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ORCiD: 0000-0003-1871-7803
February 10, 2025
Within Extended Classical Mechanics (ECM), photon dynamics describes dark energy by positing that photons, due to their unique properties within the framework, can exhibit a "negative apparent mass," causing them to effectively repel each other and contribute to the observed accelerating expansion of the universe, which is the primary characteristic of dark energy; this negative mass arises from the complex interaction of photon momentum and energy within the ECM equations, leading to an "effective acceleration" that counteracts gravitational pull.
Photon Dynamics and Dark Energy in the Framework of Extended Classical Mechanics (ECM)
In the framework of Extended Classical Mechanics (ECM), photon dynamics and dark energy are intricately linked through the concepts of effective mass (Mᵉᶠᶠ) and apparent mass (Mᵃᵖᵖ). This framework provides a novel perspective on how gravitational interactions can induce mass in initially massless particles, such as photons, and how these interactions relate to the observed phenomena of dark energy.
Photon Dynamics and Effective Mass
Effective Mass and Apparent Mass:
In ECM, the effective mass (Mᵉᶠᶠ) of a photon is a dynamic property that combines the rest mass (Mᴍ​) and the apparent mass (Mᵃᵖᵖ). For photons, which have zero rest mass, their apparent mass dictates their energy-momentum exchanges and response to forces. This leads to the reformulated force equation:
Fₚₕₒₜₒₙ =−Mᵃᵖᵖ aᵉᶠᶠ
The apparent mass (Mᵃᵖᵖ) can be negative, which is crucial for understanding antigravitational effects and dark energy.
Gravitational Redshift and Photon Energy:
The total energy of a photon is analysed as the sum of its inherent energy (E) and gravitational interaction energy (Eg​). As photons escape a gravitational field, they retain their inherent energy while gradually expending their gravitational energy. This leads to gravitational redshift, where the photon's frequency shifts due to the gravitational potential.
Dark Energy and Negative Effective Mass
Dark Energy as a Gravitational Interaction:
In ECM, dark energy is not treated as a conventional field or particle but as a gravitationally interactive background that influences mass distributions at intergalactic scales. It acts on cosmic scales by modifying the gravitational potential, leading to the observed cosmic acceleration.
Negative Effective Mass and Antigravitational Effects:
The negative effective mass (Mᵉᶠᶠ<0) is a key feature of ECM, particularly in the context of dark energy. This negative mass can lead to antigravitational effects, where objects experience repulsion rather than attraction. This phenomenon echoes the behaviour of dark energy, which accelerates the universe's expansion by generating antigravitational effects.
Gravitational Mass and Dark Energy:
The gravitational mass (Mg​) in ECM is given by:
Mɢ = Mᴍ + (-Mᵃᵖᵖ)
At intergalactic scales, the interaction of dark matter with dark energy results in an effective mass contribution (Mᴅᴇ​), which is represented by:
Mɢ = Mᴍ + Mᴅᴇ
This additional inferred mass component (Mᴅᴇ) is an emergent gravitational effect, not a fundamental mass term.
Implications for Photon Dynamics and Dark Energy
Unified Framework:
ECM provides a unified framework that bridges classical mechanics, quantum principles, and cosmological implications. By incorporating the concept of apparent mass, ECM offers a cohesive mechanism to reconcile classical, quantum, and cosmological phenomena.
Cosmic Acceleration:
The negative effective mass associated with dark energy explains the observed cosmic acceleration. This antigravitational effect is crucial for understanding the expansion of the universe and the role of dark energy in shaping cosmic dynamics.
Gravitational Collapse at the Planck Scale:
At the Planck scale, gravitational interactions can induce mass in massless particles, leading to gravitational collapse. This transition from massless to massive states is a direct consequence of ECM's mass induction principle, where increasing energy (via frequency) leads to mass acquisition.
Conclusion
The framework of Extended Classical Mechanics (ECM) offers a detailed and nuanced understanding of photon dynamics and dark energy. By incorporating the concepts of effective mass and apparent mass, ECM provides a unified perspective on gravitational interactions across quantum and cosmological scales. This approach not only aligns with fundamental principles but also offers potential explanations for cosmic-scale phenomena involving dark matter, dark energy, and exotic gravitational effects.
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view works by Lebedev V.A.
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The assertion that "antigravity is an unlikely phenomenon" is inconsistent with established observations. The behaviour of photons provides direct evidence to the contrary. According to its energy, a photon possesses effective mass and is observed to escape gravitational wells, demonstrating a counteracting effect against gravity. Extended Classical Mechanics (ECM), a framework built upon classical mechanics principles, provides a clear formulation of this phenomenon. ECM reveals that photons exert an antigravitational force on massive bodies, accelerating at twice the speed of light within gravitational influence. As a photon leaves a gravitational well, it expends energy but retains its inherent energy, continuing to travel at the speed of light in free space. This indicates that antigravitational effects are an intrinsic feature of certain mass-energy interactions, contradicting the claim that antigravity is unlikely.
The notion that "dark energy is not real" is only partially correct. While dark energy is not a physical object with rest mass, its effects are observable. ECM equations establish dark energy as a form of potential energy with a dynamic nature, existing only as a consequence of gravitational and motion dynamics of massive bodies. Rather than being an independent entity, dark energy emerges from the interplay of gravity and motion at cosmic scales, reinforcing its role in large-scale universal dynamics.
Similarly, the claim that "negative mass lacks a physical description and remains unproven" overlooks key insights provided by ECM. Rather than considering negative mass as a standalone entity, ECM introduces the concept of negative apparent mass, which arises from motion and gravitational interactions. This phenomenon does not imply an intrinsic negative mass but rather an emergent property influenced by both baryonic matter and dark matter. ECM principles illustrate how apparent mass contributes to gravitational effects, expanding the understanding of mass-energy interactions beyond conventional classical mechanics.
These refinements in ECM extend classical mechanics while maintaining consistency with empirical observations, providing a structured approach to understanding gravitational repulsion, dark energy, and the role of apparent mass in astrophysical phenomena.
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Antigravity - in the shadow side of the comet, dark matter - ether with a density contained in Planck's constant, negative apparent mass - in the mechanics of the mass defect of nucleons: see the works of Lebedev V.A.
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We all know that energy density entanglements undoubtedly exist since they are measured almost daily.
We also know that all the giant scientists Einstein, Schrödinger, Minkowski, Hilbert, Hamilton... . etc.  didn't understand the physics of entanglement.
We assume that the reason is that the entanglement is related to the correct definition of time, which is more complex and hidden than the entanglement itself.
In the following, some true but simplified quotes about entanglement:
1- Most of the time, everything gets tangled up with everything.
2-The true geometry of nature implies that
The problem of time and entanglement is a conceptual conflict between quantum mechanics and general relativity.
3-Quantum mechanics considers the flow of time as universal and absolute, while general relativity considers the flow of time as malleable and relative.
4-why time seems to flow in only one direction, (Arrow of time)
5- In classical mechanics and quantum mechanics, time has a separate status in the sense that it is treated as a classical background parameter, external to the system itself.
6-In Copenhagen interpretation of quantum mechanics: all measurements of observables are made at certain instants of time and probabilities are assigned only to these measurements. Additionally, the Hilbert space used in quantum theory relies on a complete set of observables that commute at a specific time.
7-What is the entanglement theory of time?
Work started by Don Page and William Wootters suggests that the universe appears to evolve for observers on the inside because of energy entanglement between an evolving system and a clock system, both within the universe. In this way the overall system can remain timeless while parts experience time via entanglement.
8- It is possible to go to quantum mechanics from statistical mechanics by PROJECTION OF CLASSICAL STATISTICAL MECHANICS ONTO PRESPACE.
This means in that 4D statistical classical physical space is equivalent to 3D quantum space and so on.
9- etc .. .etc.
*Looking forward to responses and comments from our respectable readers and contributors, please focus on a few ideas for a thorough break.
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Dear Ismail: The 2022 Nobel Prize was given to the scientist who verified the apparent non-locality of this phenomenon. Nonetheless, up to today, there has been no detailed explanation of how nature acts in that way. From 2021 there is a novel interpretation (Theory of space) that clarifies this and many other quantum characteristics mentioned in your 8 points. For example, it says that quantum systems can be divided and still be one system; i.e., beam splitter mirrors, two-slit experiments, etc. Now, entangled particles are one divided system where one particle is at one zone and the other at the other zone. The key idea is that existence in 3D is in oscillation with the 4th D (4thD = C*tau, where tau = h/Energy or Planck´s periodicity); so, the system can be quite separated in 3D space BUT it still is LOCAL at this 4th D. A simple model that explains this crucial quantum behavior. I recommend the attached paper where many of your points are answered (read projected probability for the measurement problem). I hope that it will inspire you in your research, regards.
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February 07, 2025
The foundation of Extended Classical Mechanics (ECM) is constructed upon classical mechanics principles, as formulated by Newton, Lagrange, and Hamilton, yet it aims to transcend the limitations encountered at quantum scales, relativistic speeds, and in complex systems.
A central innovation within ECM is the introduction of the concepts of apparent mass (Mᵃᵖᵖ) and effective mass (Mᵉᶠᶠ). These constructs extend the traditional framework to incorporate the effects of dark matter and dark energy, offering a more comprehensive understanding of gravitational dynamics.
The concept of apparent mass (Mᵃᵖᵖ) is established in classical mechanics, specifically through the fundamental relationship between force, mass, and acceleration (F = ma). However, it also integrates observational evidence from phenomena like dark energy, bridging classical principles with contemporary cosmological insights.
Extended classical mechanics offers a unified perspective on photon dynamics. It synthesizes classical principles with modern observations, emphasizing the conservation of photon energy (E) and the symmetry of gravitational interactions (Eg). This approach posits that photons maintain their intrinsic energy (E) while interacting with gravitational fields, dynamically exchanging gravitational interactional energy (Eg) during their trajectories.
In summary, ECM weaves together classical mechanics with modern astrophysical phenomena through the constructs of Mᵃᵖᵖ and Mᵉᶠᶠ. This cohesive model not only respects the heritage of classical mechanics but also embraces the complexities revealed by modern science, offering new avenues for exploring the cosmos.
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@ Soumendra Nath Thakur
However I will like to inform you that publications in an ordinary peer-reviewed journal supported by open challenge and attempted by some scientists to disprove the basis of open challenge is twenty times more important than the papers published in Nature or Physical Review D.
So far as dark energy is concerned what I can discuss when I have confirmed the existence of aether without any doubt whatsoever. When I have shown light/radiation per se is 'nothing' but the capacity of making electric dipoles to vibrate whereas it took me just half a page of research paper to show that E=mc^2 is absolutely baseless and when I have shown that space is absolute without any doubt whatsoever.
Let me inform you straight and bluntly that because of the introduction of contraction of space by Lorentz and Fitzgerald which converted absolute space into emergent space was the beginning of the end of the physics they have adopted and then why nobody could do anything to this whole issue was because transverse Doppler effect which was predicted by theory of relativity was experimentally seen as absent in the series of experiments which started in the year 1975 and so much so the absence of transverse Doppler effect was confirmed even in microwaves, with the highest possible experimental accuracy ever, was confirmed and that was the final nail in the coffin of theories of relativity, Space-time concept and Big Bang paradigm. The climax of everything is that there is not a SINGLE EXPERIMENTAL EVIDENCE of contraction of space in the direction of motion till date which theory of relativity predicted. It is me only who has the right to claim the discovery of fifth constituent of universe besides the alternative theory and also the alternative transformation to Lorentz transformation. They cannot utter a word against the open challenge not to speak of accepting the challenge. As a hard working young person of the same country in which I live I thought you have an open field for research. You should bear in mind that you are in conversation with a scientist who has proved Einstein was a scientific fraud without any doubt whatsoever and nobody can do anything about it.
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The concept of negative apparent mass in extended classical mechanics is a groundbreaking innovation. It marks a turning point in classical mechanics, introducing negative mass and expanding its capabilities beyond traditional frameworks. This extension enhances classical mechanics, making it more powerful than relativistic mechanics.
Furthermore, velocity-induced relativistic Lorentz's transformations are flawed because they neglect classical acceleration between the rest and moving frames. They also overlook material stiffness in calculations, relying solely on the speed of light as the defining dynamic factor. For these reasons, extended classical mechanics stands as a far superior framework compared to the flawed foundations of relativistic mechanics.
Effective Mass and Acceleration Implications of Negative Apparent Mass in Extended Classical Mechanics (ECM):
Newton's Second Law and Acceleration:
In classical mechanics, Newton's second law is typically expressed as:
F = ma
This shows that force (F) is directly proportional to acceleration (a) and mass (m).
