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The vacuum is not always stable Using the nonlinear Klein-Gordon equation, bubbles of a lower-energy state erupt across the fabric expand, collide and leave oscillating remnant behind called Oscillons.

Mathelirium

80,917 subscribers

10,768 views • 11 days ago •via X (Twitter)

Anya Rossi• Live Now

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13 Comments

Rozmowy z Bogiem11 days ago

Where does the cause lie?

andy11 days ago

another banger

Brian Jordan11 days ago

Next level, keep exploring!!

Edwin VanGorder11 days ago

the curve to corners modells the heptagon saddleback geometry to hyperbolic plane linking split octonions cosmogenesis on numberline to spectral grading through the pseudo algebras...where an apeirogon models inversion to Holographic horizon transport

Monsol10 days ago

It's hard to visualize this as 3d model bubbles inside bubbles affecting other bubbles.

Carlos ‘Cacho’ Contreras11 days ago

What song is that?

Carlos ‘Cacho’ Contreras11 days ago

OMG, that's so nice of you, thank you so much! 🫶

Mathelirium11 days ago

Youre welcome! Im using a cleaner version from AppleMusic but I forgot the name of the song. Mayne you can if you know some Arabic

Carlos ‘Cacho’ Contreras11 days ago

I don't know any Arabic, but I'll find it, BELIEVE ME! Love it.

Heather Davis11 days ago

Cymatics

V. W.11 days ago

In what sense, then, is anything truly stable?

ArtisanTony11 days ago

But the vacuum does don’t have edges to bounce off of ;)

PoetinAz11 days ago

You mean your vacuum oscillates like an old fan in your grandma’s house?? Wow that is awesome!!

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Mathelirium

40,978 views • 9 months ago

Final Lecture of our Statistical Mechanics Series. Lecture 2 showed how we move from the Full Phase-Space Density ρ(q₁, …, qₙ, p₁, …, pₙ, t) to smaller statistical objects by integrating out variables we do not want to keep. That gives reduced descriptions like the One-Particle Density f₁(q₁,p₁,t) and the Two-Particle Density f₂(q₁,p₁,q₂,p₂,t) This was the simplification. Now comes the catch. If the Full Density obeys Liouville’s Equation, the reduced densities do not evolve independently. The equation for one level depends on the next one and this is referred to as the BBGKY hierarchy. The One-Particle Density depends on the Two-Particle Density. The Two-Particle Density depends on the Three-Particle Density. And the chain keeps going. That happens because particles interact. Once one particle feels the rest, one-particle information is no longer enough. Correlations enter, and the lower level is fed from above. If the full Hamiltonian is H = Σᵢ pᵢ²/(2m) + Σᵢ U(qᵢ) + (1/2) Σᵢ Σⱼ≠ᵢ Φ(qᵢ − qⱼ) then reducing the full density does not make the interaction terms disappear. It leaves behind coupling to higher-order reduced densities. So, schematically, ∂f₁/∂t + transport of one particle = interaction term involving f₂ and more generally the heirarchy is such that ∂fₛ/∂t + s-particle transport = interaction term involving fₛ₊₁ Therefore, Lecture 3 is really about the price of reduction. We simplify the description, but the information we remove comes back as coupling to higher-order correlations. So, how do you actually compute anything if every level depends on the next one? This is the so-called Closure Problem. To make the hierarchy usable, you need an extra assumption that cuts the chain. You replace the exact higher-order object by an approximation in terms of lower-order ones. The most basic example is a factorized closure at the pair level, where the exact correlated Two-Particle Density is replaced schematically by a product of One-Particle Densities: f₂(q₁,p₁,q₂,p₂,t) ≈ f₁(q₁,p₁,t) f₁(q₂,p₂,t) That approximation is not exact. It throws away part of the correlation structure. But it gives you something the raw hierarchy does not... a closed equation for the lower-level description. That is why closure matters so much. Without it, the hierarchy is exact but open. With it, the theory becomes approximate but usable. Thus, the combined point of this final Statistical Mechanics post is simple. First, reduced descriptions are not closed because interactions generate correlations across levels. Second, if you want a workable Kinetic Theory, you must close the hierarchy by approximating those higher-order correlations. It is the bridge from formal many-body mechanics to equations people can actually solve. In the render, that is exactly the story you are seeing. The first part shows the hierarchy itself: one reduced level feeding the next, with lower descriptions inheriting structure from higher ones. The second part shows the closure step where the exact correlated pair level is replaced by a factorized ansatz, and that approximation gives back a closed one-particle description. That is, the animation moves from dependence to approximation, and from approximation to solvability. #StatisticalMechanics #BBGKY #ClosureProblem #KineticTheory #PhaseSpace #ReducedDistribution #HamiltonianMechanics #MathematicalPhysics #Mathematics #Physics

