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	2022-06-15: Can Wormholes Solve The Black Hole Information Paradox? 08:14: ... path integral you analyze some patch of spacetime changing from one geometry to   another. And you do this by adding up all ... 08:36: ... didn’t think it was necessary to consider   a lot of different geometries - after all,  black holes are pretty simple objects - ... 09:17: ... geometries should be included which include spacetime folding into itself in a ... 09:36: ... like?   It’s very difficult to properly picture  these geometries since they’re so weird,   the image wouldn’t fit in our ... 10:42: ... is found using the gravitational path integral. For a spacetime geometry where none   of the black holes interact with each other, ... 08:14: ... path integral you analyze some patch of spacetime changing from one geometry to   another. And you do this by adding up all possible geometries that ...
	2022-05-25: The Evolution of the Modern Milky Way Galaxy 07:58: ... into thin gas disks, and then produce stars that share that geometry. ...
	2022-05-04: Space DOES NOT Expand Everywhere 02:38: ... just as latitude and longitude describe the spherical geometry of the surface of the Earth, the FLRW metric gives the geometry or shape ...
	2022-04-20: Does the Universe Create Itself? 15:24: ... of Perístanom asks if the geometry of the universe - close, open, flat - dictates the “temporal shape”. As ...
	2022-03-23: Where Is The Center of The Universe? 04:37: We can’t visualize the center of a geometry if we can’t fit it in our heads. 08:48: No matter the geometry of our FLRW universe, all geodesics converge to a single point in the past, and end there.
	2022-02-16: Is The Wave Function The Building Block of Reality? 09:25: ... two facts together, and you will get a superposition of two different geometries of space-time. According to Penrose, this isn’t possible. The ...
	2022-02-10: The Nature of Space and Time AMA 00:03: ... frame the best place to explore that is the episode we did on the geometry of causality but i suppose still space and time remained a type of ...
	2022-01-27: How Does Gravity Escape A Black Hole? 06:08: Now in quantum mechanics - or more specifically quantum field theory - forces are mediated by particles, not by the geometry of spacetime.
	2021-12-20: What Happens If A Black Hole Hits Earth? 18:51: ... best math-inspired computer graphics, including various many-dimensional geometries, I recommend you check out their channel - link in the ...
	2021-06-16: Can Space Be Infinitely Divided? 07:48: ... measure a size smaller than the Planck length,   the warped geometry changes that size to give 100% uncertainty. This explains why the ...
	2021-04-21: The NEW Warp Drive Possibilities 03:29: It’s a sp acetime geometry that is a valid solution to the equations general theory of relativity. The Einstein Field Equation. 04:01: ... of mass, energy, on the right side and it spits out the spacetime geometry on the ... 04:11: ... instead solved the equations backwards - he figured out the geometry of a warp bubble, and then ran it backwards through the equations to see ... 04:23: You can do this with any geometry, but almost every geometry will produce an impossible mass-energy distribution. 08:20: The velocity of the bubble is baked into the equation for the field geometry, but it’s not clear how you change that velocity.
	2021-01-19: Can We Break the Universe? 12:16: ... asked the very similar questions regarding length-contracting closed geometries that inspired this episode - guys, i hope this helped clarify matters a ...
	2020-08-10: Theory of Everything Controversies: Livestream 00:00: ... so his claim is i it looks like these could generate differential geometry and therefore the underpinnings of the standard model in gr in ...
	2020-06-15: What Happens After the Universe Ends? 05:17: By the way, our episode on the geometry of causality goes into all of this in more detail.
	2020-06-08: Can Viruses Travel Between Planets? 15:49: ... those plates - its conductive and dialectric properties, as well as the geometry of the plates, and for the most part that dependency agrees with ...
	2020-05-27: Does Gravity Require Extra Dimensions? 10:15: ... geometry of modern devices allow more precise positioning between the test ...
	2020-04-28: Space Time Livestream: Ask Matt Anything 00:00: ... rules by which they can evolve and then you can produce all sorts of geometries and according to Stephen Wolfram you can basically recover the laws of ...
	2020-04-22: Will Wormholes Allow Fast Interstellar Travel? 07:52: ... the matter and energy that spacetime contains. In fact by defining the geometry you want - eg a wormhole - the required matter distribution is ... 10:15: ... wormholes, fixed this last problem by constructing a number of wormhole geometries that kept the exotic matter out of the way of travelers. For example, he ... 12:51: ... suggested that on the smallest possible scales, the geometry and even the topology of the fabric of spacetime may fluctuate wildly, ...
	2020-02-03: Are there Infinite Versions of You? 10:31: ... to greater and greater precision and see if it has an open or closed geometry... but even then we still have to hope that it’s reasonable to extrapolate ...
