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	2022-10-26: Why Did Quantum Entanglement Win the Nobel Prize in Physics? 19:52: ... breaks off from the rest of reality, slipping backwards into this infinite regress of imaginary ...
	2022-10-19: The Equation That Explains (Nearly) Everything! 04:36: ... the behavior of particles in a certain volume, we have to add up infinitely many Lagrangian Densities over that volume. Although in practice ...
	2022-10-12: The REAL Possibility of Mapping Alien Planets! 20:21: ... then I realized that pi is an irrational number with   infinite digits, which means if you look far  enough it says “LOL noobs”. ...
	2022-08-17: What If Dark Energy is a New Quantum Field? 12:31: ... -1 - that’s the big rip, in which all points in space eventually become infinitely far apart. Fortunately, that seems ...
	2022-08-03: What Happens Inside a Proton? 08:58: ... for a single Feynman diagram   you’re actually adding infinite possible  trajectories using Feynman path ... 09:50: ... any patch of spacetime technically   contains an infinite number of points and  no computer can hold an infinite amount ...
	2022-07-27: How Many States Of Matter Are There? 04:16: ... example solids are rigid having effectively infinite viscosity; liquids are viscous and are incompressible; gasses are ...
	2022-06-15: Can Wormholes Solve The Black Hole Information Paradox? 07:24: ... the “classical” and sensible path that we observe is the sum of infinite paths, many ...
	2022-05-25: The Evolution of the Modern Milky Way Galaxy 18:41: ... light - that’s the velocity  of an inertial frame that falls from infinite   distance towards a black hole. In the same way, an  inertial frame ...
	2022-05-04: Space DOES NOT Expand Everywhere 02:38: ... a space that loops back on itself in all directions. Or it could be an infinite plane, either flat or hyperbolic. These shapes can be thought of as 2-D ... 09:16: ... general relativity, space can be infinitely divided. That means we can start with a universe that’s small and grid ... 10:06: ... we’ve talked about before. All spacetime paths can be traced to the infinite future or past until they hit a singula,rity - the big bang or a black ... 10:33: ... all works if space is infinitely divisible. But we know that at the smallest scales, general relativity ... 10:52: ... which must expand out of the old Planck lengths. That implies an infinitely divisible space emerging from within each Planck ... 11:22: ... fabric of space, it’s still possible to expand it or condense it infinitely without changing its fundamental nature. Empty space can be rescaled ... 12:56: ... there’s your answer. The infinite scalability of space means the universe can and probably will expand ... 13:16: ... horizon, in which case we never would have even known that we live in an infinitely expanding ... 16:05: ... the issue the Wheeler was trying find his way around - the issue of infinite regress. How to you identify a founding cause by tracing the causal ... 16:38: ... wavefunction is the just that wavefunction in the space of  infinite possible wavefunctions  that constructively interferes to reinforce ...
	2022-03-30: Could The Universe Be Inside A Black Hole? 00:28: Both of these involve matter being packed to infinite densities - they are singularities where the mathematics of GR breaks down. 01:01: In general relativity, that looks like a point of infinite density surrounded by an event horizon. 01:30: ... time at the beginning of the universe when all matter was compressed to infinite density and all points in space ... 02:46: ... is that the black hole singularity seems to us to be a point of infinite density in space, while the big bang singularity is a time of infinite ... 04:24: ... you can keep tracing the geodesic into the infinite future or all the way back to the Big Bang - it’s defined for all past ... 12:16: ... black hole and so on ad infinitum in a series of black holes, forming an infinitely nested space ...
	2022-03-23: Where Is The Center of The Universe? 08:09: ... 2-D analog of the flat universe is an infinite flat plane, while the open universe corresponds to a sort of saddle ... 10:01: But what about an infinite universe? 10:13: But at the same time there are infinite points. 10:16: So did the universe start out pointlike at t=0 and then suddenly become infinite in size? 11:35: ... of Hubble’s observation of the receding galaxies that doesn’t require an infinite universe, nor a hyperspherically looping ...
	2022-02-16: Is The Wave Function The Building Block of Reality? 16:48: ... the event horizon is defined from the perspective of an observer at “infinite distance” - aka very very far away, which is after all where you wanna ... 17:28: ... by escape I mean reach YOU at your “infinite distance”. And it’s the surface from which light is infinitely ... 17:42: ... emitted at the moment it crosses the horizon from its perspective takes infinite time to reach us. So to lose an object beneath a growing black hole ...
