Addressing the Question: "Is There a Reasonable Alternative to the Theory of the Expanding Universe?"

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

December 10, 2024

1. The Concept of a Static Universe

Historically, the static universe model was considered a viable alternative but was ultimately disproven by observational evidence. Albert Einstein initially proposed a static, isotropic, and homogeneous universe, introducing the cosmological constant (Λ) to counteract gravitational collapse and maintain stability. However, in 1929, Edwin Hubble's discovery of the redshift of galaxies provided definitive evidence of an expanding universe. Hubble's law demonstrated that the redshift of galaxies is proportional to their distance, signifying that galaxies are receding from each other at speeds increasing with distance.

In light of this discovery, Einstein abandoned the static universe model, calling his introduction of the cosmological constant "the biggest blunder of my life." Consequently, the expanding universe model became the cornerstone of modern cosmology, and no reasonable alternative to it has been validated since.

2. Mass Loss and Gravitational Redshift

The claim that mass loss from stars or galaxies should result in a decreasing gravitational redshift is not scientifically accurate. Gravitational redshift, also known as the Einstein shift, depends on the gravitational potential of the source and the intrinsic and interactional energy of the photon at the point of emission, not on gradual mass changes over time.

3. Photon energy is a key parameter influenced by gravitational and cosmological phenomena during its journey through space. At emission, a photon’s total energy includes:

Eₜₒₜₐₗ,ₚₕₒₜₒₙ = E + Eg

 

• Intrinsic Energy (E): The inherent energy of the photon, proportional to its frequency.

• Interactional Energy (Eg): The energy gained from gravitational interaction with the source's gravitational potential.

Within the gravitational influence of massive bodies, photons expend Eg to escape the gravitational well, leading to gravitational redshift. However, the intrinsic energy (E) of the photon remains intact, as this component is unaffected by gravitational interactions.

Therefore, as the photon escapes the gravitational influence of the source, it does not lose its intrinsic energy (E); instead, it expends its interactional energy (Eg). The observed gravitational redshift arises from this expenditure, leading to a decrease in the total energy (Eₜₒₜₐₗ,ₚₕₒₜₒₙ) of the photon as it climbs out of the gravitational well.

4. Why Mass Loss Does Not Affect Gravitational Redshift:

• Gravitational redshift is determined by the gravitational potential at the point of photon emission. For a star or galaxy, this potential remains effectively constant over short timescales compared to the gradual mass loss caused by electromagnetic radiation or particle emissions.

• A photon's interaction with gravity is independent of the source's gradual mass changes, as long as the emission conditions remain unchanged.

5. Doppler and Relativistic Contributions:

Gravitational redshift is distinct from the relativistic Doppler effect, which arises due to the relative motion between the photon source and the observer. The Doppler factor, which relates the source and observed frequencies, is given by:

Doppler Factor = √(1−β)/(1+β), β = v/c 

Here, v is the relative velocity of the source, and c is the speed of light. The Doppler effect affects photon frequency (f) and wavelength (λ) based on relative motion, whereas gravitational redshift results solely from energy interactions with the gravitational potential.

Illustration:

For a typical photon with intrinsic energy E = 4.0 × 10⁻¹⁹ J, its emission frequency corresponds to f = 6.0368 × 10¹⁴ Hz. The gravitational redshift arises as the photon expends its interactional energy (Eg) while escaping the gravitational field, leading to an observed decrease in frequency (fr) and a proportional increase in wavelength (λr).

In summary, a photon retains its intrinsic energy (E) as it escapes the gravitational influence of a massive object, while the redshift results from the loss of interactional energy (Eg). Gradual mass loss from stars or galaxies has no direct impact on this process, as gravitational redshift is governed by the gravitational potential at the point of emission and the photon's total energy interaction with that potential.

6. Photon Behaviour in Dark-Energy-Dominated Cosmic Space

As a photon exits the zero-gravity sphere of gravitationally bound systems and enters dark-energy-dominated intergalactic space, its energy behaviour changes due to the increasing distances between receding galaxies. In this interpretation, the increased separation of galaxies is treated as a physical increment of distances rather than an expansion of the natural spacetime fabric. The implications for photon energy are as follows:

• Loss of Intrinsic Energy (E):

In contrast to its behaviour within gravitationally bound regions, a photon traveling through intergalactic space experiences a permanent loss of intrinsic energy (E). This energy loss is caused by the photon having to traverse additional physical distances created by the increasing separation of galaxies. The longer the photon’s journey, the greater the energy it expends to cover these growing distances, manifesting as a reduction in frequency (cosmological redshift).

• Physical Increment of Distance:

Rather than attributing this phenomenon to the relativistic expansion of spacetime, the interpretation focuses on the physical increase in distances between galaxies driven by dark energy. The receding galaxies contribute to a lengthening of the photon’s travel path, resulting in greater energy expenditure.

Comparison with Gravitational Redshift:

• Gravitational Redshift: Results from a photon expending Eg while escaping a gravitational well, with E remaining unaffected.

• Cosmological Redshift (Revised): Results from the photon losing intrinsic energy (E) due to the extended physical travel distance required in intergalactic space dominated by dark energy.

7. Implications for Photon Energy Dynamics

This interpretation of distance increment between galaxies provides an alternative framework for understanding cosmological redshift. It underscores that the photon's energy loss during its journey is linked to the physical realities of increasing galaxy separations rather than the relativistic notion of spacetime fabric expansion. The observed redshift is thus a direct consequence of the photon's traversal of additional, physically real distances, reinforcing the role of dark energy in driving the universe's large-scale structure.

Conclusion

In summary, photons retain their intrinsic energy (E) within the gravitational influence of massive bodies, expending only their interactional energy (Eg) to escape gravitational wells. This ensures that the photon’s inherent properties remain intact. However, in dark-energy-dominated intergalactic space, the photon loses intrinsic energy due to the physical increment of distances between receding galaxies. This energy loss, observed as cosmological redshift, arises not from a relativistic expansion of spacetime but from the tangible elongation of the photon’s travel path in an evolving universe.

Addressing the broader question, "Is there a reasonable alternative to the theory of the expanding universe?"—the overwhelming observational evidence, including the cosmic microwave background (CMB), large-scale galaxy distributions, and redshift-distance relationships, firmly supports the theory of increasing distances between galaxies driven by dark energy. The notion of a static universe, previously proposed as an alternative, has been empirically invalidated by Hubble’s discoveries and subsequent advancements in astrophysical observations.

While interpretations of cosmic expansion may vary, such as the preference for framing the phenomenon as physical distance increments rather than spacetime fabric expansion, these distinctions do not undermine the fundamental premise of an evolving, dynamic cosmos. As of now, no alternative model has provided a comparable explanatory and predictive framework for the observable universe. Thus, while scientific exploration should always remain open to novel ideas, the theory of increasing distances between galaxies—whether interpreted as spacetime expansion or physical separation—remains the most reasonable and well-supported explanation for the universe’s large-scale behaviour.