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Why String Theory Won't Die The string theory idea refuses to die because it's one of the few frameworks that forces a quantum object and spacetime geometry into the same picture. In the render, a closed string isn’t just a loop doing pretty vibrations. Its internal phase pattern is...

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Mathelirium

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13,635 次观看 • 5 个月前 •via X (Twitter)

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What String Theory Does That Classical Physics Doesn’t Classical Physics begins with a point particle. Its position is described by one function of time x = x(t) As time passes, that point traces a curve through Spacetime called a worldline. String theory changes the starting object. A string has length, so time alone is not enough. We also need a coordinate along the string Xᵘ = Xᵘ(τ, σ) Here τ is worldsheet time, and σ labels position along the string. As the string moves, it sweeps out a surface called a worldsheet. The action measures the area of that surface S = -T ∫ dτ dσ √[-det hₐᵦ] This is where string theory begins. #StringTheory #ClassicalMechanics #TheoreticalPhysics #Worldsheet #QuantumGravity #MathematicalPhysics #Spacetime #PhysicsVisualization #ScienceEducation
0:55

What String Theory Does That Classical Physics Doesn’t Classical Physics begins with a point particle. Its position is described by one function of time x = x(t) As time passes, that point traces a curve through Spacetime called a worldline. String theory changes the starting object. A string has length, so time alone is not enough. We also need a coordinate along the string Xᵘ = Xᵘ(τ, σ) Here τ is worldsheet time, and σ labels position along the string. As the string moves, it sweeps out a surface called a worldsheet. The action measures the area of that surface S = -T ∫ dτ dσ √[-det hₐᵦ] This is where string theory begins. #StringTheory #ClassicalMechanics #TheoreticalPhysics #Worldsheet #QuantumGravity #MathematicalPhysics #Spacetime #PhysicsVisualization #ScienceEducation

Mathelirium

18,446 次观看 • 12 天前

String Theory Lecture 1 A String Does Not Move Like a Point A point particle traces a line through spacetime. A string traces a surface. This is the first geometric shift in String Theory. Particle mechanics asks where one object is at time t, so its history is a curve. String Theory asks where every point of an extended object is at worldsheet time τ, so we need another coordinate telling us where we are along the string. For a point particle x(t) So, for one input of time we get a position in Spacetime. For a string Xᵘ(τ,σ) Here τ plays the role of time on the worldsheet, while σ labels position along the string. Freeze τ and vary σ, and you see the string at one instant. Let τ move, and that curve sweeps out a two-dimensional surface... the worldsheet. The same comparison appears in the action. For a relativistic point particle, the geometric action measures worldline length S = −m ∫ ds If we parameterize the path by t, the action has one integral, one parameter, and one tangent vector dxᵘ/dt For a string, the same idea grows by one dimension. The action measures area, not length. In Nambu-Goto form, S = −T ∫ dτ dσ √[−det hₐᵦ] Here T is the string tension. It plays a role similar to mass, but for an extended object. It weights the area of a surface rather than the length of a line. The particle action has ∫ dt because the history is one-dimensional. The string action has ∫ dτ dσ because the history is two-dimensional. We are no longer summing along a path, we are summing over a surface. The geometry changes for the same reason. For the particle, one derivative is enough dxᵘ/dt For the string, the geometry is built from two derivatives: ∂τXᵘ and ∂σXᵘ The first tells you how the string changes as worldsheet time flows. The second tells you how the embedding changes as you move along the string. Together they define the induced worldsheet metric hₐᵦ = ∂ₐXᵘ ∂ᵦXᵤ In plain terms, hₐᵦ measures tangent lengths and tangent angles on the worldsheet. From it, the area element is dA = dτ dσ √[−det hₐᵦ] This, the Nambu-Goto action is the direct analogue of the point-particle length action. The point particle extremizes length and the string extremizes area. For calculations, people usually switch to the Polyakov action: S = −(T/2) ∫ dτ dσ √[−γ] γᵃᵇ ∂ₐXᵘ ∂ᵦXᵤ This describes the same classical string dynamics, but the algebra is cleaner. After choosing conformal gauge, varying with respect to Xᵘ gives (∂²/∂τ² − ∂²/∂σ²) Xᵘ = 0 This is the first real dynamical payoff... a two-dimensional wave equation on the worldsheet. For a point particle, the equation of motion tells you how one position evolves along one path. For a string, it tells you how an entire curve evolves, with waves traveling along it. The term ∂²Xᵘ/∂τ² measures acceleration in worldsheet time, while ∂²Xᵘ/∂σ² measures curvature along the string. The time evolution is balanced by how the string bends along its own length. This is why strings have oscillation modes. A point particle has one trajectory. A string has many possible vibration patterns, each one a normal mode of the worldsheet wave equation. For a closed string, σ wraps around the loop Xᵘ(τ, σ + 2π) = Xᵘ(τ, σ) For an open string, one standard free-end condition is ∂σXᵘ = 0 at the endpoints. Solving the wave equation gives waves moving in opposite directions along the string Xᵘ(τ,σ) = Fᵘ(τ + σ) + Gᵘ(τ − σ) A function of τ + σ moves one way. A function of τ − σ moves the other. Therefore, a particle has a worldline, its action measures length, and its geometry uses one tangent. The string has a worldsheet, its action measures area, and its geometry uses two tangent directions. #StringTheory #TheoreticalPhysics #MathematicalPhysics #Physics #Spacetime
0:34

