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2022-10-12: The REAL Possibility of Mapping Alien Planets!

  • 04:12: ... general theory of relativity   tells us that gravity is due to curvature in the fabric of spacetime due to massive objects. But   ...

2022-03-30: Could The Universe Be Inside A Black Hole?

  • 07:34: The curvature changes dramatically as you approach the singularity.
  • 07:48: And the space-time curvature is nearly flat, so no crazy tidal forces like in a white or black hole.

2022-03-23: Where Is The Center of The Universe?

  • 03:04: General relativity can be used to calculate the spacetime curvature produced by the Earth or the Sun to determine their gravitational effects.
  • 04:03: The FLRW metric also predicts that there are only three possible global shapes to 4D spacetime, determined entirely by one number- the curvature.
  • 04:14: ... on whether the average curvature is positive, negative, or zero, we get one of three shapes- which we ...
  • 04:30: The presence of matter increases the curvature and the presence of dark energy decreases the curvature.
  • 05:52: Space can have curvature without there being anything for it to curve into.

2022-03-08: Is the Proxima System Our Best Hope For Another Earth?

  • 17:27: ... by the non-linearities across the wavefunction introduce by spacetime curvature. ...
  • 17:38: And on the subject of gravity, Jan Wester asks why the curvature of spacetime can’t be in a superposition.
  • 17:45: ... for sure that it can’t - just that if you try to have a superposition of curvature you get unresolvable infinities at large curvatures that produce ...

2022-02-10: The Nature of Space and Time AMA

  • 00:03: ... in the sense of the x-z axes um it is the degree of freedom is the curvature of the space itself um the density of the lines in the grid so maybe ...

2022-01-27: How Does Gravity Escape A Black Hole?

  • 00:35: ... describe gravity not as a traditional force, but rather in terms of the curvature of the fabric of space and ...
  • 03:34: In GR, the gravitational field - the curvature of spacetime - has an independent existence to the mass that causes it.
  • 05:34: Depending on how you think about it, the curvature or the motion of each patch influences the next.
  • 10:06: ... gravity is communicated by the curvature of spacetime or by virtual gravitons, we maintain a causal connection to ...
  • 11:18: You interact with the local curvature of spacetime, which is produced by the past mass, which from your point of view is on the event horizon.

2021-11-10: What If Our Understanding of Gravity Is Wrong?

  • 02:52: ... his general theory  of relativity, which explains gravity as the curvature in the fabric of space and time  rather than just as a classical ...
  • 08:35: ... call a tensor  field - a multi-component object that describes the curvature of ...

2021-06-16: Can Space Be Infinitely Divided?

  • 09:58: ... that scale,   Heisenberg’s principle tells us that the  curvature of space is fundamentally uncertain.   In the same way that ...

2021-05-11: How To Know If It's Aliens

  • 14:48: ... motion must allow time travel. A simple example is that the extreme curvature in the warp bubble walls should produce something like Hawking ...

2021-04-21: The NEW Warp Drive Possibilities

  • 03:37: It includes a comfortable, flat region of space surrounded by a region of extreme spatial curvature.

2021-02-17: Gravitational Wave Background Discovered?

  • 00:00: ... electromagnetic and gravity but if gravity is really due to space-time curvature surely it's fundamentally different to the other three which appear to ...

2021-02-10: How Does Gravity Warp the Flow of Time?

  • 01:30: General relativity, or “GR” explains the force of gravity as being due to curvature in space and time.
  • 02:12: ... one thing, it implies that curvature in the fabric of space is the cause of gravitation - but that’s only ...
  • 02:22: Matter tells space AND time how to curve, and it’s the curvature of time that’s mostly responsible for telling matter how to move.
  • 02:43: ... ultimately, we’ll use what we learn to understand how curvature in time - this gradient of time dilation - can be thought of as the true ...
  • 11:51: The curvature of space by matter isn’t nearly enough to give gravity at the strength we feel it.
  • 11:56: You’re held in your chair right now by the curvature in time.

2020-11-04: Electroweak Theory and the Origin of the Fundamental Forces

  • 13:57: ... when some property blows up to infinite values, like the density or curvature at the center of a black ...

2020-10-27: How The Penrose Singularity Theorem Predicts The End of Space Time

  • 08:49: ... These holes tend to be associated with infinite spacetime curvature - infinite gravity. In other   words, singularities. Penrose ...

2020-07-28: What is a Theory of Everything: Livestream

  • 00:00: ... that many of us including you brian have worked on measuring like the curvature space that's supposed to be omega's total is supposed to be one and ...