Final Lecture of our Statistical Mechanics Series. Lecture 2 showed how we move from the Full Phase-Space Density ρ(q₁, …, qₙ, p₁, …, pₙ, t) to smaller statistical objects by integrating out variables we do not want to keep. That gives reduced descriptions like the One-Particle Density f₁(q₁,p₁,t) and the Two-Particle Density f₂(q₁,p₁,q₂,p₂,t) This was the simplification. Now comes the catch. If the Full Density obeys Liouville’s Equation, the reduced densities do not evolve independently. The equation for one level depends on the next one and this is referred to as the BBGKY hierarchy. The One-Particle Density depends on the Two-Particle Density. The Two-Particle Density depends on the Three-Particle Density. And the chain keeps going. That happens because particles interact. Once one particle feels the rest, one-particle information is no longer enough. Correlations enter, and the lower level is fed from above. If the full Hamiltonian is H = Σᵢ pᵢ²/(2m) + Σᵢ U(qᵢ) + (1/2) Σᵢ Σⱼ≠ᵢ Φ(qᵢ − qⱼ) then reducing the full density does not make the interaction terms disappear. It leaves behind coupling to higher-order reduced densities. So, schematically, ∂f₁/∂t + transport of one particle = interaction term involving f₂ and more generally the heirarchy is such that ∂fₛ/∂t + s-particle transport = interaction term involving fₛ₊₁ Therefore, Lecture 3 is really about the price of reduction. We simplify the description, but the information we remove comes back as coupling to higher-order correlations. So, how do you actually compute anything if every level depends on the next one? This is the so-called Closure Problem. To make the hierarchy usable, you need an extra assumption that cuts the chain. You replace the exact higher-order object by an approximation in terms of lower-order ones. The most basic example is a factorized closure at the pair level, where the exact correlated Two-Particle Density is replaced schematically by a product of One-Particle Densities: f₂(q₁,p₁,q₂,p₂,t) ≈ f₁(q₁,p₁,t) f₁(q₂,p₂,t) That approximation is not exact. It throws away part of the correlation structure. But it gives you something the raw hierarchy does not... a closed equation for the lower-level description. That is why closure matters so much. Without it, the hierarchy is exact but open. With it, the theory becomes approximate but usable. Thus, the combined point of this final Statistical Mechanics post is simple. First, reduced descriptions are not closed because interactions generate correlations across levels. Second, if you want a workable Kinetic Theory, you must close the hierarchy by approximating those higher-order correlations. It is the bridge from formal many-body mechanics to equations people can actually solve. In the render, that is exactly the story you are seeing. The first part shows the hierarchy itself: one reduced level feeding the next, with lower descriptions inheriting structure from higher ones. The second part shows the closure step where the exact correlated pair level is replaced by a factorized ansatz, and that approximation gives back a closed one-particle description. That is, the animation moves from dependence to approximation, and from approximation to solvability. #StatisticalMechanics #BBGKY #ClosureProblem #KineticTheory #PhaseSpace #ReducedDistribution #HamiltonianMechanics #MathematicalPhysics #Mathematics #Physics

Mathelirium

10,998 views • 5 months ago

This reminds me of how the orbs spin around the plane. I think they figured out how to teleport by scaling up quantum tunneling. The 'barrier' is spacetime itself. The ZPE that also causes mass/inertia. They thinned the barrier enough by causing vacuum decay when the orbs converge. Huge amount of EM flux pushed aside the ZPE for a brief moment. The false vacuum dropped to a lower energy state of a true vacuum, and the plane teleported.

This reminds me of how the orbs spin around the plane. I think they figured out how to teleport by scaling up quantum tunneling. The 'barrier' is spacetime itself. The ZPE that also causes mass/inertia. They thinned the barrier enough by causing vacuum decay when the orbs converge. Huge amount of EM flux pushed aside the ZPE for a brief moment. The false vacuum dropped to a lower energy state of a true vacuum, and the plane teleported.