String Theory Lecture 1 A String Does Not Move Like a Point A point particle traces a line through spacetime. A string traces a surface. This is the first geometric shift in String Theory. Particle mechanics asks where one object is at time t, so its history is a curve. String Theory asks where every point of an extended object is at worldsheet time τ, so we need another coordinate telling us where we are along the string. For a point particle x(t) So, for one input of time we get a position in Spacetime. For a string Xᵘ(τ,σ) Here τ plays the role of time on the worldsheet, while σ labels position along the string. Freeze τ and vary σ, and you see the string at one instant. Let τ move, and that curve sweeps out a two-dimensional surface... the worldsheet. The same comparison appears in the action. For a relativistic point particle, the geometric action measures worldline length S = −m ∫ ds If we parameterize the path by t, the action has one integral, one parameter, and one tangent vector dxᵘ/dt For a string, the same idea grows by one dimension. The action measures area, not length. In Nambu-Goto form, S = −T ∫ dτ dσ √[−det hₐᵦ] Here T is the string tension. It plays a role similar to mass, but for an extended object. It weights the area of a surface rather than the length of a line. The particle action has ∫ dt because the history is one-dimensional. The string action has ∫ dτ dσ because the history is two-dimensional. We are no longer summing along a path, we are summing over a surface. The geometry changes for the same reason. For the particle, one derivative is enough dxᵘ/dt For the string, the geometry is built from two derivatives: ∂τXᵘ and ∂σXᵘ The first tells you how the string changes as worldsheet time flows. The second tells you how the embedding changes as you move along the string. Together they define the induced worldsheet metric hₐᵦ = ∂ₐXᵘ ∂ᵦXᵤ In plain terms, hₐᵦ measures tangent lengths and tangent angles on the worldsheet. From it, the area element is dA = dτ dσ √[−det hₐᵦ] This, the Nambu-Goto action is the direct analogue of the point-particle length action. The point particle extremizes length and the string extremizes area. For calculations, people usually switch to the Polyakov action: S = −(T/2) ∫ dτ dσ √[−γ] γᵃᵇ ∂ₐXᵘ ∂ᵦXᵤ This describes the same classical string dynamics, but the algebra is cleaner. After choosing conformal gauge, varying with respect to Xᵘ gives (∂²/∂τ² − ∂²/∂σ²) Xᵘ = 0 This is the first real dynamical payoff... a two-dimensional wave equation on the worldsheet. For a point particle, the equation of motion tells you how one position evolves along one path. For a string, it tells you how an entire curve evolves, with waves traveling along it. The term ∂²Xᵘ/∂τ² measures acceleration in worldsheet time, while ∂²Xᵘ/∂σ² measures curvature along the string. The time evolution is balanced by how the string bends along its own length. This is why strings have oscillation modes. A point particle has one trajectory. A string has many possible vibration patterns, each one a normal mode of the worldsheet wave equation. For a closed string, σ wraps around the loop Xᵘ(τ, σ + 2π) = Xᵘ(τ, σ) For an open string, one standard free-end condition is ∂σXᵘ = 0 at the endpoints. Solving the wave equation gives waves moving in opposite directions along the string Xᵘ(τ,σ) = Fᵘ(τ + σ) + Gᵘ(τ − σ) A function of τ + σ moves one way. A function of τ − σ moves the other. Therefore, a particle has a worldline, its action measures length, and its geometry uses one tangent. The string has a worldsheet, its action measures area, and its geometry uses two tangent directions. #StringTheory #TheoreticalPhysics #MathematicalPhysics #Physics #Spacetime

