Dual Mass Properties of Semi-Dirac Fermions: Theoretical Insights and Technological Implications

This study provides a theoretical explanation of semi-Dirac fermions using the extended classical mechanics framework, emphasizing the duality of mass properties and their implications for technological advancements.

Soumendra Nath Thakur, Tagore's Electronic Lab, WB. India 

January 11, 2025.

Abstract

Semi-Dirac fermions are unique quasiparticles that exhibit dual mass properties, being massless in one direction and massive in another. This phenomenon is explained using the extended classical mechanics framework, which distinguishes the behaviour of particles with rest mass (Mᴍ > 0) from those that are massless (Mᴍ = 0). For particles with rest mass, the effective mass (Mᵉᶠᶠ > 0) results in forces aligned with external gravitational influences, ensuring classical motion. Conversely, massless particles with negative effective mass (Mᵉᶠᶠ​ < 0) experience forces opposing gravitational fields. This duality underpins the behaviour of semi-Dirac fermions, which were recently observed in zirconium silicon sulphide (ZrSiS) crystals. The discovery, published in Physical Review X by researchers at Penn State and Columbia University, marks a significant advancement in condensed matter physics and offers exciting potential for technological innovations, including quantum devices, batteries, and sensors.

Description 

The following description provides the explanation of the dual mass properties of semi-Dirac fermions within the framework of extended classical mechanics, their experimental confirmation in ZrSiS crystals.

Semi-Dirac fermions exhibit a unique duality in their mass properties, being massive in one direction and massless in another, for reasons rooted in the extended classical mechanics framework.

For particles with rest mass Mᴍ > 0:

The force equation is expressed as:

F = (Mᴍ − Mᵃᵖᵖ)⋅aᵉᶠᶠ

Where Mᴍ > 0 represents the rest mass, Mᵃᵖᵖ denotes the apparent mass, and Mᵉᶠᶠ = (Mᴍ − Mᵃᵖᵖ) is the effective mass. For such particles, an effective mass Mᵉᶠᶠ > 0 leads to a positive force aligned with the external gravitational influence, ensuring classical motion under gravitational forces.

For massless particles with Mᴍ = 0:

The force equation simplifies to: 

F = −Mᵉᶠᶠ ⋅ aᵉᶠᶠ

Where Mᵉᶠᶠ = −Mᵃᵖᵖ < 0. Here, the negative effective mass results in a force opposing the direction of the external gravitational field, distinguishing their behaviour from particles with positive effective mass.

This distinct behaviour of massless particles aligns with the characteristics of semi-Dirac fermions, which exhibit massless motion in one direction while being massive in another. This duality has been experimentally confirmed in zirconium silicon sulphide (ZrSiS) crystals, a semi-metal material. First theorized 16 years ago, semi-Dirac fermions have now been directly observed, representing a significant milestone in condensed matter physics.

A research team from Penn State and Columbia University identified these quasiparticles and published their ground breaking findings in the journal Physical Review X. Their discovery holds immense promise for advancing emerging technologies, such as next-generation batteries and highly sensitive sensors. By bridging the gap between massless and massive particle behaviour, semi-Dirac fermions could provide a foundation for transformative quantum and technological applications, opening new horizons in material science and quantum mechanics.

Conclusion

The observation of semi-Dirac fermions in ZrSiS crystals represents a milestone in the study of quasiparticles and their dual mass properties. Using the framework of extended classical mechanics, their unique behaviour—massless in one direction and massive in another—has been effectively explained. This discovery not only validates theoretical predictions made over 16 years ago but also opens new avenues for research in material science and quantum mechanics. The potential applications of semi-Dirac fermions in advanced technologies such as sensors and energy storage systems underscore their importance. By bridging the gap between massless and massive particle behaviour, this breakthrough paves the way for transformative innovations, highlighting the far-reaching implications of fundamental research in physics.