Ashton Forbes

819,121 views • 1 year ago

The Mathematics of Moving a Cursor with Neural Signals What might Neuralink Neuralink be doing Mathematically? Consider the task of moving a cursor without touching it. The machine is not looking for a full thought, a sentence, or an image. For this Control problem, the useful object is an intended movement state. sₜ = (pₜ, vₜ) Here, pₜ is the cursor position at time t, and vₜ is the velocity the user is trying to express. The implant records neural activity through many electrode channels, then the decoder tries to estimate vₜ from that activity. Neuralink’s PRIME material describes the N1 Implant as recording and transmitting brain activity with the goal of enabling computer control. For channel i, a simple population model is rᵢ(t) ≈ bᵢ + aᵢ max(0, dᵢ · vₜ) + ηᵢ(t) where rᵢ(t) is the measured activity, bᵢ is baseline activity, aᵢ is channel gain, dᵢ is the channel’s preferred movement direction, and ηᵢ(t) is noise. One channel is not the command. The useful signal is the pattern across many channels: rₜ = (r₁(t), r₂(t), …, rₙ(t)) The decoder subtracts the baseline vector b and applies a learned map W: v̂ₜ = W(rₜ − b) This gives an estimate of the intended velocity. The cursor then updates by pₜ₊₁ = pₜ + Δt v̂ₜ This is the loop shown in the render: neural activity -> decoded velocity -> cursor motion The cortical network and electrode threads show the measurement side. The N1 Implant is described as using 1,024 electrodes distributed across 64 flexible threads, each thinner than a human hair. The decoder panel shows the computational side with activity rₜ, decoded velocity v̂ₜ, and the cursor state pₜ changing over time. A noisy biological pattern becomes a state estimate. That estimate becomes motion on a screen. Therefore, the first lesson is not that Neuralink makes the brain a screen. For cursor control, the Mathematics is more precise: A small piece of intention is represented as a hidden state, measured through neural activity, decoded as a vector, and turned into action. #Neuralink #BrainComputerInterface #NeuralEngineering #Mathematics #StateEstimation #Neuroscience #MachineLearning #BiomedicalEngineering

The Mathematics of Moving a Cursor with Neural Signals What might Neuralink Neuralink be doing Mathematically? Consider the task of moving a cursor without touching it. The machine is not looking for a full thought, a sentence, or an image. For this Control problem, the useful object is an intended movement state. sₜ = (pₜ, vₜ) Here, pₜ is the cursor position at time t, and vₜ is the velocity the user is trying to express. The implant records neural activity through many electrode channels, then the decoder tries to estimate vₜ from that activity. Neuralink’s PRIME material describes the N1 Implant as recording and transmitting brain activity with the goal of enabling computer control. For channel i, a simple population model is rᵢ(t) ≈ bᵢ + aᵢ max(0, dᵢ · vₜ) + ηᵢ(t) where rᵢ(t) is the measured activity, bᵢ is baseline activity, aᵢ is channel gain, dᵢ is the channel’s preferred movement direction, and ηᵢ(t) is noise. One channel is not the command. The useful signal is the pattern across many channels: rₜ = (r₁(t), r₂(t), …, rₙ(t)) The decoder subtracts the baseline vector b and applies a learned map W: v̂ₜ = W(rₜ − b) This gives an estimate of the intended velocity. The cursor then updates by pₜ₊₁ = pₜ + Δt v̂ₜ This is the loop shown in the render: neural activity -> decoded velocity -> cursor motion The cortical network and electrode threads show the measurement side. The N1 Implant is described as using 1,024 electrodes distributed across 64 flexible threads, each thinner than a human hair. The decoder panel shows the computational side with activity rₜ, decoded velocity v̂ₜ, and the cursor state pₜ changing over time. A noisy biological pattern becomes a state estimate. That estimate becomes motion on a screen. Therefore, the first lesson is not that Neuralink makes the brain a screen. For cursor control, the Mathematics is more precise: A small piece of intention is represented as a hidden state, measured through neural activity, decoded as a vector, and turned into action. #Neuralink #BrainComputerInterface #NeuralEngineering #Mathematics #StateEstimation #Neuroscience #MachineLearning #BiomedicalEngineering

Mathelirium

14,520 views • 5 months ago