Mathelirium

31,560 次观看 • 2 个月前

Why Are Some People Still Taking String Theory Seriously? String theory is controversial, but it is still one of the few ideas that tries to describe Quantum Physics and Gravity in one picture. This animation points to one of its best-known ideas: Holography. What happens on the boundary helps determine what happens in the interior, so the edge seems to shape the bulk.
0:30

Why Are Some People Still Taking String Theory Seriously? String theory is controversial, but it is still one of the few ideas that tries to describe Quantum Physics and Gravity in one picture. This animation points to one of its best-known ideas: Holography. What happens on the boundary helps determine what happens in the interior, so the edge seems to shape the bulk.

Mathelirium

29,696 次观看 • 2 个月前

String Theory Lecture 2 In Conformal Gauge, the String Becomes a Wave Equation Episode 1 showed the geometric jump point particle -> worldline string -> worldsheet Episode 2 is the dynamical jump. The Nambu-Goto action measures the area of the worldsheet, S = −T ∫ dτ dσ √[−det hₐᵦ] but the square-root determinant is awkward to work with. So we usually rewrite the same classical theory in Polyakov form, S = −(T/2) ∫ dτ dσ √[−γ] γᵃᵇ ∂ₐXᵘ ∂ᵦXᵤ Here Xᵘ(τ,σ) tells us where each point of the string’s worldsheet sits in spacetime, and γₐᵦ is the metric we put on the worldsheet. The power of this form is that we can choose a convenient gauge. In conformal gauge, the equations of motion simplify to (∂²/∂τ² − ∂²/∂σ²) Xᵘ = 0 So the string’s spacetime coordinates behave like waves living on the worldsheet. The τ-derivative measures how the string changes in worldsheet time. The σ-derivative measures how it bends along its own length. For a closed string, σ is periodic Xᵘ(τ, σ + 2π) = Xᵘ(τ,σ) and the wave equation splits into two traveling pieces, Xᵘ(τ,σ) = Fᵘ(τ + σ) + Gᵘ(τ − σ) One family moves one way around the string and the other moves the opposite way. These are the left-moving and right-moving modes. In the render, the bright loop is the string at the present moment. The glowing cylinder behind it is the worldsheet it has swept out. The cyan curves trace one traveling family, and the gold curves trace the other. They are the visual version of τ + σ and τ − σ. Therefore, the theory has an internal wave equation, and its normal modes are the raw material for the string spectrum. #StringTheory #TheoreticalPhysics #ConformalGauge #Worldsheet #WaveEquation #Physics #Mathematics #MathematicalPhysics #QuantumGravity #ScienceVisuals
0:30

String Theory Lecture 2 In Conformal Gauge, the String Becomes a Wave Equation Episode 1 showed the geometric jump point particle -> worldline string -> worldsheet Episode 2 is the dynamical jump. The Nambu-Goto action measures the area of the worldsheet, S = −T ∫ dτ dσ √[−det hₐᵦ] but the square-root determinant is awkward to work with. So we usually rewrite the same classical theory in Polyakov form, S = −(T/2) ∫ dτ dσ √[−γ] γᵃᵇ ∂ₐXᵘ ∂ᵦXᵤ Here Xᵘ(τ,σ) tells us where each point of the string’s worldsheet sits in spacetime, and γₐᵦ is the metric we put on the worldsheet. The power of this form is that we can choose a convenient gauge. In conformal gauge, the equations of motion simplify to (∂²/∂τ² − ∂²/∂σ²) Xᵘ = 0 So the string’s spacetime coordinates behave like waves living on the worldsheet. The τ-derivative measures how the string changes in worldsheet time. The σ-derivative measures how it bends along its own length. For a closed string, σ is periodic Xᵘ(τ, σ + 2π) = Xᵘ(τ,σ) and the wave equation splits into two traveling pieces, Xᵘ(τ,σ) = Fᵘ(τ + σ) + Gᵘ(τ − σ) One family moves one way around the string and the other moves the opposite way. These are the left-moving and right-moving modes. In the render, the bright loop is the string at the present moment. The glowing cylinder behind it is the worldsheet it has swept out. The cyan curves trace one traveling family, and the gold curves trace the other. They are the visual version of τ + σ and τ − σ. Therefore, the theory has an internal wave equation, and its normal modes are the raw material for the string spectrum. #StringTheory #TheoreticalPhysics #ConformalGauge #Worldsheet #WaveEquation #Physics #Mathematics #MathematicalPhysics #QuantumGravity #ScienceVisuals