	2022-02-10: The Nature of Space and Time AMA 00:03: ... of these dimensions is continuous in that you can subdivide space uh infinitely uh you know to to uh arbitrarily small pieces and same with time you ...
	2022-01-27: How Does Gravity Escape A Black Hole? 01:01: ... reaches such a density has to collapse to a point-like singularity of infinite density surrounded by this boundary of no return - the event ... 09:46: ... collapsing star continue to make their way out into the universe over infinite ... 11:37: To get a consistent definition for mass you need to integrate - add up - the contributions to infinite distance from the black hole. 12:00: ... hole will eat you right up, and even as you’re getting crushed into an infinitesimal point, you can rest assured that your own mass will continue to exert ...
	2022-01-12: How To Simulate The Universe With DFT 14:25: Peter, the infinite dimensional universal wavefunction barely contains enough information to describe your generosity.
	2021-12-10: 2021 End of Year AMA! 00:02: ... that the electron could uh end up are realized okay so we have this infinite um or possibly infinite branching of the timeline and so to think of ...
	2021-11-17: Are Black Holes Actually Fuzzballs? 00:39: ... matter should contract to a single point of infinite density - the singularity - which is surrounded by a surface from which ... 06:12: Lose that pesky infinite density and we can start making sense of physics again. 07:04: The infinitesimal strings and branes of string theory might be the analog of the molecules that store the entropy of our room full of air. 12:04: One dimension means a line, so a 1-D black hole is just a segment of a line with a point of infinite density on it.
	2021-11-10: What If Our Understanding of Gravity Is Wrong? 16:52: Light does travel a straight line if you look at an infinitesimally small patch of space. 17:10: Well, in space the disco ball mirrors are infinitesimally small, but over those regions the path is straight.
	2021-11-02: Is ACTION The Most Fundamental Property in Physics? 17:24: ... function, which means physics is over. Or we might find there are still infinite functions that can perfectly describe the ... 17:54: ... it well: If we assume the universe operates under certain assumptions (infinite/finite, discrete/continuous spacetime, invariance, quantum etc.) then ...
	2021-10-20: Will Constructor Theory REWRITE Physics? 06:06: David Deustch gives the example of the perpetual motion machine of the first kind - a device from which infinite energy can be extracted.
	2021-08-18: How Vacuum Decay Would Destroy The Universe 11:34: ... species,  let alone your own lifetime. Of course, in an   infinitely or sufficiently large universe then vacuum decay has definitely ...
	2021-08-03: How An Extreme New Star Could Change All Cosmology 14:14: ... big bang level. Charlie, the fabric of space around us thrums with the infinitesimal vibrations of countless white dwarfs that have merged since the ...
	2021-07-21: How Magnetism Shapes The Universe 15:28: ... 2 worlds, but for every measurement of photon number we get countably infinite splits, and for particle position it’s uncountably infinite splits per ... 15:47: If you mean every possible configuration of particle properties in the universe - then the answer is there are infinite worlds. 15:54: A world for every infinitesimal difference in every particle property. 16:05: Each infinitesimal location can be thought of as a “world” and some worlds have more weight - more probability than others. 16:37: But possibly still infinite, though that’s still being debated.
	2021-06-16: Can Space Be Infinitely Divided? 01:16: ... the energy of light in this heat-glow was   not infinitely divisible. Rather came in quanta - chunks of energy that we now ... 05:08: ... space down to any conceivable precision,   perhaps even infinite precision - as long as  we’re happy to have infinite uncertainty ...
	2021-04-21: The NEW Warp Drive Possibilities 02:30: His special theory of relativity just says that it takes infinite energy to accelerate anything with positive mass all the way to light speed.
	2021-04-13: What If Dark Matter Is Just Black Holes? 11:16: ... black hole might leave behind a tiny naked singularity - a speck of infinite density weighing less than a grain of ...
	2021-03-23: Zeno's Paradox & The Quantum Zeno Effect 00:33: ... time is composed of an infinite number of these snapshots, and the arrow doesn’t move in any of them, ...
	2021-03-16: The NEW Crisis in Cosmology 15:19: ... similar to the double slit experiment if   there were an infinite number of slits. Well, John Smith, you're in good company. There's ...