	2019-12-17: Do Black Holes Create New Universes? 04:27: Perhaps the configuration of the geometry string theory’s extra dimensions gets shifted - this would do the job.
	2019-12-09: The Doomsday Argument 14:22: Daniel M. and Sam Harper ask whether a universe can transition between different geometries. 14:29: ... on the largest scales the curvature does changes but the global geometry does ... 15:37: ... Spring points out that there are flat geometries that are not infinite, but rather closed - for example the 3-torus ... 16:05: ... while these are valid geometries for spacetimes that can be constructed within Einstein's general ...
	2019-12-02: Is The Universe Finite? 02:54: Before we get to the new study, let’s do a super-quick review of geometry. 02:59: Albert Einstein’s general theory of relativity allows for three simple geometries for our universe. 03:56: Parallel lines stay parallel, your high school geometry still works, and again, space in such a universe goes on forever. 04:04: The geometry of the universe is determined by two things: 1) the mass and energy it contains. 04:31: The combination of these factors determine the geometry. 04:38: For example, by looking at the geometry of gigantic triangles defined by the largest of the speckles in the CMB. 08:15: Also, beyond a certain distance from us that expansion exceeds the speed of light, so there’s no lapping the universe regardless of its geometry. 09:48: ... of the Planck data may have led to the unexpected results for both the geometry and the expansion history of the ... 12:01: ... of dark energy, and perhaps verifying the positively curved, finite geometry of space ...
	2019-11-04: Why We Might Be Alone in the Universe 12:59: Well, crudely, they're a mathematical way to describe the geometry of space - which means they aren't in space, they sort of ARE space. 13:17: But that doesn't mean the loops are physical, they're just a way to parameterize the quantum-scale geometry of space.
	2019-10-15: Loop Quantum Gravity Explained 02:11: It requires some giant hacks to even attempt regular quantum calculations in a non-flat geometry. 02:41: ... precisely, the metric - the object encapsulating the geometry and causal structure of spacetime - evolves in the equations of GR. So ... 05:45: ... maybe there’s an equation that describes the quantum evolution of the geometry of ... 06:32: As you move through this coordinate system, the geometry of space changes. 07:52: And the amount of rotation encodes information about the changes in geometry along the path. 09:29: ... realized it was possible to define any geometry of 3-D space out of a sort of weave of these closed loops, with each ... 11:37: ... LQG has background independence in terms of different 3-D spatial geometries, it’s not actually clear that this independence extends to 4-D ...
	2019-08-06: What Caused the Big Bang? 00:55: - and why is the geometry of the universe so flat?
	2019-04-10: The Holographic Universe Explained 17:02: Measurements of the geometry of the universe indicate flatness, but we may never know whether it's truly flat, or just flat as far as we can see.
	2019-04-03: The Edge of an Infinite Universe 02:52: Geometry is a bit broken in such a universe – for example, two parallel lines will eventually converge and cross each other. 03:00: In general relativity we call a universe with this geometry de Sitter space, after Dutch astronomer Willem de Sitter. 03:08: Then there’s the flat universe – classic, straightforward geometry – parallel lines stay parallel – and it goes on forever. 03:36: In this geometry parallel lines actually diverge from each other. 10:22: Those circle segments represent the straight lines of a hyperbolic geometry projected onto the disk. 10:30: We can see the hyperbolic behavior these arcs – they are geodesics – the straightest-possible paths in the geometry. 03:00: In general relativity we call a universe with this geometry de Sitter space, after Dutch astronomer Willem de Sitter. 03:36: In this geometry parallel lines actually diverge from each other. 10:22: Those circle segments represent the straight lines of a hyperbolic geometry projected onto the disk.
	2019-02-20: Secrets of the Cosmic Microwave Background 07:42: ... the presence of matter and energy as well as cosmic expansion cause geometry to be curved which would mess up our basic trig So here we have a test ...
	2019-01-30: Perpetual Motion From Negative Mass? 06:36: ... mass, and of energy, momentum, pressure, and more, change the geometry of spacetime and that new geometry defines the paths objects can ... 10:58: ... geodesics of general relativity – the paths carved into the geometry of Einstein’s spacetime – are the GR analogs of Newton’s second law and ... 06:36: ... pressure, and more, change the geometry of spacetime and that new geometry defines the paths objects can ...
	2018-12-20: Why String Theory is Wrong 06:32: What differs is the detailed geometries and symmetries of those spaces, and the way strings vibrate within them. 12:43: In all superstring theories the extra spatial dimensions are wrapped, not in simple loops, but in complicated geometries called Calabi-Yau manifolds. 13:08: ... more worrying, there are countless possible geometries, countless Calabi-Yau manifolds, to choose from. The standard number ... 13:44: ... model lives somewhere in the string landscape, but without knowing the geometry of the extra dimensions, this can't be verified nor can we make testable ...