Links to the discovery, research paper:

1.https://doi.org/10.1103/PhysRevX.14.041057

2.https://modernsciences.org/new-particle-shifts-massless-massive-states-semi-dirac-fermion-december-2024/

References: 

[1]. Thakur, S. N. (2024). Extended Classical Mechanics: Vol-1 - Equivalence Principle, Mass and Gravitational Dynamics. doi: https://doi.org/10.20944/preprints202409.1190.v3

[2]. Thakur, S. N. (2024) Photon Dynamics in extended classical mechanics: Effective mass, negative inertia, momentum exchange and analogies with Dark Energy. doi: 10.20944/preprints202411.1797.v1

[3]. Thakur, S.N. (2024) A symmetry and conservation framework for photon energy interactions in gravitational fields. doi: 10.20944/preprints202411.0956.v1

[4]. Thakur, S.N. (2024) Photon interactions with external gravitational fields: True cause of gravitational lensing. doi: 10.20944/preprints202410.2121.v1

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Comment:

The above presentation consistently evaluates the alignment of the discovery research with the theoretical focus, highlighting the following:

Theoretical Framework:

The  above presentation acknowledges the accurate emphasis on the extended classical mechanics framework, which forms the foundation of the explanation for the dual mass properties of semi-Dirac fermions.

Mass Properties:

The  distinction  between   rest  mass (Mᴍ > 0) and massless (Mᴍ = 0) particles, along with the roles of effective mass (Mᵉᶠᶠ > 0 and Mᵉᶠᶠ < 0) is clearly reiterated,  aligning with the presented work.

Observations and Implications:

The above presentation appropriately notes the reference to semi-Dirac fermions' experimental observation in ZrSiS crystals and their technological potential, confirming the coherence of these aspects with the presentation.

Focus:

It recognizes the presentation's intentional narrowing of focus to theoretical insights and technological implications, while omitting experimental details and topological aspects, which were not central to the scope of the presentation.

Conclusion:

The conclusion in the above presentation reaffirms the consistency, clarity, and relevance of the presentation, accurately reflecting the theoretical and applied aspects while justifying the selective omission of experimental specifics.

Final Assessment:

The above presentation effectively supports and reinforces the coherence and focus of the Dual Mass Properties of Semi-Dirac Fermions: Theoretical Insights and Technological Implications. It aligns with the intentions and scope of the presentation while maintaining clarity and logical flow.

Dark Matter, Higher Dimensions, and the Vibrational Essence of the Universe:

Johnny5 Alive questioned, "Dark matter: Could it just be some influence from a different dimension, which would explain never finding it?"

January 09, 2025

Dear Johnny5 Alive,

You have raised an abstract question that holds merit but requires further refinement for clarity. Let me guide you through the necessary enhancements in your question.

1. Exploring "Different Dimensions"

Before delving into hyper-dimensions, let’s examine the term “different dimension” that you mentioned. This phrase could refer to dimensions beyond or below the three spatial dimensions we naturally observe in our universe.

• Hyper-dimensions: These refer to dimensions beyond the three spatial dimensions and are commonly explored in theoretical physics, often associated with higher-dimensional models like string theory.

• 0ₜₕ Dimension: This pertains to systems with fewer than three spatial dimensions, often conceptualized at scales well below the Planck length (ℓₚ ≈ 1.616255 x 10⁻³⁵ m), a range imperceptible to human senses.

Perceptibility of Dimensions

Both hyper-dimensions and the 0ₜₕ dimension are beyond human perception. Even within our familiar three spatial dimensions, scales below the Planck length are permanently imperceptible. Examples in this realm include:

• One-dimensional black holes

• Strings in string theory

Such phenomena exist in a regime far removed from observable scales, challenging our ability to comprehend them naturally.

2. Gamma Rays and Planck Scales

Gamma rays represent the highest-frequency electromagnetic (EM) waves. While ultra-high-energy gamma rays can exceed 2.42 × 10²⁸ Hz, they remain significantly below the Planck frequency (fᴘ ≈ 2.952×10⁴² Hz). Even the most powerful gamma rays detected, such as those at 10³⁰ Hz in 2024 by China’s LHAASO, fall short of Planck scales.

3. String Theory: Vibrating Strings and Fundamental Frequencies

String theory posits that the universe’s fundamental components are tiny, vibrating strings. These strings are hypothesized to vibrate at frequencies calculated using the formula:

f = n/2L√T/m

​

Where:

• f: Frequency of vibration

• T: Tension in the string

• L: String length

• n: Number of harmonics

Key properties of strings include:

• String Length: In the given model, the calculated string length (3.232 x 10⁻³⁴ m) is approximately 20 times larger than the Planck length (ℓₚ ≈ 1.616255 x 10⁻³⁵ m). This ratio aligns with popular string theory models, such as Type I and heterotic string theory, where ℓₛ/ℓₚ is predicted to be 20–30 times ℓₚ.