Mathelirium

15,295 次观看 • 2 个月前

D-Branes and the Expansion of String Theory String Theory was already attempting to do something huge by trying to describe particles, forces, and gravity in one framework. Branes made that picture much richer. When Physicists found that open strings can end on objects called D-branes, many important ideas became easier to organize. Things like gauge fields, black hole microstates, holography, and deep dualities gained a clearer place inside the theory. They showed that String Theory is not only about tiny vibrating strings, but also about larger structures that help connect Quantum Physics, Geometry, and Gravity.
0:30

D-Branes and the Expansion of String Theory String Theory was already attempting to do something huge by trying to describe particles, forces, and gravity in one framework. Branes made that picture much richer. When Physicists found that open strings can end on objects called D-branes, many important ideas became easier to organize. Things like gauge fields, black hole microstates, holography, and deep dualities gained a clearer place inside the theory. They showed that String Theory is not only about tiny vibrating strings, but also about larger structures that help connect Quantum Physics, Geometry, and Gravity.

Mathelirium

21,515 次观看 • 2 个月前

String Theory tries to unify Quantum Mechanics and gravity into a single framework by replacing particles with strings whose vibrations also shape Spacetime.
0:30

String Theory tries to unify Quantum Mechanics and gravity into a single framework by replacing particles with strings whose vibrations also shape Spacetime.

Mathelirium

28,212 次观看 • 1 个月前

In String Theory, we ask a deceptively simple question What happens when you replace a point with something stretched across space and time? On one side, the particle draws a world line. On the other, a string fills out a world-sheet as every point along it evolves together.
0:58

In String Theory, we ask a deceptively simple question What happens when you replace a point with something stretched across space and time? On one side, the particle draws a world line. On the other, a string fills out a world-sheet as every point along it evolves together.

Mathelirium

16,325 次观看 • 1 个月前

The Non-Traversable Bridge Einstein Found Inside Gravity Einstein’s equations not only describe gravity as a force but as the shape of Spacetime as well. In 1935, Einstein and Rosen found that the Schwarzschild solution could be written in a way that reveals something astonishing: Two separate exterior regions of Spacetime joined by a bridge-like throat Rᵤᵥ = 0 This became known as the Einstein-Rosen Bridge. It is often called a Wormhole, but the classical Einstein-Rosen bridge is not a science-fiction tunnel. In the standard Schwarzschild geometry, it is non-traversable. The throat does not remain open long enough for ordinary travel from one region to the other. Its real power is mathematical. It shows that General Relativity is not merely about objects moving through space. The theory allows Spacetime to have global structure such as different regions, horizons, extensions, and hidden connections that are not visible from one local patch alone. The Einstein-Rosen bridge is one of the earliest glimpses of that deeper idea. Gravity is geometry. And sometimes, geometry has two worlds joined by a throat. #Astrophysics #GeneralRelativity #Einstein #BlackHole #Spacetime #Cosmology #Gravity #Wormhole #Mathematics #Physics
0:56

The Non-Traversable Bridge Einstein Found Inside Gravity Einstein’s equations not only describe gravity as a force but as the shape of Spacetime as well. In 1935, Einstein and Rosen found that the Schwarzschild solution could be written in a way that reveals something astonishing: Two separate exterior regions of Spacetime joined by a bridge-like throat Rᵤᵥ = 0 This became known as the Einstein-Rosen Bridge. It is often called a Wormhole, but the classical Einstein-Rosen bridge is not a science-fiction tunnel. In the standard Schwarzschild geometry, it is non-traversable. The throat does not remain open long enough for ordinary travel from one region to the other. Its real power is mathematical. It shows that General Relativity is not merely about objects moving through space. The theory allows Spacetime to have global structure such as different regions, horizons, extensions, and hidden connections that are not visible from one local patch alone. The Einstein-Rosen bridge is one of the earliest glimpses of that deeper idea. Gravity is geometry. And sometimes, geometry has two worlds joined by a throat. #Astrophysics #GeneralRelativity #Einstein #BlackHole #Spacetime #Cosmology #Gravity #Wormhole #Mathematics #Physics

