Conservation Laws - Science topic

I need to find support prior to submission because the journal editors are sabotaging my paper’s chances by refusing to even do a peer review of what is a perfect qualified and rigorous paper.

They dishonestly bypass the quality control that would have my controversial paper published.

I need a professor of physics with the balls to kick the ass of the system into the next epoch in the name of science.

My paper Angular Energy shows that fundamentals need to be overturned.

The paper has never been genuinely shown to contain any error, because I have honed it to perfection over years of unforeseen and unfortunately hostile debate, by listening to everything.

The only thing it needs is to be published in a peer reviewed journal in order to be taken seriously and it must be taken seriously.

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

Match 16, 2025

Abstract:

Extended Classical Mechanics (ECM) refines the classical understanding of force, energy, and mass by incorporating the concept of negative apparent mass. In ECM, the effective force is determined by both observable mass and negative apparent mass, leading to a revised force equation. The framework introduces a novel energy-mass relationship where kinetic energy emerges from variations in potential energy, ensuring consistency with classical conservation laws. This study extends ECM to massless particles, demonstrating that they exhibit an effective mass governed by their negative apparent mass components. The connection between ECM’s kinetic energy formulation and the quantum mechanical energy-frequency relation establishes a fundamental link between classical and quantum descriptions of energy and mass. Furthermore, ECM naturally accounts for repulsive gravitational effects without requiring a cosmological constant, reinforcing the interpretation of negative apparent mass as a fundamental aspect of energy displacement in gravitational fields. The framework is further supported by an analogy with Archimedes’ Principle, providing an intuitive understanding of how mass-energy interactions shape particle dynamics. These findings suggest that ECM offers a predictive and self-consistent alternative to relativistic mass-energy interpretations, shedding new light on massless particle dynamics and the nature of gravitational interactions.

Keywords:

Extended Classical Mechanics (ECM), Negative Apparent Mass, Effective Mass, Energy-Mass Relationship, Kinetic Energy, Massless Particles, Quantum Energy-Frequency Relation, Archimedes’ Principle, Gravitational Interactions, Antigravity

Extended Classical Mechanics: Energy and Mass Considerations

1. Force Considerations in ECM:

The force in Extended Classical Mechanics (ECM) is determined by the interplay of observable mass and negative apparent mass. The force equation is expressed as:

F = {Mᴍ +(−Mᵃᵖᵖ)}aᵉᶠᶠ

where: Mᵉᶠᶠ = {Mᴍ +(−Mᵃᵖᵖ)}, Mᴍ ∝ 1/Mᴍ = -Mᵃᵖᵖ

Significance:

- This equation refines classical force considerations by incorporating negative apparent mass −Mᵃᵖᵖ, which emerges due to gravitational interactions and motion.

- The effective acceleration aᵉᶠᶠ adapts dynamically based on motion or gravitational conditions, ensuring consistency in ECM's mass-energy framework.

- The expression (Mᴍ ∝ 1/Mᴍ) provides a self-consistent relationship between observable mass and its apparent counterpart, reinforcing the analogy with Archimedes' principle.

2. Total Energy Considerations in ECM:

Total energy in ECM consists of both potential and kinetic components, adjusted for mass variations:

Eₜₒₜₐₗ = PE + KE

By incorporating the variation in potential energy:

Eₜₒₜₐₗ = (PE − ΔPE) + ΔPE

where:

- Potential Energy: PE = (PE - ΔPE)

- Kinetic Energy:( KE = ΔPE)

Since in ECM, (ΔPE) corresponds to the energy displaced due to apparent mass effects:

Eₜₒₜₐₗ = PE + KE

⇒ (PE − ΔPE of Mᴍ) + (KE of ΔPE) ≡ (Mᴍ − 1/Mᴍ) + (-Mᵃᵖᵖ)

Here, Potential Energy Component:

(PE − ΔPE of Mᴍ) ≡ (Mᴍ − 1/Mᴍ)

This represents how the variation in potential energy is linked and identically equal to mass effects.

Kinetic Energy Component:

(KE of ΔPE) ≡ (-Mᵃᵖᵖ)

This aligns with the ECM interpretation where kinetic energy arises due to negative apparent mass effects.

Significance:

- Ensures energy conservation by explicitly including mass variations.

- Demonstrates that kinetic energy naturally arises from the variation in potential energy, aligning with the effective mass formulation.

- Strengthens the analogy with fluid displacement, reinforcing the concept of negative apparent mass as a counterpart to conventional mass.

3. Kinetic Energy for Massive Particles in ECM:

For massive particles, kinetic energy is derived from classical principles but adjusted for ECM considerations:

KE = ΔPE = 1/2 Mᴍv²

where:

Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ)

Significance:

- Maintains compatibility with classical mechanics while integrating ECM mass variations.

- Reflects how kinetic energy is influenced by the effective mass, ensuring consistency across different gravitational regimes.