2020-06-30: Dissolving an Event Horizon

  • 12:00: Then the third dimension is just a way to represent the strength of the spatial curvature and the connections between different regions.

2020-05-04: How We Know The Universe is Ancient

  • 15:09: ... is the sheet depressing into? None - it's a representation for the curvature of ...

2020-02-03: Are there Infinite Versions of You?

  • 12:56: That's because objects in orbit are all moving, so the curvature of the background spacetime is constantly changing.

2019-12-09: The Doomsday Argument

  • 13:39: ... the discord: Habunelahack asks if it's ever be possible to measure the curvature of space to get an estimate on the size of the entire ...
  • 13:51: ... the answer is maybe: if the universe is closed and has positive curvature then measuring that curvature absolutely will give us the total volume ...
  • 14:06: ... or infinite because it may be that there's a slight positive or negative curvature just beyond the sensitivity of our ...
  • 14:29: ... where matter and energy is evenly distributed on the largest scales the curvature does changes but the global geometry does ...
  • 14:50: That said, patchs of the universe CAN change in curvature depending on the behavior of matter in those patches.
  • 16:21: ... signatures seen in galaxy clusters are an independent measure of curvature, and these point to a much flatter universe than implied by this new ...
  • 16:49: In short, there's still significantly more evidence in favour of flatness than positive curvature.

2019-12-02: Is The Universe Finite?

  • 03:04: We have 1) a universe with positive curvature.
  • 03:50: And finally 3) the universe with zero curvature - a geometrically flat universe.
  • 04:10: ... gravity, which tends to pull a universe in on itself - it gives positive curvature and closes the universe - making it ...
  • 04:26: Rapid expansion tends to give negative curvature and open the universe - make it infinite.
  • 04:46: ... curvature measured was consistent with being zero - flat - but there’s always a ...
  • 04:56: ... curvature COULD have been very slightly positive or very slightly negative - just ...
  • 05:04: It’s only when you get some elevation that you see the curvature.
  • 05:07: But it turns out that evidence of very slight curvature may have been hiding in the Planck data all along.
  • 06:51: Remember that more energy density tends to introduce positive curvature.
  • 07:25: They found the range of models that fit the shape of the power spectrum, and for the most part those pointed to positive curvature.
  • 07:33: That curvature was slight - meaning the universe is still unthinkably vast, but if this is right then it’s not infinitely large.
  • 07:42: The researchers claim a greater than 99% statistical confidence for positive curvature in this analysis.
  • 10:18: ... redid part of the Planck analysis to claim this evidence of positive curvature - which the Planck team had themselves decided wasn’t ...
  • 10:38: If this lensing signal is real then maybe there’s curvature, or maybe its an indication of some unknown physics.

2019-10-21: Is Time Travel Impossible?

  • 03:16: ... relativity, but also explains the force of gravity as a result of curvature in the fabric of spacetime due to the presence of mass and ...

2019-04-10: The Holographic Universe Explained

  • 11:15: While the original space was flat, the new space had negative curvature – it was a hyperbolic, anti-de Sitter or AdS space.
  • 16:40: KI9 asks whether the things we learn from AdS/CFT are applicable to the universe we live in given that our universe doesn't have negative curvature.
  • 16:50: ... we don't know for sure that it doesn't have negative curvature - just that any curvature - negative or positive - is very weak compared ...

2019-04-03: The Edge of an Infinite Universe

  • 02:46: We call that positive curvature.
  • 03:25: Finally there’s the universe with negative curvature, and the 2-D analog of that is the hyperbolic surface, like an infinite saddle or pringle.
  • 03:40: In GR this is anti-de Sitter space because it’s the “opposite” of the positive curvature de Sitter space.
  • 07:44: ... a universe that is “asymptotically flat” – it may have some local curvature due to gravity of massive objects inside, but at its boundaries the ...

2019-02-20: Secrets of the Cosmic Microwave Background

  • 07:42: ... us the total amount of energy in the Universe Energy results in positive curvature due to its positive gravitational effect On the other hand an expanding ...

2019-01-30: Perpetual Motion From Negative Mass?

  • 07:26: Positive mass causes spacetime to curve inwards – what we call positive curvature.
  • 08:01: Negative mass causes negative curvature, which in our sheet analogy looks like pulling the sheet up.

2018-09-20: Quantum Gravity and the Hardest Problem in Physics

  • 08:59: Any energy must cause space-time curvature.
  • 09:14: The energy of those excitations should themselves precipitate more space-time curvature, represented as further excitations.

2018-06-13: What Survives Inside A Black Hole?

