A photon passes near a massive object simultaniously gains and loses momentum:

The momentum of a photon is given by the equation p = E/c, where p represents momentum, E represents energy, and c represents the speed of light. Since the energy of a photon is directly related to its frequency or inversely related to its wavelength, any change in the photon's energy will result in a corresponding change in its momentum.

When a photon passes near a massive object, it simultaniously gains and loses energy (and thus momentum) due to gravitational interactions. This exchange of momentum causes the photon's path to be curved or deflected in the presence of a gravitational field.

Despite the exchange of momentum, a photon continues to travel at the speed of light (c) and covers the same distance (d) relative to its constant speed. The curvature of the photon's path is a result of the gravitational interaction and exchange of momentum.

Redshift due to motion, when phase shift T(deg) of the observed frequency and the source frequency f(rest) are know.:

Redshift due to motion - an alternative formula. 

A 1° phase shift in the wave oscillation is due to motion, we can calculate the redshift using the formula.

z = {1 - 360 * f(rest)} / {360 * f(rest)}.

Where, T(deg) represents the phase shift in degrees and f(rest) represents the source frequency

Frequency and phase in sin:

The equation y(x) = sin(f * x + p). What does f represent and what does p represent?

In the equation y(x) = sin(f * x + p), the variables f and p represent parameters that affect the behavior of the sine function.

f: The variable f represents the frequency of the sine wave. It determines how many oscillations occur over a given interval of x values. The frequency f controls the rate at which the sine function completes a full period, which is 2π radians or 360 degrees. Higher values of f result in more oscillations within the same interval, while lower values lead to fewer oscillations.

p: The variable p represents the phase shift of the sine wave. It indicates the horizontal displacement or translation of the wave along the x-axis. Specifically, it determines the initial position of the wave at x = 0. The phase shift p is measured in radians or degrees and can move the wave to the left or right. Positive values of p shift the wave to the left, while negative values shift it to the right.

By adjusting the values of f and p, you can modify the frequency and position of the sine wave, respectively, in the y(x) equation.

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