- Provides a basis for extending kinetic energy considerations to cases involving negative apparent mass.

4. Kinetic Energy for Conventionally Massless but Negative Apparent Massive Particles:

For conventionally massless particles in ECM, negative apparent mass contributes to the effective mass as follows:

Mᵉᶠᶠ = −Mᵃᵖᵖ + (−Mᵃᵖᵖ)

Since in ECM:

Mᴍ ⇒ −Mᵃᵖᵖ

it follows that:

Mᵉᶠᶠ = −2Mᵃᵖᵖ

Significance:

- Establishes that even conventionally massless particles possess an effective mass due to their negative apparent mass components.

- Provides a self-consistent framework that supports ECM's interpretation of mass-energy interactions.

- Highlights the role of negative apparent mass in governing the energetic properties of massless particles.

5. Kinetic Energy for Negative Apparent Mass Particles, Including Photons:

For negative apparent mass particles, such as photons, kinetic energy is given by:

KE = 1/2 (−2Mᵃᵖᵖ)c²

where:

v = c

Since:

ΔPE = −Mᵃᵖᵖ.c²

it follows that:

ΔPE/c² = −Mᵃᵖᵖ

Thus:

KE = ΔPE/c² = −Mᵃᵖᵖ

Significance:

- Establishes a direct relationship between kinetic energy and the quantum mechanical frequency relation.

- Demonstrates that photons, despite being conventionally massless, exhibit kinetic energy consistent with ECM’s negative apparent mass framework.

- Reinforces the view that negative apparent mass plays a fundamental role in governing mass-energy interactions at both classical and quantum scales.

6. ECM Kinetic Energy and Quantum Mechanical Frequency Relationship for Negative Apparent Mass Particles:

KE = ΔPE/c² = hf/c² = −Mᵃᵖᵖ

This equation establishes a direct link between the kinetic energy of a negative apparent mass particle and the quantum energy-frequency relation. The expression ensures consistency with quantum mechanical principles while reinforcing the role of negative apparent mass in energy dynamics.

7. Effective Mass and Apparent Mass in ECM:

In ECM, the Effective Mass represents the overall mass that is observed, while the Negative Apparent Mass (−Mᵃᵖᵖ) emerges due to motion or gravitational interactions. This distinction provides deeper insight into how mass behaves dynamically under varying conditions, differentiating ECM from conventional mass-energy interpretations.

8. Direct Energy-Mass Relationship in ECM:

hf/c² = −Mᵃᵖᵖ

This equation is inherently consistent with dimensional analysis, showing that negative apparent mass naturally arises from the energy-frequency relationship without requiring any extra scaling factors. This highlights ECM's compatibility with established quantum mechanical formulations and reinforces the role of negative apparent mass as an intrinsic component of energy-based mass considerations.

9. Effective Mass for Massive Particles in ECM

For a massive particle in ECM, the effective mass is given by:

Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ)

where:

- Mᴍ is the conventional mass.

- −Mᵃᵖᵖ is the negative apparent mass component induced by gravitational interactions and acceleration effects.

ECM establishes the inverse proportionality of apparent mass to conventional mass:

Mᴍ ∝ 1/Mᴍ ⇒ Mᴍ = − Mᵃᵖᵖ

Thus, we obtain:

Mᵉᶠᶠ = Mᴍ − Mᴍ = 0

which represents a limiting case where effective mass cancels out under specific conditions.

10. Effective Mass for Massless Particles in Motion

For massless particles such as photons, the conventional mass is:

Mᴍ = 0

However, in ECM, massless particles exhibit an effective mass due to the interaction of negative apparent mass with energy-mass dynamics.

From ECM’s force equation for a photon in motion:

Fₚₕₒₜₒₙ = −Mᵃᵖᵖaᵉᶠᶠ

This indicates that the apparent mass governs the photon’s dynamics.

Since massless particles always move at the speed of light (v = c), ECM treats their total apparent mass contribution as doubled due to energy displacement effects (analogous to Archimedean displacement in a gravitational-energy field):

Mᵉᶠᶠ = (−Mᵃᵖᵖ) + (−Mᵃᵖᵖ) = −2Mᵃᵖᵖ

Thus, for massless particles in motion:

Mᵉᶠᶠ = −2Mᵃᵖᵖ

This confirms that even though Mᴍ = 0, the particle still possesses an effective mass purely governed by negative apparent mass interactions.

11. Archimedes’ Principle Analogy in ECM

ECM’s treatment of negative apparent mass is closely related to Archimedes’ Principle, which describes the buoyant force in a fluid medium. In classical mechanics, a submerged object experiences an upward force equal to the weight of the displaced fluid. Similarly, in ECM:

- A mass moving through a gravitational-energy field experiences an **apparent reduction** in mass due to energy displacement, akin to an object losing effective weight in a fluid.