  • 03:24: In Einstein's general theory of relativity, we think of the gravitational field as curvature in the fabric of spacetime.
  • 04:20: ... black hole, but that mass is remembered in the gravitational field, the curvature of spacetime above the event ...

2018-04-04: The Unruh Effect

  • 01:19: To understand this, we don't need general relativity with its space-time curvature and conflicts with quantum mechanics.

2018-03-15: Hawking Radiation

  • 04:11: But spatial curvature can mess with the balance of the underlying quantum field modes by introducing horizons.
  • 04:25: Stephen Hawking knew that black holes with their insane spacetime curvature would wreak havoc on quantum fields in their vicinity.

2017-11-08: Zero-Point Energy Demystified

  • 05:36: That means the vacuum energy between Casimir plates still produces positive spatial curvature, not the negative curvature required for warp drives.

2017-11-02: The Vacuum Catastrophe

  • 05:26: It should also massively increase the spatial curvature of the universe.

2017-10-25: The Missing Mass Mystery

  • 11:29: Yet, it would still push the universe towards positive spatial curvature.

2017-03-29: How Time Becomes Space Inside a Black Hole

  • 00:49: First we'll think about what the flow of time looks like without black holes or even spacetime curvature.

2017-01-19: The Phantom Singularity

  • 03:09: I mean, the curvature and the density are infinite from any frame of reference.
  • 06:53: When you use the Schwarzschild metric to calculate the curvature at r equals 0, that curvature is infinite.

2017-01-04: How to See Black Holes + Kugelblitz Challenge Answer

  • 09:39: Just above the sphere, which is only a bit larger than that event horizon that was going to form, the spacetime curvature is pretty insane.

2016-11-09: Did Dark Energy Just Disappear?

  • 09:36: It would have a weird, hyperbolic curvature.

2016-06-15: The Strange Universe of Gravitational Lensing

  • 00:00: [MUSIC PLAYING] The curvature of spacetime plays tricks on our eyes.
  • 01:41: The curvature produced by mass gives gravity.
  • 01:45: Light follows this curvature, and so gravity bends the path of light.

2016-05-18: Anti-gravity and the True Nature of Dark Energy

  • 05:17: Instead, the overall effect of pressure on the curvature of space time is a purely relativistic effect.

2016-04-27: What Does Dark Energy Really Do?

  • 08:03: We know that the universe is flat, so the curvature is also zero.
  • 10:02: We can't rule out curvature below our current best sensitivity, which at the moment is 0.4% of perfect flatness.
  • 10:32: ... the degree of curvature required by the first Friedmann equation to agree with the balance ...

2016-04-20: Why the Universe Needs Dark Energy

  • 02:30: It describes the curvature of space.
  • 02:35: k is, in a sense, the shape of the universe-- its spatial curvature, as well as its spatial extent, finite or infinite.
  • 02:44: Notice I said "spatial" curvature.
  • 04:13: Zero spatial curvature, at any given time.
  • 06:13: This is totally inconsistent with the level of positive curvature we'd expect from an infinitely expanding universe.

2016-04-13: Will the Universe Expand Forever?

  • 01:50: And it defines the shape, the curvature, of spacetime.
  • 02:16: ... perspective-- as a force, rather than as an Einsteinian spacetime curvature. ...
  • 08:35: It describes the shape of the universe-- its spatial curvature.

2016-04-06: We Are Star Stuff

  • 10:58: ... describe it as flat positive or negatively curved, I should say that the curvature of space at a single, constant moment in time has to be one of these ...
  • 11:10: So constant time spatial curvature, which is different to the curvature of spacetime.
  • 11:39: ... spatial curvature refers to the fact of the geometry of space on the largest scales in the ...

2016-03-23: How Cosmic Inflation Flattened the Universe

  • 01:51: Draw the same triangle on the surface of a sphere, which has what we call positive curvature, and the angles add up to more than 180.
  • 02:00: On a negative curvature hyperbolic plane-- a saddle-like structure-- they add up to less.
  • 02:07: Triangles in 3D space obey exactly the same rules as on 2D surfaces, and their geometry measures the curvature of space.
  • 02:57: Based on the precision of our measurements so far, we know that the curvature is within 0.4 of 1% of perfect flatness.
  • 03:35: If the center of the alley represents a flat universe, then the gutters represent extreme curvature in the positive or negative directions.

2016-03-16: Why is the Earth Round and the Milky Way Flat?

  • 01:07: ... in New York, has to factor in the changing direction of down due to the curvature of Earth's surface over its four mile ...