Mathelirium

91,291 次观看 • 18 天前

Why quantum theory could have a fractal structure: explained in 83 minutes. The notion of true quantum nonlocality is absurd. In the latest episode of the Quantum Foundations Podcast, Prof Tim Palmer from the University of Oxford suggests that there is a hidden assumption in standard quantum mechanics, and dropping it will save us from this absurdity. Namely, the reality of counterfactuals: the physics of what could have happened but did not. Inspired by chaos theory and the fractal structure widespread in atmospheric physics, Palmer has developed a new underlying structure for quantum theory, with radical implications for our fundamental principles of quantum physics; the limits of quantum computation; and perhaps even the search for quantum gravity. Watch on my YouTube channel, or listen on Spotify and Apple Podcasts!
1:34

Why quantum theory could have a fractal structure: explained in 83 minutes. The notion of true quantum nonlocality is absurd. In the latest episode of the Quantum Foundations Podcast, Prof Tim Palmer from the University of Oxford suggests that there is a hidden assumption in standard quantum mechanics, and dropping it will save us from this absurdity. Namely, the reality of counterfactuals: the physics of what could have happened but did not. Inspired by chaos theory and the fractal structure widespread in atmospheric physics, Palmer has developed a new underlying structure for quantum theory, with radical implications for our fundamental principles of quantum physics; the limits of quantum computation; and perhaps even the search for quantum gravity. Watch on my YouTube channel, or listen on Spotify and Apple Podcasts!

Dr Maria Violaris

18,259 次观看 • 5 个月前

Eric Weinstein unleashes a bombshell: Theoretical physics froze in 1973—right as "Crocodile Rock" topped the charts—and hasn't advanced at the deepest level since. Youngest living Nobel in theoretical physics? Always under 50... until string theory took over as "quantum gravity." Now it's over 70. The field stopped producing breakthroughs. His wild claim: The Biden White House reportedly told Marc Andreessen they deliberately stagnated parts of theoretical physics—cocooning string theory as the "only game in town." Dissenting ideas? Career suicide. The trick? Hammer "quantum gravity is the holy grail" on repeat until it feels true. (Weirdly, that phrase barely appears in books before 1972.) Safe, harmless pursuit—no real risk even if foreign students dive in. Why? To avoid dangerous progress that could shatter the speed-of-light limit and get us to the stars... before humanity's tools become too lethal on one fragile planet. Weinstein's rallying cry: Physics is our only path off Earth. Break the stagnation, surpass Einstein, reach the cosmos. The end of physics as we know it might be glorious—if we seize this brief window before wars erupt. Clip from his ARC 2025 talk (4:05 of high-stakes provocation). Does this ring true—the deliberate stall on breakthrough physics? Or is string theory just a victim of its own complexity? What's your take on the "holy grail" mantra?
4:05

Eric Weinstein unleashes a bombshell: Theoretical physics froze in 1973—right as "Crocodile Rock" topped the charts—and hasn't advanced at the deepest level since. Youngest living Nobel in theoretical physics? Always under 50... until string theory took over as "quantum gravity." Now it's over 70. The field stopped producing breakthroughs. His wild claim: The Biden White House reportedly told Marc Andreessen they deliberately stagnated parts of theoretical physics—cocooning string theory as the "only game in town." Dissenting ideas? Career suicide. The trick? Hammer "quantum gravity is the holy grail" on repeat until it feels true. (Weirdly, that phrase barely appears in books before 1972.) Safe, harmless pursuit—no real risk even if foreign students dive in. Why? To avoid dangerous progress that could shatter the speed-of-light limit and get us to the stars... before humanity's tools become too lethal on one fragile planet. Weinstein's rallying cry: Physics is our only path off Earth. Break the stagnation, surpass Einstein, reach the cosmos. The end of physics as we know it might be glorious—if we seize this brief window before wars erupt. Clip from his ARC 2025 talk (4:05 of high-stakes provocation). Does this ring true—the deliberate stall on breakthrough physics? Or is string theory just a victim of its own complexity? What's your take on the "holy grail" mantra?