	2021-03-09: How Does Gravity Affect Light? 04:27: ... be sapped of ALL energy - redshifted so the wavelength is effectively infinite. ... 04:47: ... the bizarre thing is that the density of mass required to produce this infinite redshift is exactly the same as is required to turn a light-speed ... 07:40: The idea is that any wave can be described as an infinite number of point-like oscillations, each of which produces new waves. 07:58: At any point in time, the expanding ripple can be thought of as an infinite number of sources of new circular ripples, or wavelets. 08:23: A plane wave of light is just an infinite number of new sources of light that generate the next step in the plane wave.
	2021-02-24: Does Time Cause Gravity? 07:29: It’s enough to imagine clocks that are infinitesimally separated and we still have our time gradient.
	2021-01-19: Can We Break the Universe? 08:02: Our own universe also has a special frame - whether it’s closed or infinite.
	2020-11-04: Electroweak Theory and the Origin of the Fundamental Forces 13:45: ... why are we then typically ok that the size of the universe is infinite? ... 13:57: ... type is considered a bad one - that’s when some property blows up to infinite values, like the density or curvature at the center of a black ... 14:19: ... infinite universe doesn’t have the same problem, and I guess it’s often accepted ...
	2020-10-27: How The Penrose Singularity Theorem Predicts The End of Space Time 00:00: ... every black hole contains a place of   infinite gravity - a singularity. But the true  impact of Penrose’s ... 01:17: ... At that so-called singularity, the  gravitational field becomes infinite. But   physicists tend to be dubious about infinities ... 03:18: ... hole in Einstein’s theory. In it, the central point of infinite gravity is spun out into a   ring - but it was a singularity ... 08:49: ... have holes in it.   These holes tend to be associated with infinite spacetime curvature - infinite gravity. In other   words, singularities. ... 10:15: ... and weave past each other in an insanely dense but not   infinitely dense knot. This might be the case if the universe underwent cyclic ... 12:51: ... by no means geodesically incomplete - rather it extends   infinitely into the future AND the past. With your help Space Time might do ...
	2020-09-28: Solving Quantum Cryptography 05:16: For the full explanation, I’m going to point you to the episodes made by Infinite Series a while back.
	2020-08-10: Theory of Everything Controversies: Livestream 00:00: ... objects that you were talking about before but you should form the infinite dimensional gauge group and just as you form the inhomogeneous ...
	2020-07-28: What is a Theory of Everything: Livestream 00:00: ... indicate that something has gone horribly wrong you know things like infinite energies or probabilities greater than one these kinds of things ...
	2020-07-20: The Boundary Between Black Holes & Neutron Stars 00:29: ... though it’s no big deal that we regularly read the infinitesimal ripples in the fabric of spacetime due to a cataclysmic collision of ...
	2020-06-30: Dissolving an Event Horizon 01:12: Without it, the infinitely dense singularity and its surrounding madness is exposed to the outside universe. 02:57: Inside, we found that the rapid rotation has spun the point-like singularity into a ring of infinite density. 12:54: ... cosmology, in which the big bang is hypothesized to be the rescaled infinite late-time forever of a previous universe, leading to a potentially ... 13:11: ... conformal cyclic cosmology: the space between atoms in one aeon would be infinite from the point of view of observers from the previous ... 13:27: ... yes - Each new infinitessimally small Big Bang corresponds not to just the very, very large late time of ...
	2020-06-15: What Happens After the Universe Ends? 00:45: ... goes like this: the infinitely far future, when the universe has expanded exponentially to to an ... 09:34: ... are ways of mathematically transforming our grid of spacetime to fit infinite distance and time into the one map, while at the same time preserving ... 09:48: The edges of this map represent “conformal infinity” - where infinite space and time are compressed onto an edge. 10:00: ... the full 4-D spacetime the edge becomes a 3-D “hypersurface” in which infinite distance and time are compressed or “conformally rescaled” into a finite ... 10:12: Similarly, the infinitesimal or “zero-sized” point of the Big Bang can be rescaled into a finite space. 12:20: In CCC, all of the energy - and, importantly, the gravitational field - is smoothed out over infinite time between aeons. 13:06: Wait infinite time and see if you find yourself in a big bang? 14:24: ... up your aeon, remember to eat your greens, and try to have fun in this infinite chain of conformally rescaled ...
	2020-05-27: Does Gravity Require Extra Dimensions? 13:29: ... of a rotating black hole - regions like the Carter time machine and the infinite string of parallel ... 15:44: ... right, Polygondwanaland: in reality, impossible-seeming things like an infinite string of universes or a time machine indicate that the math may have ...