- For massive particles, this effect reduces their observed mass through the relation:

Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ)

- For massless particles, the displacement effect is **doubled**, leading to:

Mᵉᶠᶠ = −2Mᵃᵖᵖ

This is analogous to how a fully submerged object displaces its entire volume, reinforcing the interpretation that massless particles inherently interact with the surrounding energy field via their negative apparent mass component.

Physical & Theoretical Significance

(A) Massless Particles Exhibit an Effective Mass

- This challenges the traditional view that massless particles (e.g., photons) have no mass at all. ECM reveals that while they lack conventional rest mass, their motion within an energy field naturally endows them with an effective mass, explained by negative apparent mass effects.

(B) Quantum Mechanical Consistency

- The ECM kinetic energy relation aligns with quantum mechanical frequency-based energy expressions:

KE = hf/c² = −Mᵃᵖᵖ

This suggests that negative apparent mass is directly linked to the fundamental nature of wave-particle duality, reinforcing ECM’s consistency with established quantum mechanics principles.

(C) Natural Explanation for Antigravity

- The doubling of negative apparent mass for massless particles introduces a natural anti-gravity effect, distinct from the ad hoc introduction of a cosmological constant Λ in relativistic models.

- Since massless particles propagate via their effective mass Mᵉᶠᶠ = −2Mᵃᵖᵖ, ECM naturally incorporates repulsive gravitational effects without requiring modifications to spacetime geometry.

(D) Reinforcement of ECM’s Fluid Displacement Analogy

- The analogy with Archimedes’ Principle provides a strong conceptual foundation for negative apparent mass. Just as an object in a fluid experiences a buoyant force due to displaced volume, mass in ECM interacts with gravitational-energy fields via displaced potential energy, leading to apparent mass effects.

Conclusion

ECM’s interpretation of effective mass provides a self-consistent framework where both massive and massless particles exhibit observable mass variations due to negative apparent mass effects. The Archimedean displacement analogy reinforces this concept, offering an intuitive understanding of how energy-mass interactions govern particle dynamics.

This formulation provides a clear, predictive alternative to conventional relativistic models, demonstrating how massless particles still exhibit mass-like behaviour via their motion and interaction with energy fields.

12. Photon Dynamics in ECM & Archimedean Displacement Analogy

Total Energy Consideration for Photons in ECM

In ECM, the total energy of a photon is composed of:

Eₚₕₒₜₒₙ = Eᵢₙₕₑᵣₑₙₜ + E𝑔

where:

- Eᵢₙₕₑᵣₑₙₜ is the inherent energy of the photon.

- E𝑔 is the interactional energy due to gravitational effects.

When a photon is fully submerged in a gravitational field, its total energy is doubled due to its interactional energy contribution:

Eₚₕₒₜₒₙ = Eᵢₙₕₑᵣₑₙₜ + E𝑔 ⇒ 2E

This represents the energy displacement effect, aligning with ECM’s formulation that massless particles experience a doubled apparent mass contribution in motion:

Mᵉᶠᶠ = −2Mᵃᵖᵖ

Photon Escaping the Gravitational Field

As the photon escapes the gravitational field, it expends E𝑔, reducing its total energy:

Eₚₕₒₜₒₙ ⇒ Eᵢₙₕₑᵣₑₙₜ, E𝑔 ⇒ 0

Thus, once the photon is completely outside the gravitational influence:

Eₚₕₒₜₒₙ = E, E𝑔 = 0

This describes how a photon’s energy and effective mass vary dynamically with gravitational interaction, reinforcing the ECM perspective on gravitational influence on energy-mass dynamics.

Alignment with Archimedean Displacement Analogy

This ECM interpretation strongly aligns with Archimedes' Principle, where:

- A photon in a gravitational field is analogous to an object fully submerged in a fluid, experiencing an energy displacement effect.

- As the photon leaves the gravitational field, it expends its interactional energy E𝑔, similar to how an object leaving a fluid medium loses its buoyant force.

This analogy further strengthens ECM’s concept of negative apparent mass, where the gravitational interaction displaces energy similarly to how a fluid displaces volume.

Conclusion & Significance

- The ECM photon dynamics equation aligns with the Archimedean displacement analogy, reinforcing the physical reality of negative apparent mass effects.

- This provides a natural, intuitive explanation for how photons interact with gravitational fields without requiring relativistic spacetime curvature.

- It further supports the energy-mass displacement framework, demonstrating how photons dynamically exchange energy with gravitational fields while maintaining ECM’s effective mass principles.

This formulation elegantly unifies photon energy dynamics with mass-energy interactions, further validating ECM as a robust framework for fundamental physics.