Camus

150,275 次观看 • 4 个月前

Can Spacetime Move Faster Than Light? In 1994, Miguel Alcubierre proposed a strange solution to Einstein’s field equations: A Spacetime geometry where a compact region could be transported without the object inside locally breaking the speed of light. The idea is not that a ship accelerates through space faster than light. The local interior remains comparatively calm. The violent part is the surrounding geometry. Space contracts in front of the bubble, expands behind it, and forms a moving transport shell that carries the interior region forward. A simplified form of the Alcubierre metric is ds² = −dt² + [dx − vₛ f(rₛ)dt]² + dy² + dz² where f(rₛ) shapes the warp bubble and vₛ describes the motion of its centre. The physics is still highly speculative, especially because the original construction requires exotic stress-energy, but the mathematical idea is powerful. #GeneralRelativity #AlcubierreDrive #WarpDrive #Spacetime #EinsteinEquations #Relativity #Physics #Astrophysics #Cosmology
0:56

Can Spacetime Move Faster Than Light? In 1994, Miguel Alcubierre proposed a strange solution to Einstein’s field equations: A Spacetime geometry where a compact region could be transported without the object inside locally breaking the speed of light. The idea is not that a ship accelerates through space faster than light. The local interior remains comparatively calm. The violent part is the surrounding geometry. Space contracts in front of the bubble, expands behind it, and forms a moving transport shell that carries the interior region forward. A simplified form of the Alcubierre metric is ds² = −dt² + [dx − vₛ f(rₛ)dt]² + dy² + dz² where f(rₛ) shapes the warp bubble and vₛ describes the motion of its centre. The physics is still highly speculative, especially because the original construction requires exotic stress-energy, but the mathematical idea is powerful. #GeneralRelativity #AlcubierreDrive #WarpDrive #Spacetime #EinsteinEquations #Relativity #Physics #Astrophysics #Cosmology

Mathelirium

37,986 次观看 • 14 天前

Google’s Quantum AI Found Something Disturbing in String Theory. The Results Are Unsettling...🧐🤔 Google’s Quantum AI may have just opened a door that scientists weren’t ready for. While running experiments connected to string theory, researchers claim the system uncovered results that were not only unexpected — but deeply unsettling. Could this be the first sign that our understanding of the universe is incomplete? In this documentary-style breakdown, we’ll look at what the AI discovered, why physicists are both excited and disturbed, and how these findings could change the future of science. This is not just theory anymore — it’s a glimpse into something far bigger than we imagined...
18:18

Google’s Quantum AI Found Something Disturbing in String Theory. The Results Are Unsettling...🧐🤔 Google’s Quantum AI may have just opened a door that scientists weren’t ready for. While running experiments connected to string theory, researchers claim the system uncovered results that were not only unexpected — but deeply unsettling. Could this be the first sign that our understanding of the universe is incomplete? In this documentary-style breakdown, we’ll look at what the AI discovered, why physicists are both excited and disturbed, and how these findings could change the future of science. This is not just theory anymore — it’s a glimpse into something far bigger than we imagined...

UFO mania

196,710 次观看 • 7 个月前

Why does String Theory keep introducing extra dimensions? Because once you quantize a relativistic string consistently, the Mathematics stops working cleanly in ordinary 3+1 dimensions.
0:45

Why does String Theory keep introducing extra dimensions? Because once you quantize a relativistic string consistently, the Mathematics stops working cleanly in ordinary 3+1 dimensions.

Mathelirium

67,374 次观看 • 1 个月前

The Chinese Physicist Who Turned Force Into Geometry In 1954, Chinese physicist Chen-Ning Yang, together with Robert Mills, introduced a new idea that changed modern physics: Maybe a force is not just something that pushes or pulls. Maybe a force can come from geometry. In Yang-Mills Theory, every point in space carries a hidden internal direction. As you move through space, that direction can twist. If you go around a closed loop and the direction does not return exactly the same, the field has curvature. That curvature is what we see as force. In this animation, the glowing surface shows where the gauge field is strongest. The changing colours show how the hidden internal direction varies across space. The moving rectangular loops are Wilson loops. They travel through the field and measure how much the internal direction changes after completing a closed path. The key equation behind the scene is Fₓᵧ = ∂ₓAᵧ - ∂ᵧAₓ + Aₓ × Aᵧ. The final term, Aₓ × Aᵧ, is the special part. It means the field can interact with itself. That self-interaction is one reason Yang-Mills theory became one of the foundations of particle physics. #China #ChinesePhysics #YangMills #GaugeTheory #QuantumFieldTheory #NonAbelianGeometry #WilsonLoops #ModernPhysics #STEM
0:30

