The Planck Equation and the Limits of Energy Quantization:

Soumendra Nath Thakur

December 21, 2024

Abstract:

This paper explores the fundamental relationship between photon energy and frequency, encapsulated by the Planck equation E=hf, which has been pivotal in shaping quantum mechanics. It discusses the independence of the Planck equation from relativistic frameworks and its integration into the Planck scale, where quantum and cosmological phenomena converge. By examining energy quantization at the Planck scale, the text highlights the theoretical boundaries defined by Planck units, including Planck frequency, time, and length. The paper further explores the implications of reaching these limits, where current physical theories break down, leading to the necessity of new frameworks. The Planck frequency is emphasized as a crucial threshold that challenges established understandings of physics, offering a path toward a unified theory of fundamental forces.

Keywords:

Planck Equation, Energy Quantization, Planck Scale, Photon Energy, Quantum Mechanics, Planck Frequency, Quantum Gravity, Energy-Frequency Relationship, Wave-Particle Duality, Fundamental Physics, Cosmology, Quantum Field Theory,

1. The Planck Equation and Energy Quantization:

The Planck equation, E = hf, introduced by Max Planck in 1900, established a fundamental relationship between a photon’s energy (E) and its frequency (f), where h is Planck’s constant. This equation resolved the ultraviolet catastrophe by quantizing energy and became a cornerstone of quantum mechanics. It is foundational in linking energy and frequency, demonstrating that energy exists in discrete packets proportional to frequency, fundamentally shaping our understanding of the quantum world.

2. Independence of E=hf from Relativistic Frameworks

The Planck equation, introduced long before Einstein's theories of relativity (1905 and 1916), operates independently of relativistic concepts such as time dilation and spacetime curvature. It quantizes energy through a direct relationship between frequency and energy, remaining rooted in quantum mechanics without the need for relativistic adjustments. By focusing solely on the energy-frequency relationship, E=hf operates on its own merits, unaffected by the complexities of relativistic time transformations or spacetime warping.

3. The Planck Scale: A Universal Framework.

The Planck scale represents a universal framework for understanding the limits of physical phenomena, determined by five fundamental constants: c (speed of light), G (gravitational constant), ℏ (reduced Planck constant), kʙ (Boltzmann constant), and e (elementary charge). These constants define the Planck units—length, mass, time, temperature, and charge—which are used to describe extreme physical conditions. The Planck scale bridges quantum realms and cosmological phenomena, providing a foundation for theories like string theory. By connecting energy quantization and wave-particle duality with discrete measures of space and time, the Planck equation E=hf fits seamlessly into this framework, emphasizing its universal relevance across physical scales.

4. Energy Quantization and the Planck Scale:

The equation E=hf inherently aligns with the Planck scale, which defines discrete units of energy, frequency, and wavelength. The equation demonstrates energy quantization, with photons carrying energy in packets proportional to their frequency. The frequency f is linked to the photon's wavelength λ through the speed of light c, as f=c/λ, further reinforcing the wave-particle duality of photons. In terms of Planck units, the equation can be expressed as E ≈ Eᴘ⋅(f/fᴘ), where Eᴘ and fᴘ are the Planck energy and Planck frequency, respectively. This connection ensures dimensional consistency within the Planck framework, highlighting the quantum mechanical nature of energy at the Planck scale.

5. Planck Units and the Speed of Light:

The Planck length (ℓᴘ) and Planck time (tᴘ) are fundamental units that determine the speed of light c. The relationship c = ℓᴘ/tᴘ connects these two units, where Planck length, ℓᴘ ≈ 1.616 × 10⁻³⁵ meters and Planck time, tᴘ ≈ 5.391 × 10⁻⁴⁴ seconds. The speed of light, a cornerstone of quantum physics, governs the propagation of electromagnetic waves and establishes a fundamental connection between space, time, and energy. This intrinsic relationship ties together Planck units, reinforcing the coherence and dimensional consistency of the Planck scale, connecting fundamental constants to the structural framework within space and time and the nature of light.

