Nath Thakur. 

  Author ORCID: 0000-0003-1871-7803

The redshifts correspond to distortion in time: - The effects of redshift on wavelength, frequency, and time.

Authored by Soumendra Nath Thakur. 

  Author ORCID: 0000-0003-1871-7803

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