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We know gravity pulls things together in space...but have you ever seen what it does in phase space? In this scene we're not watching a blob of matter in x–space. We're watching a thin probability sheet in (x, v).... position–velocity space... being pulled by its own gravity. In the...

47,586 次观看 • 7 个月前 •via X (Twitter)

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Warmup to Statistical Mechanics What Exactly is a Hamiltonian A System? In ordinary Mechanics, you might begin with position and velocity. Hamiltonian Mechanics rewrites the same motion in a different language. Instead of position and velocity, it uses position and momentum. We write the position variables as q and the momentum variables as p. Then the full state of the system at one instant is (q, p) That pair is one point in phase space. Why do we do this? Because in these variables, the equations of motion take a remarkably clean form. Everything is generated by one single function, the Hamiltonian H(q, p) and in the simplest cases this Hamiltonian is just the total energy written in terms of position and momentum. So if you know H, you know the dynamics. You might wonder, but how can one function generate motion? The rule is dqᵢ/dt = ∂H/∂pᵢ dpᵢ/dt = −∂H/∂qᵢ These are Hamilton’s equations. Now read them slowly 😄 The rate of change of position comes from differentiating H with respect to momentum. The rate of change of momentum comes from differentiating H with respect to position, with a minus sign. This constitutes the whole engine. A simple example makes this less abstract: Take one particle of mass m moving in a potential V(q). Then the Hamiltonian is H(q, p) = p²/(2m) + V(q) The first term is kinetic energy. The second term is potential energy. Now apply Hamilton’s equations. First, dq/dt = ∂H/∂p = p/m So momentum tells you how position changes. Second, dp/dt = −∂H/∂q = −dV/dq Thus, momentum changes because of force. If you now combine these two equations, you recover ordinary Newtonian mechanics. Since p = m dq/dt, we get m d²q/dt² = −dV/dq So, Hamiltonian mechanics is not a different theory. It is the same mechanics, written in a form that exposes its geometric structure much more clearly. The animation The full 3D surface is the Hamiltonian itself, the energy landscape H(q, p). The floor underneath is phase space, marked by energy contours and the local flow field. The bright moving point is one actual state (q(t), p(t)) evolving under Hamilton’s equations. Its trail shows that the motion is not arbitrary. It is guided everywhere by the geometry of the same single function H. The render is doing more than illustrating a particle moving, it is showing how one function organizes the whole phase-space motion. The math breakdown: Start with one degree of freedom. The state is described by position q and momentum p. So the system lives in a two-dimensional phase space with coordinates (q, p) Now choose a Hamiltonian H(q, p) Think of H as the energy function. In many standard systems, H(q, p) = kinetic energy + potential energy For a particle of mass m in a potential V(q), this becomes H(q, p) = p²/(2m) + V(q) Hamilton’s equations say dq/dt = ∂H/∂p dp/dt = −∂H/∂q Now substitute this specific H. First compute the p derivative: ∂H/∂p = ∂/∂p (p²/(2m) + V(q)) = p/m So dq/dt = p/m Now compute the q derivative: ∂H/∂q = ∂/∂q (p²/(2m) + V(q)) = dV/dq So dp/dt = −dV/dq These two first-order equations completely determine the motion. Now, connect this back to Newton’s law. From dq/dt = p/m we get p = m dq/dt Differentiate both sides with respect to time: dp/dt = m d²q/dt² But Hamilton’s second equation gives dp/dt = −dV/dq So , together they imply m d²q/dt² = −dV/dq This is exactly Newton’s second law for motion in the potential V(q). Thus, Hamilton’s equations do not replace mechanic, they reorganize it. #HamiltonianMechanics #PhaseSpace #ClassicalMechanics #MathematicalPhysics #DifferentialEquations #Mathematics #Physics