6. Photons as Quantum Carriers of Electromagnetic Force:

Photons are the gauge bosons responsible for carrying the electromagnetic force across the entire spectrum of electromagnetic radiation. This spectrum includes radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays, ordered by increasing frequency. Within the visible light spectrum, human perception ranges from red (approximately 4 × 10¹⁴ Hz) to violet (approximately 8 × 10¹⁴ Hz ), with photons mediating the interactions between charged particles across these frequencies. The photon’s frequency is pivotal in determining its energy, as described by the Planck equation, E = hf. For instance, an emitting photon from a star might have an initial frequency of 6.0368 × 10¹⁴ Hz, placing it in the visible range. 

7. The Broad Frequency Range of Photons:

Visible light constitutes only a small segment of the electromagnetic spectrum, while photons span an extensive range of energy levels. Within this spectrum, gamma rays typically achieve frequencies as high as 10¹⁹ Hz, whereas radio waves exhibit much lower frequencies, around 10⁵ Hz. Remarkably, the highest observed gamma-ray frequencies can extend up to 10³⁰ Hz, highlighting the immense breadth of the electromagnetic spectrum. Beyond gamma rays, cosmic rays are theorized to reach even higher frequencies. At the theoretical Planck frequency, a photon’s energy becomes so extreme that it could collapse into a black hole, representing a fundamental boundary of our current understanding of physics. This wide frequency range underscores the photon’s dual wave-particle nature, its quantum mechanical properties, and its capacity to mediate electromagnetic interactions throughout the universe.

8. Planck Frequency: Theoretical Boundaries.

At the Planck frequency (fᴘ = 1/tᴘ), oscillatory phenomena reach theoretical limits. The angular Planck frequency (ωᴘ=2ϖfᴘ) is approximately 1.885 × 10⁴³ s⁻¹, while the standard Planck frequency (fᴘ) is 2.952×10⁴² Hz. At these frequencies, a photon’s energy (E = hfᴘ) approaches levels where gravitational effects dominate, potentially collapsing the photon into a black hole, marking the boundaries of current physical theories. The Planck frequency represents a fundamental upper limit for oscillatory phenomena in the universe. Beyond this frequency, the current understanding of physical laws breaks down, emphasizing the boundary defined by the Planck scale. This framework highlights the profound interplay between quantum mechanics and cosmological scales, anchoring the Planck equation E = hf in the realm of fundamental physics.

Note: The constant 2π serves as a consistent multiplier or divider when converting between angular frequency (ωp) and linear frequency (fp). This conversion essentially represents the process of expressing angular frequency in terms of linear frequency in hertz (Hz).

9. The Significance of Planck Frequency in Fundamental Physics

The Planck frequency (fᴘ) represents a fundamental limit in our understanding of oscillatory phenomena in the universe. Derived from the Planck angular frequency (ωᴘ) through the relationship ωᴘ=2ϖfᴘ, the Planck frequency is calculated as fᴘ = ωᴘ/2ϖ = 2.952 × 10⁴² Hz. This theoretical construct defines the upper boundary at which the laws of physics, as currently understood, cease to apply, marking the transition into regimes where quantum gravity effects dominate.

At the Planck frequency, the energy associated with a photon reaches the Planck energy (Eᴘ = hfᴘ), corresponding to an extreme energy density where spacetime becomes highly curved. The wavelength (λ) of such a photon approaches the Planck length (ℓᴘ ≈ 1.616 × 10⁻³⁵ m), and its oscillation period (T = 1/fᴘ) aligns with the Planck time (tᴘ ≈ 5.391 × 10⁻⁴⁴ s).

These scales signify the breakdown of classical and quantum mechanical laws, as neither general relativity nor quantum field theory adequately describes physics in such extreme conditions. The Planck frequency sets the threshold for phenomena where new theories, such as loop quantum gravity or string theory, are expected to provide insights.

