Soumendra Nath Thakur
ORCiD: 0000-0003-1871-7803
09-06-2024
Abstract:
The speed of light (c) is governed by the equation c=f⋅λ, where frequency (f) and wavelength (λ) are inversely proportional. This relationship ensures that in the absence of external forces, both frequency and wavelength remain constant. However, photons emitted by gravitationally bound bodies experience a gravitational force, described by Fg = G⋅(m₁⋅m₂)/d², influencing their wavelength and causing redshift. Despite this, the speed of light (c) remains unchanged due to the compensatory relationship between frequency and wavelength. As gravitational redshift reduces the frequency, the energy of the photon decreases according to E=hf. Beyond the gravitational influence, photons encounter the effects of dark energy, which exhibits antigravitational properties and becomes significant in cosmic expansion. This study highlights that while light travels at a constant speed in a vacuum, the increasing distance due to cosmic expansion can be perceived as (c+Δd)>c, though the intrinsic speed of light remains c. These findings underscore the importance of gravitational and dark energy influences on light while affirming the constancy of the speed of light in a vacuum.
Keywords: Gravitational redshift, Cosmic redshift, Dark energy, Cosmic expansion, Photon energy, Frequency-wavelength relationship, Antigravity, Zero-gravity radius,
The speed of light (c) is given by the equation c=f⋅λ, where frequency (f) is inversely proportional to wavelength (λ), i.e., f∝1/λ. This means that in the absence of any external forces acting on a wave or photon, both the frequency and wavelength would remain unchanged. However, the source emitting a photon is a gravitationally bound body. Therefore, a gravitational force acts on the wave or photon from the moment of its emission until it exits the gravitational influence of its source. This force is expressed as:
Fg = G⋅(m₁⋅m₂)/d²
The gravitational force (Fg) influences the wavelength (λ), causing redshift, although c remains constant. This is possible because the frequency (f) of the wave or photon must also change due to their relationship f∝1/λ. As the wavelength increases due to the gravitational force (Fg), the frequency (f) correspondingly decreases, ensuring that c remains constant. A reduction in f leads to a reduction in the energy (E) of the wave, as described by E=hf. Consequently, the energy of the wave or photon decreases due to the gravitational force (F_g) until this force becomes negligible, according to the relationship Fg = G⋅(m₁⋅m₂)/d².
When the wave or photon moves beyond the gravitational influence, it no longer experiences redshift or blueshift due to gravity. Beyond gravitational influence, dark energy, which exhibits antigravitational properties, can become significant. This is discussed in the study "Dark energy and the structure of the Coma cluster of galaxies" by Chernin et al. (2013), where dark energy's repulsive effect influences the structure of the Coma cluster. The effective mass of dark energy is considered negative due to its repulsive nature, impacting the cluster's dynamics.
In the context of cosmic expansion, this means that as the wave or photon travels through regions where dark energy dominates, the increasing distance due to cosmic expansion affects the observed wavelength (λ) and frequency (f). While light always travels at the speed c in a vacuum, the increasing distance (c+Δd) due to cosmic expansion can be interpreted as (c+Δd)>c. However, the intrinsic speed of light remains c.
Thus, gravitational influences and cosmic expansion affect the frequency and wavelength of light but do not alter the constancy of the speed of light (c) in a vacuum.
References:
Chernin, A. D., Bisnovatyi-Kogan, G. S., Teerikorpi, P., Valtonen, M. J., Byrd, G. G., & Merafina, M. (2013). Dark energy and the structure of the Coma cluster of galaxies. Astronomy & Astrophysics, 553, A101. https://doi.org/10.1051/0004-6361/201220781
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