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String Theory makes an ambitious proposal: Quantum excitations and Spacetime geometry may arise from the same extended objects.

Mathelirium

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32,499 次观看 • 1 个月前 •via X (Twitter)

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String Theory is one of the few frameworks that tries to describe Quantum Physics and Gravity in the same mathematical language. In this animation, the glowing loop is the string, the shifting color along it represent its quantum vibration modes, and the surrounding fabric is a proxy for Spacetime responding. When you quantize a string, one of its vibration modes behaves like a graviton. So, geometry shows up as part of the same quantum system. #StringTheory #QuantumGravity #GeneralRelativity #QuantumPhysics #TheoreticalPhysics #PhysicsVisualization

String Theory is one of the few frameworks that tries to describe Quantum Physics and Gravity in the same mathematical language. In this animation, the glowing loop is the string, the shifting color along it represent its quantum vibration modes, and the surrounding fabric is a proxy for Spacetime responding. When you quantize a string, one of its vibration modes behaves like a graviton. So, geometry shows up as part of the same quantum system. #StringTheory #QuantumGravity #GeneralRelativity #QuantumPhysics #TheoreticalPhysics #PhysicsVisualization

Mathelirium

42,172 次观看 • 6 个月前

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 a quantum degree of freedom, shown as color. At the same time, its motion stirs ripples in the surrounding metric, shown as the fabric below. One object, two roles. A wave-like state living on the string, and a curvature-like response spreading through the background. You can literally watch quantum stuff and gravity stuff talk to each other in the same scene. #StringTheory #Physics #QuantumMechanics #GeneralRelativity #MathematicalPhysics #SciComm

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 a quantum degree of freedom, shown as color. At the same time, its motion stirs ripples in the surrounding metric, shown as the fabric below. One object, two roles. A wave-like state living on the string, and a curvature-like response spreading through the background. You can literally watch quantum stuff and gravity stuff talk to each other in the same scene. #StringTheory #Physics #QuantumMechanics #GeneralRelativity #MathematicalPhysics #SciComm

Mathelirium

13,657 次观看 • 7 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.

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 • 3 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.

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 • 4 个月前

White Holes Don’t Push You Way. Spacetime Refuses Your Future. A White Hole appears in the maximally extended Schwarzschild solution of General Relativity, the full mathematical extension of the Spacetime around an eternal, non-rotating Black Hole. The exterior geometry is the same Schwarzschild geometry ds² = −(1 − 2M/r)dt² + (1 − 2M/r)⁻¹dr² + r²dΩ² But the causal direction is reversed. For a Black Hole, future-directed paths can cross the horizon inward. For a White Hole, future-directed paths can emerge from the horizon, but outside particles cannot enter that region. The object has not been observed in nature. But inside the Mathematics of General Relativity, it is a real sector of the extended Schwarzschild Spacetime... the Black Hole’s time-reversed counterpart.

White Holes Don’t Push You Way. Spacetime Refuses Your Future. A White Hole appears in the maximally extended Schwarzschild solution of General Relativity, the full mathematical extension of the Spacetime around an eternal, non-rotating Black Hole. The exterior geometry is the same Schwarzschild geometry ds² = −(1 − 2M/r)dt² + (1 − 2M/r)⁻¹dr² + r²dΩ² But the causal direction is reversed. For a Black Hole, future-directed paths can cross the horizon inward. For a White Hole, future-directed paths can emerge from the horizon, but outside particles cannot enter that region. The object has not been observed in nature. But inside the Mathematics of General Relativity, it is a real sector of the extended Schwarzschild Spacetime... the Black Hole’s time-reversed counterpart.

Mathelirium

31,146 次观看 • 3 个月前

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

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

18,616 次观看 • 2 个月前

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

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 • 4 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

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

91,963 次观看 • 2 个月前

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

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

198,712 次观看 • 7 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.