	2018-11-21: 'Oumuamua Is Not Aliens 02:17: The geometry is very unusual for an asteroid or comet.
	2018-10-25: Will We Ever Find Alien Life? 14:04: ... manifolds that string theorists need to search through to find the geometry of our universe's extra ...
	2018-09-20: Quantum Gravity and the Hardest Problem in Physics 04:30: In fact, it's very possible to shoehorn the curved geometry of general relativity into the way quantum field theory deals with space and time.
	2018-02-28: The Trebuchet Challenge 04:46: ... Newton's laws, with a complicated series of force vectors, some gnarly geometry, and of course, some ...
	2017-09-20: The Future of Space Telescopes 03:16: ... you'll have a flower-like shape, whose cleverly calculated petal geometry is designed to diffract light away from the central axis, not towards ...
	2017-03-29: How Time Becomes Space Inside a Black Hole 00:55: ... we talked about the geometry of causality, we saw that this quantity that we call the spacetime ...
	2017-03-15: Time Crystals! 01:44: That may have been Arthur Winfree in his "The Geometry of Biological Time," where it's used to describe periodic biological systems.
	2017-03-08: The Race to a Habitable Exoplanet - Time Warp Challenge 00:42: This question will draw a lot on our recent episode on the geometry of causality.
	2017-02-15: Telescopes of Tomorrow 11:10: So last time, I showed you how you can visualize the effects of special relativity on spacetime using geometry. 11:39: ... few of you wondered about the relationship between the geometry I depicted on the space-time diagram and the geometry that comes from ... 11:57: The hyperbolic geometry is just what you did when you map the space-time interval to a third dimension.
	2017-02-02: The Geometry of Causality 02:57: We'll see our causal geometry emerge plain as day, even in this simplified picture. 04:47: Instead of doing that with equations, we can see it with geometry. 06:56: We just performed a Lorentz transformation, but using geometry rather than math. 02:57: We'll see our causal geometry emerge plain as day, even in this simplified picture.
	2016-11-16: Strange Stars 11:10: A flat 3D space means that the rules of geometry in that space work just like on an actually flat 2D surface. 11:45: ... definitely have weird angles, less than 180 degrees for a hyperbolic geometry, more than 180 for a spherical ... 12:04: Your comparison was for people living in a 2D flatland universe that has the geometry of the surface of a 3D sphere.
	2016-11-09: Did Dark Energy Just Disappear? 09:04: Another really powerful piece of evidence is that the balance of Omega-Lambda and Omega-m define the geometry of the universe. 09:12: ... angles of triangles add up to 180 degrees, and all the regular rules of geometry ... 09:38: ... going to have to refer you to another vid for details on universe geometries, but the main point is that we can also figure out where we should be on ... 10:03: Their geometry appears to be very flat, so our universe should lie on this line here. 11:03: ... there countering the gravitational effect of matter and flattening the geometry of ... 10:03: Their geometry appears to be very flat, so our universe should lie on this line here. 09:12: ... angles of triangles add up to 180 degrees, and all the regular rules of geometry work. ...
	2016-11-02: Quantum Vortices and Superconductivity + Drake Equation Challenge Answers 01:07: ... studies the geometry of shapes under what we call "continuous deformation." So, changes in ...
	2016-05-18: Anti-gravity and the True Nature of Dark Energy 07:33: It has to be, because dark energy helps regular matter flatten the geometry of the universe.
	2016-04-20: Why the Universe Needs Dark Energy 01:48: Today, let's look at one of these measurements-- the geometry of the universe, which points to a discrepancy in the first Friedmann equation. 02:53: But the spatial geometry of the universe at a fixed instant in time can be flat or curved. 03:05: "k equals plus 1" means the universe has a positive-curvature spatial geometry. 03:23: In a universe like that, geometry is weird. 03:43: And we call that a "closed geometry." If k is minus 1, the universe is the 3D version of a negatively curved hyperbolic plane. 04:16: Geometry works just as you learned in school, and a flat universe is still infinite-- open-- in all three spatial dimensions. 04:47: An overdense, recollapsing universe should have a spherical geometry. 05:17: See, we can measure the shape of the universe and, so, measure k, just by checking how geometry works on cosmic scales. 05:26: Now, if we got everything right so far, the geometry should turn out to be hyperbolic. 05:58: That's the straight-up geometry of a flat, Euclidean universe-- flat to within 0.4%. 06:40: ... can also fix this little problem with the first Friedmann equation and geometry. ... 07:13: ... too low to reverse the expansion, with this new player in the game, geometry is no longer tied to the fate of the ... 04:16: Geometry works just as you learned in school, and a flat universe is still infinite-- open-- in all three spatial dimensions. 05:17: See, we can measure the shape of the universe and, so, measure k, just by checking how geometry works on cosmic scales.
