Clarification on Photon Mass and Energy Transfer in Atomic Absorption:

Photons are gauge bosons, not made of quarks, so they do not have rest mass. When a photon is absorbed by an electron in an atom, it transfers its energy to the electron, but the photon itself ceases to exist in its original form. However, the photon always remains as energy, even though it doesn't have mass in the traditional sense. A phonon, which is a quasiparticle representing quantized vibrations in a lattice, is also distinct from photons and doesn't have mass either.

Key Clarifications:

• Photon and mass: While photons have no rest mass, they do carry energy and momentum, which are related to their frequency and wavelength.
• Phonon: Phonons are not the same as photons. They are quasi-particles arising from lattice vibrations in a material and also do not have rest mass, but they are fundamentally different from photons.

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.

The Evolution of the Early Universe: From Atomic Formation to Galactic Development.

Soumendra Nath Thakur

December 10,2024

Stable atoms began to form in the universe approximately 380,000 years after the Big Bang. While the first elements—primarily hydrogen, helium, and trace amounts of lithium—were created within minutes of the Big Bang during a process known as Big Bang nucleosynthesis, it took hundreds of thousands of years for the universe to cool and expand enough for electrons to be captured by nuclei. This critical phase, known as recombination, allowed neutral atoms to form over a span of about 100,000 years cantered around the 380,000-year mark. The newly formed atoms entered their lowest energy states, releasing excess energy as photons. This released light persists as the cosmic microwave background (CMB), a faint glow that provides a snapshot of the universe in its infancy.

Galaxies began to form roughly one billion years after the Big Bang, which itself is estimated to have occurred 13.8 billion years ago. The first stars emerged a few hundred million years after the Big Bang during a period called the cosmic dawn. These stars coalesced into protogalaxies during the cosmic dark ages, a time lasting around 100 million years when hydrogen gas cooled and collected into dark matter halos. Early galaxies were smaller and more irregular than modern ones, and their continued evolution has been shaped by collisions and mergers. For instance, the Andromeda galaxy is currently on a collision course with the Milky Way, with the two expected to merge in the distant future.

The Big Bang primarily created hydrogen and helium, with trace amounts of lithium, but it left the universe devoid of heavier elements. These elements, including carbon, oxygen, and iron, were synthesized later in the cores of massive stars through nuclear fusion. About 150–200 million years after the Big Bang, the first stars formed from primordial gas clouds. These stars exhausted their hydrogen and helium fuel and forged heavier elements in their cores. The most massive stars ended their lives as supernovae, dispersing these heavier elements into the cosmos and enriching the interstellar medium. This process paved the way for the formation of subsequent generations of stars, planets, and eventually, life as we know it.

References:

[1] Peacock, J. A. (1999). Cosmological Physics. Cambridge University Press.

This textbook provides a comprehensive overview of cosmological phenomena, including the formation of atoms, galaxies, and elements in the early universe.

[2] Planck Collaboration (2020). Planck 2018 Results: Cosmological Parameters. Astronomy & Astrophysics, 641, A6.

The Planck mission's findings give precise measurements of the cosmic microwave background (CMB) and the timeline of early universe events.

[3] Carroll, B. W., & Ostlie, D. A. (2017). An Introduction to Modern Astrophysics. Cambridge University Press.

This resource explores stellar evolution, nucleosynthesis, and the development of cosmic structures like galaxies and stars.

Ensuring Objective Evaluation in Scientific Discourse

The merit of a scientific study lies in its internal consistency, mathematical rigor, and the potential for empirical validation, rather than its accessibility to human intuition or comprehension. Highlighting human limitations in understanding advanced concepts risks diverting attention from the study's foundational arguments, thereby underestimating its scientific value.

To maintain the integrity of scientific discourse, it is essential to use objective and neutral language, refrain from subjective judgments, and focus solely on the scientific merits of the study. This approach ensures a fair and unbiased evaluation, fostering a constructive exchange of ideas.

Periodicity and Phase Shift Dynamics between the Big Bang and Planck Time: A Micro-Scale Approach to Frequency and Time Shifts.