As force F increases, acceleration a increases proportionally. However, the relationship a ∝ 1/m means that if mass m increases, acceleration a will decrease, assuming force is constant.
In this framework, if acceleration increases while force increases, it suggests that mass must decrease to maintain the inverse relationship between acceleration and mass.
Apparent Mass and Effective Mass in ECM:
In Extended Classical Mechanics (ECM), this relationship is reflected in the equation:
F = (Mᴍ − Mᵃᵖᵖ) aᵉᶠᶠ
The term (Mᴍ − Mᵃᵖᵖ) implies that the effective mass is the difference between matter mass and apparent mass, which is a dynamic concept.
Apparent mass reduction:
If the apparent mass Mᵃᵖᵖ decreases (or becomes negative), this results in an increase in effective mass, which in turn causes an increase in acceleration a when the force F remains constant.
Thus, in ECM, a reduction in apparent mass leads to a corresponding increase in acceleration, aligning with the inverse relationship a ∝ 1/m, where m is the effective mass. This supports the idea that acceleration can increase without an actual increase in matter mass Mᴍ but rather a reduction in apparent mass Mᵃᵖᵖ.
Supporting Observational Findings:
The expression Mᵉᶠᶠ = Mᴍ + Mᴅᴇ, where Mᴅᴇ is negative, aligns with this reasoning. If the apparent mass Mᵃᵖᵖ (which could be represented Mᴅᴇ in this framework) is negative, the effective mass becomes:
Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ)
This negative apparent mass Mᵃᵖᵖ or, effective mass of dark energy (Mᴅᴇ), reduces the total effective mass, causing an increase in acceleration when force is applied, consistent with the relationship a ∝1/m.
Conclusion:
In this framework, the concept of effective mass Mᵉᶠᶠ is key to understanding how acceleration behaves when apparent mass changes. When apparent mass decreases (or becomes negative), the effective mass also decreases, leading to an increase in acceleration. This theory not only aligns with the classical force-acceleration-mass relationship but also supports observational findings, particularly the role of negative apparent mass in cosmological models or exotic gravitational effects.
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Thank you sir,,,,❤️
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It is predicted but was never experimentally confirmed because technical limitations but also physical observation limitation of HUP (Heisenberg Uncertainty Principle) that an electron at rest has an intrinsically caused jittery motion similar as an analogy, to the Brownian vibration motion observed on atoms. Although the Brownian motion of atoms we must differentiate here, in a fluid for example, is not caused intrinsically inside the atom, but rather due to extrinsic causes like different atoms bumping on each other all the time.
Nevertheless, the Zitterbewengung (German term for jittery vibrational motion) of the electron is predicted to be twice the electron's Compton frequency fc :
fc ~ 127 EHz (i.e. one ExaHertz [EHz] unit is 1018 Hz)
Thus,
fZ = 2fc~254 EHz
which is an enormous high frequency vibration.
However, if the cause of the electron's Zitterbewengung at rest, is to be attributed to the unknown possible intrinsic mechanics of the electron then this also possible mean, and also predicted by de Broglie theory about every subatomic particle, that a kind of intrinsic harmonic energy oscillation exists for the electron that is the classical cause for the electron Zitterbewengung.
My question here is and discussion topic, what do you think is the physical reason (please do not use just equations to explain or abstract effective terminology) this frequency to be twice the Compton frequency?
I found this question always to be a big mystery which however if answered could be the key for deciphering the electron.
Emmanouil
p.s. In my "Intrinsic Mechanics" for example model of the electron, the electron undergoes in superposition two overlapping different harmonic energy oscillations at a 90º angle. One latitudinal and one longitudinal harmonic oscillation of its energy string :
This combinatoric motion is of two harmonic oscillations is in my theory and model, is the reason why the zitter vibration of the electron is twice its Compton frequency.
Relater paper of my model:
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The question
“Predicted Zitterbewengung of electron thought similar to Brownian vibration motion of atoms”
- relates to a really fundamental physical problem – “what is Z”itterbewengung”? ”
- which – as any other really fundamental problem - really can be, and in this case is, scientifically rationally solved only in the Shevchenko-Tokarevsky’s Planck scale informational physical model, in this case it is enough to read one of two main papers
- where the scientifically rational model of “particle” is given. In the model particles are some cyclic disturbances - cyclic algorithms that tick with frequencies ω - in the Matter’s ultimate base – the (at least) [4+4+1]4D dense lattice of primary elementary logical structures – (at least) [4+4+1]4D binary reversible fundamental logical elements [FLE],
- which [lattice] is placed in the Matter’s fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct). FLE “size” and “FLE binary flip time” are Planck length, lP, and Planck time, tP, correspondingly the always constantly running algorithms-particles move constantly in the utmost universal, “kinematical” 4D space with metrics (at least) (cτ,X,Y,Z) with the speed of light, c, c= lP/tP,
So a particle’s “Zitterbewegung” is just the particle’s algorithm ticking. When a having rest mass particle is at rest in the 3DXYZ space, it moves only in the-dimension with the speed of light and its algorithm ticks with maximal frequency, when the particle moves also in the 3D space, the algorithm’s FLE sequence is diluted by [in certain sense, but that isn’t essential here] “blank” FLE steps ; so the algorithm ticks slower in Lorentz factor, unstable particles live longer,
- and Zitterbewengung can be experimentally observed. What seems was really made, see for example https://arxiv.org/pdf/1409.0888.pdf
Cheers
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Quantum mechanics is 9ne of the most succesfull theories (if not the most, empirical) yet at its roots ontological vaqueness thrives.
In QM, physicists are not sticking to the standards they set in classical mechanics: clear ontological status.
Here we had better at least be clear whether we are talking about mental states, or physical ones out there in the world, and whether the theory implies that there uncountably many other versions of our everyday reality out there, or not.
Few however believe that remaining ambivalent about this kind of thing is just not acceptable.
"Note that this is not a choice imposed on us by physics. It is a choice that we can make depending on what kind of thing we think science should be".
The obove is the view of some such as Paul Msibwood, Ph. D Philosophy of Physics, that this approach is the only defensible option.
He thinks that exploring the basic ontology of the theory and its implications is something rich and valuable to the progress of science, and more generally, a real addition to human knowledge.
Do you agree?
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Questions related to the ontology of QM, and to the 30-odd interpretations of QM, themselves classifiable into three main broad categories (Bohmian, Objective Collapse, or Everett), have all been IMMO extremely well addressed in Shan Gao's superb 2017 book "The Meaning of the Wave Function" (published by Cambridge University Press), a book which itself built on earlier works.
By "addressed" is not necessarily always meant fully resolved : some questions are indeed resolved, some others set forth in terms of what they imply, and what their various alternatives would entail, and what may drive alternative worldviews and why.
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The question is if the Relativistic Kinetic Energy formula:
KE_rel = (gamma -1) mc**2
Has it been verified using thermal calorimetry?
SINCE I WROTE THIS QUESTION, I FOUND OUT ABOUT THE BERTOZZI EXPERIMENT ON RELATIVISTIC ELECTRONS. THAT SETTLES THE ISSUE OF RELATIVISTIC KINETIC ENERGY. THAT IS THE CORRECT ANSWER.
MY THEORY PREDICTS WEAKENED FORCES AT HIGH ABSOLUTE VELOCITIES. THAT IS CONSISTENT WITH OBSERVATIONS AND ANATOLI BUGORSKI ACCIDENT.
READ ABOUT THE HYPERGEOMETRICAL UNIVERSE THEORY HERE:
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I was wrong, although I knew I could be wrong here.
Upon relaxing the condition of "thermal calorimetry measurement of relativistic kinetic energy using protons" to electrons, I was able to find the Bertozzi's Experiment.
That is a nail in the coffin. There is nothing to argue and I moved on and retracted the work.
I still went one more time to do Bethe-Block modeling and it yielded small absorption. That was the second nail...:)
I think this subject is very clear to me now...:)
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2) How is the formation of the universe?
The universe, at its most fundamental level, appears to operate according to the principles of quantum mechanics, where uncertainty and indeterminacy play key roles in shaping its evolution. In classical computational theory, Turing’s Halting Problem demonstrates that it is impossible to predict whether a system will reach a final state or run indefinitely. This raises profound questions about the nature of the universe: could it, too, one day halt, reaching a state where no further evolution is possible? However, the inherent unpredictability of quantum mechanics—through phenomena like superposition, quantum fluctuations, and entanglement—may offer a safeguard against such a scenario. This paper explores the intersection of quantum mechanics and the Halting Problem, suggesting that quantum uncertainty prevents the universe from settling into a static, final state. By continuously introducing randomness and variation into the fabric of reality, quantum processes ensure the universe remains in perpetual motion, avoiding a halting condition. We will examine the scientific and philosophical implications of this theory and its potential to reshape our understanding of cosmology.
Stam Nicolis added a reply:
The evolution of the universe, from the inflationary epoch onwards, is described by classical, not quantum, gravity.
Stam Nicolis added a reply:
Turing's halting problem doesn't have anything to do with the subject of cosmology, or any subject, where the equations that describe the evolution of the system under study are known.
In particular the answer to the question of the evolution of the universe is known: It's described by the de Sitter solution to Einstein's equations, that is its expansion is accelerating, although with a very slow rate. The question, whose answer isn't, yet, known is what happened before the inflationary epoch. It is for this question that a new theory is needed, that can match to classical description of spacetime and the quantum description of matter that emerged from it.
Stam Nicolis added a reply:
That quantum mechanics provides a probabilistic description isn't particular to it. Classical mechanics, also provides a probabilistic description, since classical systems are, typically, chaotic and integrable systems are the exception, not the rule. The only difference between a quantum system and its classical limit is the space of states.
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Dear Abbas We must realize that our universe is a complete entity that it is running billions of galaxies and place billions solar systems in each galaxy in most accurate way is not result of accident big bang, or run mechanically as our past icons (quantum mechanics, or any mechanical entanglement) stated it. Our universe like anything else (inside of it) has born and it has a natural journey. If you accept this fact, then we are in right track as far as knowing intelligent atom, not mechanical atom.
Unfortunately science believes someone imagination of collapsing our mechanical physics into nature (atom)
Reading this unprecedented articles might help your view of this magnificent universe of ours.
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This is a simple proof the guitar is Hamiltonian. Then by deconstruction so is string vibration because the string is the smallest open set on guitar.
The time-independent Hamiltonian has the form H(p, q) = c and dH/dt = 0.
All I need is to define p and q.
So p will be the center of harmonic motion, and q will be a potential energy gradient that reads off the differential between any two points.
Consider the set of notes for the guitar tuning known as standard: E A D G B E.
The tuning naturally separates into two vectors in this way: Indexing the tuning notes by counting up from the low E the pitch values are equivalent to p: 0 5 10 15 19 24.
Now taking the intervals between the notes we have a second vector q: 0 5 5 5 5 4.
It is important to notice that tuning vectors p and q are equal, opposite, and inverse, which is expected since the orbit and center have this relation in the Hamiltonian.
For instance, p is the summation of q and q is the differential of p. The points in p and the intervals in q together make a unit interval in R.
Most important, p = 1/q means the tuning is the identity of the guitar. If you know the tuning, you know everything (all movement). You can learn guitar without learning anything but the tuning.
The proof the vectors are Hamiltonian is this, p is the center of motion in R6, and q is the gradient of the potential field surface in R5 where every vibrational state is presented by a single point.
The coordinates of notes on guitar chord charts given by the gradient function
form a union as a smooth atlas.
Therefore, it must be true the guitar is Hamiltonian. How else could the symplectic manifold be smooth?
Physicists and mathematicians have no choice but to accept that one degree of freedom is better than two. The fact that they cannot see it implies an illness of the public mind that cannot think straight about classical mechanics.
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Also, this is a normed metric space because of the octave.
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A minion is a low-level official protecting a bureaucracy form challengers.
A Kuhnian minion (after Thomas Kuhn's Structure of Scientific Revolutions) is a low-power scientist who dismisses any challenge to existing paradigm.
A paradigm is a truth structure that partitions scientific statement as true to the paradigm or false.
Recently, I posted a question on Physics Stack Exchange that serves as a summary of the elastic string paradigm. My question was: “Is it possible there can be a non-Fourier model of string vibration? Is there an exact solution?”
To explain, I asked if they knew the Hamiltonian equation for the string vibration. They did not agree it must exist. I pointed out there are problems with the elastic model of vibration with its two degrees of freedom and unsolvable equations of motion can only be approximated by numerical methods. I said elasticity makes superposition the 4th Newtonian law. How can a string vibrate in an infinite number of modes without violating energy conservation?