• Planck Frequency (fᴘ) 2.952×10⁴² Hz: Represents the highest possible frequency, associated with the smallest wavelength.

4. Sample Calculation

Using the specific equation for a vibrating string’s fundamental frequency:

f= c/2ℓₛ

Where c is the speed of light, we find:

f = 299792458 m/s / 2×(10×1.616×10⁻³⁵ m)

f ≈ 9.276 x 10⁴¹ Hz

For the corresponding wavelength:

λ = c/f yields

λ ≈ 3.232 x 10⁻³⁴ m

Conclusion

The calculated string length (ℓₛ) is approximately 20 times larger than the Planck length (ℓₚ). This refined understanding aligns with string theory's predictions and highlights the extraordinary scales involved in these theoretical constructs.

By refining the scope of your question and clarifying these concepts, we can delve deeper into the exciting realms of higher dimensions, Planck scales, and string theory.

5. The Law of Vibration

The Law of Vibration asserts that everything in the universe—whether visible or invisible—when reduced to its most fundamental essence, consists of pure energy or light. This energy resonates and manifests as vibratory frequencies or patterns.

• Universal motion: Nothing in the universe is at rest. All things, including living beings like you and me, vibrate continuously at atomic and subatomic levels.

• Vibratory essence: The universe and all that it contains are ultimately expressions of pure vibratory energy, taking on various forms.

Matter as Vibrational Energy

Despite our perception of solidity, the universe lacks true "solidity." Matter, as we perceive it, is merely energy in a specific state of vibration. This perspective highlights the interconnectedness of all things, where existence is a continuum of vibrational energy.

Energy Across Dimensions

Energy exhibits different behaviours in different dimensions: 

• Primordial energy: Before the Big Bang, energy likely existed without events or dimensions as we know them. In the absence of interactions, there was no time or space in our conventional understanding.

• Time and space: Both require the interplay of existence and events. Primordial energy, therefore, existed outside the three-dimensional framework of our universe.

• Higher dimensions: Energy in dimensions beyond our own may behave in fundamentally different ways, revealing properties and dynamics that challenge current scientific understanding.

Conclusion

To answer the question, "Can different forms of energy exist in different dimensions?" the response is an unequivocal "Yes." Primordial energy that existed before the Big Bang, as well as energy in higher dimensions, may behave uniquely, showcasing the adaptability and versatility of vibrational energy in varied dimensional realms.

6. Dark Matter and Dark Energy

As previously discussed, energy behaves differently across dimensions. The Law of Vibration suggests that all entities in the universe—visible or invisible—consist of pure energy or light when reduced to their most fundamental nature. This energy resonates as vibratory frequencies or patterns.

Dark matter and dark energy, though imperceptible to us, likely exist in energetic forms as vibratory frequencies or patterns in dimensions beyond our perception. Their behaviours transcend our current understanding, emphasizing the dynamic and versatile nature of vibrational energy across multiple dimensions. 

Best regards,

Soumendra Nath Thakur

Relativistic re-interpretation of curvature in spacetime:

Soumendra Nath Thakur

December 29, 2024

Photons do not possess rest mass, but this does not imply they lack effective mass. In fact, photons have an effective mass given by m_eff = E/c ^2 . Moreover, photons exhibit a negative apparent mass, which exceeds their matter mass, resulting in a net negative effective mass.

This negative effective mass generates an anti-gravitational force, enabling photons to escape gravitational wells.

The idea of spacetime curvature as a manifestation of gravity fundamentally contradicts the concept of gravity as a classical force. Both concepts—gravity as a force and gravity as spacetime curvature—cannot simultaneously hold validity in scientific reasoning.

Experimental evidence and observations strongly support gravity as a force, while the notion of physical spacetime curvature producing tangible gravitational effects lacks empirical grounding. The concept of spacetime curvature stems from speculative assumptions rather than validated scientific principles.

Since no human can physically realize or measure spacetime curvature, the relativistic interpretation of gravity should be reconsidered, favoring a framework grounded in observable and verifiable phenomena.

