We believe that in nature, the rotational angular velocity of structural body cannot be infinite and should have a maximum limit value, denoted as Ωmax = c/2π, with units of rad/s, where c is the speed of light. It should be noted that the angular velocity referred to here is the rotational angular velocity of an object with a certain "structural shape" (such as a rigid body disk), rather than the "angular velocity" of a point (or particle) moving around another point in a pure mathematical (geometric) sense! Photons in vacuum are the "structural body" with the fastest rotational angular velocity (Ωmax = c/2π, unit: rad/s),Therefore, photons in vacuum have dual properties: they are both the fastest moving “particles” and the "structural body" with the fastest rotating angular velocity at the same time in nature!

You can also look at the dependence of relativistic and angular motion within the framework of the oscillations of a metaphysical pendulum.

Preprint Chaotic dynamics of an electron

Dear Pu Guangyi ,

The two substances, electromagnetic and ordinary matter, should not be considered in the same category... In some cases they behave similarly, but in other cases differently. Based on: the essence of natural phenomena is similar in many cases, but their expression is different. For example, this is the basis for solving the mystery of the phenomenon of ball lightning:

Preprint A villámok anyaga és a Föld térfázisának hiánya mint kulcsté...

Regards,

Laszlo

In fact, there may exist some potential connections between the photon angular velocity hypothesis and the Larmor clock model.

In the angular displacement spacetime (φ(τ)), Pu Guangyi suggests that the time τ should be described using a ​Larmor clock (Larmor Clock)

In fact, in a uniformly rotating reference frame, a "structure" does not necessarily have to be a rigid body. For example, an elastic disk under uniform rotation can have a constant deformation amount and maintain an unchanged shape in the rotating frame. In this case, it can be effectively regarded as a rigid body. This approach is known in engineering as the "rigidification principle." Therefore, combining the photon angular displacement hypothesis with the rigidification principle greatly expands its range of applicability.

The photon angular velocity hypothesis is still in its early stages and currently remains within the kinematic phase of the angular displacement spacetime φ(τ). It has not yet been extended to the dynamic phase (such as the “alternative mass-energy equation” in the angular displacement spacetime φ(τ). Ultimately, the theory aims to expand from uniform rotational frames to non-uniform rotational frames, thereby completing the theoretical framework of angular displacement spacetime. Therefore, it is neither comprehensive nor correct to directly compare the photon angular velocity hypothesis, which is still in the initial kinematic stage, to well-established theories such as special relativity, general relativity, and quantum mechanics, which have been developed for over a century! In quantum theory, the photon's “spin angular momentum” is considered an intrinsic property (with a value of ℏ=h2π), a quantized non-classical rotation unrelated to the macroscopic object's “rotational angular velocity.” Quantum mechanics denies that a photon, as a point particle, possesses a classical sense of rotational angular velocity. Its spin is a property in relativistic quantum field theory and is independent of spatial coordinates. Clearly, spin angular momentum is a dynamic concept, whereas the angular displacement spacetime φ(τ) currently does not involve the photon's spin angular momentum. Additionally, unlike macroscopic scenarios, at the microscopic scale, the photon's spin angular momentum in the angular displacement spacetime also faces the issue of “quantization.” Therefore, one cannot simply conclude that the photon angular velocity hypothesis (i.e., the constancy of photon angular velocity) is irreconcilably contradictory with the quantum notion of photon spin angular momentum. In the photon angular velocity hypothesis, angular velocity is defined as the first derivative of angular displacement φ(τ) with respect to time τ: ω=dφ/dτ​. Within this framework, a pure point mass has no rotational angular velocity, while general relativity studies point masses. Hence, besides differing research objects, the concept of “rotation” in general relativity and the rotation defined by Pu Guangyi are distinct; their definitions and meanings of “rotation” differ fundamentally.

This article: 'On the Alternative Special Theory of Relativity Applicable to Physical Theorems of Rotation in the Uniform Rotating Frames' is dedicated to the great theory of relativity. Happy 120th birthday to the theory of relativity!"