10. Implications of the Planck Frequency

At the Planck frequency, the effects of quantum gravity become dominant, rendering the laws of general relativity and quantum mechanics inadequate in their current forms. The associated energy density surpasses that of a black hole, presenting challenges to the application of established physical laws, including thermodynamics. At this frequency, time and space scales approach the Planck time (tᴘ ≈ 5.391 × 10⁻⁴⁴ s) and Planck length (ℓᴘ ≈ 1.616 × 10⁻³⁵ m), where conventional physics—formulated for larger scales—struggles to remain valid.

The Planck frequency also disrupts conventional notions of causality, as time intervals near tᴘ blur the distinction between cause and effect. This extreme oscillatory regime challenges the boundaries of current theoretical frameworks, including the Standard Model and general relativity. Addressing these limitations requires new theories, such as loop quantum gravity or string theory, which aim to provide a unified understanding of physics at these scales.

In essence, the Planck frequency encapsulates the intersection of quantum mechanics and cosmology, providing a pivotal anchor in the ongoing quest to unify the fundamental forces of nature. Its exploration remains a cornerstone of theoretical physics, pointing toward the next frontier in our understanding of the universe.

Experimental Evidence for Negative Mass and Theoretical Implications:

"What experiment has been done to verify the existence of negative mass?"

Soumendra Nath Thakur
December 20, 2024

1. The Context of Negative Apparent Mass:

The concept of negative apparent mass (−Mᵃᵖᵖ) differs fundamentally from intrinsic negative mass. It arises as a contextual property, emerging from the equations of effective mass (Mᵉᶠᶠ) under extreme conditions. The term "apparent" signifies that this property is not an inherent attribute of the particle but is instead influenced by external factors.

Key insights include:

• Apparent mass: A dynamic result influenced by energy, momentum, and the interplay with external forces, not a static characteristic of matter.

• Negative apparent mass: Emerges under specific conditions, particularly when the energy contributions from potential and kinetic dynamics surpass the rest mass energy.

This theoretical framework aligns with phenomena where gravitational dynamics deviate from classical predictions, including dark energy interactions.

Reference: Observational research by A.D. Chernin et al., "Dark Energy and the Structure of the Coma Cluster of Galaxies," supports the interpretation of dark energy dynamics in systems where apparent mass plays a role.

2. "Matter to Antimatter" Transition:

The proposed transition from matter to antimatter-like behaviour under extreme conditions is unconventional but extends the understanding of particle dynamics. When negative apparent mass dominates, the following occurs:

• Structural disintegration: Negative apparent mass exerts pressure that challenges the electron's structural integrity. This pressure increases as the electron's velocity approaches the speed of light (c), rendering its rest mass negligible. This is a consistent mathematical prediction of physical consequences.

• Transition dynamics: The effective mass (Mᵉᶠᶠ) becomes dominated by (−Mᵃᵖᵖ), leading to repulsive (antigravitational) effects. The electron no longer adheres to conventional matter dynamics.

• Antigravity effects: As negative apparent mass dominates at light's speeds, repulsion from gravitational sources occurs. This behaviour aligns with the theoretical underpinnings of antimatter-like states in extreme conditions.

3. Gravitational Bound Systems and Structural Breakdown:

The inability of matter to survive as conventional matter at light's speeds in gravitationally bound systems highlights the interplay between −Mᵃᵖᵖ, and matter M:

• Increasing speed and Mᵃᵖᵖ: As the electron accelerates, Mᵃᵖᵖ grows while matter M diminishes. A tipping point is reached where structural forces are overwhelmed.

• Collapse or dissipation: At this point, the electron ceases to behave as traditional matter. Instead, it transitions to state resembling antimatter, characterized by antigravitational interactions.