13. Effective Acceleration and Apparent Mass in Massless Particles

For photons in ECM, the effective force is given by:

Fₚₕₒₜₒₙ = −Mᵉᶠᶠaᵉᶠᶠ, Where: aᵉᶠᶠ = 6 × 10⁸ m/s²

- Negative Apparent Mass & Acceleration:

Photons possess negative apparent mass (−Mᵃᵖᵖ), which leads to an anti-gravitational effect. Their effective acceleration (aᵉᶠᶠ) is inversely proportional to Mᵉᶠᶠ and radial distance r.

- Within a gravitational field, the photon has more interactional energy E𝑔, increasing aᵉᶠᶠ.

- Escaping the field, it expends E𝑔, reducing Mᵃᵖᵖ and lowering aᵉᶠᶠ.

- Acceleration Scaling with Gravitational Interaction:

E𝑔 ∝ 1/r

- At r₀ ⇒ E𝑔,ₘₐₓ ⇒ Maximum −Mᵃᵖᵖaᵉᶠᶠ ⇒ aᵉᶠᶠ = 2c.

- At rₘₐₓ ⇒ E𝑔 = 0 ⇒ Minimum −Mᵃᵖᵖaᵉᶠᶠ ⇒ aᵉᶠᶠ = c.

This confirms that effective acceleration (2c) is a function of gravitational interaction, not an intrinsic speed change, reinforcing ECM’s explanation of negative apparent mass dynamics.

14. Extended Classical Mechanics: Effective Acceleration, Negative Apparent Mass, and Photon Dynamics in Gravitational Fields

Analytical Description & Significance:

This paper refines and extends the framework of Extended Classical Mechanics (ECM) by establishing a comprehensive formulation for effective acceleration, negative apparent mass, and their implications for massless and massive particles under gravitational influence. The analysis revises ECM equations to incorporate Archimedes' principle as a physical analogy for negative apparent mass, clarifies the role of effective acceleration (2c) in different gravitational conditions, and demonstrates how negative apparent mass serves as a natural anti-gravity effect, contrasting with the relativistic cosmological constant (Λ).

A key highlight is the kinetic energy formulation for negative apparent mass particles, which aligns with quantum mechanical frequency relations for massless particles. This formulation provides deeper insight into how negative apparent mass influences energy and motion without requiring conventional mass assumptions.

Key Implications & Theoretical Advancements:

Refined Effective Acceleration Equation for Massless Particles:

- ECM establishes that photons, despite being massless in the conventional sense, exhibit negative apparent mass contributions, leading to an effective acceleration of aᵉᶠᶠ = 6 × 10⁸ m/s² = 2c inside gravitational fields.

- This acceleration naturally arises due to the relationship between negative apparent mass −Mᵃᵖᵖ and gravitational interaction energy E𝑔.

- The effective acceleration decreases as a photon exits the gravitational field, reaching c in free space.

Negative Apparent Mass as a Replacement for Cosmological Constant (Λ):

- Unlike Λ, which assumes a uniform energy density, negative apparent mass dynamically varies with gravitational interaction energy.

- This formulation provides a self-consistent explanation for observed cosmological effects, particularly in gravitational repulsion and expansion scenarios.

Physical Analogy with Archimedes’ Principle:

- The ECM framework aligns negative apparent mass effects with Archimedean displacement, where gravitational interaction leads to energy displacement effects analogous to buoyant forces in fluids.

- In gravitational fields, a photon's interactional energy (E𝑔) contributes to its total energy, analogous to an object submerged in a fluid experiencing an upward force.

- As the photon escapes, the loss of E𝑔 mirrors an object emerging from a fluid losing its buoyant support.

4. Revision in the Energy-Mass Relation for Massless Particles:

- The study revise prior inconsistency by explicitly linking the kinetic energy of negative apparent mass particles to quantum mechanical frequency relations, ensuring consistency between ECM and established quantum principles.

Conclusion:

This research enhances ECM’s predictive power by clarifying the role of negative apparent mass in gravitational dynamics and demonstrating its relevance to photon motion, cosmological expansion, and gravitational interactions. By introducing effective acceleration (2c) as a natural consequence of gravitational interaction, ECM provides a compelling alternative to relativistic formulations, reinforcing the practical applicability of classical mechanics principles in modern physics.

I just posted a preprint article, as the original approach to this topic.

Every critical remarks would be welcome.

I heard its because Wigner spin conservation law , I don't know how it makes T-T transition forbidden

Noether's theorem is a fundamental result in physics stating that every symmetry of the dynamics implies a conservation law. It is, however, deficient in several respects: for one, it is not applicable to dynamics wherein the system interacts with an environment; furthermore, even in the case where the system is isolated, if the quantum state is mixed then the Noether conservation laws do not capture all of the consequences of the symmetries[1].

In SR, force-free motion in an inertial frame of reference takes place along a straight-line path with constant velocity. Viewed from a non-inertial frame, on the other hand, this path of motion will be a geodesic curve in a flat spacetime. Einstein made the plausible assumption that this geodesic motion also holds in the non-flat case, i.e. in a spacetime region for which it is impossible to find a coordinate system that leads to the Minkowski metric in SR[2].