The Chinese Physicist Who Turned Force Into Geometry In 1954, Chinese physicist Chen-Ning Yang, together with Robert Mills, introduced a new idea that changed modern physics: Maybe a force is not just something that pushes or pulls. Maybe a force can come from geometry. In Yang-Mills Theory, every point in space carries a hidden internal direction. As you move through space, that direction can twist. If you go around a closed loop and the direction does not return exactly the same, the field has curvature. That curvature is what we see as force. In this animation, the glowing surface shows where the gauge field is strongest. The changing colours show how the hidden internal direction varies across space. The moving rectangular loops are Wilson loops. They travel through the field and measure how much the internal direction changes after completing a closed path. The key equation behind the scene is Fₓᵧ = ∂ₓAᵧ - ∂ᵧAₓ + Aₓ × Aᵧ. The final term, Aₓ × Aᵧ, is the special part. It means the field can interact with itself. That self-interaction is one reason Yang-Mills theory became one of the foundations of particle physics. #China #ChinesePhysics #YangMills #GaugeTheory #QuantumFieldTheory #NonAbelianGeometry #WilsonLoops #ModernPhysics #STEM

Mathelirium

80,867 次观看 • 14 天前

If you’re an engineer, physicist, or CS person and you’ve been telling yourself that Pure Mathematics is optional, and you’re anywhere between an ambitious undergrad and a beginning PhD, gravity is usually where that story ends. Not because mathematicians are trying to show off, but because the basic object in the theory is Spacetime, and Spacetime is already a pure mathematical structure. It’s a Manifold with Topology built in. Sure you can get pretty far by memorising formulas, but at some point you realise you’re no longer reading the theory, you’re just reciting it. In 2015, during the 100th anniversary of general relativity and the International Year of Light, the Scientific Organizing Committee released a central set of 24 lectures by Frederic P. Schuller. The series is titled: A thorough introduction to the theory of general relativity. It builds the subject carefully from first principles, step by step, across 24 self-contained lectures. #GeneralRelativity #Spacetime #MathematicalPhysics #DifferentialGeometry #PhysicsEducation #Relativity
2:46

If you’re an engineer, physicist, or CS person and you’ve been telling yourself that Pure Mathematics is optional, and you’re anywhere between an ambitious undergrad and a beginning PhD, gravity is usually where that story ends. Not because mathematicians are trying to show off, but because the basic object in the theory is Spacetime, and Spacetime is already a pure mathematical structure. It’s a Manifold with Topology built in. Sure you can get pretty far by memorising formulas, but at some point you realise you’re no longer reading the theory, you’re just reciting it. In 2015, during the 100th anniversary of general relativity and the International Year of Light, the Scientific Organizing Committee released a central set of 24 lectures by Frederic P. Schuller. The series is titled: A thorough introduction to the theory of general relativity. It builds the subject carefully from first principles, step by step, across 24 self-contained lectures. #GeneralRelativity #Spacetime #MathematicalPhysics #DifferentialGeometry #PhysicsEducation #Relativity

Mathelirium

198,381 次观看 • 5 个月前

India Hits a Quantum Milestone! 🇮🇳 🇮🇳India just had a quantum breakthrough that went pretty unnoticed! 🔥 Kaveri is a 64-qubit quantum chip built in Bengaluru, and it’s the first time India has crossed 50 qubits, putting it in the same quantum league as the U.S., China, and Europe. 🔥🔥🔥
1:06

India Hits a Quantum Milestone! 🇮🇳 🇮🇳India just had a quantum breakthrough that went pretty unnoticed! 🔥 Kaveri is a 64-qubit quantum chip built in Bengaluru, and it’s the first time India has crossed 50 qubits, putting it in the same quantum league as the U.S., China, and Europe. 🔥🔥🔥

JIX5A

93,915 次观看 • 5 个月前

Ever Heard of a Metric in Differential Geometry? How About a Geodesic? These two ideas are central to how Mathematics and Physics describe Spacetime. A metric is how a surface measures distance and angle. A geodesic is the path that counts as "straight" after that measuring rule is chosen. Once the metric changes from point to point, straightness is no longer something you judge by eye. On a curved surface, the shortest paths are geodesics. They are chosen by the metric. Take a surface written as r(x,y) = (x, y, f(x,y)) Its metric is gᵢⱼ = ∂ᵢr · ∂ⱼr A geodesic q(t) = (x(t), y(t)) obeys q̈ᵏ + Γᵏᵢⱼ q̇ᶦq̇ʲ = 0 where Γᵏᵢⱼ are the Christoffel symbols of the surface metric. Launch many almost-parallel paths. At the start, they look like a clean beam until curvature takes over. Some paths focus, others separate and some slide around ridges. The surface is essentially the rulebook for motion. The shortest path is local. The geometry remembers everything. #DifferentialGeometry #Geodesics #RiemannianGeometry #MathematicalPhysics #Curvature #TensorCalculus #AppliedMathematics #Geometry #ScienceAnimation
0:33