4. Supporting Evidence and Theoretical Alignment:

While direct experimental validation of negative apparent mass remains an open frontier, theoretical consistency with extended classical mechanics offers promising pathways for exploration:

• Alignment with dark energy dynamics: The interpretation of negative apparent mass mirrors the influence of dark energy on cosmic expansion, as shown in the work of A.D. Chernin et al.

• High-energy phenomena: Observations of high-energy particles near black holes or data from particle accelerators could provide indirect evidence of these transitions.

5. Transition to Antimatter-like Behaviour:

The transition described is not conventional antimatter (as defined in particle physics, with opposite charge but identical mass). Instead, it represents a novel state governed by:

• Negative effective mass: This leads to repulsion from gravitational sources, creating antigravity effects.

• Dynamic behaviour under extreme at light's speeds, conventional properties of matter cease to apply, resulting in a fundamentally different state of existence.

Conclusion:

The theoretical framework for the "Matter to Antimatter" transition provides a robust model for understanding high-energy dynamics and structural transformations under extreme conditions. While experimental validation is pending, its consistency with extended classical mechanics and alignment with observed phenomena (e.g., dark energy effects) support its plausibility. Further research and experimentation are essential to substantiate these claims and deepen our understanding of particle behaviour near the speed of light.

Invalidating Relativistic Time Dilation: A Re-assessment of Time, Measurement Errors, and Cosmic Time.

Soumendra Nath Thakur 

ORCiD: 0000-0003-1871-7803

December 16, 2024

The explanation of time as presented in relativity is widely regarded as the best description of time, primarily due to its reliance on relativistic principles. This interpretation has remained influential and largely unchallenged since the publication of Einstein's theory of special relativity in 1905. However, recent research and advancements in scientific understanding challenge the relativistic notion of time.

Einstein's dismissal of the classical interpretation of time in favour of the relativistic framework went unopposed for decades. Yet, contemporary findings suggest that time does not dilate in the manner proposed by relativity. Instead, any perceived alteration in the natural progression of time should be treated as an error in time measurement rather than an actual dilation. Furthermore, the concept of time dilation inherently invites its counterpart—time contraction—when the influencing factors are reversed. This duality contradicts the fundamental principle that the scale of time (∆t) must remain constant. Any deviation, whether a dilation (t′) or contraction (-t′), leads to errors in time measurement, as standard clock mechanisms cannot accommodate these variations. A dilated time scale (∆t+t′) exceeds the standard scale, while a contracted time scale fails to complete it.

For instance, the clock face represents a fixed 360° cycle, symbolizing the uniform progression of time. A dilated time cannot fit within this 360° framework, while a contracted time would fall short of completing the cycle, resulting in measurement inaccuracies. Furthermore, while clock time is a representation of cosmic time, the relativistic interpretation focuses solely on clock time and violates the very essence of cosmic time.

Cosmic time is defined as the continuous and irreversible progression of existence and events through the past, present, and future, regarded as an integrated whole. It exists beyond spatial dimensions in the fourth dimension and progresses without reversal. Relativity, however, imposes an artificial ordering of events based on natural time, failing to recognize that existential events invoke conceptual time rather than natural time.

My research, supported by mathematical formulations and experimental evidence, challenges this relativistic perspective. I have explored time distortion through piezoelectric oscillator experiments, the human perception of time, and the role of entropy in defining time. These studies highlight flaws in the experiments supporting time dilation, which were biased and employed improper techniques. Instead of identifying the true cause of errors—namely, distortions in the wavelength of oscillations—these experiments prematurely concluded that time dilation was occurring.

Wavelength, being directly proportional to the time period, shows that errors in wavelength lead to errors in time measurement—not to time dilation. Relativistic time dilation fails to account for this fundamental relationship and overlooks the broader context of wavelength distortion, which is a more general phenomenon. Consequently, the concept of relativistic time dilation is fundamentally flawed in its understanding of time and its measurement. Time dilation is rather error in time reading.

Redefining 'Nothing': A Scientific Perspective on the Universe's Creation.