Analytical Insights into Time Dilation and Time Distortion:

Soumendra Nath Thakur

December 28, 2024

Abstract

This study, Analytical Insights into Time Dilation and Time Distortion, provides a critical examination of the relativistic and conceptual interpretations of time, serving as a supplementary resource to the research titled Effect of Wavelength Dilation in Time - About Time and Wavelength Dilation. It investigates the distinction between time dilation—a relativistic phenomenon—and time distortion, a conceptual deviation defined as t±Δt, which accommodates both dilation and contraction.

Time dilation, introduced in Einstein’s theory of relativity, describes the difference in elapsed time observed between two reference frames due to relative velocity or gravitational effects. Conversely, time distortion highlights perceived temporal alterations caused by measurement inaccuracies rather than fundamental changes in time itself. This study emphasizes that relativistic time dilation (t′) does not equate to time distortion (±Δt), as t′≠±Δt, underscoring the distinct scientific frameworks of these concepts.

The research also explores time measurement within the standardized 360° framework of clocks, which provides a geometric and intuitive structure for representing temporal progression. This framework ensures uniformity, with 30° corresponding to an hour, 6° to a minute, and 6° to a second, maintaining consistency across temporal units. However, the study identifies inherent challenges in reconciling time dilation and contraction within this fixed framework, exposing limitations in accommodating relativistic variations.

Further critique of Einstein’s relativistic framework challenges its dominance in physics, suggesting that perceived changes in time’s progression are better understood as errors in time measurement. By prioritizing localized relativistic effects, the theory inadvertently overlooks the intrinsic constancy and uniformity of cosmic time—a universal continuum governing natural processes.

Lastly, the study connects time with oscillatory motion through the expression T=2π/ω, linking time to energy and frequency via Planck’s constant. This reinforces the broader physical understanding of time as a fundamental dimension tied to energy and motion, surpassing the constraints of relativistic interpretations.

This work, grounded in theoretical critique and geometric representation, provides a nuanced perspective on time, challenging established relativistic paradigms while advancing the discourse on temporal measurement and interpretation.

Comment: This study is a supplementary resource of the research titled, "Effect of Wavelength Dilation in Time. - About Time and Wavelength Dilation."

In the framework of special relativity, time dilation refers to the difference in elapsed time as measured by two observers, typically arising from differences in relative velocity or gravitational influence. For example, a clock in motion relative to an observer appears to tick more slowly than one at rest. This physical phenomenon, first introduced by Albert Einstein, has been central to relativistic physics for decades.

On the other hand, time distortion, represented mathematically as t±Δt, encapsulates the notion of perceived temporal alteration, where Δt can signify either an increase or decrease in time’s progression relative to a reference frame. Time dilation and time distortion are distinct: relativistic time dilation (t′) does not equate to ±Δt, as t′ ≠ ±Δt. Specifically, time dilation (t′) involves a systematic slowing of time for a moving observer, while time distortion implies a bidirectional deviation (either dilation or contraction), potentially leading to inaccuracies in time measurement.

This distinction highlights a critical issue: the direct comparison of t′ with ±Δt is scientifically incorrect. Time dilation is a relativistic effect described within the confines of Einstein’s theory, whereas time distortion relates to deviations observed in standardized timekeeping.

Time Measurement and the 360° Framework

Clocks are meticulously designed using standardized mechanisms to represent universal time (e.g., Coordinated Universal Time, UTC) with precision and consistency. Each ideal clock is calibrated to measure proper time (t), the temporal progression experienced in its local inertial frame. Within the standardized 360° framework of timekeeping:

• Each 30° segment represents one hour, completing a 12-hour cycle in 360° (30°×12=360°).

• Each 6° segment signifies one minute, culminating in 60 minutes per 360° (6°×60=360°).

• Similarly, each 6° division also denotes one second, amounting to 60 seconds per minute (6°=360°/60).

This geometric division ensures a consistent and intuitive representation of time across all temporal units, maintaining uniformity within the standardized clock framework.