All spacetime models can be expressed in terms of the gμν = {4x4} matrix, differing only in the distribution of matrix elements. The gμν of Minkowski spacetime is the unit diagonal matrix {1 -1 -1 -1}; the gμν of Riemann spacetime is { X }. If a new spacetime model is introduced gμν={a0,-a1,-a2,-a3}, which is a non-unit diagonal matrix. (ds)^2=(a0)^2+(a1)^2+(a2)^2+(a3)^2, always holds, interpreting it as a non-uniformly flat spacetime, generalised Minkowski spacetime, and no longer a curved spacetime. Should Noether's theorem maintain its validity in this case.

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References

[1] Marvian, I., & Spekkens, R. W. (2014). Extending Noether's theorem by quantifying the asymmetry of quantum states. Nature Communications, 5(1), 3821. https://doi.org/10.1038/ncomms4821 ;

[2] Rowe, D. E. (2019). Emmy Noether on energy conservation in general relativity. arXiv preprint arXiv:1912.03269.

This is to provide updates on my research as a backup communication channel for my project Multidimensional Integrable Systems

should Researchgate go through with its plan to discontinue the project feature altogether on March 31, 2023.

For the previous update log please see this snapshot

made on April 1, 2023.

You are welcome to follow this question, especially if you are interested in my research, and/or have already followed or intend to follow the above project.

For now, here are the links

0) to my lab

1) to the presentation explaining the most important research results in the project

2) to the key paper of the project

and to the other works in the project

which is now a spotlight, see

In teaching, or as a student in physics, oftentimes a difficulty becomes a motivation for new understanding. In this context, what difficulty do you see in using Lagrangian or Hamiltonian methods in physics, also thinking of avoiding difficulties ahead, for example, in teaching or learning Quantum Mechanics?

As a reference, please read the following. "Consider the system of a mass on the end of a spring. We can analyze this, of course, by using F=ma to write down mx'' = −kx. The solutions to this equation are sinusoidal functions, as we well know. We can, however,  figure things out by using another method, which doesn’t explicitly use F=ma. In many (in fact, probably most) physical situations, this new [150 years old] method is far superior to using F=ma. You will soon discover this for yourself when you tackle the problems and exercises for this chapter [see instructions below, or search in Google]. We will present our new [150 years old] method by  rst stating its rules (without any justi cation) and showing that they somehow end up magically giving the correct answer. We will then give the method proper justification.", in Chapter 6, The Lagrangian Method, Copyright 2007 by David Morin, Harvard University.

Morin continues, "At this point it seems to be personal preference, and all academic, whether you use the Lagrangian method or the F = ma method. The two methods produce the same equations.However, in problems involving more than one variable, it usually turns out to be much easier to write down T and V , as opposed to writing down all the forces. This is because T and V are nice and simple scalars. The forces, on the other hand, are vectors, and it is easy to get confused if they point in various directions. The Lagrangian method has the advantage that once you’ve written down L ≡ T − V , you don’t have to think anymore."

instructions: search in Google, or please write requesting the link.

There is something in the relation between the charge conservation law and the electrons/holes continuity equations in semiconductors that I couldn't resolve.

In steady state, charge conservation law is:

Div(J)=0

Or

Div(Jn+Jp)=0

On the other hand, the continuity equations are:

Div(Jn)=q(R-G)

Div(Jp)=-q(R-G)

Thus, the sum of the two continuity equations satisfy the charge conservation law which is good.

But there are cases when Recombination/Generetion are not equal for electrons and holes, for example when there are traps only for one type of charge.

In such case it seems that the charge conservation law is not satisfied.

Sure it is not possible, so how should I think about this situation?

Thanks

There is lot of emphasis on expansion of green cover or trees on farms (asfForest being common resources even after so conservation laws and efforts forest degradation and deforestation is still on) through agroforestry and tree farming can be a cheaper solution for mitigating climate change effects. If so why in UNFCC only 10-15% projects on A/R under carbon credits framework? If developing countries opting for CDM projects under A/R categories to reach out poor farmers in tropics, rules need to be made simpler and affordable fees for registration for carbon finance. Why only corporate plantations are having edge in projects. How farmers friendly tree farming policies at national level harmonized with climate change & UNFCC.

The importance of the conservation laws in physics, if they not more than the physical constants, certainly, is not less than them. The conservation laws in physics define the boundary between possible events and the impossible.

If we ignore the law of conservation of energy, we can build a machine in our imagination that produces energy from nothing. That is, we will have an erratic universe that is more compatible with our imaginations than with observable realities.

Over the course of the last century, physics has been plagued by many problems, and their numbers are increasing day by day, to the point where modern physics is in a state of stagnation and crisis.