Here are some comments I got in response:
“What does string is not Fourier mean? – Qmechanic
“ ‘String modes cannot superimpose!’ Yet, empirically, they do.” – John Doty
“ A string has an infinite number of degrees of freedom, since it can be modeled as a continuous medium. If you manage to force only the first harmonic, the dynamics of the system only involve the first harmonic and it’s a standing wave: this solution does depend on time, being (time dependence in the amplitude of the sine). No 4th Newton’s law. I didn’t get the question about Hamilton equation.
“What do you mean with ‘archaic model’? Can I ask you what’s your background that makes you do this sentence? Physics, Math, Engineering? You postulate nothing here. You have continuum mechanics here. You have PDEs under the assumption of continuum only. You have exact solutions in simple problems, you have numerical methods approximating and solving exact equations. And trust me: this is how the branch of physics used in many engineering fields, from mechanical, to civil, to aerospace engineering.” – basics
I want to show the rigid versus elastic dichotomy goes back to the calculus wars. Quoting here from Euler and Modern Science, published by the Mathematical Association of America:
"We now turn to the most famous disagreement between Euler and d’Alembert … over the particular problem of the theory of elasticity concerning a string whose transverse vibrations are expressed through second-order partial differential equations of a hyperbolic type later called the wave equation. The problem had long been of interest to mathematicians. The first approach worthy of note was proposed by B. Taylor, … A decisive step forward was made by d’Alembert in … the differential equation for the vibrations, its general solution in the form of two “arbitrary functions” arrived at by means original with d’Alembert, and a method of determining these functions from any prescribed initial and boundary conditions.”
[Editorial Note: The boundary conditions were taken to be the string endpoints. The use of the word hyperbolic is, I believe, a clear reference to Taylor’s string. A string with constant curvature can only have one mathematic form, which is the cycloid, which is defined by the hyperbolic cosh x function. The cosh x function is the only class of solutions that are allowed if the string cannot elongate. The Taylor/Euler-d’Alembert dispute whether the string is trigonometric or hyperbolic.
Continuing the quote from Euler and Modern Science:
"The most crucial issue dividing d’Alembert and Euler in connection with the vibrating string problem was the compass of the class of functions admissible as solutions of the wave equation, and the boundary problems of mathematical physics generally, D’Alembert regarded it as essential that the admissible initial conditions obey stringent restrictions or, more explicitly, that the functions giving the initial shape and speed of the string should over the whole length of the string be representable by a single analytical expression … and furthermore be twice continuously differentiable (in our terminology). He considered the method invalid otherwise.
"However, Euler was of a different opinion … maintaining that for the purposes of physics it is essential to relax these restrictions: the class of admissible functions or, equivalently, curves should include any curve that one might imagine traced out by a “free motion of the hand”…Although in such cases the analytic method is inapplicable, Euler proposed a geometric construction for obtain the shape of the string at any instant. …
Bernoulli proposed finding a solution by the method of superimposition of simple trigonometric functions, i.e. using trigonometric series, or, as we would now say, Fourier series. Although Daniel Bernoulli’s idea was extremely fruitful—in other hands--, he proved unable to develop it further.
Another example is Euler's manifold of the musical key and pitch values as a torus. To be fair, Euler did not assert the torus but only drew a network show the Key and Pitch can move independently. This was before Mobius's classification theorem.
My point is it should be clear the musical key and pitch do not have different centers of harmonic motion. But in my experience, the minions will not allow Euler to be challenged by someone like me. Never mind Euler's theory of music was crackpot!
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Physic Stack Exchange is not peer review, it is sneer review. I show then their answers are not correct but I am shut out.
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In trigonometry we know that frequency and amplitude are independent because they have independent variables.
Then frequency and amplitude do not have the same equation of motion.
But according to Newtonian determinism, all of the motion of a system is determined an equation that depends only on the initial state of the string, being the totality of points on string and their velocities. The initial velocity is zero.
In a closed system, all of the movement must include both frequency and amplitude. That is, frequency and amplitude have the same equation of motion.
On the elastic string, the false assumption the string wave is trigonometric by itself implies amplitude and frequency have independent equations. Indeed, in the literature when mathematicians and physicists want the standing wave to stand down, they just add another arbitrary real-valued function. The frequency and amplitude are parameterized by sine wave and exponential functions, and each has its own time variable. Frequency and amplitude do not map on to the same interval of time.
But under one degree of freedom the standing wave never stands down because it is a surface defined by the potential energy. The surface being precisely those lines of motion along which energy is conserved.
So please tell why are two equations better than one? Why are two degrees of freedom better than one? Some even say the string has infinite degrees of freedom as if the string is not subject holonomic constraint.
You guy’s think the frequency is a velocity, but it's not. Frequency is a potential. Constant velocity and constant potential are both measure by a time unit.
Apparently, physicists and mathematicians think the velocity of the string is constant right up to the point in time when the string stops moving. Because the frequency is constant. That is, you think dv/dt = df/dt = 0. Then you write a partial differential equation that has the form of a sine wave. But your equation in the form u(x. t) is parameterized by time but contain coefficients that are not determined by the initial condition of the string. And it is not continuous on the lower limit.
That is to say the trigonometric string cannot map onto the string at rest. The trigonomtric string has no natural vector field.
Furthermore, the assumption of a continuous trig function implies that you are not required to have a lower semi-continuous boundary, without which it is not possible to formulate the law of string motion in terms of a minimum principle. (See Critical Point Theory by Mawhin and Willem)
There is a stumbling block here because it may seem that it is obvious that amplitude is dependent on time, since it occupies an interval of time. In fact, it is independent of time because decay always consumes the same amount of time regardless of amplitude magnitude.
the rate of amplitude decay da/dt2 = 0 is constant just like the frequency. They have the same Hamiltonian minimizing functions.
The equation da/dt2 = 0 is possible mathematically if the external derivative of amplitude decay is a tautochrone formed by the cycloidal involution of the cycloidal string manifold.
On a tautochrone, a rolling ball always arrives at the bottom of the curve at the same time regardless of how high the ball in dropped from.
This shows that frequency and amplitude are subject to the same holonomic restraint imposed by energy conservation.
When you give up your false assumption frequency is a velocity and change to frequency is a potential, you should see energy conservation is equivalent to volume preservation according to the principle of Liouville integration.
In attached diagrams I show the string manifold and amplitude decay manifold are both minimal surfaces of revolution and they have the same submanifold in Liouville integration except that amplitude is the involution of the cycloid at constant volume. Both manifolds uniform rectilinear motion. The frequency and amplitude run on the same time interval and clearly are not independent.
The trigonometric law of frequency/amplitude independence is not a natural Newtonian law, it is just an illusion that results from the assumption that frequency itself is sinusoidal.
But potential energy is a real number. You guys are just assuming frequency is real (so continuity seems to demand a trigonometric form).
Finally, if the moving string keeps moving until external force stops it, what force stops the string? Clearly not gravity, friction, or viscosity.
The answer is that the motion of the string is quasi-periodic meaning that perturbation involves only the loss of kinetic energy. Potential and kinetic energy do not alternate like a pendulum. When the string is deformed, the potential increases, but quickly the excess goes to kinetic energy and never returns to potential energy. Amplitude decay is simply the loss of kinetic energy doing work against the inertial mass of the string. Since it must be true that potential and kinetic energy have the same Hamiltonian equation, they cannot be independent.
Fig 1 The string manifold and amplitude decay manifold have the same submanifold
Fig 2 Amplitude Decay Manifold
Fig 3 Path of a Cycloidal Pendulum
Fig 4 Amplitude decay is the cycloidal involution of the Cycloidal Manifold.
Fig 5 Volume-preserving Liouville Integration
Fig 6 Constructing a cycloid geometrically using a horocycle give the string a constant radius of curvature.
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If the equation of motion is a sine wave, then of course amplitude and frequency are independent of each other. It's built into your assumption of an arbitrary real-valued function.
You have to use classic mechanics to answer the question formally. You can also use logical deduction.
I mean the frequency and amplitude decay have exactly the same time interval.
How does your sine wave run down?
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1. Dark energy has been a subject of considerable debate since its discovery due to its association with the accelerated expansion of the universe. Traditionally perceived as an unknown force or substance, dark energy is better understood as a by-product of the universe’s dynamic processes, particularly the transformation of potential energy into kinetic energy during and after the Big Bang. This work explores the interconnected roles of gravitational forces, kinetic energy, and apparent negative mass, highlighting that dark energy results from the complex interplay between these elements rather than being an independent substance.
2. Initial State of the Universe and Energy Transformation
Immediately after the Big Bang, the universe's total energy consisted of potential and kinetic components:
Eᴛₒₜ,ᴜₙᵢᵥ = PEᴜₙᵢᵥ + KEᴜₙᵢᵥ
In the earliest moments, the universe was dominated by potential energy, which rapidly approached zero as kinetic energy surged from zero to infinity:
PEᴜₙᵢᵥ: ∞ → 0, KEᴜₙᵢᵥ: 0 → ∞
This energetic shift was driven by gravitational dynamics, where the rapid conversion of potential energy into kinetic energy fuelled the universe’s expansion.
3. Emergence of Dark Energy: A Dynamic Outcome
Dark energy did not pre-exist the universe but emerged from the dynamic interactions between mass, gravity, and kinetic energy. As the universe’s initial potential mass accelerated due to gravitational forces, an apparent negative mass effect arose, which we interpret as dark energy:
Fᴜₙᵢᵥ = (Mᴘᴇ,ᴜₙᵢᵥ - Mᵃᵖᵖ,ᴜₙᵢᵥ)·aᵉᶠᶠ,ᴜₙᵢᵥ
Here, the apparent mass (Mᵃᵖᵖ,ᴜₙᵢᵥ) represents the dynamic influence of dark energy, emerging from the acceleration of potential mass under universal forces.
4. Inverse Relationship Between Potential and Kinetic Energy
The universe’s potential energy is inversely related to its kinetic energy, illustrating the natural balance that dictates cosmic evolution:
PEᴜₙᵢᵥ ∝ 1/KEᴜₙᵢᵥ
This relationship underscores the continuous transformation and reactivation of dark energy as the kinetic energy of the universe’s matter evolves.
5. Dark Energy's Dormancy and Reactivation
Dark energy enters a dormant state when kinetic energy and potential energy achieve equivalence. However, as the universe’s matter mass persists in motion, dark energy reactivates, leading to the accelerated expansion observed today. This cyclical behaviour underscores the transient nature of dark energy:
When PEᴜₙᵢᵥ = KEᴜₙᵢᵥ , Mᵃᵖᵖ = 0
As the universe continues to expand, dark energy becomes dominant once again, reflecting the evolving interplay of mass-energy dynamics.
6. Conclusion
Dark energy is not a fundamental substance but a manifestation of the universe’s dynamic processes. The accelerated expansion is driven by the continuous transformation of kinetic and potential energies, highlighting that dark energy is a consequence of the cosmic gravitational and kinetic interplay. This understanding shifts the perspective from viewing dark energy as an isolated force to recognizing it as an emergent property of the universe’s mass-energy transformations.
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Hi, Soumendra Nath Thakur
The idea is interesting, but some details need further consideration. You mentioned MG​, which represents the effective mass, defined as MG=Meff=MM−Mapp​. The effective mass appears in the equation for force as F=(MM−Mapp)⋅aeff​. However, this force must also be equivalent to the gravitational force Fg=G⋅(MG⋅M2)/r2.
How is M2​ related to (MM−Mapp), and is it included in the concept of negative mass?
Best regards Ittipat Roopkom
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Can somebody point to publications describing essential logic gates (e.g. AND and NOT) implemented in the most basic model of classical mechanics - bistable systems consisting of point masses (point charges) in external potential fields, manipulated by other external potential fields.
E.g., a single bit can be implemented in this classical mechanics framework as a bistable system consisting of a single charged particle trapped in one of two nearby potential wells of the field interacting with the charge of the particle. The time-dependent external field can be applied to move the particle between these two wells, thus implementing flipping the bit between 0 and 1. Perhaps, other time-dependent fields can be suggested, acting on a single and multiple bits, thus implementing the logic gates? See below.
The question is motivated by the physics of quantum computing (QC), where QC practitioners use external fields to manipulate qubits, thus implementing quantum gates, claiming that many/most/all quantum gates can be implemented by properly modulated external fields.
Thank you!
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Here is some information on mechanical logic gates and some thoughts on potential approaches to the implementation of such logic gates in simple classical mechanics model.