The Relationship between the Photon Angular Velocity Hypothesis and General Relativity:

1. Different Research Objects: In angular displacement spacetime, the research objects are "structured objects," whereas in General Relativity, the research objects are point masses.

2. Different Concepts of "Rotation": In the photon angular velocity hypothesis, angular velocity is defined as the first derivative of the angular displacement ϕ(τ) with respect to time τ: (ω = dϕ/dτ). Within this framework, a mere point has no rotational angular velocity. This differs entirely from the definition and content of "rotation" in General Relativity.

3. Conclusion: The "alternative special relativity" in angular displacement spacetime does not conflict with General Relativity.

Note: The "alternative special relativity" in angular displacement spacetime focuses on "structured objects," which are not necessarily rigid bodies! For example, in a uniformly rotating frame, an elastic disk with a constant deformation under uniform rotation will not change its shape, and can be equivalently treated as a rigid body in this case. This method, known as the "rigidification principle" in engineering, significantly expands the applicable scope of the photon angular velocity hypothesis by combining it with the rigidification principle.

The Similarities and Differences Between the Photon Angular Velocity Hypothesis and Quantum Mechanics on Photon Spin:

1. Common Ground on Point Particles: Quantum mechanics denies that a photon, as a point particle, has rotational angular velocity in the classical sense. In the photon angular velocity hypothesis, angular velocity is defined as the first derivative of angular displacement ϕ(τ) with respect to time τ: (ω = dϕ/dτ). Within this framework, a mere point particle has no rotational angular velocity, or its rotational angular velocity is considered zero. If the photon is treated as a point particle, the perspective of quantum mechanics aligns completely with angular displacement spacetime theory—both conclude that the photon has no rotational angular velocity. Of course, in Pu’s hypothesis, the photon is treated as a "structured entity" rather than a point particle, possessing a maximum angular velocity: Ωmax = c/2π.

2. Differences in Spin Angular Momentum: Quantum mechanics states that while photons lack rotational angular velocity, they have spin angular momentum (with a value of ℏ, where ℏ = h/2π) and emphasizes that "spin angular momentum" is an intrinsic property of photons. ◦ The photon angular velocity hypothesis proposes that photons have both the maximum rotational angular velocity Ωmax = c/2π and spin angular momentum. Since this hypothesis is still in its infancy, currently confined to the kinematic stage within angular displacement spacetime ϕ(τ) and not yet extended to the dynamical stage, it has not provided a definite numerical value for the photon’s spin angular momentum. Additionally, at the microscopic level, the spin angular momentum of photons in angular displacement spacetime will encounter the issue of "quantization," which remains unaddressed (again, due to the hypothesis being in its early stages).

3. Conclusion on Compatibility: For the reasons above, it is currently inappropriate to simply conclude that the photon angular velocity hypothesis (i.e., the constant angular velocity of photons) and the concept of "spin angular momentum" in quantum mechanics are irreconcilably contradictory.

If the hypothesis of the photon's angular velocity is experimentally confirmed, we will further extend the current kinematics in angular displacement spacetime to dynamics, and ultimately expand to the dynamics of variable angular velocity rotation. This will contribute to theoretical extensions (such as to variable angular velocity frames and quantum field scenarios). In this way, the complete theoretical framework for the angular displacement spacetime ϕ(τ) can be established. Therefore, the current key is to experimentally falsify or verify the hypothesis of a maximum angular velocity. In fact, as long as experiments confirm that a maximum angular velocity limit exists in nature—even if the maximum angular velocity limit value is not equal to c/(2π), that is, Ω_max ≠ c/(2π)—we can set Ω_max = k * c/(2π), where k is a constant coefficient. Under this condition, the theoretical framework based on the hypothesis of the photon's angular velocity remains valid.

The photon's angular frequency ν and angular velocity ω are two different concepts and should not be confused. The angular velocity is defined as: ω = dϕ/dτ. We consider the principle of the invariance of the speed of light (c) and the principle of the constancy of the photon's angular velocity (Ωₘₐₓ = c/(2π)) as two parallel universal laws in nature.

