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A Pulsar (the tiny, ultra-dense core left behind after a massive star explodes) is one of the most accurate clocks in the Universe. But when its radio pulses pass near a Black Hole, gravity delays their arrival. In other words, the pulse never changed and the clock stayed perfect... show more

Mathelirium

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The Elusive Concept of Time - Part II Pulsar Timing The first scene showed you Time as a local rate...clocks nearer the hole run slower, light gets redshifted, and spin drags the geometry around. This follow-up keeps the same idea, but turns it into a timing experiment. Instead of watching a clock face, we watch a receiver compare what arrives versus what flat space would predict. In the animation, the three small orange dots are the pulsars...orbiting emitters that flash regularly (in their own proper time). The larger white dot is the receiver sitting off to the side, and the little dark nub next to it is a tiny craft/antenna marker to make it feel like an instrument, not a star. When a pulsar lines up behind the hole relative to the receiver, the arrival times jump, because curved spacetime added extra delay and bent the path. #Physics #GeneralRelativity #PulsarTiming #BlackHoles #FrameDragging #Spacetime #Astrophysics #Time

The Elusive Concept of Time - Part II Pulsar Timing The first scene showed you Time as a local rate...clocks nearer the hole run slower, light gets redshifted, and spin drags the geometry around. This follow-up keeps the same idea, but turns it into a timing experiment. Instead of watching a clock face, we watch a receiver compare what arrives versus what flat space would predict. In the animation, the three small orange dots are the pulsars...orbiting emitters that flash regularly (in their own proper time). The larger white dot is the receiver sitting off to the side, and the little dark nub next to it is a tiny craft/antenna marker to make it feel like an instrument, not a star. When a pulsar lines up behind the hole relative to the receiver, the arrival times jump, because curved spacetime added extra delay and bent the path. #Physics #GeneralRelativity #PulsarTiming #BlackHoles #FrameDragging #Spacetime #Astrophysics #Time

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Near a Black Hole, gravity stretches time so profoundly that seconds for one observer can become centuries for another. So the question isn’t what time is it? The question is: When are we?

Near a Black Hole, gravity stretches time so profoundly that seconds for one observer can become centuries for another. So the question isn’t what time is it? The question is: When are we?

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Gravity Makes Light Arrive Late Shapiro delay is the weird fact that gravity doesn’t only bend a light path, it also makes the signal arrive late, even after you subtract the usual distance/c travel time. On the our beautiful spacetime fabric stage, a transmitter sends clean pulses across the scene to a reflector and back. When the pulses skim the deep region near the horizon ring, they stretch into long faint filaments and the echo returns after the flat-space prediction. *Python Script Available for Subscribers

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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 collisionless limit, Liouville’s theorem says this sheet can stretch, fold, and swirl, but never tear or change area. Collapse in x is "paid for" by stretching in v. Numerically, this is a 1D cold-dark-matter toy universe: a sheet of particles evolved under the Vlasov-Poisson system. We solve Poisson on a periodic line, get the self-consistent gravitational field, then integrate Hamilton’s equations so the sheet folds into a multi-layer spiral. The glowing filaments are where the sheet keeps revisiting, carving out dense caustics in phase space. It's gravity not as "stuff falling down," but as area-preserving origami in phase space. #Mathelirium #VlasovPoisson #PhaseSpace #Liouville #DarkMatter #HamiltonianFlow #ProbabilityFlow

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 collisionless limit, Liouville’s theorem says this sheet can stretch, fold, and swirl, but never tear or change area. Collapse in x is "paid for" by stretching in v. Numerically, this is a 1D cold-dark-matter toy universe: a sheet of particles evolved under the Vlasov-Poisson system. We solve Poisson on a periodic line, get the self-consistent gravitational field, then integrate Hamilton’s equations so the sheet folds into a multi-layer spiral. The glowing filaments are where the sheet keeps revisiting, carving out dense caustics in phase space. It's gravity not as "stuff falling down," but as area-preserving origami in phase space. #Mathelirium #VlasovPoisson #PhaseSpace #Liouville #DarkMatter #HamiltonianFlow #ProbabilityFlow