Ever Heard of a Metric in Differential Geometry? How About a Geodesic? These two ideas are central to how Mathematics and Physics describe Spacetime. A metric is how a surface measures distance and angle. A geodesic is the path that counts as "straight" after that measuring rule is chosen. Once the metric changes from point to point, straightness is no longer something you judge by eye. On a curved surface, the shortest paths are geodesics. They are chosen by the metric. Take a surface written as r(x,y) = (x, y, f(x,y)) Its metric is gᵢⱼ = ∂ᵢr · ∂ⱼr A geodesic q(t) = (x(t), y(t)) obeys q̈ᵏ + Γᵏᵢⱼ q̇ᶦq̇ʲ = 0 where Γᵏᵢⱼ are the Christoffel symbols of the surface metric. Launch many almost-parallel paths. At the start, they look like a clean beam until curvature takes over. Some paths focus, others separate and some slide around ridges. The surface is essentially the rulebook for motion. The shortest path is local. The geometry remembers everything. #DifferentialGeometry #Geodesics #RiemannianGeometry #MathematicalPhysics #Curvature #TensorCalculus #AppliedMathematics #Geometry #ScienceAnimation

Mathelirium

22,170 次观看 • 17 天前

In this episode, I speak with Professor Felix Finster, a radical thinker reimagining the foundations of physics. We explore his theory of causal fermion systems, where reality emerges from quantum correlations—without assuming spacetime or geometry. From the Dirac sea to quantum gravity, this conversation challenges familiar concepts and offers a glimpse into where the next physics revolution might begin.
1:30

In this episode, I speak with Professor Felix Finster, a radical thinker reimagining the foundations of physics. We explore his theory of causal fermion systems, where reality emerges from quantum correlations—without assuming spacetime or geometry. From the Dirac sea to quantum gravity, this conversation challenges familiar concepts and offers a glimpse into where the next physics revolution might begin.

Curt Jaimungal

16,924 次观看 • 11 个月前

Phase Space Is the Real Stage of Dynamics. So, Stop Watching the Object and Watch the State. Ordinary Space tells you where something is. Phase Space tells you what state it is in. Position alone is not enough because you also need the variable that tells you where the system is trying to go. In the animation, the left panel shows the particle moving in Ordinary Space, while the right panel shows the same system as a moving point in Phase Space. For one degree of freedom, the state is (x, p) and as time evolves, that state traces a trajectory t ↦ (x(t), p(t)) Instead of thinking of a differential equation as just a formula, Phase Space lets you see it as a flow on the space of states. For this lecture we use ẋ = p ṗ = x − x³ with Hamiltonian H(x,p) = 0.5 p² + 0.25 x⁴ − 0.5 x² #PhaseSpace #DynamicalSystems #NonlinearDynamics #HamiltonianMechanics #Mathematics
0:30

Phase Space Is the Real Stage of Dynamics. So, Stop Watching the Object and Watch the State. Ordinary Space tells you where something is. Phase Space tells you what state it is in. Position alone is not enough because you also need the variable that tells you where the system is trying to go. In the animation, the left panel shows the particle moving in Ordinary Space, while the right panel shows the same system as a moving point in Phase Space. For one degree of freedom, the state is (x, p) and as time evolves, that state traces a trajectory t ↦ (x(t), p(t)) Instead of thinking of a differential equation as just a formula, Phase Space lets you see it as a flow on the space of states. For this lecture we use ẋ = p ṗ = x − x³ with Hamiltonian H(x,p) = 0.5 p² + 0.25 x⁴ − 0.5 x² #PhaseSpace #DynamicalSystems #NonlinearDynamics #HamiltonianMechanics #Mathematics

Mathelirium

30,340 次观看 • 3 个月前

In String Theory, a tiny compact circle can be physically equivalent to a large one. This is known as T-duality.
0:40

In String Theory, a tiny compact circle can be physically equivalent to a large one. This is known as T-duality.

Mathelirium

23,897 次观看 • 1 个月前