	2016-04-06: We Are Star Stuff 10:51: Let me clarify a few things about space geometry first, and I'll get to what flat means in a minute. 10:58: ... I talk about the geometry of the universe and describe it as flat positive or negatively curved, I ... 11:39: ... spatial curvature refers to the fact of the geometry of space on the largest scales in the universe works just like the ...
	2016-03-23: How Cosmic Inflation Flattened the Universe 02:07: Triangles in 3D space obey exactly the same rules as on 2D surfaces, and their geometry measures the curvature of space.
	2015-10-28: Is The Alcubierre Warp Drive Possible? 05:21: Happily, recent reworkings of the bubble geometry have cut this down further.
	2015-09-30: What Happens At The Edge Of The Universe? 05:04: Well, that all depends on the geometry of the universe. 05:07: On the largest scales, the geometry of spacetime is very flat. 06:59: We also have to keep in mind that these geometries assume that we can just extrapolate Einstein's equations in the most simplistic way. 07:22: Now, bubble universes may be finite in size regardless of internal geometry.
	2015-08-27: Watch THIS! (New Host + Challenge Winners) 02:43: Now explaining the answer to the Einsteinian challenge is a bit more involved because we don't know the geometry from the outset. 04:53: In every problem, the rules of geometry change.
	2015-08-19: Do Events Inside Black Holes Happen? 04:56: ... determines the spacetime geometry in its neighborhood, the resulting geodesics of which correspond to ... 05:19: So as far as Earth is concerned, that black hole generates the same spacetime geometry out here that the Sun does. 06:26: See, spacetime geometry in this region is very foreign. 07:28: ... it's not being "pulled." Instead, the insane curvature there has made geometry so weird that radially out is simply not an available ...
	2015-08-12: Challenge: Which Particle Wins This Race? 02:26: ... that fact, plus the fact that the density is uniform, plus some basic geometry about spheres, you should be able to get a formula for the gravitational ...
	2015-07-22: SPECIAL ANNOUNCEMENT + Flat Spacetime Geometry Comments 00:03: Last week, part 2 of our general relativity series went a little deeper into some aspects of flat space time geometry.
	2015-07-15: Can You Trust Your Eyes in Spacetime? 00:02: But before we can graduate to the curves version and general relativity, we need a stronger foundation in spacetime geometry. 00:51: They look like flat spacetime, which although not curved, still has a geometry that doesn't always agree with our visual intuitions. 01:07: Now, we're not going to do a complete treatment of special relativity or all aspects of flat spacetime geometry. 01:22: Our principle tool for exploring flat spacetime geometry will be something called a spacetime diagram for representing physical events. 06:57: ... space, we can discover facts about physics just by exploring geometry in that ...
	2015-07-08: Curvature Demonstrated + Comments 06:29: I wanted to make sure this was on better footing before we moved on to flat spacetime geometry in the next episode.
	2015-07-02: Can a Circle Be a Straight Line? 01:33: ... part one we're going to put physics aside and focus on geometry, specifically on what we really mean by straight line and by flat verses ... 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. 01:57: We'll end up seeing that all the supposedly gravitational effects on motion can be accounted for just by the geometry of spacetime. 02:17: Today is part one, that's straight lines and curved spaces with no physics, just geometry. 02:33: ... if we want to do geometry on arbitrary spaces like on the surface of a sphere or a saddle or on ... 06:38: ... those lines might close on themselves, but locally, snippet by snippet, geometry and straightness and tangency and parallelism all work just like they do ... 06:53: Topology is global, but geometry and curvature are local. 07:31: To understand that, we need to get a better grip on how geometry works in flat spacetime. 07:36: And remember, even without curvature, that geometry is super weird. 07:49: Flat spacetime geometry is part two, which is next week. 07:31: To understand that, we need to get a better grip on how geometry works in flat spacetime.
	2015-06-17: How to Signal Aliens 06:55: ... common sense that can only be resolved once we change our concept of the geometry of the world, including the fact that time has a geometric ...
	2015-06-03: Is Gravity An Illusion? 08:52: The rule that inertial frames can't accelerate relative to each other turns out only to be true if the world has what's called a flat geometry. 09:49: Wait a minute-- how can geometry and straight lines possibly work the way I just said?
	2015-04-22: Are Space and Time An Illusion? 06:47: ... mix, we'll find that there are many possible spacetimes with different geometries, making it hard to ascertain which one this ...

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