Additionally, in wave mechanics, such as in vibration and wave equations, ϕ is often used to represent the phase (typically combined with trigonometric functions like sine or cosine). In this context, the concept of phase velocity emerges. It is important to note that phase is not the same as angular displacement; similarly, phase velocity is not equivalent to angular velocity, and these concepts should not be confused with each other! Understanding these distinctions is crucial for avoiding confusion between concepts in wave mechanics and rotational dynamics, especially when relating physical concepts such as "maximum angular velocity" and "phase velocity."

We list the angular displacement spacetime (φ(τ)) and the linear displacement spacetime r(t) as two parallel spacetimes in nature, and take the falsifiable maximum angular velocity principle Ω max (Ω max = c/2π, unit: rad/s) as a universal limit, paralleling the speed of light c, thus forming the translation-rotation symmetry hypothesis.

Meanwhile, do not directly and casually use the concepts familiar in the linear displacement spacetime to judge phenomena in the angular displacement spacetime. For example, when discussing forces (including inertial forces such as centrifugal force and Coriolis force) in the angular displacement spacetime, the "force" in the angular displacement space is the moment of force (couple)! Additionally, do not directly apply the clock in linear displacement spacetime to angular displacement spacetime. For instance, on a uniformly rotating disk, two points A and B at different radii have different linear velocities, so according to special relativity, the time lapse t at the two points is different. However, according to the alternative special relativity, since the angular velocity is the same, the time τ lapse at both points is the same! Using the same clock from linear displacement spacetime would lead to contradictory conclusions! We define time as: Time = t + iτ, where t is the linear displacement clock and τ is the angular displacement clock. It is suggested that in the angular displacement spacetime, a "Larmor clock"-like device can be used to describe τ.

We list the angular displacement spacetime (φ(τ)) and the linear displacement spacetime r(t) as two parallel spacetimes in nature, and take the experimentally falsifiable maximum angular velocity principle Ω max (Ω max = c/2π, unit: rad/s) as a universal limit, juxtaposed with the speed of light c. We define the complex time as Time = t + iτ, where t is the clock in linear displacement and τ is the angular displacement spacetime, thus forming a symmetry hypothesis of translation-rotation.

Meanwhile, we emphasize: do not directly and arbitrarily apply the concepts familiar in the linear displacement spacetime r(t) to judge phenomena in the angular displacement spacetime (φ(τ)). For example, in the linear displacement spacetime r(t), if two places A and B are 20,000 kilometers apart, it means they are very distant; however, in the angular displacement spacetime (φ(τ)), distance is not measured in meters but in radians. Perhaps the same places A and B are "together" in the angular displacement spacetime (φ(τ)), meaning that the locality and non-locality in the linear displacement spacetime r(t) do not hold in the angular displacement spacetime (φ(τ))!

Additionally, in the linear displacement spacetime r(t), the transmission of information (such as changes in momentum) cannot exceed the speed of light c; similarly, in the angular displacement spacetime (φ(τ)), the transmission of information (such as changes in angular momentum) cannot exceed the maximum angular velocity (Ω max = c/2π). Therefore, observing changes in angular momentum far exceeding the speed of light in the linear displacement spacetime r(t) may be considered inconsistent with relativity and difficult to understand, but such phenomena are entirely normal in the angular displacement spacetime (φ(τ)) (since the change in angular momentum does not actually exceed c/2π). It is crucial to recognize this!

Reinterpretation of Quantum Entanglement Non-locality​

In the traditional ​linear displacement spacetime framework (r(t))​, the collapse of quantum entanglement appears as "​instantaneous action-at-a-distance," seemingly violating relativity’s light-speed limit. For example, two entangled particles separated by 20,000 km are considered "distant" in linear spacetime, yet the instantaneous collapse of entanglement remains experimentally uncontradicted by light-speed constraints.

If quantum entanglement properties correlate with ​rotational backgrounds​ (e.g., particle spin, photon polarization, and other angular momentum attributes), the phenomenon should be attributed to ​angular displacement spacetime (φ(τ))​. In this framework:

​Theoretical Implications & Experimental Prospects​

​Conclusion​

The angular displacement spacetime theory offers a new paradigm for rotational physics, including quantum entanglement and rotating-body time paradoxes. Its validity hinges on experimental confirmation of:

• The existence of ​Ω_max,
• The consistency of ​complex time frameworks.