The Inherent Challenges of Time Dilation and Contraction

The concept of time dilation inherently implies its counterpart—time contraction—when the conditions inducing dilation are reversed. However, this duality presents a contradiction: the scale of time (Δt) must remain constant. Any deviation, whether dilation (t′>t) or contraction (t′<t), introduces inaccuracies in measurement, as standard clock mechanisms are incapable of accommodating such variations.

• A dilated time scale (Δt+t′) exceeds the standardized cycle, disrupting uniformity.

• A contracted time scale (Δt-t′) falls short of completing the temporal framework, leading to incomplete cycles.

For instance, a clock face, operating within a fixed 360° framework, symbolizes the uniform progression of time. A dilated time cannot fit seamlessly into this cycle, while a contracted time fails to complete it. These discrepancies reveal the limitations of relativistic interpretations, which focus on clock time rather than the broader, unaltered continuum of cosmic time.

Critique of Relativistic Time

Einstein’s relativistic framework replaced the classical interpretation of time, emphasizing time dilation and its dependence on motion and gravity. While this paradigm dominated physics for decades, contemporary insights suggest that time does not dilate as proposed by relativity. Instead, any perceived alteration in time’s natural progression is better understood as an error in time measurement, not an actual modification of time itself.

Relativistic interpretations emphasize clock time but fail to account for the essence of cosmic time—the universal, unaltered continuum governing the natural universe. By prioritizing localized relativistic effects, these interpretations inadvertently diverge from the intrinsic uniformity and constancy of cosmic time.

Time and Oscillatory Motion

In physics, time (T) is often linked to the period of oscillation, defined as T=2π/ω, where ω is the angular frequency. The reciprocal of the period, or frequency (f), is given by f=1/T=ω/2π=v/λ=E/h, where h is Planck’s constant, and f, v, λ, T, and E represent frequency, velocity, wavelength, time period, and energy, respectively.

This connection underscores the fundamental nature of time as a dimension intimately tied to motion and energy, offering a broader perspective that transcends the limitations of relativistic time dilation.

Reference:

[1] Thakur, S. N. & Tagore’s Electronic Lab. (2023). Effect of Wavelength Dilation in Time. - About Time and Wavelength Dilation. In EasyChair Preprint. http://dx.doi.org/10.13140/RG.2.2.34715.64808

[2] Thakur, S. N., Samal, P., & Bhattacharjee, D. (2023). Relativistic effects on phaseshift in frequencies invalidate time dilation II. TechRxiv. https://doi.org/10.36227/techrxiv.22492066.v2

The contrast between gravitational lensing and Plasma interaction of photon:

Soumendra Nath Thakur 

December 26, 2924

Gravitational lensing, as the term suggests, arises from the interaction between electromagnetic radiation (photons) and a gravitational field. Specifically, it involves the symmetric energetic interaction of photons with the gravitational field, resulting in balanced blueshifts and redshifts of the photon’s energy. This symmetry causes the photon’s trajectory to curve, deviating from its linear path during transit through the gravitational field. Once the photon exits the field, it retains its energy and resumes its inherent linear trajectory.

The question of whether energetic plasma can cause gravitational lensing must be examined by understanding how photons interact with ionized gas during transit. Unlike the photon-gravitational field interaction, which is energetically symmetric, the interaction between photons and ionized plasma is fundamentally different. This is an electromagnetic-electromagnetic interaction where photons interact with charged particles (electrons and ions) via electromagnetic forces.

Such interactions are inherently asymmetric and often involve absorption, scattering, or redistribution of photon energy due to the charged nature of plasma constituents. Consequently, these processes result in photon scattering rather than the curvature of the photon’s path seen in gravitational lensing.

While hot plasma may facilitate symmetric energy exchanges, it primarily causes photon scattering rather than maintaining the conditions necessary for gravitational lensing. This distinction highlights that the nature of photon interactions with ionized plasma differs fundamentally from the interaction with a gravitational field.

Electrons and ions, due to their electric charge, always interact with photons via electromagnetic forces. However, this interaction leads to scattering and absorption, making it unlikely that hot plasma could produce the phenomenon of gravitational lensing.

In conclusion, photon interaction with a gravitational field and photon interaction with ionized plasma are fundamentally different processes. Gravitational lensing remains a unique phenomenon tied to the symmetric energetic interaction of photons with gravitational fields, distinct from the asymmetric scattering processes characteristic of plasma interactions.