These problems are due to the fact that in modern physics, there is a law of mass-energy conservation, but there is no law of conservation of amount of speed. I first proposed the conservation law of the amount of speed in 1387 (1992 AD) and published it in the Persian language.

The conservation law of the amount of speed shows that the universe behaves more realistically and accurately than we ever imagined and that the whole universe is an automated and highly precise system.

Generalization of the Dirac’s Equation and Sea, 2016

Many conservation laws are found in references, also selection rules and exclusion rules. Time passage is taken for granted, but I don't find any law that compels time to pass.

Discussions in other threads explored that possibility that passage of time is started by creating particle pairs with mass out of a swarm of photons. Mass experiences the passage of time while photons do not.

Consider an end of time. In theory all the mass would convert to photons including black holes. Entropy the arrow of time would go to zero. Distances could not be measured, and might not continue to exist. This begins to sound much like descriptions of our early universe many researchers have given, which is the reason for this question.

Roger Penrose in the book Cycles of Time and in many speeches has a dilemma that enormous length of time is required for black holes to evaporate in the manner of Stephen Hawking. A remedy might be found in some other mechanism for time to stop passing sooner.

Comparing other laws, it seems likely that time should continue to pass unless something causal occurs or a permissive is lost in physical cosmos.

In other threads topics were explored about possible ways time might stop by natural processes, and other possibilities that human activities working with extreme high energy densities might cause time to stop locally in a bubble of quantum modified space.

Researchers debate what might happen to a modified bubble, and how large it would need to be before it could begin to expand uncontrollably to fill the cosmos. Also they make theories about how a bubble might be stopped. A few researchers look to such bubbles as a source of dark energy.

The question is asking if researchers have other information or theories about passage of time.

Does Any Law Of Science Require Time To Continue Passing?

The Lorentz transformations were introduced after 1905 , since the Galilean transformations could not maintain the invariance of Maxwell equations between IRFs. They implement the postulates of the constancy of the speed of light and relativity of motion.

LT SIMPLEST FORM t'= γ(t -vx/c²), x'=γ(x - vt)

some algebraic passages are needed to get the

LT ALTERNATIVE FORM t'= γ^-1 t - vx'/c², x'= γ(x-vt)

A consequence of their application is the relativity of simultaneity which has never been tested experimentally.

They do not reduce to Galilean transformations at low speeds but to

t'= γ^-1t - vx'/c² for |v|/c<<1, γ gets close to 1, hence

t'= t – vx’/c² , x'= x-vt

a further condition is necessary to make vx’/c² negligibly small. That has to be much smaller than t: t >>vx’/c² , ct/x’ >> v/c: x' has to be very small in comparison to the light path length.

The relativity of simultaneity depends strictly on the term vx’/c²

As it was measured by Lorentz and Maxwell,  physically LT express the transformation of the radiation exchanged between relative moving  objects at constant speed whose direct consequence is the RDE.

How does one combine the basis of Quantum Physics that the information cannot be destroyed with the GR statement that black holes destroy the info?

In typical, three-dimensional context, classical fluid flow is described by 3D velocity vector, fluid density and pressure function. This is all required information.

These functions are obtained from conservation laws, in some sense. Conservation of mass gives rise to continuity equation, from which, knowing the velocity vector, we can, in principle, determine the density. Euler's equation, being simply second Newton's law, hence "preservation of momentum", allows us to derive Bernoulli's law (preservation of energy), therefore finding the pressure function. All above is done assuming that we already know velocity.

That's it for three dimensions, however analogous question in higher-dimensional-framework seems to me at least puzzling, since everywhere I looked for an answer, I've found only familiar three-dimensional setting.

My core question is that in three dimensions I need five functions in order to fully describe fluid, so in n (arbitrary) dimensions I need n+2 quantites(scalar fdunctions)? Or is this a simplistic view and this number n+2 becomes more ccomplicated function Z(n)?

Does continuity , momentum and energy laws remain conserved when we use local refinement in adaptive meshes ?

A soliton (such as, KdV soliton) has to satisfy an infinite number of conservation laws. What are the physical names and significances of such solitonic conserved properties? Please explain elaborately with examples, illustrations and references.

If you have a symmetry and use the principle of least action, you will get a conservation law! This is the Noether theorem. The "symmetry" is time and the Lagrangian mathematically describes this principle of least action. Which is very useful because you arrive to a conservation law. Nevertheless, thermodynamics tells that time is not a symmetry! the time in the future will have more entropy than the one in the pass. How can we put a non-symmetrical time in the Noether theorem? A entropic Lagrangian? I think there is a very big problem with time!