Mechanical logic gates exist - see, for instance:
However, these mechanical logic gates are more complex than just point charges in external fields - they involve solid bodies (of certain dimensions and shapes), interacting with each other.
For the bit implemented as a single charged particle trapped in one of two adjacent potential wells, as described above, perhaps the following approaches can be used to implement the NOT and AND logic gates.
To implement the NOT logic gate, consider the field that would drag the particle from the well 0 to the well 1, combined with the simultaneously applied field, dragging the particle from the well 1 to the well 0, along the non-intersecting paths. Regardless of the original position of the particle (well 0 or well 1), such time-varying field will flip the value of the bit from 0 to 1 or from 1 to 0. This time-varying field implements the NOT gate.
The AND gate can be constructed using the fact that the field from the charged particle trapped in the well compensates, in part, the field of this well. So, if the "depth" of the well is properly chosen, and the second particle is dragged through the well with another particle already trapped there, this second particle will not be trapped in this well, which can be used to implement the AND gate.
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It might be interesting to study latest research results on emergent information processing, which is basically finding computational methods that are capable to perform complicated computations by using self-organization and emergent computations without using their manual design.
The review with incorporated research results is here:
There is existing a database of videos depicting animatuins of simulations, see the link in the review. The software used to create those animations is open souce.
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Discussion:
This discussion explores the inherent limitations of the Lorentz transformation, a cornerstone of special relativity, particularly concerning its treatment of acceleration. While the Lorentz transformation adeptly describes relativistic effects such as time dilation, length contraction, and mass increase, it falls short in directly accommodating acceleration. This discrepancy becomes pronounced when the velocity-dependent Lorentz transformation fails to reconcile velocities between rest and inertial frames without the presence of acceleration, thus highlighting a significant gap in its applicability.
The discussion delves into the historical context of the Lorentz transformation, acknowledging its development by Mr. Lorentz and its status as a final form in science. However, it also underscores the expectation for accurate physics within its framework, especially considering the pre-existence of the concept of acceleration predating Mr. Lorentz. This expectation includes honouring Isaac Newton's second law, which governs the dynamics of accelerated motion in classical mechanics.
While the scientific community initially accepted the Lorentz transformation without questioning its treatment of acceleration, there is now a growing recognition of the importance of integrating principles from classical mechanics, such as Newton's second law, to address these limitations. The discussion emphasizes the need for a more comprehensive theoretical framework that harmonizes the principles of classical mechanics and relativity, thereby offering a more unified and accurate depiction of physical phenomena.
The Impact of Acceleration on Kinetic Energy in the Relativistic Lorentz Factor in Motion?
The Lorentz factor (γ) becomes relevant when the object attains its desired velocity and is in motion relative to the observer. Initially, when both reference frames are at rest, the object's energetic state reflects its lack of motion, resulting in zero kinetic energy (KE). As the frames separate, the moving object undergoes acceleration until it reaches its desired velocity. At this stage, the object's energetic state reflects its motion, and it possesses kinetic energy (KE) due to its acceleration. This acceleration is not accounted for in the Lorentz factor (γ). Once the object reaches its desired velocity, its energetic state reflects its motion, and it possesses kinetic energy (KE) due to its velocity. The Lorentz factor (γ) and kinetic energy (KE) play significant roles in relativistic motion. However, the acceleration component is not considered in the Lorentz factor (γ).
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The subject of discussion is really interesting. However, the author should have formulated his initial positions in an acceptable form - not so vague, but in generally accepted terms and comparisons.
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This discussion delves into the intricate relationship between acceleration, inertial reference frames, and Relativistic Lorentz transformation. It scrutinizes how the necessity of different velocities for separated reference frames underscores the pivotal role of acceleration in achieving this transition. By integrating classical mechanics concepts like Newton's second law and Hooke's Law with relativistic physics theories, the discussion enriches our comprehension of motion in diverse reference frames.
The initial motion and separation of inertial reference frames are crucial for their physics, but once they separate, they must have different velocities, with the first frame's velocity (v₀) and the second frame's velocity (v₁) needing acceleration to achieve v₁ > v₀. This acceleration is essential in both classical mechanics and Relativistic Lorentz transformation. The Lorentz factor (γ) is a velocity-dependent factor that involves velocity-induced forces, affecting the behaviour of objects in motion. It is based on the equation E = KE + PE, where KE is treated as 'effective mass'. Piezoelectric materials can convert mechanical energy from vibrations, shocks, or stress into electrical energy, typically an alternating current (AC). This process involves force-mass conversion, where the force applied to the piezo actuator results in a deformation or displacement. The displacement ΔLɴ of the actuator is inversely proportional to the stiffness, highlighting the interplay between force, stiffness, and displacement in force-mass conversion.
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Mr. Preston Guynn,
Thank you for sharing your insights and research on the role of acceleration in special relativity, particularly concerning rotational motion and its implications for particle characteristics. Your work undoubtedly provides valuable contributions to the field.
However, I must point out that your reply deviates from the objectives outlined in the initial discussion topic, "The Role of Acceleration in Relativistic Lorentz Transformation." While your emphasis on acceleration in rotational motion within special relativity is fascinating, it shifts the focus away from the broader discussion on acceleration across diverse reference frames and its relation to relativistic Lorentz transformations.
Furthermore, the specific mention of your research papers and poster, while informative, detracts from the aim of engaging in a meaningful discussion centred around the broader topic. While your proofs and correlations between physical constants are undoubtedly significant, they are more specialized and detailed than what the original discussion topic intended to explore.
In essence, for reasons to accept a meaningful discussion within the scope of "The Role of Acceleration in Relativistic Lorentz Transformation," it would be more beneficial to focus on broader concepts and their implications across various reference frames, rather than specific aspects of rotational motion within special relativity.
Best regards,
Soumendra Nath Thakur
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This discussion aims to delve deeper into the interconnectedness of classical mechanics, wave mechanics, and relativistic physics, alongside an exploration of piezoelectricity, guided by the fundamental concepts of velocity, speed, and gravitational dynamics. Drawing inspiration from recent research, we seek to unravel the intricate relationships between external forces, atomic structures, and wave phenomena, shedding light on potential advancements in materials science, physics, and engineering.
Join us as we navigate this interdisciplinary landscape and contemplate its implications for future scientific endeavours.
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I for one am not clear what the overall purpose of the discussion will be. It starts off being remarkably general and universal, then lurches into the very specific piezoelectricity. However, if we are looking for a theory of everything I would start with the Principle of Least Action. It applies to all of classical mechanics, relativity, quantum mechanics and anything involving waves, including light. Accordingly, I would recommend for any such study to first think about minimizing the generated action.
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I can measure positions in classical mechanics because my measurements do not disturb the state of the system.
Why measurements cannot be used without perturbation of the system for atomic or subatomic interactions, for example using smaller scale interactions like neutrinos?
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I think it's a bit crackpot, maybe in 50 years!
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In classical mechanics, an important principle is the principle of relativity: the physical laws are invariant with respect to the transformation from one inertial frame into another. Maxwell's equations seem to violate this principle, because they contain a distinguished speed -- the speed of light c. It was this apparent conflict between mechanics and electrodynamics that led Albert Einstein in 1905 to his special theory of relativity. By a careful analysis of the concept of time, he realized that Maxwell's equations do indeed obey the relativity principle, although the transformation law becomes more complicated (Lorentz instead of Galileo transformations).
Einstein was very aware of the problem of the speed of light inconcitensy with Newton's laws (and Maxwell's equations). We was also aware of the observer effects (relative velocity effects) and he married the two, being the fist to explain the constancy of speed of light or reconcile classical mechanics with that fact.
This has been the only (albeit successful) attempt. Are you aware of any others >
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Robert A. Phillips
: " What about fluid dynamics as an option to gravitomagnetism? "
Fluid dynamics sounds good! But it's a way outside my area of expertise, so I'll have to leave that to other people. There's also a strong overlap with acoustic metrics:
I do accept that imposing strong gravitomagnetism just to fix Newtonian theory is a bit extreme, and a slightly "ad hoc" solution. But there are also quite a few other reasons why we seem to need gravitomagnetism:
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In classical mechanics, kinetic energy is KE = ½mv², where m is mass and v is velocity. So mass multiplied by the square of the speed is an energy. The concept of energy plays a fundamental role in understanding the behaviour of objects in motion. One of the key forms of energy is kinetic energy, which is intimately linked to an object's mass and velocity. Additionally, in the realm of relativity, Einstein's famous equation E = mc² introduces a profound understanding of energy in terms of mass and the speed of light. This discussion aims to delve into the classical expression for kinetic energy KE = ½mv² and its connection to relativistic energy (mc²).
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Dear Mr. Stam Nicolis The main question is, "Is relativistic 'energy' the same representation of kinetic energy as 'energy' in classical mechanics, which is questioned on the basis that the main point of discussion is, "mass multiplied by the square of speed is 'energy'.” The question is between relativistic and mechanical 'energy', it doesn't ask the differences between relativistic and mechanical processes. The relativistic energy, as represented by the mass-energy equivalence principle (E = mc²), can be seen as a similar representation of energy as kinetic energy in classical mechanics. Both concepts involve the multiplication of mass by the square of speed to yield energy. In classical mechanics, kinetic energy (KE = ½mv²) quantifies the energy associated with the motion of an object. This expression illustrates that there's an energy associated with the mass of an object and its velocity squared.
Regards
Soumendra Nath Thakur
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We assume that the accepted definition of a quantum particle is one subject to Schrödinger dynamics as opposed to Newtonian dynamics.
This implies some limitation on the size or volume of the quantum particle V.
In other words there exists a critical volume Vc where if V<< Vc the particle obeys quantum dynamics and for V >> Vc the particle is subject to Newtonian classical mechanics.
The question arises: is there an accepted estimate of the critical size Vc?
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Dear All,
I have succeeded to formulate a concept that is realistic and that captures reality in metaphysical terms, which can be used to prove the existence of the graviton particle:
(Hungarian)
Has English translation:
- abstract:
- conclushion:
and graviton:
Onto this article, where was created the term of a priori entity an universal form of electric-magnetic matter can be said that the quantum is an elementary a priori entity which is the building particle of ordinary matter every particle sub this dimenshion is a quantum... somewhat here cen be used definition of Prof. Ismail Abbas : a bit transformed
'This implies some limitation on physical size or volume V.
In other words there exists a critical volume Vc where if V<< Vc' (when the particle phisical dinamics cannot be related to our dimension, which is why quantum dynamics was formulated to make possible phisical description on this scale). §
'The quantum particle itself has a wave function which is the Schrödinger solution which extends'(to the outer boundary of the space phase of the a priori entity).
On the other hand, the world of quantum particles is the one that is estimated to be equal or smaller than an atom (atomic and subatomic world), which means that Vc is approximately the size of an atom.
Regards,
Laszlo
§-'and for V >> Vc the particle is subject to Newtonian classical mechanics.'
(In my opinion, these is an erroneous conclusions:
Newton's concept can only be applied to the solid state of ordinary matter; Newton could not plausibly explain the cause of the phenomenon of garvitation! )
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Since Einstein proposed the fundamental shiftbin thinking, that time and space are interwoven, people began to doubt time's fundamental it. Althoughtbitbis still ladenly agreed to be so.
Einstein made the proposal to deal with incompatibilities between properties of light and principles of classical mechanics, the science of describing motion its causes and what its possible (given certain kinematics and so-called dynamics parameters in a system) . This then led to the most hroad, novel and consistent confirmstions of any theory in science. Yet, doubt remains.
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Time is not fundamental property of the universe!
The time Is a a reference tool to describe physical phenomena, and useful for our social environment functionality .
Regards,
Laszlo
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Current classical mechanics, Newtonian, are force causality centered.
However, linear ordering of events (LOoE) based causality and teleological are also options. Here I present the basics of LOoE and a glimpse of the challenges to odopting it to low speed mechanics.
Linear ordering based
**Speed of light-based i.e light cone causality is fundamental
** Newtonian force-based causality is fundamental in SR, GR but needs to be extented in all physics
Challenges
**problem of adopt ing low speed Requirements of classic mechanics to light speed causality
** force causality must be eliminated and still low speed mechanics work
To develop a full outline of the challenges, what do you think one should add ?
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The question is why we defined a field i.e classical mechanics not by domain of definition i.e low speed mechanics, small masses, highly restricted motion, but by the principles Newton adopted.
