Soumendra Nath Thakur
ORCID: 0000-0003-1871-7803
Tagore's Electronic Lab, India.
March 10, 2025
A fundamental and precise understanding of the speed of light (c) in relation to the observer's speed (S), along with a clear explanation of why the observer's speed is negligible, is presented through a nuanced, non-relativistic scientific framework grounded in consistent physical principles.
The principle of special relativity asserts that the laws of physics remain the same for all observers in any inertial frame of reference. As a result, the relativity's understanding of light’s constant speed originates from Einstein’s theory of special relativity (1905), which states that the speed of light in a vacuum is a universal constant, unaffected by the motion of the light source or the observer.
Mathematically, this is expressed as:
λ f = c
where:
c represents the speed of light,
λ is the photon's wavelength,
f is the photon's frequency.
The equation
λ f = c
can also be rewritten as:
f = c/λ
This highlights the inverse relationship between wavelength and frequency while maintaining the constant speed of light. However, in logical terms, this inverse relationship implies that their ratio must always yield c.
However, the equation λ f = c is primarily a mathematical convenience derived from the known frequency-wavelength inverse relationship. While effective in describing wave behaviour, it does not fully explain the fundamental reason why light's speed remains constant.
Here on, we will discuss a fundamental and precise understanding of the speed of light (c) in relation to the observer's speed (S);
Each observer in question is characterized not only by their matter mass (Mₘ) but also by the gravitational mass (M𝗀), which includes both the observer’s own mass and the gravitational influence of the massive body they reside on. Matter mass of the observer’s host body is a crucial factor in this physical consideration.
In addition to ordinary (baryonic) mass, the mass of dark matter is also accounted for and included in the total matter mass (Mᴍ). In classical mechanics, inertial mass is traditionally considered equivalent to gravitational mass, expressed as m = m𝗀. However, recent observations of the gravitational effects of dark matter and dark energy on ordinary (baryonic) inertial mass have necessitated an extension of this classical equation.
Extended Classical Mechanics (ECM), in alignment with established observational evidence and theoretical formulations, refines this understanding by recognizing that gravitational mass is equivalent to the sum of matter mass and negative apparent mass, which can dynamically modify the effective mass—potentially turning it negative at intergalactic scales. — This relationship is expressed as:
Mg = Mᴍ + (−Mᵃᵖᵖ)
When considering the speed of light in relation to the speed of an observer, the scale of measurement should be at least planetary. Consequently, the speed (S) of the planet on which the observer is located must be taken into account and included in the calculation.
According to the principles of Extended Classical Mechanics (ECM), a photon possesses negative apparent mass (-Mᵃᵖᵖ) where: Mᴍ = 0 for photons, which, unlike matter mass (Mᴍ), exhibits an anti-gravitational property.
As a result, photons are not inherently restricted by an upper speed limit when external influences (gravitational fields, Planck-scale constraints) are absent.
However, Planck units impose a fundamental limit, restricting the smallest possible wavelength to the Planck length (ℓP) and the shortest measurable time to the Planck time (tP), thereby constraining a photon's behaviour within permissible limits.
Beyond the Planck scale, classical, relativistic and even quantum descriptions of spacetime break down. At the Planck length (ℓP ≈ 1.616 × 10⁻³⁵ m) and Planck time (tP ≈ 5.391 × 10⁻⁴⁴ s), gravitational and quantum effects become inseparable, implying that distances smaller than ℓP and times shorter than tP lose physical significance. This arises because, at these scales, quantum fluctuations of spacetime dominate, leading to a breakdown of continuous space and time concepts. Hence, any attempt to define a wavelength smaller than ℓP or a frequency beyond the Planck frequency (fP = 1/tP) is meaningless in a physically observable sense.
The Planck scale imposes a fundamental limit on measurable space-time intervals, ensuring that beyond these limits, conventional descriptions of motion—including those of photons—lose physical meaning. This restriction provides a natural boundary for photon behavior before additional external influences, such as gravitational redshift and cosmic expansion, further alter their observed properties.
Within a gravitational field, a photon expends energy while escaping, leading to a redshift in its wavelength. However, beyond significant gravitational influence, a photon's speed—defined by the ratio of its wavelength (λ) and frequency (f)—further changes due to the cosmic recession of galaxies, resulting in an additional energy loss.
The Planck length (ℓP) and Planck frequency (fP), as defined in Planck units, are derived from Planck’s constant and other fundamental constants. They establish a theoretical limit on the smallest meaningful measurements of space and time, where our current physical understanding, including relativity, breaks down and quantum gravity effects become dominant.