	2020-05-18: Mapping the Multiverse 04:54: The singular, central point has been spun out into a ring of infinite density. 06:33: Only the ones exactly on the equator hit the ring and, those geodesics do end - same infinite squish as in a Schwarzschild black hole. 07:58: Surrounding the ring on this side is a toroidal region in which it’s possible to accelerate to infinite speed. 16:27: So in an infinite universe, every definable galaxy or definable location ends up right here on top of us at some point in the rewind. 16:36: The universe approaches infinite density in the limit as time approaches zero.
	2020-05-11: How Luminiferous Aether Led to Relativity 14:06: ... Lord asks how we reconcile the idea that "the universe is infinite in size" and "the universe has a finite age" if the universe started ... 14:23: ... let's pretend that the expansion rate is constant. And for an infinite universe the "size" is just the average distance between galaxies. Half ... 14:42: ... even when the universe was a tiny fraction of a second old, it was still infinite, even though ALL of the galaxies we can see were compacted into a tiny ... 15:13: ... all that aside - we don't actually know A) if the universe truly is infinite, or B) what happened before 10^-43 seconds - the so-called Planck time. ...
	2020-04-28: Space Time Livestream: Ask Matt Anything 00:00: ... now this doesn't sound very intuitive because you know you could just infinitely create an enormous amount of mass if you're allowed to continually ...
	2020-04-07: How We Know The Earth Is Ancient 03:43: ... Hutton didn’t propose a beginning for the Earth - instead he assumed an infinite series of cycles. This was also the notion of the great German ...
	2020-03-31: What’s On The Other Side Of A Black Hole? 00:37: ... singularities. A singularity is where a variable in the equation becomes infinite - and a single swivel at a pole carries you through the longitudes at an ... 03:14: ... that depends on their latitude - and that multiplication factor becomes infinite at the poles, to cancel out the converging lines of longitude. For black ... 04:31: ... travelers. On Penrose diagrams, space and time also bunch up at infinite distance so tha t the entire universe fits on the one diagram. Well, the ... 05:00: ... we see that light rays can either travel away from the black hole to infinite distance, or they can travel towards the center of the black hole and be ... 07:32: ... imagine you could travel at infinite speed - then you could take these horizontal which would dip beneath the ... 08:44: ... as an inevitable crushing future, in which the space around you becomes infinitely ...
	2020-03-03: Does Quantum Immortality Save Schrödinger's Cat? 11:06: So let’s stick it to all those alternate realities, and make this the best of infinitely many diverging histories of space time.
	2020-02-18: Does Consciousness Influence Quantum Mechanics? 16:39: ... then we had various defenses of my using chimps to represent infinite typing monkeys - from the status of "monkey" in common vernacular to ...
	2020-02-11: Are Axions Dark Matter? 03:59: ... in QCD, where there isn’t just one lowest energy state - there are infinite lowest energy ... 12:33: ... week we tried to figure out whether a universe that is infinite in size should contain infinite repetitions of everything it contains, ... 14:39: ... eternal inflation must have had a beginning, so it hasn't yet lasted for infinite time - well also true, but there's no reason to imagine we are near that ... 16:00: ... quite detail-oriented. And so I was terrified you'd be mad that the infinite typewriter monkey we showed was actually a chimpanzee - so, a great ape ...