Principles and theoretical framework, even if successful, do not defined the context of a field. With this in mind, can relativistic framework be applied? In the end CM is still natural and some insights from GR might find expression, not complete description
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Modern quantum mechanics is based on the Shrödinger equation (SE) with the Bohr-Copenhagen interpretation.
As far as I understand, SE creates its own independent world outside of classical mechanics or any other world of measurement and/or interaction.
The box itself, with a cat and a bomb inside, constitutes the separation or boundary between the QM world and the other worlds of measurement and interaction.
In other words, the box creates a pure quantum mechanical statistical system (world) with its own QM states where their linear superposition is possible.
And yet, there are many solutions for SEs where the essential box is poorly taken into account, how?
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This is just an introductory approach to the most important unanswered question:
What would happen if the box was transparent?
My personal view is briefly as follows:
Modern quantum mechanics is based on the Shrödinger equation (SE) with the Bohr-Copenhagen interpretation.
It creates its own independent world extending throughout x-t space outside of classical mechanics or any other world of measurement and/or interaction.
And yet, there are many solutions for SEs where the essential box is poorly taken into account.
Indeed, the box itself is not part of modern QM but it is the ignorance of the state of the system which introduces QM.
Therefore, E. Schrödinger assumed that the box itself, containing a cat and a bomb inside, must be non-transparent to prevent photons carrying information about the state of the system from escaping into the world real.
In other words, the non-transparent box constitutes the separation or boundary between the QM world and the other worlds of measurement and interaction.
And yet, what would happen if the box was transparent?
This is equivalent to removing the box as a whole and hence we cannot create a pure quantum mechanical statistical system (world) with its own unknown QM states where their linear superposition is possible.
To be continued.
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Most masters focus on general review of qm, classical mechanics, assesing students skills in classical yet heneric and self-value calculative and interpreting capabilities.
The English MSc's on the other hand, provide an introduction to the physical principles and mathematical techniques of current research in:
general relativity
quantum gravity
quantum f. Theory
quantum information
cosmology and the early universe
There is also a particular focus on topics reflecting research strengths.
Graduates are more well equiped to contribute to research and make impressive ph. D dissertations.
Of course instructors that teach masters are working in classical and quantum gravity, geometry and relativity, to take the theoretical physics sub-domain, in all universities but the emphasis on current research's mathematical techniques and principles is only found in English university'masters offerings.
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Μr Verch indeed My research, which was not fully developped at the time I asked my question, showed that this the case.
Still, a 30% offer the classic calculative phys quantities - based skills of big 4 (and less conceptual understanding assesment or less actual "doing the science" skills of qm, CM, statistical and thermal. Physics) which trends to be considered classic masters structilure or outdated.
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I think these phenomena follow the scientific facts defined in the classical mechanics, but not theories or definitions in Einstein's mechanics.
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Stam Nicolis. We are living in electrical, electronics, and digital world.
Because Newton(atom), J. J. Thomson (Electron), Niels Bohr (motion of electron in outer orbits of atom), Rutherford (nuclear physics), ..., etc. These are the development/growth of science.
Please don't escape by saying these are history of physics.
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A review of analogies used in high energy physics is a 2020 Ph.D dissertation by Gunnar Kreisel, Analogies in Physics — Analysis of an Unplanned Epistemic Strategy, Gottfried Wilhelm Leibniz Universitat Hannover.
Are there any books or articles for analogies in classical mechanics?
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Sure! Regarding articles on the subject, cf. Dirac's article https://www.informationphilosopher.com/solutions/scientists/dirac/Lagrangian_1933.pdf
in particular his equations (8) and (9).
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We assume that the conservation of probability does not exist in quantum mechanics as in the case of classical mechanics.
According to Shrodinger's equation, there is a continuous generation of probability density in subatomic systems.
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*** Answer continued part III.
This question is not just about physics (classical/quantum) or mathematics, but a rigorous and comprehensive combination or incorporation of all three.
I'm sure many researchgate contributors can answer this question as well as I, if not better.
In fact, it is possible to solve the Schrödinger equation via a statistical transition matrix without needing the Schrödinger equation itself in the same way as solving the heat diffusion PDE, in his case the most general, without needing the heat equation itself.
The only requirement is the ability to imagine nature in 3D geometry (solid geometry) and then, in a later stage, in 4D x-t unit block space.
The energy field in 4D x-t unit space is resolved in B-matrix chains and can also be resolved via any other suitable statistical transition matrix.
My recommendation here is not to listen to those "scientists" who dismiss the whole matter as insignificant due to their own lack of imagination and understanding.
While waiting for your answers or suggestions, I am preparing my own answer based on a modified B-Transition matrix (we call it Q-matrix).
Therefore, in a following answer, we provide our own numerical answers (where I assume you can personally provide answers that are adequate or better than mine) calculations of the outputs of the Schrödinger equation in an infinite potential well via the technique of the Q-matrix for the quantum transition.
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I uploaded an article on research gate with a wrong date of publication. The article is "Investigating Students’ Physico-mathematical Difficulties in Classical Mechanics and Designing an Instructional Model". The article was published in 2018 by American Journal of Educational Research, 2018, Vol. 6, No. 8, 1127.
When uploaded on research gate it picked the date it was uploaded April 2023
How can the date of publication be corrected?
Waiting to hear from you soon.
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The method I mentioned is also given there.
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I am new to modeling, i am only familiar with Gaussian (quantum mechanics only)
And I want to model the adsorption mechanism of Dye Methylene blue on metal carbonate because therir are many psoible mechanisms like elecrostatic attraction force or Hydrogen bond. I don't know if it works with quantum mechanics or classical mechanics.
plz advice me
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You're welcome Aly Reda.
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Physics is Stalled by Politics - Paper with solutions to 64 significant problems published in #3 journal but rejected by arXiv.org. The new paper entitled, Measurement Quantization, published Jan. 25, 2023 in the Intl. J. Geom. Methods Mod. Phys., lays out the foundations of quantum behavior using existing classical expressions, expanded to account for the discrete internal frame of the universe. The paper presents predictions of a length contraction effect unrelated to that described by Einstein and then presents measurement data to support the approach. It then derives the physical constants and the laws of nature from first principles. It unifies gravity with electromagnetism and writes both SR and GR anew from first principles, therein leading to a derivation of the equivalence principle. It presents simple classical solutions to dark energy, dark matter and a no free parameter description of early universe events. But we should restate, this paper is classical mechanics, offering 530 equations describing phenomena across the entire measurement domain. While extensive support is offered, additional support rests on a long history of support for classical mechanics. In regards to posts regarding the heated debate about the absurdity of new research being filtered, I agree! Even though this paper is published in the #3 mathematical physics journal in the world (by SJR ranking) and is indexed to NASA’s ADS, it was rejected by arXiv.org. I then sought the assistance of a top five ranked astrophysicist in the world. The case was reopened, reconsidered and then rejected a second time, as though classical mechanics was of questionable scientific merit. The point is, classical mechanics is worthy of arXiv.org. We must conclude that the paper was rejected because of a higher cultural mandate, that breakthroughs that impact the existing funding model cannot appear as though they enjoy support by the community. For insight, see this post by Avi Loeb: https://avi-loeb.medium.com/how-to-navigate-academia-6e8c4feea460 I will state, this paper presents solutions to 82.5% of all outstanding problems in cosmology among many other classical and quantum problems. If community leaders really want to effect change, they would use well-vetted publications as example of this cultural absurdity and the need for change. And the best way to affect that change is to begin by supporting breakthroughs in existing classical mechanics on their blogs, in videos, in presentations and at conferences. Community leaders should not be posting literature as unanswered (i.e., dark matter, dark energy) where existing classical mechanics offers insight with straight-forward calculations. Otherwise, such individuals mimic the same cultural bias they are arguing against.
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It is essential for community leaders to recognize and address these issues by actively supporting breakthroughs in classical mechanics and other fields. This support can be demonstrated through various platforms, including blogs, videos, presentations, and conferences. By acknowledging the value of new research and encouraging open-mindedness, community leaders can help foster an environment that welcomes diverse perspectives and drives scientific progress.
To truly effect change, community leaders must also be willing to question established beliefs and paradigms, including those related to dark matter and dark energy. By remaining open to alternative explanations and solutions, they can help ensure that innovative ideas are not prematurely dismissed or overlooked. In doing so, they can pave the way for a more inclusive and dynamic scientific community that is better equipped to tackle the challenges of modern physics.
Regards, Alessandro Rizzo
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Start with a purely classical case to define vocabulary. A charged marble (marble instead of a point particle to avoid some singularities) is exposed to an external electromagnetic (E&M) field. "External" means that the field is created by all charges and currents in the universe except the marble. The marble is small enough for the external field to be regarded as uniform within the marble's interior. The external field causes the marble to accelerate and that acceleration causes the marble to create its own E&M field. The recoil of the marble from the momentum carried by its own field is the self force. (One piece of the charged marble exerts an E&M force on another piece and, contrary to Newton's assumption of equal but opposite reactions, these forces do not cancel with each other if the emitted radiation carries away energy and momentum.) The self force can be neglected if the energy carried by the marble's field is negligible compared to the work done by the external field on the marble. Stated another way, the self force can be neglected if and only if the energy carried by the marble's field is negligible compared to the change in the marble's energy. Also, an analysis that neglects self force is one in which the total force on the marble is taken to be the force produced by external fields alone. The key points from this paragraph are the last two sentences repeated below:
(A) An analysis that neglects self force is one in which the total force on the marble is taken to be the force produced by external fields alone.
(B) The self force can be neglected if and only if the energy carried by the marble's field is negligible compared to the change in the marble's energy.
Now consider the semi-classical quantum mechanical (QM) treatment. The marble is now a particle and is treated by QM (Schrodinger's equation) but its environment is an E&M field treated as a classical field (Maxwell's equations). Schrodinger's equation is the QM analog for the equation of force on the particle and, at least in the textbooks I studied from, the E&M field is taken to be the external field. Therefore, from Item (A) above, I do not expect this analysis to predict a self force. However, my expectation is inconsistent with a conclusion from this analysis. The conclusion, regarding induced emission, is that the energy of a photon emitted by the particle is equal to all of the energy lost by the particle. We conclude from Item (B) above that the self force is profoundly significant.
My problem is that the analysis starts with assumptions (the field is entirely external in Schrodinger's equation) that should exclude a self force, and then reaches a conclusion (change in particle energy is carried by its own emitted photon) that implies a self force. Is there a way to reconcile this apparent contradiction?
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I am studying Finite element method and Classical Mechanics. I have come across three important terms
  1. Principle of virtual work (found in Classical Mechanics)
  2. Principle of minimum potential energy (found in Finite element method)
  3. Calculus of variation (found in Mathematics while searching concept of Variational method of Finite element method)
All above terms are being used interchangeably and in bits and pieces in different book and no book did not explain properly about the relation of those three terms.
I feel that there are some relationship but not able to figure it out. Can someone explain all these three terms and how these are inter related?
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Sorry outside of my especilest
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No way to find out unless you do the actual proposed experiment:
This guy here:
claims he made an interference Galton board https://en.wikipedia.org/wiki/Galton_board experiment and got an interference pattern. This would explain that quantum randomness originates from determinism and is a result of hidden local variables possible in the photon's environment in contrast to the Bell inequality EPR experiment?
Note:
As a reminder this is nothing extremely new, actually a deterministic explanation of the quantum DS single photon experiment was previously demonstrated by this experimental application of the pilot-wave theory using bouncing droplets:
The photons which are epicenters of electromagnetic distortions when translating in space distort the EM mass fiel of the environment they move in.These distortions of the mass field environment are feedback at the photon as alterations in its motion trajectory. Photons as massless particles may pass through each other without being affected but dynamic EM flux coming from the mass field of their environment they interact with can affect their trajectory.
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Good points. However, I cannot see why the EM wig the photon lefts behind at its passage interacting with the matter field of its environment cannot be regarded as a local hidden variable.
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Hamiltonian mechanics is a theory developed as a reformulation of classical mechanics and predicts the same outcomes as non-Hamiltonian classical mechanics. It uses a different mathematical formalism, providing a more abstract understanding of the theory. Historically, it was an important reformulation of classical mechanics, which later contributed to the formulation of statistical mechanics and quantum mechanics.
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This is my humble opinion about your interesting question:
  • In classical mechanics, we start from the Hamilton formulation leading us to the concept of the phase space, which is used in the microcanonical ensemble widely studied in statistical mechanics, & where energy must be preserved in order to have some classical perspective of what happens with millions of microscopical states.
  • In quantum mechanics, we have a sort of similar approach when we use elastic scattering theory which uses an energy conservation principle and a phase space, & which allows observing a classical perspective of the quantum micro world.