2016-01-06: The True Nature of Matter and Mass

  • 07:23: The presence in the flow of energy and momentum as well as pressure all have their quite different effects on the curvature of space-time.
  • 07:33: And when you trap them in a box, the curvature that they produce looks just like gravity.

2015-12-09: How to Build a Black Hole

  • 00:21: ... as general relativistic entities, as space time regions whose boundary curvature effectively removes the interior from our observable ...
  • 07:41: The space time curvature at the neutron star's surface is pretty extreme.
  • 09:03: All paths lead to the central point of infinite curvature, the singularity.

2015-10-28: Is The Alcubierre Warp Drive Possible?

  • 02:24: ... a volume of nice, flat spacetime enclosed in a bubble of extreme curvature, a pinching or warping of spacetime in the surrounding shell that causes ...
  • 03:34: That means our ship looks something like this in order to produce a spacetime curvature like this.
  • 04:21: One possible quantum disaster is that the extreme spacetime curvature of the warp bubble walls would roast the interior with crazy Hawking radiation.

2015-10-07: The Speed of Light is NOT About Light

  • 11:26: ... 18 times the particle horizon, only applies if the universe has positive curvature, making it a hyposphere and the curvature is the maximum that it could ...

2015-09-30: What Happens At The Edge Of The Universe?

  • 00:41: Are you sure you measured the universe's curvature with infinite precision?
  • 06:01: The surface of the Earth looks pretty flat to us because we really can't see the curvature locally.
  • 06:12: What if the curvature of the universe is so small that we're just not seeing far enough or measuring precisely enough to detect it?
  • 06:21: It's very possible that the universe has curvature just inside the uncertainty range of the best measurements to date.
  • 06:28: If that curvature is positive, then it may be that the universe is really the surface of a hypersphere, the 3D surface of a 4D sphere.
  • 06:46: ... on a recent estimate of the minimum radius of the curvature of the universe, you'd need to travel an absolute minimum of 18 times ...

2015-08-19: Do Events Inside Black Holes Happen?

  • 07:28: ... move radially inward, it's not being "pulled." Instead, the insane curvature there has made geometry so weird that radially out is simply not an ...
  • 10:53: Is it associated with the curvature of spacetime, with all of spacetime?

2015-08-05: What Physics Teachers Get Wrong About Tides!

  • 10:18: So if gravity is not a force and it's considered spacetime curvature, then why do people talk about gravitons?
  • 10:28: Thinking about things in terms of gravitons and thinking about spacetime curvature are not necessarily mutually exclusive.
  • 12:04: A lot of you wanted clarification on how curvature of time is what's responsible for, say, circular orbits around the Earth being geodesics.
  • 12:13: There's really only spacetime curvature.
  • 12:14: You can't really break it up into separate space and time curvatures.

2015-07-29: General Relativity & Curved Spacetime Explained!

  • 06:36: ... effects on earth that Newton would attribute to gravity are due to curvature in ...
  • 06:48: ... the pictures we sometimes use on this show, they all suggests spatial curvature only, so they're somewhat ...
  • 07:02: And around Earth, spacetime curvature manifests itself in clocks much more than in rulers.
  • 07:32: Its curvature in geodesics are determined by how much energy is present at those events via set of rules called, no surprise, the Einstein equations.
  • 08:32: ... or whatever, it's just a lot easier to say the word gravity than say curvature of four dimensional ...

2015-07-15: Can You Trust Your Eyes in Spacetime?

  • 00:28: In the episode on curvature, we saw that tiny patches on the surface of a sphere look like the Euclidean plane.

2015-07-08: Curvature Demonstrated + Comments

  • 04:19: ... is embedded-- namely, the 3D ambient space-- affects the discussion of curvature on the ...
  • 06:34: ... after that, we'll be putting the notions of curvature and flat space time together to discuss what curved space time is, what ...

2015-07-02: Can a Circle Be a Straight Line?

  • 00:05: Instead, he said, it's a manifestation of spacetime curvature.
  • 00:09: Now what's curvature?
  • 01:42: In part two we'll acquaint ourselves with the specific geometry of 4D flat spacetime, which is already weird, even without curvature present.
  • 01:50: ... finally, in part three we'll put curvature and spacetime together to tie up all the loose ends that we raised at ...
  • 05:41: Again, we can end up defining curvature using parallel transport.
  • 06:04: Now you may have heard an alternate definition of curvature that involves parallelism.
  • 06:24: Note that this notion of curvature does not always agree with your 3D visual intuitions.
  • 06:53: Topology is global, but geometry and curvature are local.
  • 06:57: Now in a three dimensional space you can test curvature the same way we've been describing.
  • 07:36: And remember, even without curvature, that geometry is super weird.
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