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 • 4 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

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

15,607 次观看 • 4 个月前

🌀🌌 What if gravity isn’t really a force? Einstein’s general relativity gives us a radically different picture: mass and energy curve the fabric of spacetime, and objects follow paths shaped by that geometry. Even light bends when passing through strongly curved spacetime. In this view, planets aren’t simply being “pulled” by the Sun they’re moving through curved spacetime created by its mass. Gravity may be less like an invisible force… and more like the geometry of the universe itself. 🕳️✨

🌀🌌 What if gravity isn’t really a force? Einstein’s general relativity gives us a radically different picture: mass and energy curve the fabric of spacetime, and objects follow paths shaped by that geometry. Even light bends when passing through strongly curved spacetime. In this view, planets aren’t simply being “pulled” by the Sun they’re moving through curved spacetime created by its mass. Gravity may be less like an invisible force… and more like the geometry of the universe itself. 🕳️✨

The Universe

33,055 次观看 • 16 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.

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

16,977 次观看 • 1 年前

A Black Hole Can Be Dragged Through Spacetime A Black Hole does not have to sit still. Einstein’s equations allow a stranger possibility... a Black Hole that accelerates. This is the C-metric, an exact solution of General Relativity describing an accelerating Black Hole. The Black Hole accelerates because the geometry of Spacetime says it must. The C-metric is one of those exact solutions that reminds us how wild General Relativity really is. Gravity is not just attraction, and Spacetime is not just a stage. Sometimes the stage itself contains the force. #Astrophysics #GeneralRelativity #Einstein #CMetric #BlackHole #CosmicStrings #Spacetime #Cosmology #Mathematics #Physics

A Black Hole Can Be Dragged Through Spacetime A Black Hole does not have to sit still. Einstein’s equations allow a stranger possibility... a Black Hole that accelerates. This is the C-metric, an exact solution of General Relativity describing an accelerating Black Hole. The Black Hole accelerates because the geometry of Spacetime says it must. The C-metric is one of those exact solutions that reminds us how wild General Relativity really is. Gravity is not just attraction, and Spacetime is not just a stage. Sometimes the stage itself contains the force. #Astrophysics #GeneralRelativity #Einstein #CMetric #BlackHole #CosmicStrings #Spacetime #Cosmology #Mathematics #Physics

Mathelirium

789,660 次观看 • 2 个月前

General Relativity allows a geometry where two distant regions of Spacetime become connected through a curved throat. In 1935, Albert Einstein and Nathan Rosen showed that the Schwarzschild solution can be extended into a bridge-like structure. The metric is ds² = −(1 − 2M/r)dt² + (1 − 2M/r)⁻¹dr² + r²dΩ² Under maximal coordinate extension, the Spacetime splits into two asymptotically flat regions joined through a narrow throat called, the Einstein–Rosen bridge. It's a geometric structure emerging directly from Einstein’s field equations. #EinsteinRosenBridge #GeneralRelativity #SpacetimeGeometry #BlackHolePhysics #EinsteinFieldEquations #Relativity

General Relativity allows a geometry where two distant regions of Spacetime become connected through a curved throat. In 1935, Albert Einstein and Nathan Rosen showed that the Schwarzschild solution can be extended into a bridge-like structure. The metric is ds² = −(1 − 2M/r)dt² + (1 − 2M/r)⁻¹dr² + r²dΩ² Under maximal coordinate extension, the Spacetime splits into two asymptotically flat regions joined through a narrow throat called, the Einstein–Rosen bridge. It's a geometric structure emerging directly from Einstein’s field equations. #EinsteinRosenBridge #GeneralRelativity #SpacetimeGeometry #BlackHolePhysics #EinsteinFieldEquations #Relativity

Mathelirium

26,356 次观看 • 3 个月前

Faster Than Light Without Moving Faster Than Light In 1994, Miguel Alcubierre discovered a solution to Einstein’s Field Equations where a region of Spacetime can effectively travel faster than light without anything locally breaking Relativity. The object inside the bubble never outruns light in its own local frame. Instead, Spacetime contracts ahead of the bubble, expands behind it, and carries the interior forward. The motion comes from geometry itself.