Interesting question, Best Regards.
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The electron and photon are extensively interrelated, and therefore should share many common properties, equalities and laws. According to De Broglie, one such law is the Planck-Einstein relation, stating that as wavelength (i.e. radial orbit path) decreases, energy increases. An electron at a smaller orbit (today believed to be the ground state) most assuredly has a lower wavelength, and therefore should display a higher energy, not a “lower” energy level of the so called ground state.
Bringing this question up previously, two primary responses are typically offered... the "negative energy" aspect taught in high school, and the "pay no attention to classical mechanics" response. The last I checked, negative energy does not exist. Even it if did, a "zero" electron energy believed to exist at ionization is still greater than a -13.6eV at the believed minimum radius ground state, and therefore does not answer the question. As far as the second typical response, some sort of waving of the hands is offered, stating that the electron does not obey classical mechanics. Ok, I'll bite for argument sake, but then please explain why even the Schrodinger probability wave function also states that electron energy is minimum at a smaller radius ground state, and increases with a radial distance increase away from the proton. No so-called classical mechanics here.
I propose a model of Hydrogen for consideration, and welcome any peer review comments:
1) When the electron gains photonic energy, its orbiting radius is reduced and therefore its orbiting path per cycle decreases, equating to a higher cyclic frequency, equating to a higher energy per the Planck-Einstein relationship [so far so good, nothing strange here].
2) As it’s radius (r) decreases its Coulomb attraction force to the proton increases by r squared, and therefore so does its Potential Energy (PE) by 1/r (since E=F x dist). Therefore to remain in this particular lower radius increased energy level state, its orbiting velocity must then also increase to remain in this stable orbit, thereby increasing its associated Kinetic Energy (KE). [if you’re going to wave your hands here and say that classical mechanics doesn't apply to atomics, then state WHY and give an explanation, please don’t just regurgitate something you have read. Electrons have mass, and it is orbiting another mass. A very "classical" situation].
3) This increasing orbital velocity (frequency) has two limits: a) The speed of light, and b) Ionization "escape velocity" of the electron mass.
4) Once either of these velocities occur, the electron must then, a) convert completely into a photon at the speed of light, b) completely ionize (escape) from the proton, or c) convert part of its energy into a photon plus transform itself to a lower energy (higher radius) energy level [nothing too strange here unless there is a classical hand waving fetish].
In other words, attempt to purge the incorrect visualization thinking that as an electron gets further and further away from the proton, that it is closer and closer to becoming ionized. Attempt to think about WHY and HOW the electron would want to ionize, and you’ll come up with the above postulate. In fact, attempt to think about WHY only particular wavelength photons will be absorbed by the Hydrogen electron. Perhaps it is because it has the same geometric orbital size or a harmonic of that size. I have actually derived this harmonic to be the Fine Structure Constant / 2 utilizing classical mechanics, and by doing so, believe I have also discovered why and how the quantum aspect of the electron energy levels must occur.
- J.L. Brady
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Radial gravitational wave study, physical interpretation of the fine-structure constant, resolution of the problem of wave-particle duality for electromagnetic radiations, and quantization of space-time :
Have a nice day :)
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the radial gravitational wave depends on amplitude , potential of energy .It introduced a good idea about dilations of space and the radiation.
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I am asking this question on the supposition that a classical body may be broken down in particles which are so small in size that quantum mechanics is applicable on each of these small particles. Here number of particles tends to uncountable (keeping number/volume as constant).
Now statistical mechanics is applicable if practically infinite no. of particles are present. So if practically infinite number of infinitely small sized particles are there, Quantum Statistical Mechanics may be applied to this collection. (Please correct me if I have a wrong notion).
But this collection of infinitesimally small particles make up the bulky body, which can be studied using classical mechanics.
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There is no difference Prof. Manish Khare, we have two windows to watch the physical world, the classical & the quantum approaches, but there is a window, they are the Wigner probabilistic distributions.
Best Regards.
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Dear Sirs,
R Feynman in his lectures, vol 1, chapter 12, Characteristics of force wrote:
"The real content of Newton’s laws is this: that the force is supposed to have some independent properties, in addition to the law F=ma; but the specific independent properties that the force has were not completely described by Newton or by anybody else, and therefore the physical law F=ma is an incomplete law. ".
Other researchers may consider the 2nd Newton's law as a definition of force or mass. But R. Feynman did not agree with them in the above chapter.
What is your view on the 2nd Newton's law?
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Dear Mr khripov,
I prefer that we agree on the questions you ask.
For me F'=-kx is Hook's law.
For me F=ma is Newton's second law.
If in a given problem F=F', then -kx=ma.It is Newton's law particularized to the case where the force applied is that of a spring (Hook's law).
At static equilibrium, we have theoretically kx=mg. The theory tells you that kx=mg.
You want to check this relation experimentally. Fabricate identical objects of the same mass m. Hang on the spring one object, then two objects, then three objects, etc.... At the first elongation mark the elongation with a pen x=X0. You will notice experimentally that for 2m you will have an elongation of 2(X0), for 3m you will have 3(X0), etc ..... Plot on a graph the elongation of the spring as a function of the hooked mass. You will see that the curve is a straight line and that the slope of this line is (1/k) in the system of units you have used.
Conclusion:
1) You have therefore verified the linearity of x as a function of m and this is the verification you wanted to make.
2) You have deduced the value of k.
Important remark:
Clearly, the measurements you have made do not depend on any law (including the law of the relation you want to verify).
I hope I have answered your question.
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Dear Sirs,
Everyone knows the derivation of Lorentz transformations from electromagnetic wave front propagation. But Lorentz transformations are the basis of the general mechanics theory. It seems to me it is logically correct to derive the transformations from purely mechanical grounds. But how to do this? Mechanical (sound) waves are not of course applicable here. Or there is only purely mathematical approach? I The later is also not good in physics. Could it be derived from gravitational wave propagation? If it is so is there any controversy because General relativity is based on special relativity? I would be grateful for your suggestions.
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Length contraction CAN be deduced by purely mechanical processes. The other Transformations are substituted by other mechanical means. For example, time dilation can be speed of light changes in different media density.
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Dear Sirs,
I would like to find out whether galilean relativity principle (which means the same
form of three Newton's laws in all inertial frames) is derived from the three Newton's laws or
any other classical mechanics statements.
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Dear Anatoly,
If you are satisfied by the 1st Newton's law, which is basically equivalent to Galilean relativity, there is nothing to prove.
But if you mean to axiomatically construct a logically self-consistent mechanics without Galilean relativity, like non-Euclidean geometries proposed by mathematicians in 19th century, that should be possible, of course.
There are plenty of mechanical systems without translation invariance - a pendulum, a bent railway, a body in an "irremovable potential field", etc. But they are used to be well handled by existing formalism: systems with nonlinear constraints - by Lagrangian, potential motions - by Hamiltonian.
So, it is unobvious whether there is need for something new physically. And mathematically, it must be just part of non-Euclidean geometry, already well developed.
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Hello Dear colleagues:
it seems to me this could be an interesting thread for discussion:
I would like to center the discussion around the concept of Entropy. But I would like to address it on the explanation-description-ejemplification part of the concept.
i.e. What do you think is a good, helpul explanation for the concept of Entropy (in a technical level of course) ?
A manner (or manners) of explain it trying to settle down the concept as clear as possible. Maybe first, in a more general scenario, and next (if is required so) in a more specific one ....
Kind regards !
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Dear F. Hernandes
The Entropy (Greek - ἐντροπία-transformation, conversion, reformation, change) establishes the direct link between MICRO-scopic state (in other words orbital) of some (any) system and its MACRO-scopic state parameters (temperature, pressure, etc).
This is the Concept (from capital letter).
Its main feature – this is the ONLY entity in natural sciences that shows the development trend of any self-sustained natural process. It is the state function; it isn’t the transition function. That is why the entropy is independent from the transition route, it depends only from the initial state A and final state B for any system under consideration. Entropy has many senses.
In the mathematical statistics, the entropy is the measure of uncertainty of the probability distribution.
In the statistical physics, it presents the probability (so-caled *statistical sum*) of the existence of some (given) microscopic state (*statistical weight*) under the same macroscopic characteristics. This means that the system may have different amount of information, the macroscopic parameters being the same.
In the information approach, it deals with the information capacity of the system. That is why, the Father of Information theory Claude Elwood Shannon believed that the words *entropy* and *information* are synonyms. He defined entropy as the ratio of the lost information to the whole of information volume.
In the quantum physics, this is the number of orbitals for the same (macro)-state parameters.
In the management theory, the entropy is the measure of uncertainty of the system behavior.
In the theory of the dynamic systems, it is the measure of the chaotic deviation of the transition routes.
In the thermodynamics, the entropy presents the measure of the irreversible energy loss. In other words, it presents system’s efficiency (capacity for work). This provides the additivity properties for two independent systems.
Gnoseologically, the entropy is the inter-disciplinary measure of the energy (information) devaluation (not the price, but rather the very devaluation).
This way, the entropy is many-sided Concept. This provides unusual features of entropy.
What is the entropy dimension? The right answer depends on the approach. It is dimensionless figure in the information approach (Shannon defined it as the ratio of two uniform values; therefore it is dimensionless by definition). On the contrary, in the thermodynamics approach it has a dimension (energy to temperature J/K)
Is entropy parameter (fixed number) or this is a function? Once again, the proper answer depends on the approach (point of view). It is a number in the mathematical statistics (logarithm of the number of the admissible (unprohibited) system states, well-known sigma σ). At the same time, this is the function in the quantum statistics. Etc., etc.
So, be very cautious when you are operating with entropy.
Best wishes,
Emeritus Professor V. Dimitrov vasili@tauex.tau.ac.il
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Many have asked, why does a theory fail? The challenge is establishing a physical connection. You have to step back and look at it this way. Anyone can take classical mechanics and introduce a variable to produce a ‘new’ approach. This is a critical problem pervasive throughout the community. This is NOT what physicists are looking for.
You might ask, isn’t that the point? No. Here’s why. Let us say that classical mechanics is a model described by A+B=C. But there is some unknown quality such that many results are askew.
Someone introduces a new idea E. It doesn’t matter what it is. But consider E(A+B)=EC. Now, maybe EC=h. So we have E(A+B)=h. Boom! We think E is this missing physics that solves amazing problems. All calculations result in perfect matches to the measured values.
Why is this a failure? We took something we already knew and multiplied it by a random value. Most physicists see through this right away. We’ve done this so many times that we can see it immediately.
MQ differs. Frames of reference are well understood. Discrete and non-discrete measure are well-understood. Planck Units are well-known. We ask only that one frame be discrete, the other not. This is a clear physical foundation without a concept E.
For clarity, LQG considers all frames discrete. Supersymmetry does not address discreteness. String Theory is in all likelihood and example of E, but so complex we cannot resolve it.
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Willem Marinus de Muynck , I think that this modern trend for rejecting the idea that theories can be true or false is unscientific, and indicative of a rot in modern physics, in which "everyone must have prizes", and everyone has to be protected against their precious theories being overturned.
This seems to be to just be a way of protecting bad science and/or the status quo, and trying to eliminate the possibility of an inconvenient future scientific revolution.
In reality, scientific theories are disproved all the time (or at least, they used to be).
Phlogiston theory (~1667-), was the greatest theory of chemistry that had ever been proposed, it put chemistry onto a more solid footing, and it even had elements of mass-energy conversion, in that it related weight-change to energy output or input. It arguably deserved to be true, and it was our major theory for about a hundred years. Then we found out that these weight-changes were due to standard chemical reactions with previously-unisolated element, oxygen, and the hypothesis of an additional attribute of matter, phlogiston, was set aside.
Phlogiston theory did not live on as a limiting case of subsequent chemical theory, with its own domain of applicability: it was simply the wrong explanation.
Similarly, Newton's explanation for lightbending at an air/glass boundary as being the idea that light bends towards the region of fastest lightspeed - it (in its assumed sense) simply didn't agree with the experimental evidence.
And how about "creation science" which claims that the Earth was created by God in maybe about 5,000-10,000 BC? Would you say that that's true, within a given domain? Or how about the tobacco industry's early assertions that smoking tobacco was not implicated in raised levels of lung cancer? How about magical healing crystals?
Part of the point of science is supposed to be an attempt to head towards the truth (even if we can't guarantee that we'll ever quite get there), and part of that is about eliminating possibilities and establishing what appears NOT to be true (as in Popper's principle that a theory that doesn't allow at least the chance of invalidation isn't "scientific"). This useful (and efficient) process of elimination is not served by saying that all theories are true.