In classical mechanics, speed is determined using the values of distance and time associated with a given motion. The fundamental equation for speed is:
S = d/t
At the quantum scale, this equation is expressed as:
ΔS = Δd/Δt
where:
Δd corresponds to the Planck length (ℓP),
1/Δt corresponds to the Planck frequency (fP), where Δt represents the Planck time.
The expression c = λf, where f = 1/Δt, translates directly into the quantum-scale speed equation ΔS = Δd/Δt. Here, wavelength (λ) corresponds to a measurable distance (Δd), and its division by the time period of one oscillation (1/Δt) mirrors the definition of speed as distance per unit time. This consistency shows that the speed of light (c) is fundamentally a ratio of measurable spatial and temporal quantities, reinforcing that c = λ(1/Δt) is structurally identical to the speed equation ΔS = Δd/Δt, where ΔS represents velocity measured within a defined quantum reference frame.
Thus, the equation
ΔS = Δd/Δt
can be interpreted as:
c = fλ
where:
ΔS represents c (the speed of light),
Δd represents the photon's wavelength (λ),
1/Δt represents the frequency (f).
Additionally, the speed of light can be expressed in terms of the Planck scale:
c/ℓP = fP
Since the Planck length (ℓP) is the smallest meaningful spatial unit, and the Planck frequency (fP) is the highest fundamental oscillation frequency in the universe, their ratio is equivalent to the ratio of a photon's wavelength to its inverse frequency (which corresponds to the Planck time).
I have previously mentioned that photons are not inherently restricted by an upper speed limit when external influences (gravitational fields, Planck-scale constraints) are absent. This distinction is crucial in understanding the fundamental difference between the speed of observers and the speed of photons.
Photons, having negative apparent mass (-Mᵃᵖᵖ), exhibit fundamentally different gravitational properties than observers with positive matter mass (Mᴍ).
Photons exhibit an anti-gravitational nature, meaning they follow the dynamics of negative apparent mass, which aligns with negative effective mass (-Mᵉᶠᶠ) contributions in the universe (similar to dark energy).
Observers and massive objects exhibit gravitational properties, meaning their motion is bound to the gravitational pull of the universal potential centre (i.e., the tendency toward gravitational collapse).
Because the forces governing these entities are opposite in nature, their respective speeds must also be opposite in direction. The observers’ movement is toward the universal gravitational potential, while photons move away from the universal potential due to their anti-gravitational nature. This opposition results in an effective cancellation of speed components between the two systems.
Since an observer's speed is defined in a gravitational reference frame and a photon's speed in an anti-gravitational reference frame, their effective speeds appear in opposite directions. Given that the magnitude of negative effective mass (-Mᵃᵖᵖ) dominates, the observer's gravitational speed is effectively negligible when compared to the anti-gravitational motion of photons.
The anti-gravitational motion of photons, driven by negative apparent mass (-Mᵃᵖᵖ), aligns with the large-scale acceleration of cosmic structures. This is evident in the recession of galaxies, where the dominance of negative effective mass (-Mᵉᶠᶠ) contributes to the observed cosmic expansion, reinforcing the fundamental opposition between gravitationally bound matter and anti-gravitational dynamics.
Moreover, since the measurement system itself is dictated by the dominant mass-energy contribution, we must recognize that:
The negative measurement system dominates due to the overwhelming contribution of negative apparent mass (-Mᵃᵖᵖ) and negative effective mass (-Mᵉᶠᶠ), which surpasses the contribution of positive matter mass (Mᴍ).
In a mass-energy dominated measurement framework, where the contribution of -Mᵃᵖᵖ vastly exceeds that of positive matter mass, the effective measurement system aligns with anti-gravity, making the observer’s motion negligible in contrast to the dominant anti-gravitational dynamics.
Gravitational deceleration in a positive mass system corresponds to anti-gravitational acceleration in a negative effective mass system, reinforcing that the observer’s motion is measured within a negative measurement framework when compared to photons.
The speed of photons in the anti-gravitational system is vastly superior to the speed of observers in the gravitational system . This makes the gravitational motion of observers negligible compared to the anti-gravitational motion of photons.
Thus, the ultimate outcome is that the speed of observers with positive mass is rendered insignificant when contrasted against the anti-gravitational speed of photons with negative apparent mass, which follows an opposite trajectory—away from the universal potential. The dominance of the negative measurement system further amplifies this effect, reinforcing the fundamental asymmetry between the two domains.