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A White Hole is a Black Hole Running Backward A Black Hole is famous because it lets things fall in, but never lets them come back out. A White Hole is the time-reversed version of that idea. In the full Schwarzschild solution of General Relativity, the Black-Hole region and the White-Hole region appear as two different causal parts of the same exact geometry. Outside the horizon, the metric is the usual Schwarzschild metric ds² = -(1 - 2M/r)dt² + (1 - 2M/r)⁻¹dr² + r²dΩ². The horizon sits at rₛ = 2M, using G = c = 1. For an ordinary Black Hope, future-directed paths can cross this surface inward. Once they do, they cannot return to the outside universe. For a White Hole, the arrow is reversed and particles and light can come out from the horizon, but outside observers cannot enter it. No one has observed a physical White Hole. It may be an ideal solution rather than an object that nature actually forms. But as Mathematics, it is one of the strangest lessons of General Relativity: The equations allow a horizon that throws the universe outward. #WhiteHoles #GeneralRelativity #Schwarzschild #Spacetime #BlackHoles #Cosmology #Physics #Mathematics #Astrophysics #Astronomy

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In String Theory, it has been shown that one vibration of a closed string behaves like a graviton, the Quantum particle of gravity, revealing that gravity is already built into String Theory’s spectrum.

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The High-Dimensional Ball Is Full, but Its Probability Mass Lives Near the Boundary High-dimensional probability is weird. As the dimension grows, a uniform point in the ball does not usually land deep inside. Most of the mass gets pushed into a very thin shell near the boundary.

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The Elusive Concept of Time. Your instincts treat time like a background meter the whole universe shares. Relativity does not take time away, it forces you to earn it operationally. Events are points. Motion is a curve through them. A clock is not a metaphor, it is a worldline with a number attached to it. Two observers can disagree on which distant events are simultaneous, and nothing contradictory happens, because causal structure is still pinned down by light cones and invariants. Even in weak gravity the rule shows up. A clock deeper in a gravitational potential ticks more slowly relative to one far away. Near a compact object the difference becomes hard to ignore. Add rotation and spacetime itself picks up a twist. That twist is frame dragging, not a new force, just geometry telling you that time and angle are coupled in a rotating spacetime. In the animation You are watching a geometry lesson disguised as a black hole scene. The fabric is a visualization of the field shaping clock-rates and the paths light can take. The ripples are driven by local proper time, so their phase visibly slows as you approach the horizon. The accretion disk is lensed through Kerr ray tracing, and its brightness is pushed by redshift and beaming so the approaching side can flare while the receding side dims. Beacon points at different radii pulse at different rates, so you can see time dilation without any labels. The bead ring is a redshift tracer, with intensity scaled by a g³ proxy so deeper emission arrives weaker and shifted. The math breakdown Start with what a clock actually measures. Proper time τ is the accumulated time along an observer’s worldline. In special relativity, the invariant interval is ds² = c² dt² − dx² − dy² − dz² Along a timelike path, dτ = (1/c) √(ds²) = √( dt² − (1/c²)(dx²+dy²+dz²) ) If the observer moves with speed v, so dx²+dy²+dy²+dz² = v² dt², then dτ = dt √(1 − v²/c²) That is time dilation as geometry. The moving clock accumulates less τ between the same pair of events. Now add gravity. General relativity replaces the flat interval with a metric gᵤᵥ that depends on position: ds² = gᵤᵥ dxᵘ dxᵛ For a stationary clock in Schwarzschild geometry (mass M), the time component is g_tt = −(1 − 2GM/(rc²)) If the clock sits at fixed r (no spatial motion), ds² = g_tt c² dt², so dτ = dt √(1 − 2GM/(rc²)) Closer to the mass means a smaller factor, so the clock ticks more slowly relative to a clock far away. That is the rule used to drive the fabric phase in the animation. Now connect time to light. A gravitational field shifts photon frequency. Between an emitter at rₑ and an observer at rₒ, f_obs / f_emit = √( (1 − 2GM/(rₑ c²)) / (1 − 2GM/(rₒ c²)) ) For a far-away observer rₒ → ∞, f_obs / f_emit = √(1 − 2GM/(rₑ c²)) Deeper emission arrives redshifted. Lower frequency. Lower energy per photon. In the render, the disk intensity uses a Kerr-derived redshift factor g (clipped for stability). The bead ring uses a simple radiative proxy I_obs ∝ g³ I_emit to make that effect visible. Finally, why rotation looks like a twist. A rotating black hole is Kerr geometry. The key structural change is a nonzero g_tφ term, which couples time to angle. That coupling is frame dragging in equations. Near the hole, being stationary is not the same notion everywhere, because the local inertial frames are being pulled around the spin axis. So the moral stays clean. Time is not a universal substance flowing everywhere at one rate. It is what clocks accumulate along worldlines. Light cones constrain what can influence what. Invariants are what everyone agrees on. The rest is operational detail that only feels universal because our daily corner of the universe is slow and mild. #GeneralRelativity #Gravity #FrameDragging #BlackHoles #Spacetime