Faster Than Light Without Moving Faster Than Light In 1994, Miguel Alcubierre discovered a solution to Einstein’s Field Equations where a region of Spacetime can effectively travel faster than light without anything locally breaking Relativity. The object inside the bubble never outruns light in its own local frame. Instead, Spacetime contracts ahead of the bubble, expands behind it, and carries the interior forward. The motion comes from geometry itself.

Mathelirium

17,688 次观看 • 3 个月前

General Relativity Keeps Revealing Unexpected Spacetime Geometries That Go Far Beyond Everyday Intuition. In 1988, Kip Thorne and Michael Morris described a traversable Wormhole geometry that strangely connects two distant regions of Spacetime without an event horizon or central singularity. No traversable Wormhole has ever been observed. Within General Relativity, though, these solutions are mathematically valid if Spacetime is supported by exotic stress-energy that violates classical energy conditions. It's a solution Einstein’s field equations allow, but nature has not confirmed. #Einstein #GeneralRelativity #Wormholes #Spacetime #Physics #Relativity

General Relativity Keeps Revealing Unexpected Spacetime Geometries That Go Far Beyond Everyday Intuition. In 1988, Kip Thorne and Michael Morris described a traversable Wormhole geometry that strangely connects two distant regions of Spacetime without an event horizon or central singularity. No traversable Wormhole has ever been observed. Within General Relativity, though, these solutions are mathematically valid if Spacetime is supported by exotic stress-energy that violates classical energy conditions. It's a solution Einstein’s field equations allow, but nature has not confirmed. #Einstein #GeneralRelativity #Wormholes #Spacetime #Physics #Relativity

Mathelirium

24,117 次观看 • 3 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.

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 • 3 个月前

What If a Black Hole Shredded Worlds Before They Fell In? Far away from a Black Hole, an object can orbit, drift past, or escape. But if its path carries it too close, the geometry decides its fate. The exterior geometry is Schwarzschild-like ds² = -(1 - 2M/r)dt² + (1 - 2M/r)⁻¹dr² + r²dΩ² The event horizon sits at rₛ = 2M The photon sphere sits at rₚₕ = 3M #Astrophysics #GeneralRelativity #Einstein #BlackHole #Spacetime #TidalForces #PhotonSphere #Cosmology #Mathematics

What If a Black Hole Shredded Worlds Before They Fell In? Far away from a Black Hole, an object can orbit, drift past, or escape. But if its path carries it too close, the geometry decides its fate. The exterior geometry is Schwarzschild-like ds² = -(1 - 2M/r)dt² + (1 - 2M/r)⁻¹dr² + r²dΩ² The event horizon sits at rₛ = 2M The photon sphere sits at rₚₕ = 3M #Astrophysics #GeneralRelativity #Einstein #BlackHole #Spacetime #TidalForces #PhotonSphere #Cosmology #Mathematics

Mathelirium

40,811 次观看 • 2 个月前

For decades, string theory promised a “theory of everything” that described all particles and forces as tiny vibrating strings. Physicists hoped it could also solve one of the field’s deepest problems: reconciling quantum mechanics with gravity. But as string theory grew increasingly elaborate—and experimentally unreachable—many physicists lost hope. Now, some researchers are revisiting the theory from first principles. Learn more:

For decades, string theory promised a “theory of everything” that described all particles and forces as tiny vibrating strings. Physicists hoped it could also solve one of the field’s deepest problems: reconciling quantum mechanics with gravity. But as string theory grew increasingly elaborate—and experimentally unreachable—many physicists lost hope. Now, some researchers are revisiting the theory from first principles. Learn more:

Science Magazine

61,475 次观看 • 13 天前