	2020-02-03: Are there Infinite Versions of You? 00:00: If the universe goes on forever, does that mean there are infinite versions of you? 00:14: ... in the most straightforward way, they tell us that the universe may be infinite. ... 00:37: But according to our best theoretical understanding, an infinite universe seems at least possible - and some would say likely. 00:50: An infinite universe may literally contain every possible thing allowable by the laws of physics - each in infinite multitude. 00:59: And that includes infinite versions of you. 01:12: In fact, we need infinite monkeys. 01:15: ... may have heard the old thought experiment - if an infinite number of monkeys tap randomly on an infinite number of typewriters, ... 01:26: This proposition is the infinite monkey theorem. 03:01: ... it’s not zero probability, and the Infinite Monkey Theorem tells us that any non-zero probability event will ... 03:13: Perhaps you can start to see how this applies to there being infinite yous in an infinite universe. 04:06: ... it’s not a zero probability, and so with infinite regions of the universe - infinite trials, the infinite monkey theorem ... 04:17: In fact, it’s got to happen infinite times and with infinite variations. 04:22: So infinite yous and infinite versions of you. 04:36: ... up, in such an infinite universe we wouldn’t find everything - only everything that COULD happen ... 04:48: ... Infinite monkeys with standard English typewriters will eventually reproduce all ... 05:14: OK, so refining our question: in an infinite universe, does every POSSIBLE thing happen infinite times? 05:24: If there are infinite possible starting configurations for any one region of the universe, then there can be infinite regions without any doubling up. 05:32: But if there are finite starting points then at least SOME of those starting configurations have to be repeated infinite times. 06:53: We can’t tune the starting conditions to an infinite degree and still get different results - and that’s the key point. 07:04: That means at least some regions must be repeated infinitely. 07:24: ... in most cases we expect these values to repeat themselves infinite times in an infinite universe - eventually leading to an exact-enough ... 07:48: If one or more properties of the universe can take on values over an infinite range then no repetitions would be necessary. 07:55: ... like the mass or charge or other properties of individual particles, an infinite range means going to very, very high values for these properties - and ... 08:27: In fact that’s essentially the eternal inflation picture - one of the most popular ways to produce infinite universes. 08:48: ... that still doesn’t give us an infinite number of distinguishable histories because the number of possible ... 10:10: ... weird hiding in the laws of physics that we don’t understand, an infinite universe probably does duplicates its parts infinite ... 10:28: That the universe is actually infinite at all. 10:47: ... verify the eternal inflation picture then it’s very hard to avoid an infinite universe, or at least one that’s infinite-enough to duplicate ... 11:12: But let’s get back to the real question: in an infinite universe, is it inevitable that somewhere a monkey will type out Shakespeare? 11:39: ... just long strings of S’s underscored with fecal smears - and where the infinite monkey theorem has been experimentally ... 11:54: As for whether there are infinite versions and variations of you. 12:04: Now I think it’s hard to avoid that conclusion ... assuming an infinite universe. 12:10: And at risk of over quoting whatshisname: I could be bounded in a nutshell, and count my self a King of infinite spacetime.
	2020-01-27: Hacking the Nature of Reality 02:16: ... and all interactions are calculated by adding up the exchanges of infinite number of virtual ... 02:41: Early quantum theory was plagued by problems - for example, how do you compute infinite interactions? 02:48: And how do you avoid the infinite interaction strengths produced by some of those infinite sums? 09:45: ... gluons revealed that the strong nuclear force does not actually approach infinite strength as was once feared, and so a full quantum field theoretic ...
	2020-01-20: Solving the Three Body Problem 12:21: ... was a converging infinite series that added together an endless chain of terms to solve the ...
	2019-12-17: Do Black Holes Create New Universes? 03:26: ... black hole collapses, its mass doesn’t all end up stuck in the central, infinitely dense ... 07:16: ... near vacuum will cause black holes to spontaneously appear - and given infinite time these will eventually outnumber those produced by stars or stellar ...
	2019-12-09: The Doomsday Argument 13:31: OK, so our last episode was a journal club looking at a study that claimed to have evidence that the universe is not infinite after all. 14:02: If it turns out to the universe is negatively curved then well it's infinite. 14:06: ... geometric flatness we'll never actually know whether it's finite or infinite because it may be that there's a slight positive or negative curvature ... 14:39: ... universe remains flat or hyperbolic respectively and so remains infinite, while a positively curved universe remains positively curved and ... 15:07: That means it's also possible to produce a closed, positively curved bubble universe within an infinite inflating multiverse. 15:16: One commenter, O.N., pointed out that an infinite universe is technically possible within a bubble that otherwise looks finite from the outside. 15:37: ... Spring points out that there are flat geometries that are not infinite, but rather closed - for example the 3-torus embedded which is like a ...
	2019-12-02: Is The Universe Finite? 00:11: Although according to a new paper, it may literally be infinitely smaller than we previously thought. 01:38: ... the initial analysis from the Planck map, pointed to a universe that is infinitely large and geometrically flat, and is dominated by the influences of dark ... 02:24: ... that the universe is, as close as we can tell, geometrically flat and infinite. ... 02:50: If they’re right, the universe is not infinite in extent. 03:36: Then there’s 2) the negatively curved universe, analogous to a hyperbolic plane - an infinite saddle shape. 04:26: Rapid expansion tends to give negative curvature and open the universe - make it infinite. 06:56: ... close the universe into a finite hypersphere surface rather than an infinite flat ... 07:33: That curvature was slight - meaning the universe is still unthinkably vast, but if this is right then it’s not infinitely large.