The Elusive Concept of Time. Your instincts treat time like a background meter the whole universe shares. Relativity does not take time away, it forces you to earn it operationally. Events are points. Motion is a curve through them. A clock is not a metaphor, it is a worldline with a number attached to it. Two observers can disagree on which distant events are simultaneous, and nothing contradictory happens, because causal structure is still pinned down by light cones and invariants. Even in weak gravity the rule shows up. A clock deeper in a gravitational potential ticks more slowly relative to one far away. Near a compact object the difference becomes hard to ignore. Add rotation and spacetime itself picks up a twist. That twist is frame dragging, not a new force, just geometry telling you that time and angle are coupled in a rotating spacetime. In the animation You are watching a geometry lesson disguised as a black hole scene. The fabric is a visualization of the field shaping clock-rates and the paths light can take. The ripples are driven by local proper time, so their phase visibly slows as you approach the horizon. The accretion disk is lensed through Kerr ray tracing, and its brightness is pushed by redshift and beaming so the approaching side can flare while the receding side dims. Beacon points at different radii pulse at different rates, so you can see time dilation without any labels. The bead ring is a redshift tracer, with intensity scaled by a g³ proxy so deeper emission arrives weaker and shifted. The math breakdown Start with what a clock actually measures. Proper time τ is the accumulated time along an observer’s worldline. In special relativity, the invariant interval is ds² = c² dt² − dx² − dy² − dz² Along a timelike path, dτ = (1/c) √(ds²) = √( dt² − (1/c²)(dx²+dy²+dz²) ) If the observer moves with speed v, so dx²+dy²+dy²+dz² = v² dt², then dτ = dt √(1 − v²/c²) That is time dilation as geometry. The moving clock accumulates less τ between the same pair of events. Now add gravity. General relativity replaces the flat interval with a metric gᵤᵥ that depends on position: ds² = gᵤᵥ dxᵘ dxᵛ For a stationary clock in Schwarzschild geometry (mass M), the time component is g_tt = −(1 − 2GM/(rc²)) If the clock sits at fixed r (no spatial motion), ds² = g_tt c² dt², so dτ = dt √(1 − 2GM/(rc²)) Closer to the mass means a smaller factor, so the clock ticks more slowly relative to a clock far away. That is the rule used to drive the fabric phase in the animation. Now connect time to light. A gravitational field shifts photon frequency. Between an emitter at rₑ and an observer at rₒ, f_obs / f_emit = √( (1 − 2GM/(rₑ c²)) / (1 − 2GM/(rₒ c²)) ) For a far-away observer rₒ → ∞, f_obs / f_emit = √(1 − 2GM/(rₑ c²)) Deeper emission arrives redshifted. Lower frequency. Lower energy per photon. In the render, the disk intensity uses a Kerr-derived redshift factor g (clipped for stability). The bead ring uses a simple radiative proxy I_obs ∝ g³ I_emit to make that effect visible. Finally, why rotation looks like a twist. A rotating black hole is Kerr geometry. The key structural change is a nonzero g_tφ term, which couples time to angle. That coupling is frame dragging in equations. Near the hole, being stationary is not the same notion everywhere, because the local inertial frames are being pulled around the spin axis. So the moral stays clean. Time is not a universal substance flowing everywhere at one rate. It is what clocks accumulate along worldlines. Light cones constrain what can influence what. Invariants are what everyone agrees on. The rest is operational detail that only feels universal because our daily corner of the universe is slow and mild. #GeneralRelativity #Gravity #FrameDragging #BlackHoles #Spacetime

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Bertrand’s Theorem states that only two central forces close every bounded orbit: F(r) ∝ - 1/r² and F(r) ∝ - r. The first gives the familiar Keplerian ellipses of Newtonian gravity. The second is the isotropic harmonic oscillator. Other central forces can still conserve energy and angular momentum, but their periapsis rotates after each revolution. A bounded orbit is therefore not necessarily a closed orbit.

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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.

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Mathelirium

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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

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Mathelirium

788,760 просмотров • 1 месяц назад

In the opening credits scene of BACK TO THE FUTURE, one of Doc’s many clocks shows a tiny figure of Harold Lloyd hanging from a clock face, directly foreshadowing Doc Brown later dangling from the Hill Valley clock tower near the climax.