Soumendra Nath Thakur 

December 13, 2024

Religious individuals who strictly believe in divine creation often reject the idea that scientific laws, such as gravity, could spontaneously create the universe from nothing. Similarly, many philosophical thinkers argue that 'something' cannot emerge from 'nothing,' asserting that nothingness inherently lacks the capacity to produce existence.

However, both perspectives tend to overlook the nuanced interpretation of 'nothing' in an inter-dimensional context. As three-dimensional beings, our perception is inherently limited, and what we define as 'nothing' might merely reflect our inability to detect phenomena beyond our dimensional framework. For instance, dimensions below the Planck scale, imperceptible to human senses and instruments, might harbour vibrational energies, such as strings, which are mathematically plausible but empirically unverifiable due to our limitations.

This perspective is further supported by the understanding that the universe appears as a continuously fluctuating field of matter whose quanta are fermions, i.e., leptons and quarks, and a force field whose quanta are bosons, i.e., photons and gluons. All of these fields have zero-point energy. Even at absolute zero, atoms and molecules maintain some vibrational motion, known as zero-point energy. Moreover, the empty space of a vacuum also exhibits these properties. This suggests that what we perceive as 'nothing' is far from an empty void; instead, it is imbued with subtle, energetic fluctuations that could serve as the foundation for the emergence of existence.

In this light, the universe's creation from 'nothing,' as we perceive it, aligns with a scientific understanding that what appears as 'nothing' may, in fact, be a subtle, energetic substrate capable of generating existence.

"Because there is a law such as gravity, the Universe can and will create itself from nothing. Spontaneous creation is the reason there is something rather than nothing, why the Universe exists, why we exist. "It is not necessary to invoke God to light the blue touch paper and set the Universe going.

Stephen Hawking"

Exploring Energy, Existence, and Hypothetical Dimensions

December, 2024

Dear Mark Jagg,

Thank you for your intriguing perspective. Here's my opinion based on the points raised:

Existence as Vibration or Oscillation:

I agree with your assertion that all forms of existence, whether energetic or mass-based, inherently involve vibration or oscillation. This aligns with the fundamental principles of quantum mechanics, where oscillations and wave-like properties underpin reality. The Planck equation provides strong evidence for this energy-frequency relationship, reinforcing the notion of "existence vibration."

Primordial Energy and Dimensionality:

The idea of primordial energy existing without spatial dimensions resonates with theoretical physics, particularly in models that describe the pre-Big Bang state. While this phase remains hypothetical due to the lack of direct evidence, it is not speculative. The suggestion that energy must have a minimum dimension (frequency) adds a logical foundation to this hypothesis.

Energy as Trans dimensional:

The concept of energy manifesting across dimensions, as suggested by its wave-particle duality, holds merit. This "trans dimensional" nature can be viewed metaphorically, reflecting energy's adaptability in different frameworks. However, this idea would benefit from further clarification and rigorous theoretical development.

Dimensional Hopping Between EM and Mass Spectra:

I must respectfully challenge this idea, as it lacks empirical support. The photon is not composed of quarks, and it does not contain mass in the way that matter does. The electromagnetic spectrum and the mass spectrum operate on distinct principles, with photons being massless and non-convertible to mass. This "hopping" concept appears to misrepresent energy's interaction between these spectra.

Electro-Evolution and Atomic Structure:

The role of electromagnetic processes in shaping atomic structures is well-supported by Big Bang nucleosynthesis. This idea aligns with our understanding of the early universe's chemistry and the formation of the first elements.

Hydrogen as the First Atomic Element:

This statement is scientifically consistent, as hydrogen is indeed the simplest and most abundant element in the universe, formed shortly after the Big Bang.

In summary, while some aspects of your hypothesis align with established scientific principles, others, like "dimensional hopping," require more substantial evidence to gain acceptance. The idea of energy's inherent vibration and its foundational role in existence is both compelling and scientifically plausible.

Warm regards,

Soumendra Nath Thakur

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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