	2019-11-04: Why We Might Be Alone in the Universe 14:47: Troy Henry asked if a torus would serve as an infinitely long cylinder - well the answer is, sadly, no.
	2019-10-21: Is Time Travel Impossible? 02:15: In order for any object with regular mass to even reach light speed it would need infinite energy – which can never be obtained. 07:13: It’s simple: just build an infinitely long cylinder of extreme density and set it rotating insanely quickly about its main axis. 07:46: If you don’t have the budget for an infinitely long cylinder, you could try building just a very, very long cylinder… and be horribly disappointed. 07:55: Stephen Hawking showed that unless the cylinder is infinitely long this doesn’t work – unless you also modify the spacetime with negative energy. 10:54: ... mechanics, in which every possible universe exists, splitting off in an infinite ... 11:17: ... prohibits it - for example, the quantum vacuum may be unstable in the infinitely iterating loops of a closed timelike ...
	2019-10-15: Loop Quantum Gravity Explained 15:49: ... to the universe - or in the case of a rotating black hole, an infinite density ...
	2019-10-07: Black Hole Harmonics 00:41: ... highly theoretical objects – static, unchanging black holes viewed from “infinitely” far ...
	2019-08-19: What Happened Before the Big Bang? 09:06: ... stunning; inflation never stops, but rather forms a fractal structure of infinitely expanding space in dispersed with bubble universes of all different ... 09:40: The exponential nature of the process will take over and the speck becomes infinite universes. 09:56: Can eternal inflation last infinitely into the past as well as the future?
	2019-08-06: What Caused the Big Bang? 12:49: eternally - Only stopping in patches where a bubble universe forms. And once started, inflation should produce infinite such universes. 12:59: But these will have to wait for a follow-up episode when we step into the multiverse of an infinitely inflating...
	2019-07-18: Did Time Start at the Big Bang? 00:25: ... all space and mass and energy should once have been compacted into an infinitesimally small point - a singularity. It's often said that the universe started ... 03:27: ... idea is especially weird if the universe is infinite Now the universe may or may not be infinite but if we can understand ... 04:38: ... universe could end up as hot and dense as you like But it'll still be infinite, spatially, the scale factor is incredibly small But an incredibly small ... 05:15: ... the infinite universe becomes infinitesimal all points become the same point and ... 06:02: ... Geodesic tracks earlier and earlier times as it approaches the Big Bang infinite clocks rewinding toward zero and then they all converge and Then what? ... 09:52: ... Conformal cyclic cosmology it's even weirder because it postulates the infinite future boundary of an eternally expanding universe Looks like the Big ... 11:12: ... an extreme quantum fluctuation could initiate a new Big Bang given infinite time or The same amount of time could lead to all particles randomly ...
	2019-05-09: Why Quantum Computing Requires Quantum Cryptography 01:33: For the best description of classical internet cryptography … on the internet … head to Infinite Series.
	2019-04-24: No Dark Matter = Proof of Dark Matter? 00:03: ... space but looks like a Jedi in a three-dimensional surface infinitely far away fleam notes that this is a form of Jedi Time Lord duality try ...
	2019-04-10: The Holographic Universe Explained 00:24: ... spacetime one dimension lower – like a hologram projected from a surface infinitely far ... 01:48: ... information in a volume of space depends on the volume – like, 1 bit per infinitesimal voxel – not one bit per pixel on its ... 05:43: We see scale invariance in fractal patterns, where the rules defining the structures repeat to infinitely large or small scales. 06:36: This adds a degree of freedom everywhere – like a new infinite number line at each of the 2-D grid points. 12:37: The lower dimensional CFT space is the surface of the AdS space because the field theory exists where the new dimension becomes infinite. 12:49: That’s tough to imagine – so let’s go back to our depiction of an infinite hyperbolic space from the last episode. 13:06: Anyone inside the hyperbolic space still has to travel infinitely far to get to that edge. 14:27: An abstract mathematical surface infinitely far from our location and from our intuition, projecting inwards our familiar holographic spacetime. 14:55: Last week was the warm-up to today's episode, in which we looked out how an infinite spacetime can have a finite boundary.
