
20221012: 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 ...


20220330: Could The Universe Be Inside A Black Hole?
 07:34: The curvature changes dramatically as you approach the singularity.
 07:48: And the spacetime curvature is nearly flat, so no crazy tidal forces like in a white or black hole.


20220323: 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.


20220308: Is the Proxima System Our Best Hope For Another Earth?
 17:27: ... by the nonlinearities 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 ...


20220210: The Nature of Space and Time AMA
 00:03: ... in the sense of the xz 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 ...


20220127: 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.


20211110: 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 multicomponent object that describes the curvature of ...


20210616: 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 ...


20210511: 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 ...


20210421: The NEW Warp Drive Possibilities
 03:37: It includes a comfortable, flat region of space surrounded by a region of extreme spatial curvature.


20210217: Gravitational Wave Background Discovered?
 00:00: ... electromagnetic and gravity but if gravity is really due to spacetime curvature surely it's fundamentally different to the other three which appear to ...


20210210: 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.


20201104: 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 ...


20201027: 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 ...


20200728: 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 ...


20200630: 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.


20200504: How We Know The Universe is Ancient
 15:09: ... is the sheet depressing into? None  it's a representation for the curvature of ...


20200203: 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.


20191209: 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.


20191202: 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.


20191021: 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 ...


20190410: The Holographic Universe Explained
 11:15: While the original space was flat, the new space had negative curvature – it was a hyperbolic, antide 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 ...


20190403: 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 2D analog of that is the hyperbolic surface, like an infinite saddle or pringle.
 03:40: In GR this is antide 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 ...


20190220: 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 ...


20190130: 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.


20180920: Quantum Gravity and the Hardest Problem in Physics
 08:59: Any energy must cause spacetime curvature.
 09:14: The energy of those excitations should themselves precipitate more spacetime curvature, represented as further excitations.


20180613: 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 ...


20180404: The Unruh Effect
 01:19: To understand this, we don't need general relativity with its spacetime curvature and conflicts with quantum mechanics.


20180315: 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.


20171108: ZeroPoint 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.


20171102: The Vacuum Catastrophe
 05:26: It should also massively increase the spatial curvature of the universe.


20171025: The Missing Mass Mystery
 11:29: Yet, it would still push the universe towards positive spatial curvature.


20170329: 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.


20170119: 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.


20170104: 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.


20161109: Did Dark Energy Just Disappear?
 09:36: It would have a weird, hyperbolic curvature.


20160615: 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.


20160518: Antigravity 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.


20160427: 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 ...


20160420: 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.


20160413: 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.


20160406: 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 ...


20160323: 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 saddlelike 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.


20160316: 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 ...


20160106: 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 spacetime.
 07:33: And when you trap them in a box, the curvature that they produce looks just like gravity.


20151209: 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.


20151028: 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.


20151007: 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 ...


20150930: 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 ...


20150819: 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?


20150805: 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.


20150729: 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 ...


20150715: 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.


20150708: 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 ...


20150702: 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.