In the opening credits scene of BACK TO THE FUTURE, one of Doc’s many clocks shows a tiny figure of Harold Lloyd hanging from a clock face, directly foreshadowing Doc Brown later dangling from the Hill Valley clock tower near the climax.

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72,728 просмотров • 5 месяцев назад

Hubble Records Wandering Black Hole That Swallowed a Star NASA astronomers have recorded a rare event using the Hubble Space Telescope and other observatories — a tidal disruption event (TDE) involving a wandering black hole. It occurred 600 million light years from Earth and provided new insights into the behavior of black holes. The object was spotted due to gravitational lensing — the distortion of light from distant bodies under the influence of gravity. As it approached the star, the black hole tore it apart, creating a bright accretion disk that radiated in ultraviolet and visible light. Unlike typical black holes in the centers of galaxies, this one was located 2,600 light years from the core, where a supermassive black hole was already located. Despite their relative proximity, the two holes do not yet form a single system, but they may merge in the future.

Hubble Records Wandering Black Hole That Swallowed a Star NASA astronomers have recorded a rare event using the Hubble Space Telescope and other observatories — a tidal disruption event (TDE) involving a wandering black hole. It occurred 600 million light years from Earth and provided new insights into the behavior of black holes. The object was spotted due to gravitational lensing — the distortion of light from distant bodies under the influence of gravity. As it approached the star, the black hole tore it apart, creating a bright accretion disk that radiated in ultraviolet and visible light. Unlike typical black holes in the centers of galaxies, this one was located 2,600 light years from the core, where a supermassive black hole was already located. Despite their relative proximity, the two holes do not yet form a single system, but they may merge in the future.

Black Hole

28,483 просмотров • 1 год назад

Hubble Records Wandering Black Hole That Swallowed a Star NASA astronomers have recorded a rare event using the Hubble Space Telescope and other observatories — a tidal disruption event (TDE) involving a wandering black hole. It occurred 600 million light years from Earth and provided new insights into the behavior of black holes. The object was spotted due to gravitational lensing — the distortion of light from distant bodies under the influence of gravity. As it approached the star, the black hole tore it apart, creating a bright accretion disk that radiated in ultraviolet and visible light. Unlike typical black holes in the centers of galaxies, this one was located 2,600 light years from the core, where a supermassive black hole was already located. Despite their relative proximity, the two holes do not yet form a single system, but they may merge in the future.

Hubble Records Wandering Black Hole That Swallowed a Star NASA astronomers have recorded a rare event using the Hubble Space Telescope and other observatories — a tidal disruption event (TDE) involving a wandering black hole. It occurred 600 million light years from Earth and provided new insights into the behavior of black holes. The object was spotted due to gravitational lensing — the distortion of light from distant bodies under the influence of gravity. As it approached the star, the black hole tore it apart, creating a bright accretion disk that radiated in ultraviolet and visible light. Unlike typical black holes in the centers of galaxies, this one was located 2,600 light years from the core, where a supermassive black hole was already located. Despite their relative proximity, the two holes do not yet form a single system, but they may merge in the future.

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72,929 просмотров • 1 год назад

Gravity makes things orbit...but what happens when the mass distribution itself is rotating and dragging phase space into resonances and chaos? In this scene we follow tens of thousands of stars in a toy barred galaxy: a flat disc with a central mass and a rotating bar of extra density that is not rigid, but wobbling, swaying, and breathing in strength over time. The stars start on almost circular orbits in a calm ring, but as the bar turns and its pattern speed and strength modulate, they feel a time-dependent gravitational shove that nudges some onto resonant tracks. 🤩😍 #Mathelirium #Astrophysics #GalacticDynamics #BarredGalaxy #PhaseSpace #HamiltonianChaos #OrbitalResonance

Gravity makes things orbit...but what happens when the mass distribution itself is rotating and dragging phase space into resonances and chaos? In this scene we follow tens of thousands of stars in a toy barred galaxy: a flat disc with a central mass and a rotating bar of extra density that is not rigid, but wobbling, swaying, and breathing in strength over time. The stars start on almost circular orbits in a calm ring, but as the bar turns and its pattern speed and strength modulate, they feel a time-dependent gravitational shove that nudges some onto resonant tracks. 🤩😍 #Mathelirium #Astrophysics #GalacticDynamics #BarredGalaxy #PhaseSpace #HamiltonianChaos #OrbitalResonance

Mathelirium

152,143 просмотров • 8 месяцев назад