Shan Gao, the author of the book

proposed a new interpretation for the QM: a substructurea of QM consisting in a moving particle. But instead of moving continuously, as in Bohm's mechanics, or as in the trajectories of all forms considered by Feynman in his path-integral theory, Gao's particle performs a random, discontinuous motion (RDM) - see section 6.3.2 and 6.3.3 in his book. In short, gao's particle jumps all the time from a position to another

"consider an electron in a superposition of two energy eigenstates in two boxes. In this case, even if the electron can move with infinite velocity, it cannot continuously move from one box to another due to the restriction of box walls. Therefore, any sort of continuous motion cannot generate the required charge distribution. . . .

An important implication of the RDM interpretation is, as the author says, that the charge distribution of a single electron (for instance, in an atom) does not display self-interaction

"Visually speaking, the ergodic motion of a particle will form a particle “cloud” extending throughout space (during an infinitesimal time interval around a given instant), . . . . . . This picture . . . may explain . . . the non-existence of electrostatic self-interaction for the distribution.”

Part of the questions regarding this picture were already clarified by the posts of some users. The questions remained non-clarified are:

1) Is Gao's picture of a particle jumping from position to position, and visiting in this way all the volume occupied by the wave-function, fit for obtaining the Feynman path integral?

Feynman considered two points in tim and space (t₁, r₁) and (t₂, r₂). He also considered all the possible paths between these two points - the majority of the paths having crazy forms, though being continuous. The particle starting at (t₁, r₁) and traveling to (t₂, r₂), was supposed by Feynman to be totally non-classical - it was supposed to follow SIMULTANEOUSLY all the paths, not one path after another. This is was permitted him to do summation over the phases of the paths, and obtain the path integral.

The movement of Gao's particle is not only discontinuous and endowed with no phase, but it os also SERIAL, one point visited after another. What you think, if one would endow these discontinuous trajectories with phases, could we obtain Feynman's path integral despite the seriality of his particle's movement?

3) Gao author also says

"discontinuous motion has no problem of infinite velocity. The reason is that no classical velocity and acceleration can be defined for discontinuous motion, and energy and momentum will require new definitions and understandings as in quantum mechanics"

This statement seems to me in conflict with the QM, because the uncertainty principle says that if at a given time a particle has a definite position, the linear momentum (therefore also the velocity) would immediately become undetermined. QM doesn't say that the linear momentum does not exist.

Can somebody offer answer(s) to my questions/doubts?

FVM methods are usually used to solve the hyperbolic conservation laws. Why we can not use finite element methods for this? Is there any other reason than the inherent conservation property associated with FVM?

How do we nicely represent specific entropy conservation law in a mathematical form in diversified astrofluids?

Astrofluids are characterized with the help of various thermodynamic properties and associated conservation laws. In this context, can anyone give a realistic correlation between the specific entropy conservation and logatropic pressure of such fluids?

Relevant References and materials dealing with new equations of state are as well welcome.

Request for information

In recent times we have seen so much work being done related to fractional partial differential equations, especially in the field of Lie symmetry analysis and conservation laws. In case of partial differential equations where the conservation laws can be determined using various methods like; Noether's theorem and direct method of Bluman and Anco. For non-trivial conservation laws, the divergence expression of fluxes must annihilate on the solution space of PDE under consideration.

My query is, whether such annihilation of fluxes also holds for conservation laws of a fractional partial differential equation?

For example, in the context of this project and what students should learn in today's crowded curriculum, consider this quote from Benjamin Crowell [1]:

In many subfields of physics these days, it is possible to read an entire issue of a journal without ever encountering an equation involving force or a reference to Newton's laws of motion. In the last hundred and fifty years, an entirely different framework has been developed for physics, based on conservation laws.

The new approach is not just preferred because it is in fashion. It applies inside an atom or near a black hole, where Newton's laws do not. Even in everyday situations the new approach can be superior. We have already seen how perpetual motion machines could be designed that were too complex to be easily debunked by Newton's laws. The beauty of conservation laws is that they tell us something must remain the same, regardless of the complexity of the process.

[1] Benjamin Crowell, Light and Matter, chapter 14, retrieved from

  I try to study the existence of a time periodic solution for the compressible with a time periodic outer force (without relaxation term) . I have recently obtained .

However, this result is restrictive. Do you know a result about this problem under more weaker condition?

Hello,

If a Lagrangian is known for a given system, we can deduce its equation of motion using the Lagrange equation.

Are there any other uses of a Lagrangian?

One use I know is to find a conservation law for a mechanical system. If its Lagrangian does not include time explicitly, we can obtain a conserved quantity by Jacobi integral.

I am wondering what other applications are possible with a Lagrangian (especially for engineering fields.)

Thank you.

David

am trying to find the  conservation laws of ZK-BBM equation with multiplier method on maple where Un is appear in the PDE but maple is not working with n will any body tell me how i do it. maple is showing the results for particular value of n but in general fails.

any suggestion please??

Dirac said that a 'linear' polarized photon is a superposition of left and right rotating photons. Here is a puzzling aspect of this superposition.