Soumendra Nath Thakur
ORCiD: 0000-0003-1871-7803
Correspondence: postmasterenator@gmail.com
DOI: http://dx.doi.org/10.13140/RG.2.2.29274.25285

December 08, 2024

Abstract:

This study investigates the applicability of micro-scale equations for frequency phase shift and time shift, specifically the equation T(deg) = x°/f·360°, which accounts for 1/360th of respective time periods, wavelengths, or energy values in standard units. The equation highlights its precision in analysing periodic phenomena at the Planck scale, with a focus on the Planck time (Tₚₗₐₙₖ) and its reciprocal relationship with Planck frequency and wavelength. By dividing the Planck time by a 1° phase shift of Planck time (1.498×10⁻⁴⁶ seconds), a near-complete 360° phase cycle is observed, offering insights into the temporal structure of the universe and its origins from the Big Bang. This framework underscores the interconnectedness between time, wavelength, and energy, emphasizing the significance of phase relationships in cosmology.

Keywords:

Planck time, frequency phase shift, time shift, Big Bang, micro-scale, periodicity, phase cycle, Planck units, wavelength, energy, cosmology, temporal structure, phase relationships

The power of the derived equation for frequency phase shift and time shift:

The applicability of the micro scale derived equations for frequency phase shift and time shift, capable of accounting for 1/360th of the respective time period, wavelength, or energy values when measured in standard units:

T(deg) = Δt = x°/f·360°

This derived equation showcases its power by providing a framework to calculate precise phase relationships in terms of time, wavelength, or energy values. This equation is applicable at the micro scale and is capable of accounting for 1/360th of these respective values when measured in standard units. This precision highlights its versatility in analysing the periodic nature of fundamental physical phenomena.

The Planck time (Tₚₗₐₙₖ) is a cornerstone of this framework, with its value defined as 5.391247(60) × 10⁻⁴⁴ seconds. The divisor, 1.498×10⁻⁴⁶ seconds, represents a 1° phase shift of Planck time, emphasizing its relevance at the Planck scale. Within the domain of Planck units, fundamental constants interrelate in a profound manner, allowing the Planck time to act as the smallest meaningful unit of time, while the Planck frequency (fP) serves as the highest possible frequency. This reciprocal relationship underscores the fundamental periodicity and interconnectedness of these units.

In this context, the equation demonstrates that 1/360th of Planck time (Tₚₗₐₙₖ) aligns with 1/360th of the Planck wavelength (λₚₗₐₙₖ) and corresponds to 1/360th of the time period of Planck frequency. This alignment reinforces the inherent periodic structure embedded within the Planck units.

When dividing 5.391247(60) × 10⁻⁴⁴ seconds by 1.498×10⁻⁴⁶ seconds, the exact quotient is approximately 359.8963°, leaving a remnant of approximately 1.3427 × 10⁻⁴⁶ seconds. This remnant, being nearly equal to the divisor, suggests that it can be divided approximately 360 times, reflecting a complete 360° phase cycle. This periodicity aligns closely with the foundational moment of t₀, the beginning of the Big Bang, offering a phase-oriented perspective on the temporal structure of the universe.

Human Perception of Zero and Hyper-Dimensions:

Human perception is inherently limited when dealing with abstract mathematical constructs such as zero and hyper-dimensions. A point, symbolized as '.', represents an exact spatial location without dimensionality, serving as a cornerstone of mathematical abstraction. Real numbers, extending infinitely in both positive and negative directions from zero on a one-dimensional number line, reflect precise mathematical consistency. Yet, translating these concepts into physical realities poses significant challenges.

For instance, humans struggle to perceive infinitesimally small values such as the Planck length (ℓP), far beyond the thresholds of perceptibility. Conversely, gamma rays, with detectable wavelengths of λ, highlight the stark disparity in scales that humans can observe. This limitation underscores the vast spectrum of physical phenomena lying outside direct human experience.

Furthermore, exploring hyper-dimensions beyond the familiar three-dimensional space introduces additional complexities. These dimensions defy intuitive comprehension, existing beyond conventional spatial boundaries. Despite these challenges, the interplay between zero, hyper-dimensions, and Planck-scale phenomena provides crucial insights into the fabric of the universe. By linking mathematical abstraction to physical realities, we gain a deeper appreciation of the intricate relationship between the observable and the imperceptible, paving the way for new frontiers in understanding the cosmos.

Conclusion

The derived equation for frequency phase shift and time shift underscores the periodicity inherent in Planck units. The calculation demonstrates that the Planck time (Tₚₗₐₙₖ) can be divided by a 1° phase shift of Planck time (1.498×10⁻⁴⁶ seconds) approximately 360 times, completing a near-perfect phase cycle. This result reveals a fundamental periodic structure in the temporal framework of the universe, suggesting a profound interconnectedness between time, wavelength, and energy. The alignment of this framework with a 360° phase cycle offers a deeper understanding of the origins of the universe and its temporal dynamics, reinforcing the significance of phase relationships in cosmology.