It's also perilously close to the Trump election campaign's idea of "alternative truths", that must all be given equal airtime.
The scientific concept that things can be wrong is a precious one, and it's part of the discipline of being a scientist that sometimes we do turn out to be wrong (and sometimes even wrong about things being wrong!), and are professionally obliged to admit it when it happens. The discovery that something is wrong can be incredibly important, and when I hear people saying that theories are never "really" wrong, it gets me worried about the quality of the associated science.
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Dear Sirs,
The 1st law in Newton`s principia are now understood as two statements: the determination of inertial frame reference (if F=0 then a=0 and if F is not equal 0 then there is some body accelleration "a"); there is in nature at least one inertial frame reference. Theoretically I can understand it a little bit. As we have such a determination of inertial frame reference then the 2 nd Newton law is not directly followed from the 1 st law, or this determination is partly independent of the 2nd law. So it looks like logically good.
But what we have in experiment? I do not know whether there is any research on experimental determination of any particular inertial system (like International Celestial Reference System) using the 1 st Newton law. So in practice we use the 2 nd law (e.g. school example - foucault pendulum plane rotation). Could you clarify on the experimental and theoretical determination of inertial frame reference. You know there are teachers that see the 1st law as the consequence of the 2nd law.
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The Galilean invariance, Dr. Anatoly A Khripov, the laws of motion are the same in all inertial frames if there is no acceleration due to an external force. But sometimes a conservation law (momentum, or energy) is needed experimentally to be tested.
For example, the capillary movement without viscosity of the 4He isotope is based on the Galilean invariance of energy and momentum, despite it is a quantum liquid, showing how general is the Galilean invariance.
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I got a question (in a Question paper) as follows:-
A three-sphere is like a two-sphere. It consists of all points equidistant from a fixed point (the origin) in four dimensional space. Consider a particle free to move on a three sphere. How many conserved quantities does this system possess?
The answer say's 6 conserved quantities are there, but how is it possible? Can anyone kindly explain.
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The dynamics of a particle moving on any-fixed-manifold is given by the Lagrangian
L = (1/2)gIJ(x)(dxI/dt)(dxJ/dt)
where xI(t) are the coordinates in the ambient space and gIJ(x) is the metric of the manifold, in the present case, a 3-sphere.
Spherical symmetry means that angular momentum is conserved. The components of angular momentum are given by the tensor MIJ=xIpJ-xJpI, where pI=gIJ(x)(dxJ/dt) and pI=gIJ(x)pJ.
Said in an equivalent way: If gIJ(x) is the metric of a sphere, it's a standard exercise that these quantities are conserved for the xI(t) that solve the equations of motion.
In d dimensions there are d(d-1)/2 non-zero components of MIJ; for d=4 this gives 4x3/2 = 6.
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Suppose, in fact, our 4-dimensional space is closed and represents the product of a sphere onto a torus or a sphere onto a cylinder, and the observer's coordinate lines are helical lines of a torus or cylinder. Then in such a closed world a material particle can be represented by a rotating ring on a torus or cylinder. Let the intrinsic angular velocity of rotation of the ring be the mass of the particle, and let the winds blow in our closed world, which blow our ring according to the principle of the least number of revolutions of the ring. Does not it resemble the principle of least action of classical mechanics. And since in this case the action is the number of revolutions of the ring, then at full revolutions we get a quantized action.
If you are interested in continuing, then welcome to
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IB: You seem to jump to many different items. There's no crisis.
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One of the consequences of relativistic physics is the rejection of the well-known concepts of space and time in science, and replacing them with the new concept of Minkowski space-time or simply space-time.
In classical mechanics, the three spatial dimensions in Cartesian coordinates are usually denoted by x, y and z. The dimensional symbol of each is L. Time is represented by t with the dimensional symbol of T.
In relativistic physics x, y and z are still intactly used for the three spatial dimensions, but time is replaced by ct. It means its dimension has changed from T to L. Therefore, this new time is yet another spatial dimension. One thus wonders where and what is time in space-time?
Probably, due to this awkwardness, ct is not commonly used by physicists as the notion for time after more than a century since its introduction and despite the fact that it applies to any object at any speed.
The root of this manipulation of time comes directly from Lorentz transformations equations. But what are the consequences of this change?
We are told that an observer in any inertial reference frame is allowed to consider its own frame to be stationary. However, the space-time concept tells us that if the same observer does not move at all in the same frame, he or she still moves at the new so-called time dimension with the speed of light! In fact, every object which is apparently moving at a constant speed through space is actually moving with the speed of light in space-time, divided partially in time and partially in spatial directions. The difference is that going at the speed of light in the time direction is disassociated with momentum energy but going at the fraction of that speed in the other three dimensions accumulates substantial momentum energy, reaching infinity when approaching the speed of light.
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Dear Prof. Ziaedin Shafiei
As a conservative physicist & non-expert in relativity, I would like to answer your question in the following way, as it is elaborated in Landau & Lifschitz classical book: the Classical Theory of Fields. They introduced the idea of the light cone many years ago to described events in space-time in a general way. For them: time is an axis, space is another axis & 1/c the inverse speed of light is the slope of the plot. Hereby, my answer is: t is the time.
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In discussing Quantum Mechanics (QM), I shall restrict myself here to Schroedinger's Non-Relativistic Wave Mechanics (WM), as Dirac showed (in his 1930 text) [using Hilbert State Vectors] that Heisenberg's Matrix Mechanics (MM) was simply mathematically equivalent.
WM was invented in 1925 when Schroedinger adopted de Broglie's radical proposal that a quantum particle, like an electron, could "have" both contradictory point particle properties (like momentum, P) and wave properties, like a wave-length or wave-number K) by: K = h P; where h is Planck's constant (smuggling in quantization). Next he ASSUMED that a free electron could be represented as a spherical wave described by the Wave Equation. Then, he "joined the QM Club" by restricting his math approach to an isolated hydrogen atom, with its one orbital electron moving around the single proton (each with only one electron charge,e) at a spatial separation r at time t (i.e. x;t). He then linearized out the time by assuming a harmonic form: Exp{i w t) along with Einstein's EM frequency (photon) rule: E = h w. This gave him his famous Wave Equation [using W instead of Greek letter, psi]: H W = E W where H was the classical particle Hamiltonian H =K+U with K the kinetic energy [K= p2/2m] and U the Coulomb potential energy [U = e2/r]. Replacing the quadratic momentum term gave the Laplacian in 3D spherical polar co-ordinates [r, theta, phi]. He then remembered this resembled the 19th century oscillating sphere model with its known complete (infinite series) solution for n=1 to N=infinity for W=Y(l:cos theta) exp[i m phi] introducing the integer parameters l [angular momentum] and m [rotation around the Z axis]. By assuming the math solution is separable, he was left with the linear radial equation that could be solved [with difficulty] but approximated to Bohr's 1913 2D circular [planetary] model E values.
The "TRICK" was to isolate out from the infinite sums, all terms that only included EACH of the finite n terms [measured from n=1 to 6]. This was Dirac's key to match the nth wave function W(n:x,t) with his own Hilbert ket vector: W(n:x,t) = |n, x, t>.
So, I maintain that QM has failed to map its mathematics to a SINGLE hydrogen atom [the physical assumptions used therein] but to the full [almost infinite] collection of atoms present in real experiments. This then results in multiple epistemological nonsense such as Born's probability theory, wave function collapse and the multiverse theory.
This is NOT needed IF we reject the Continuum Hypothesis [imported from Classical Mechanics] and stick to finite difference mathematics.
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QM, like CM, imagines time as a "Fourth Dimension" (orthogonal to the 3 space directions). Physics then adopts Newton's Timeless calculus to write a set of equations that are VALID across all space at the same single time [t].
Apart from great simplifications, what is the physical justification for this model?
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I am a materials science undergrad, interested to know the algorithms for numerical integration of equation of motion in computational materials science, like molecular dynamics. It is said that, time-reversal symmetry is essential for such simulations, while classic integration schemes like Trapezoidal, simpsons or weddle methods handle previous and next time step differently. So verlet algorithm is used instead.
Position verlet indeed adds previous and past timesteps and maintains time-reversal symmetry. But velocity verlet doe not. Why is time-reversal symmetry not important for velocity? is it because time reversal symmetry is meaningful only for position and its even derivatives, as in newton's law of motion?
My knowledge on Numerical analysis is only of introductory level, and i have not deeply studied Lagrangian, chaos theory, group theory or hyper-dimensional geometry yet.
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Both satisfy the time-reversibility because the discrete flow map, F(dt), is time reversible:
F(dt) = exp(i L1 dt/2) exp(i dt L2) exp(i L1 dt/2)
where dt is the time step and
iL1 = a(t) (\partial / \partial v)
iL2 = v(t) (\partial / \partial x)
a = acceleration
v = velocity
x = position
Applying this operator (F(dt)), the velocity-Verlet algorithm is obtained. Now, check it
F(dt)F(-dt) = 1
If we take
F(dt) = exp(i L2 dt/2) exp(i dt L1) exp(i L2 dt/2)
Then, the position Verlet algorithm is obtained, which is time-reversible too, F(dt)F(-dt)=1.
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Why quantum mechanic exist?
Why the elementary particle doesn't follow newton law?
Why we need a quantum mechanic for the tiny object?
Bohr said that quantum mechanics does not produce classical mechanics in a similar way as classical mechanics arises as an approximation of special relativity at velocities very slow than light speed.
He argued that classical mechanics exists independently of quantum mechanics and cannot be derived from it.
Max Jammer has said: quantum mechanics and classical dynamics are built on fundamentally different foundations!
No one can derive the newton law from the Schrodinger equation.
only the behavior of systems described by quantum mechanics reproduces in a statistical way the classical mechanics in the limit of large quantum numbers.
I don't understand why scientists don't give this point a big attention.
The real interpretation of quantum mechanics need to give an answer to this question:
why quantum mechanic exist?
I start from the concept of the motion itself and assume that the motion (in the quantum world and classical world) is a sequence of appearances and disappearances events in space and time:
The idea that affirms that the motion happened by disappearing and appearing actions give us God willing a beautiful answer about this question.
The Newton law said:
"In an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force".
But this law is not compatible with the disappearance and appearance idea!
this law is not always acceptable since the particle might easily appear (if the quantum jump is enough) in a forbidden (have a variation to a very large potential field like for example the particle in an infinite potential well) place after some quantum jumps in the direction of the movement of the particle!
so for a huge number of particles that jump in the subatomic level, the newton law may put our universe in an unstable situation!, and this might happen specifically when the length of the jump is close (or greater) to the length of the field's fluctuations (that frequently happens in subatomic level).
But in the case where the length of the quantum jump is very small (for example for large quantum numbers or in classical case) compared to the length of the field's fluctuations then the first law of Newton will be applicable because in this case, we can be sure that the particle will feel the force before that the force gets altered.
We usually deal with the motion like it was related only with the particle itself, but in my opinion, this is not true, I think we have two players in the motion:
1- The particle itself.
2- The space-time itself.
At each time, space itself allows the particle to appear in some multiple positions with certain preferences based on a new quantum action principle named "alike action principle" (that can lead us to Schrodinger equation) that ensures the existence of physical harmony within our universe, and the particle chooses randomly between these preferences.
So this is the role of space-time in the motion process, like for example preventing the particle from easily reaching to forbidden locations (guarded by fields of great forces). Therefore, in general, this new constraint in movement could be valid at multiple positions at the same time, so in general, we have multiple acceptable positions to appear at it. Thus the probability of existence came up in our descriptions of the movement in the quantum world.
With kindest regards.
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The practical existance of Q.M is HOMO & LUMO approach of 3D -QSAR modelling .
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The 2nd law of the thermodynamics says that the entropy only increases. From this law we derived a time-axis that has only one direction - forward. Similarly, from our life-experience we know that we only grow older (fact which seems to be a consequence of the thermodynamics 2nd law), and from that we also derived a unidirectional time-axis.
The time-axis seems to be a concept emerging from irreversible processes.
However, not every process in the world has to do with an increase of entropy. The movement of the electrons in the ground state of an atom does not have to do with an increase of entropy, s.t. the atoms, at least in their stable state, are identical today with thouse that existed billions of years ago. There is an internal dynamics in these atoms, but it doesn't need a time-axis, because this dynamics is reversible.
What I am asking is which proof do we have that the macroscopic world does not admit an influence backwards in time?