If validated, it unifies phenomena previously deemed paradoxical; if falsified, relativity requires reassessment of these effects

The angular displacement space-time (φ(τ)) theory offers a unified framework that can explain both the singular behaviours in turbulence and the non-locality of quantum entanglement. What's crucial is that both of these explanations can be rigorously tested and disproven by experiments! Our work also bridges a long-standing conflict between quantum mechanics (especially the non-locality of quantum entanglement) and relativity (which emphasizes locality and the speed of light limit).

Regarding fluid mechanics, I plan to publish a specialized paper explaining the details of fluid turbulence in due course. In it, I'll mainly clarify a new hypothesis for how turbulence starts (one that doesn't rely on the Reynolds number) and explain why we see extreme nonlinearity and physical singularities emerge within turbulence. Looking at the phenomenon of turbulence, we're happy to observe that "complexity, when pushed to its limit, becomes simplicity." In a way, I also aim to indirectly validate the correctness of "Angular Displacement Space-Time Theory (φ(τ))" through its application in fluid dynamics.

Dear colleagues,

I am preparing to submit a preprint on fluid turbulence to arXiv in the category physics.flu-dyn, and I am currently seeking endorsement.

As a new contributor to the archive, I need an endorsement from an established author who has previously submitted to physics.flu-dyn. If you are willing to support my submission, I would sincerely appreciate your help.

Please feel free to contact me at: [email protected]

(The endorsement process requires only a single click via a link sent by arXiv.)

Thank you very much for your time and consideration.

Best regards,

Guangyi Pu

Jiangnan University

[email protected]

Maximal Rotational Velocity of Fluid Elements (ΩFluidMAX): A New Perspective on Turbulent Singularities

Puguangyi*

School of Mechanical Engineering，Jiangnan University, Wuxi 214122, China

E-mail：[email protected]；[email protected]

This work identifies a critical physical incompleteness in the classical Navier-Stokes (NS) equations: the absence of angular momentum conservation and inertial torque terms for fluid elements. While the NS equations successfully describe translational motion under the continuum assumption, they fail to capture the dynamics of strong rotational, nonequilibrium flows—such as those in turbulence.

To address this, I propose a testable physical hypothesis: the Maximum Rotational Angular Velocity of Fluid Elements (ΩFluidMAX). This upper bound is hypothesized to be determined by the speed of sound (a) and the characteristic length scale (ℓ) of the fluid element:  ΩFluidMAX = Kᵢ ⋅ 2a / πℓ

where Kᵢ is a dimensionless constant to be calibrated experimentally.

When external energy input drives a fluid element's rotation toward ΩFluidMAX, excess energy can no longer be stored as rotational kinetic energy and is forced to convert into thermal energy, pressure fluctuations, or wave energy (e.g., acoustic or shock waves). This leads to a sharp rise in local energy density—what I define as a *physical singularity*.

This mechanism offers a new physical interpretation of singularity formation in turbulence, providing a natural regularization that addresses both the mathematical "blow-up" problem and the physical energy dissipation process. It transforms the concept of singularity from an abstract mathematical divergence into an observable physical state.

The hypothesis calls for high-resolution experimental validation (e.g., ultra-high-speed PIV, quantum sensing) and has the potential to revolutionize turbulence modeling—enabling physics-driven subgrid-scale closures in RANS and LES, rather than empirical fitting.

Feedback from fluid dynamics, turbulence, and theoretical mechanics communities is welcome.

https://www.researchgate.net/publication/395012380_Maximal_Rotational_Velocity_of_Fluid_Elements_OFluidMAX_A_New_Perspective_on_Turbulent_Singularities

https://www.preprints.org/manuscript/202508.2019/v1

If ΩFluidMAX is experimentally confirmed, we can take a step further: establishing a deep - seated connection between ΩFluidMAX and the second law of thermodynamics (the law of entropy increase)!