Discussion

This study presents a ground breaking perspective on the temporal framework of the universe by leveraging micro-scale equations for frequency phase shift and time shift. This discussion delves into the implications, potential applications, and limitations of the research.

Implications for Cosmology

The equation offers a novel approach to understanding periodic phenomena at the Planck scale, where the foundational units of time, frequency, and wavelength are intricately interrelated. The study reveals that the Planck time (Tₚₗₐₙₖ) can be divided approximately 360 times by a 1 phase shift of Planck time, culminating in a near-complete 360 phase cycle. This finding introduces a periodic structure within the Planck units, aligning closely with the initial moments of the universe's existence, specifically the Big Bang.

This periodicity challenges traditional notions of continuous time by suggesting a discrete, cyclic framework at micro scales. Such a framework could refine our understanding of early-universe physics, offering insights into the transition from quantum-scale phenomena to macroscopic cosmological dynamics.

Bridging Mathematical Abstraction and Physical Realities

By integrating the analysis of hyper-dimensions and infinitesimal values with Planck-scale phenomena, the study addresses the inherent disconnect between human perception and abstract mathematical constructs. Human perceptual limitations hinder the direct observation of Planck-scale phenomena, yet the study bridges this gap by linking these imperceptible scales to observable cosmic phenomena, such as gamma rays. This connection underscores the importance of mathematical abstraction in unveiling the universe's hidden structures.

Exploring hyper-dimensions introduces additional complexity but offers a richer tapestry for understanding the interplay between time, space, and energy. The study’s findings, rooted in precise phase relationships, could inspire advancements in theoretical physics and quantum cosmology, enabling deeper insights into dimensions beyond our three-dimensional experience.

Applications in Modern Physics

1. Quantum Mechanics and Cosmology: The derived equation and its implications for phase cycles could enhance our understanding of quantum oscillations and their influence on large-scale cosmic phenomena.

2. Energy Distribution in Early Universe: The periodic structure of Planck time may inform models of energy distribution during the Big Bang, refining simulations of the universe’s origins.

3. Gravitational Wave Analysis: Insights from phase relationships could aid in the detection and interpretation of gravitational waves, particularly those originating from the early universe.

Limitations and Future Directions

While the study presents a compelling framework, its reliance on the precision of Planck-scale constants requires meticulous validation. The near-complete but imperfect 360 phase cycle raises questions about residual discrepancies and their physical interpretations. Additionally, extending this framework to include hyper-dimensional dynamics necessitates further exploration to ensure coherence with existing physical theories.

Future research could:

• Expand on the implications of the residual remnant (1.3427 × 10⁻⁴⁶) in phase cycle calculations.

• Integrate these findings with quantum gravity theories to explore the unification of forces.

• Investigate experimental approaches for observing phase shifts at infinitesimal scales, potentially leveraging advancements in high-energy physics.

Conclusion

This study contributes significantly to our understanding of the temporal and periodic structure of the universe at its most fundamental level. By elucidating the interconnectedness between Planck units, time, and energy, it lays the groundwork for further exploration of the universe's origins and the profound relationship between mathematical abstraction and physical reality. The findings invite continued inquiry into the intricate dance of periodicity, energy, and dimensionality that defines the cosmos.

Reference:

[1] Thakur, S. N., & Bhattacharjee, D. (2023). Phase shift and infinitesimal wave energy loss equations - [v1]. www.preprints.org/manuscript/202309.1831/v1
[2] Thakur, S. N. Description of Planck Equation and Energy-Frequency Relationship. https://www.researchgate.net/publication/375416343
[3] Thakur, S. N. (2024). Unified Quantum Cosmology: Exploring Beyond the Planck Limit with Universal Gravitational Constants. Qeios, 26U31C https://doi.org/10.32388/26u31c
[4] Thakur, S. N. (2024). Why is 1° time interval (T) the smallest meaningful mathematical expression of the Planck frequency? ResearchGate https://doi.org/10.13140/RG.2.2.32358.40001
[5] Thakur, S. N. (2023). Quantum Scale Oscillations and Zero-Dimensional Energy Dynamics: ResearchGate. https://doi.org/10.13140/RG.2.2.36320.05124
[6] Thakur, S. N. (2023) et al. Energy Persistence Beyond Planck Scale. ResearchGate https://www.researchgate.net/publication/375488896/
[7] Thakur, S. N. Human's Imperceptions of Zero and Hyper-Dimension: Mathematical Abstraction and Physical Realities https://www.researchgate.net/publication/381514768

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