Redshift, Blueshift, and Phase Shifts: A Unified Framework for Time Deviations in Oscillatory Systems Under Motion and Gravitational Effects.

Soumendra Nath Thakur

December 04, 2024

Following reasoning highlights an essential relationship between frequency, wavelength, and period in oscillatory systems, particularly under the influence of redshift (energy loss) or blueshift (energy gain). Here's a formalized explanation:

Key Relationship:

The proportionality (1/f) ∝ λ ∝ T establishes that frequency (f), wavelength (λ), and period (T) are intrinsically linked. Any change in frequency due to a phase shift (Δf) directly affects both wavelength and period, as follows:

• Redshift (Energy Loss):

If a phase shift reduces the frequency (f₀-Δf) = f₂, then: 

λ↑ and T↑

This corresponds to an elongation of the wavelength and an increase in the period (time for one cycle).

• Blueshift (Energy Gain):

If a phase shift increases the frequency (f₀+Δf) = f₃, then:

λ↓ and T↓

This corresponds to a compression of the wavelength and a decrease in the period.

Effect on Clock Time:

Since clock time (T) is derived from the oscillatory system's period, a change in frequency due to energy shifts (redshift or blueshift) will directly influence clock time. Specifically:

1. Redshift/Energy loss:

• Energy is lost (e.g., due to gravitational potential differences or relative velocity).

• Wavelength enlarges (λ↑), and the period lengthens (T↑).

• The clock runs slower compared to a reference frame.

2. Blueshift/Energy gain:

• Energy is gained (e.g., approaching a gravitational source or moving towards the observer).

• Wavelength shortens (λ↓), and the period shortens (T↓).

• The clock runs faster compared to a reference frame.

The relative frequency shift (Δf) resulting from these effects leads to phase shifts, which manifest as errors in time synchronization between clocks. These shifts are governed by:

ΔT = 360°/(f+Δf) − 360°/f.

This discrepancy affects the oscillatory synchronization, causing an observable error in clock readings.

Conclusion:

The phase shift in frequency (f₀ ±Δf) resulting from energy changes unequivocally affects both wavelength and period. This causal relationship ensures that any change in wavelength due to frequency shifts directly impacts clock time. Consequently, oscillatory dynamics influenced by redshift (energy loss) or blueshift (energy gain) manifest as measurable time deviations in clocks under conditions of motion or gravitational influence. A single phase-shift formula for frequency (f₀ ±Δf) can effectively account for these variations across both scenarios, providing a unified approach to analysing time deviations.

By emphasizing the direct and observable relationship between frequency shifts, wavelength changes, and clock time deviations, my approach effectively sidesteps the need for relativistic formulas that rely on abstract interpretations like spacetime curvature. This streamlined framework rooted in physical causality offers a more intuitive and consistent explanation for phenomena like redshift and blueshift, making it a powerful alternative to traditional relativistic models.

"Abstract: Relative time emerges from relative frequencies. It is the phase shift in relative frequencies due to infinitesimal loss in wave energy and corresponding enlargement in the wavelengths of oscillations; which occur in any clock between relative locations due to the relativistic effects or difference in gravitational potential; result error in the reading of clock time; which is wrongly presented as time dilation."

This abstract of the research titled, "Relativistic effects on phaseshift in frequencies invalidate time dilation II" by Soumendra Nath Thakur et al, presents clear and meaningful in its presentation, effectively summarizing the core idea of the research. It encapsulates the relationship between relative frequencies, phase shifts, wave energy loss, and wavelength changes, highlighting their roles in creating errors in clock time readings. Moreover, it challenges the conventional interpretation of these phenomena as time dilation, instead presenting them as measurable and quantifiable effects of oscillatory dynamics under relativistic influences or gravitational potential differences.

For the research by Soumendra Nath Thakur et al., this abstract is appropriate and aligns well with the study's focus on reframing time dilation through a more physically grounded explanation. It clearly conveys the intent to debunk the conventional time dilation narrative while proposing an alternative mechanism rooted in phase shifts and frequency dynamics.