There are dichroic materials which can absorb only left photons. What is their effect on this superposition? They would absorb the left state and let the right. It turns out that there are two photons in a 'linear' photon! The mechanical momentum of the dichroic material must be measurable in principle  (like Beth experiment). It would be expected that there is some energy hv absorbed too but it must be in the right photon also. Conservation of energy seems broken? If there is no momentum and no energy absorbed in the dichroic the conservation laws are also severely harmed. At least something happens to that photon (linear to right which is easy to show) but nothing happens to the causer of this event (namely to the dichroic). I see that there must be wavefunction collapse for the photon and in fact the question boils out to:

Is something physically happening to the machinery causing the collapse?

This question is connected to the following question:

Is there any way to split a linear polarised photon into left and right polarised photons? - ResearchGate. Available from: https://www.researchgate.net/post/Is_there_any_way_to_split_a_linear_polarised_photon_into_left_and_right_polarised_photons [accessed Feb 12, 2016].

There are many indications that this is the case today, with the added advantage that Newton's laws can then be derived rather than proposed. For example, consider this quote from Benjamin Crowell  [1]:

In many subfields of physics these days, it is possible to read an entire issue of a journal without ever encountering an equation involving force or a reference to Newton's laws of motion. In the last hundred and fifty years, an entirely different framework has been developed for physics, based on conservation laws.

The new approach is not just preferred because it is in fashion. It applies inside an atom or near a black hole, where Newton's laws do not. Even in everyday situations the new approach can be superior. We have already seen how perpetual motion machines could be designed that were too complex to be easily debunked by Newton's laws. The beauty of conservation laws is that they tell us something must remain the same, regardless of the complexity of the process.

[1] Benjamin Crowell, Light and Matter, chapter 14, retrieved from

I have not been able to find a concrete list of exactly what species are illegal to ship across state lines. Whenever I am purchasing arthropods online for research purposes, I see websites that say "We cannot ship to Florida or Hawaii," but I haven't been able to find anything explaining this in writing other than a few people telling me that they think it's illegal to ship some insects to those states but they don't know which ones.

Some websites I see say that you need an import permit for EVERY arthropod species you plan to bring across state lines. And that it is always illegal to ship any non-U.S. native insect or millipede across state lines! I find this hard to believe... for example, I know that many people purchase Dubia Roaches online to feed their reptiles, and get them shipped across the country. Dubia Roaches are native to South America, however there are thousands of people who sell them in the U.S. including legitimate businesses like DubiaRoaches.com.

I am worried that I will think I've got all the laws sorted out based on what people say, then I will go ship some of my extra research specimens to someone in another state and the USDA will pound on my door! Any help would be appreciated, thanks!

Hello everyone,

I am reading CFD by John D. Anderson. I understood the derivation of different forms of Navier-Stokes equations. But it is still unclear for me what is the fundamental difference between Integral and differential forms of the Navier-Stokes equations. It is also not clear for me where are these forms used ?

I always see all the explanations based on the Differential forms so I am wondering if the integral forms are used ?

Another thing : Please correct me if I am wrong ::

The conservative and non-conservative forms are called like that because, the conservative forms are derived from a conservation law and the non-conservative forms are not.

In spite of appeals to international and national NGOs as well as to national and regional agencies it has (so far) been impossible to obtain information on areas of highest conservation priority in the Brazil's Mata Atlântica. The goal is to purchase land for permanent conservation as a Reserva Particular do Patrimônio Natural. Any suggestions from ResearchGate will be much appreciated.

By definition, a reversible process is one that can be undone completely, leaving no trace of it having occurred. Upon reversal "it should be impossible to devise any experiment that could determine whether the process took place" (paraphrasing Planck). This means that every single bit of information that was flipped by such a process going forward, should be flipped back when the process finishes going in reverse. This really means all causal volume traces must be erased including all memories recorded in labbooks, hard drives or brains. Postulating the existence of such a process is therefore an unfalsifiable assumption (since if you succeeded in performing such a process there would be no evidence to show for it and you wouldn't even remember doing it!). This means asserting the existence of truly "reversible" processes is no more than an act of faith. Yet significant portions of physics depend on this belief and we try hard to keep the "micro" laws time-reversible. Since reversible processes are defined as those that can never make their presence known by affecting anything, it means that experimental evidence of CPT violation is inevitable and the microscopic arrow of time is down there, it's just hard to see because of the limitations of current experiments. It follows that the notions of determinism, unitarity of quantum mechanics, symmetries etc. should be understood as approximations the same way as Plato's perfect circle is never realized in any physical system. Keeping these self-contradictory notions at the heart of the mathematical underpinnings of physics as "useful approximations" is confusing physics with engineering. Worse still, our instinct to treat absolute conservation laws as sacrosanct is seriously harmful to furthering our understanding of how it all really works.