My question is motivated by the fact that in the quantum mechanics, the results of measurements produced by entangled systems tested at different times, show a clear interdependence between present and future. None of the systems produces its response independently. The response of each system depends on the type of experiment done on the other systems, and their responses, even if other systems are tested later.
NOTE: I am not asking why the time flows only in forward direction. It is we, the human beings that choose this direction because we grow only older, not younger, because our experience of life increases, etc. I am asking if we have any evidence that a future event influences a past process.
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No, Juan, I do not expect the answer to be in any direction. Personally, I believe that there is no retro-causation. A universe in which both past and future influence the present, is a universe without past and future. I don't imagine how such a universe can evolve. Even the Big Bang explosion can't happen, what was before the Big Bang should remain forever the same.
What I thought was that maybe there can be local effects in which the future may influence the past. I had in mind Maupertuis' principle, but I am not sure what we really can infer from this principle in what regards my question - see my discussion with Daniel.
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Dear Sirs,
I would like to find out more precisely whether the 2nd Newton law is valid or not in wide range of masses, accelerations, forces. Particulary I have a question whether the inertial property of body (inertial mass) is able to stop the body for small external forces or not. I have found in the Internet the fresh articles with tests of the 2nd Newton law for small accelerations (10^-10), small forces (10^-13) and SMALL masses (about 1 kg). The articles deal with the question of dark matter and MOND theory in astrophysics.
But I am interested in BIG masses. Could the test be carried out in planetary scale? Maybe for the Moon or asteroids? Or for masses like 1000 kg? Thank you very much for any references.
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- When calculating ephemeris in the most accurate models of EPM and in some DE models, only miserable corrections are obtained from the PPN formalism. The Newtonian gravitation remains in the basement of celestial mechanics and of the GR. To my point of view, and stem from the fact, that geodetic lines in the presence of masses get bent, the Newton’s gravitation law suffers from a fundamental flaw due to violation of the inverse square law, underlying it. Let's try to go down from generalizations to specifics.
For example, discussing the modification of the law of Newton, I will argue that the mass is not an invariant, and the APPARENT gravitational mass depends on the distance to the observer Ma = M (1+ KR), where, for particular body, K = const. To verify the validity of the modified law, one will have to a) recalculate the masses of all celestial bodies in accordance with modified law, and b) get the Shapiro amendment, which will also depend on the (apparent) mass. As a result, using appropriate Shapiro delay values, we may get confirmation of the modified law.
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Dear Sirs,
1, 2, 3 laws of Newtons need closed system (net force is zero). How do we practically realize, create such closed system?
One example. Let us look at a body motion. One can say If the body velocity is constant, e.g. zero then no forces act to it. Is it true? I think no. According to the 1st Newton law the velocity constance is the CONSEQUENCE of F=0.
So are there precise ways to construct closed system? Or all physical theory is just a mean to generate a hypothesis which has more higher probability to be true then other random thought?
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Dear Sir,
To the point how to construct.
Let us take component wise
Forces = Air frictional force if your relative velocity is high like 1m/s, frictional force from ground and touching surfaces, EM forces, Temperature gradients, Electrical Gradients, Gravitational forces.
Maintain constant Temperature that is generally room temperature- If temperature gradients exist then, source of it should be eliminated or considered in the system.
Use Glass material polished with talcum powder.
If any EM material Exist that is taken care by glass itself.
If high velocity Evacuate the chamber i.e. create vacuum.
Cover other surfaces also with talcum powder.
X & Z components are taken care by these.
Y component gravity is left that comes vey expensive.
So to eliminate gravity either use Archemedies Principle or do it simulation if real is not compulsory.
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Are there examples of lossless, yet time irreversible systems? I would be pleased to know if there are any in Quantum Mechanics.
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Which meaning of "irreversible"?
If it is thermodynamically irreversible, then virtually every system is irreversible (second law) and all systems are lossless (first law.) Actually, it all depends on the degrees of freedom you chose for the system. Quantum mechanical thermodynamics is no different, although it isn't obvious.
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Could you give references on mass measurement from the 3rd law (with different forces: gravitational, elastic, etc)? E.g. old articles by Saint-Venant.
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Dear Preston,
Thank you very much for your papers
Anatoly
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The physical system of a charged particle under the action of crossed electric and magnetic fields is a well-known problem in classical mechanics. In such an approach, the motion equations can be obtained for different regimens of electric and magnetic field intensities.
From a quantum mechanics point of view, it is common to solve it for the null electric field case (as can found in several textbooks); even, the coherent states formalism has been applied to describe the charged particle dynamics. However, have such treatment been also applied to the non-null electric field case?
I have not found any information about that case and I am interested in knowing how that problem has been discussed.
Regards.
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I just got done writing an answer to a similar question:
The massless photon is chiral, meaning, you cannot get in front of it and see it spinning counter-clockwise, for instance.
By Convention: the Electric and Magnetic bosons possess off-shell mass.
Therefore, the E and M bosons, the only means by which we [at this time] can interact with any phenomenon, is mass limited to:
v << c
That is helic. You can get in front of it.
As a result:
1. the only means to interact with any wave function is [our tek limit] via the E and M bosons.
2. the E and M bosons are mass limited to v << c.
3. The E and M bosons cannot represent the immediate locality, nor immediate state function, of any phenomenon, as a result.
4. there can be no propagation of a 'field' at v = c; else, the massive EM bosons, which trail at any distance, violate - everything.
5. the massless photon cannot be said to have any sequitur description regarded as 'locality.'
6. by definition, the distribution of the massless photon is infinite, assigning any weight to an infinite distribution is a violation of the fundamental Theorems of the Limits at Infinity, and is therefore non-sequitur.
7. the Near Field Effect, namely, the E and M bosons, is a population of bosons, not a 'field.' This is by convention. They are [quantized] discrete, and have a well defined half-life of 3-lambda.
8. An already existing underlying 'infinite field' [e.g. QFT] is not possible in our finite domain, as a simple violation of the aforementioned fundamental Theorem of the Limits at Infinity. [You cannot 'fit' an infinite field inside of a finite box]
I derived the masses, and all of those results in [only firefox downloads papers correctly, for whatever reason]
THE PERMITTIVITY (ELECTRIC) VS THE PERMEABILITY (MAGNETIC) DERIVATION FOR THE TWO SPECIES OF VIRTUAL PHOTONS THAT MEDIATE THE OBSERVED EFFECTS AS AN ARTIFACT OF THE EVOLUTION OF THE AdS HORIZON AS HUP CONSERVATION of ϞNQ: Force as Entropy/Ordiny
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Dear Colleagues,
1. It is known that the correspondence principle states that the behavior of systems described by quantum mechanics reproduces in a statistical way the classical mechanics in the limit of large quantum numbers, Bohr said that quantum mechanics does not produce classical mechanics in a similar way as classical mechanics arises as an approximation of special relativity at velocities very slow than light speed.
He argued that classical mechanics exists independently of quantum mechanics and cannot be derived from it.
2. For example in the case of "particle in box", if we examine the probability density for finding the particle when n growth (case of high energy) we found a sequence of peaks separated by a distance equal to half of De Broglie wavelength, so if the correspondence principle describes exactly the reality we need to accept that the motion in classical limit does not continue.
So first it is natural to assume that the motion (in classical world) is a sequence of appearances and disappearances events in space and time.
Then if we go back to the quantum world, and say okay, why the particle does not do the same for low energies too? I mean we can suppose too that it also disappears and appears as separate events in space and time, but of course, according to another law of motion(not the half of De Broglie wavelength), in fact I suggest this law in my theory:
it is called "alike action principle" it is similar to the least action principle and can lead us simply to the path integral formulation.
What do you think?
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The best approach to justify the complementary principle is the Ehrenfest theorem, but Bohr was right: it is not possible to approach classical mechanics as it is done in relativistic mechanics for v/c << 1. See the reference
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In textbooks or introductory texts on quantum mechanics, one may read that the quantum mechanical wave function changes by two fundamentally different processes. One is the deterministic and continuous evolution according to the Schrödinger equation, the other the collapse provoked by a measurement, usually discontinuous, nonlocal and disruptive. I would like to argue that this is due to overburdening the wave function in the Schrödinger picture by requiring it to describe both the state and the dynamics of a system.
The first version of modern quantum mechanics, "matrix mechanics" given in 1925 by Heisenberg, did not do this. Actually, the notion of a wave function was not present in it, even though we may nowadays apply it to Heisenberg's state concept. In the Heisenberg picture, the wave function describes only the initial state of a system. It does not change in time, only on measurement. This change is due to a change in knowledge about the system and the necessity to adapt the probability amplitude to the new knowledge and it corresponds to the collapse. But it is not a dynamical change.
Dynamics is described by the time dependence of observables, i.e. operators. It is governed by Heisenberg's equation of motion, an equation that is equivalent to the Schrödinger equation. So in the Heisenberg picture, dynamics and collapse are neatly separated. Also, the collapse of the wave function cannot be said to be due to a wave packet interacting with a detector, because the wave packet does not change in time, it never gets close to a detector, if it is far from all of them initially. It is, in fact, not a spatiotemporal wave, it is just a spatial distribution. Interaction and dynamics is between observables only. States only describe initial conditions.
Experimental observations neither concern states nor operators directly. They always refer to matrix elements, involving both. So the Schrödinger and Heisenberg pictures are equivalent, giving the same matrix elements. Nevertheless, they attribute the dynamics to different entities.
The Heisenberg picture was invented before the Schrödinger equation. Moreover, it is closer to classical mechanics in that it is straightforward to get from Hamilton's classical equations of motion to the Heisenberg equation of motion, as soon as we know how to quantize phase space functions. Once we know how to construct quantum mechanical operators, all we have to do is to replace phase space functions by operators and the Poisson brackets of classical mechanics by i \hbar times the commutator. The way to the Schrödinger equation is more convoluted. Nevertheless, essentially everybody dashed at the Schrödinger equation, once it became available in 1926, and it soon became the predominant description. Only when we are dealing with multiple-time correlation functions, we prefer the Heisenberg picture, because the consideration of multiple-time correlations functions is difficult to justify in the Schrödinger picture (where the operators whose correlations are of interest remain time independent), whereas it has a clear motivation in the Heisenberg picture.
The reason for this rush at Schrödinger's bonanza obviously was that people knew well how to work with partial differential equations but were unfamiliar with infinite-dimensional matrices. Which then led to the (doubtful) enterprise of assigning more meaning to the wave function than follows from physical considerations.
Consider wave-particle duality, for example. There is a tendency among physicists to overemphasize one of these classical limiting ways for a quantum object "to express itself". Bohmianists give the particle aspect ontological dominance. The wave function is an additional ingredient, but when we measure a quantum particle, we always measure a positional aspect (a pointer variable), and so it is a particle, and the wave is there only to guide it. Others tend to say there is only waves and their interactions with detectors are such that a particle illusion is created. There is the fraction of field theorists saying that there are no particles, only fields, but there are also some serious scientists emphasizing "field theory without fields" by pointing out that the whole physics of a field theory is present in its particle contents.
What does the Heisenberg picture suggest on the question of wave-particle duality? The dynamical entities in the Heisenberg picture are operators. Those are neither particle nor wave. The position operator does not describe an object at a particular position. It has a spectrum containing all possible positions. When it evolves in time (because it is time-dependent in the Heisenberg picture), the relative weights of the positions and, in particular, the expectation value of the position change. But the property "position", as described by the position operator, is not univalent. So the quantum object having that dynamical property cannot be a localized particle that has only one position. On the other hand, the property wave vector is proportional to the momentum operator, evolving in time, too, and having more than one momentum value in its spectrum. The quantum object having that dynamical property cannot be a wave, not a "pure" one at least, characterized by a single wave vector (or a narrow spectrum of such wave vectors). If we take the fact at face value that dynamical variables in quantum mechanics are described by operators, it immediately becomes clear, that the quantum objects are neither waves nor particles but something different -- that's why their description is by operators. Note that in the Heisenberg picture, the double slit experiment gives the same result as in the Schrödinger picture, even though no wave is moving around there (the wave function keeps its initial distribution throughout the experiment until detection of the quantum object). What is changing are the "position" and "momentum" of the quantum object and these are influenced by the presence of both slits. Because they take into account a whole set of possibilities. (The third formulation of quantum mechanics, Feynman's path integral approach turns this set into the possible paths of particles.)
What are quantum objects? Quantum objects are characterized by their properties, as are classical objects. Properties such as mass and charge are simple parameters for the elementary objects as in classical mechanics, whereas dynamic properties such as position and momentum are characterized by operators and hence different for quantum objects from corresponding properties in classical objects. Only in certain limiting cases, descri