Mathelirium

50,478 次观看 • 2 个月前

😎🤌 According to Bob Lazar, UAP operate using a gravity wave-based propulsion system that distorts space-time rather than using conventional thrust 👽🛸 The craft generate power and gravity waves through a reactor fueled by a stable isotope of Element 115. In the reactor, Element 115 is bombarded with protons, briefly becomes Element 116, decays, and releases small amounts of antimatter. This antimatter annihilates with matter to produce enormous energy (near 100% efficient), which powers the craft and also creates a unique Gravity A wave (a micro-scale gravity field Lazar says is an extension of the strong nuclear force). This Gravity A wave forms around the reactor at the top of the craft. A waveguide channels it downward into three gravity amplifiers arranged in a triangle at the base. These amplifiers run at full power at all times and can phase-shift the wave (0° to 180°) to control direction and strength. By focusing and amplifying the gravity wave, the craft creates a powerful, localized gravitational distortion: - It bends/warps space-time in front of the vehicle. - This effectively pulls the destination toward the craft (instead of pushing the craft forward through space). Operation modes: - Omicron mode (hovering/low speed): Amplifiers point downward → craft balances/sits on its own gravity field (explains the characteristic wobble/bobbing seen in many videos). - Delta mode (high speed/travel): Amplifiers point forward → extreme space-time warping for rapid movement. Key effects: - No inertia (occupants feel no acceleration). - Time dilation near the craft. - Optical distortion (gravity lensing can make the craft appear blurry, shimmering, or invisible). In essence, the craft "falls" toward its target by warping space ahead of it, allowing extreme speeds, sharp turns, and interstellar travel without conventional motion or time dilation issues for the occupants. (#UAP #UFO #UFOSighting)

★ UAP Luigi ★ 👁️⃤ 🇺🇸 👽MJ12 SOM1-01

43,212 次观看 • 6 个月前

Desveaux’s Theory of Helix Fields Tweet 1 of 2 For decades, we treated the universe like a giant stage where particles act out their lives. What if the stage itself isn't empty? What if the "void" of space is a structured, rotating medium that is constantly twisting & turning? We have been looking at the pieces of the puzzle, but ignoring the board they sit on. It’s been hiding in plain in sight? My idea on Helix Fields suggests everything we see, from the smallest atom to the largest galaxy, is actually a "corkscrew" in the fabric of reality. In standard physics, we think of particles like tiny billiard balls. In Helix Field Theory, we rethink them as solitons - essentially stable, high-energy "whirlpools" or "corkscrews" made of space itself. Imagine a ribbon. If you pull it straight, it’s flat and simple. But if you twist it, you create a spiral. That twist is what we call Torsion. My theory says that what we perceive as "matter" is simply a place where the vacuum of space is rotating so tightly that it creates a "density core." To explain how this all works, we use a mathematical roadmap called a Lagrangian. Think of it as a master recipe or cookbook for the universe. It combines four key ingredients: 1. Electricity and Magnetism: How light and energy move. 2. Scalar Fields: The underlying "pressure" of the vacuum in space itself 3. Matter: The physical "stuff" we can touch. 4. Torsion: The "twist" or rotational force of space. By looking at the universe through this "helix" lens, we can solve two of the biggest headaches in modern science: The Hubble Tension - Astronomers are currently arguing over how fast the universe is expanding because different measurements give different answers. My theory suggests this "tension" exists because we haven't accounted for the universal rotation (torsion) affecting our measurements. The Dark Sector - We know there is "Dark Matter" and "Dark Energy" out there, but we can't find it. Helix Field Theory suggests these aren't invisible particles, but rather geometric artifacts - ripples and shadows created by the rotating vacuum itself. We are moving away from a universe of "things" and toward a universe of geometry and motion. If the vacuum of space is a structured, rotating medium, then we aren't just living in the universe - we are part of its physical rotation. The "Quantum Substratum" isn't just a theory; it’s a new way to understand the very "twist" of existence. - Protons: tiny rotating black hole-like cores anchoring the scalar field - Neutrons: stabilisers that prevent proton cores from decaying - Quarks & Gluons: the deepest torsion knots; the strong force is intrinsic torsion - Electrons: corkscrew-shaped solitons producing microscopic magnetic vortices - Neutrinos: ultra-light messenger waves traveling along the field’s “communication lines.” - Photons: instruction ripples traveling at light speed - Dark Photons: the “torsion messengers” of the Helix Field. They carry the twist, regulate the twist, and stabilize the twisting motion - W and Z bosons: on/off switches and stabilising nodes in the neutrino network - Higgs field: the local density of the scalar field, giving solitons their effective mass - Dark energy: the gentle outward push caused by the field’s overall rotation - Entropy: friction in that rotation, giving time its arrow - Cosmic Microwave Background: the universal “sustain pedal” like on a guitar or piano, keeping the field’s vibrations in phase. In this vision, dark matter isn’t missing matter - it’s the gravitational echo of the scalar field itself. Exploring antiparticles further: they may regulate the flow of time itself. In a rotational and torsional universe Time is a neutral observer: the past and future are fixed, but the present - our free will - is the point where choices echo into fate. Time is the “God” of the universe: ever-present, ever-aware, never interfering - just watching, as we decide which thread to follow.

Clinton Desveaux

23,492 次观看 • 5 个月前