A conflict between time dilation and gravitational redshift:

There are three known types of redshifts, - Doppler redshift, gravitational redshift and cosmological redshift.

The corresponding formulas for this redshift are –

• Z = {λ(obs)-λ(rest)}/λ(rest);
• Z = Δλ/λ₀ and also
• Z = Δλ/λ₀,

Where,

• Z denotes the redshift factor which represents the fractional change in wavelength;
• λ(obs) represents the observed wavelength of light;
• λ(rest) represents the rest wavelength of light;
• Δλ is the change in wavelength of light as observed;
• λ₀ is the wavelength at the source.

Time dilation, based on Doppler Redshift, and the gravitational redshift; both are due to the wavelength dilation of the wave.

The distortions of wavelengths exactly correspond to time distortions; through the relationship λ∝T, where λ denotes wavelength and T denotes period of oscillation of the wave.

 

The Planck's equation conveys that a photon's wavelength is inversely proportional to the energy of that photon, which can be calculated from Planck's equation 1/λ∝E, where h Planck's constant and c constant denotes the speed at which a light photon travel.

 

1)       Doppler Redshift is the enlargement in the wavelength (λ) of the wave in relation to an observer who is moving away relative to the wave source, Z={λ(obs)-λ(rest)}/λ(rest). Whereas, time dilation, based on Doppler formula, is not understood from the wavelength (λ) distortion rather understood from Doppler Redshift. In fact, relativistic effect causes phase shift in the frequency and corresponding enlargement in the wavelength of the clock oscillation, and so results error in the reading of the clock time, wrongfully known as time dilation.

 

    2) Similarly, gravitational redshift too is the enlargement in the wavelength (λ) of the light (photons) wave moving away relative to its source or from a gravitational well. So a photon expends energy (E) while escaping the gravitational well, known as gravitational redshift.

 

3) Cosmological redshift too is the enlargement in the wavelength (λ) of the light photons traveling, through intergalactic space, relative to its gravitational well.

 

However, time distortion always originates from wavelength distortion and so, time dilation, as in special relativity, does not follow the general rules, when it should have been understood from the wavelength (λ) distortion rather than understanding it from the Doppler Redshift. As such, Special relativity does not escape the fundamental equivalent between wavelengths and time, which is much more general than special relativity. Whereas, time dilation actually wavelength dilation.

 

Therefore, time dilation is not only in conflict with gravitational redshift because it is not understood from wavelength dilation than the Doppler Redshift, but time dilation also does not escape additional wavelength dilation due to Cosmological redshift. The Planck's equation appears to be good use for the calculation of all relevant wavelength dilations.

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A conflict between gravitational redshift and time dilation:It appears that Einstein promoted Doppler more than Planck in his gravitational redshift, so as to protect his "time dilation" from an obvious conflict with "wavelength dilation" - a must requirement for both gravitational redshift as well as time dilation. 

Considering expanded energy of "photon" (wave) and an "object" under the influence of relativistic effects respectively, in relation to an observer who is moving away relative to the wave source - as in "gravitational redshift" of photon (wave) leaving gravitational well, - and as an object under the relativistic effects in time dilation respectively. In both of the incidents, energy and frequency decreased, correspondingly wavelength enlarged, resulting respective redshift and (wavelength dilation,) so called time dilation.  

 

- Soumendra Nath Thakur

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