	2019-04-03: The Edge of an Infinite Universe 00:00: Have you ever asked “what is beyond the edge of the universe?” And have you ever been told that an infinite universe that has no edge? 00:11: We can define a boundary to an infinite universe, at least mathematically. 00:29: Our universe may be infinite. 00:50: Beyond it there exists at a minimum of thousands and possibly infinitely more regions just as large. 01:42: There’s another way to define the boundary of the universe that isn’t so shy in the face of an infinite cosmos. 01:50: In fact, if we twist our human intuition and our mathematics to its limit we can build our picket fence around an infinite universe. 02:15: ... today’s episode we’re going to talk about two ways to define an infinite boundary, and this will set us up finally for laying open the ... 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. 03:51: OK, so 2 out of 3 possible universes are infinite. 03:57: ... the other hand, assuming all these types exist, there should be infinitely more people in infinite universes compared to people in non-infinite ... 04:07: You’re probably one of the former, so let’s ignore puny de Sitter space and for today assume we’re in one of the infinite ones. 04:20: ... all got going in the early 60s when physicists tried to find ways to map infinite spacetime –to the edge of an infinite universe or across the event ... 05:03: ... singularity) It was Roger Penrose who defeated the true infinity of an infinitely large ... 06:10: The boundaries themselves represent infinite distance and infinite past and future. 07:05: ... matter must originate at this point representing all of space in the infinite past, and must also converge to this point which represents all of space ... 07:25: ... can do something that seems impossible – we can track a quantum field to infinite distance and calculate its behavior ... 08:15: ... connected a quantum field between two points at infinite distance – past and future - where he could define the state of the ... 08:37: He found that two “infinitely distant” regions could not both be in a perfect vacuum state if a black hole lay between them. 09:01: Today we’re just talking about boundaries – and we need a very different infinite boundary to give us our hologram. 09:09: Penrose diagrams define the infinite boundary of a flat universe as a useful tool in calculation. 09:16: For the holographic principle we need the infinite boundary of a negatively-curved universe – an anti-de Sitter, AdS universe. 10:44: ... of these lines are preserved, and it’s compactified because an infinite hyperbolic surface fits on a finite disk, with lengths represented by ... 11:27: ... space is fascinating because there are literally infinite ways it can be tessellated with regular polygons, while spheres and flat ... 11:40: So this disk can represent an infinite anti-de Sitter universe with 2 spatial dimensions at a single instant in time. 11:56: The boundary is infinitely far away and looks the same no matter where we travel. 12:14: It’s the nature of the infinite boundary. 13:24: Compactify it so you the infinite boundary becomes a surface – that surface is a 2+1 Minkowski plain. 14:40: The hologram part is because the lower dimensional space can be thought of as the infinitely distant boundary of the higher dimensional space. 14:49: Every particle, every gravitational effect in the bulk is represented by quantum fields on an infinitely distant surface.
	2019-03-28: Could the Universe End by Tearing Apart Every Atom? 00:05: ... cats and dogs living together and then tragically separated by the infinitely accelerating expansion of space on subatomic ... 10:03: ... be nothing but hopelessly isolated elementary particles separated by infinitely expanding space. That's a hell of a ... 12:53: ... all be over much sooner when the universe is ripped to shreds by the infinitely accelerating subatomic structure of ...
	2019-03-06: The Impossibility of Perpetual Motion Machines 10:15: The result is that a positive and negative mass should accelerate indefinitely, potentially powering an infinite energy device.
	2019-02-07: Sound Waves from the Beginning of Time 13:26: ... Guy has a fun one. To paraphrase: As the universe expands towards the infinite future, does that expansion outpace the probability of collapsing into a ... 15:51: In fact, we can imagine infinitely more things than a real.
	2019-01-30: Perpetual Motion From Negative Mass? 05:08: A negative mass apple would still fall to the Earth, and you wouldn’t notice Earth’s infinitesimal repulsion from the apple. 09:46: ... certain energy conditions, but the prospect of a bottomless well of infinite negative energy breaks them all very badly, and has implications for the ... 10:03: In particular, with the idea of negative and positive masses accelerating each other to infinite energies? 13:18: ... and is repelled by negative mass, come up with a way to use a pair of infinitely accelerating positive and negative mass objects to build a perpetual ...
	2018-11-07: Why String Theory is Right 04:02: The energy density at that point becomes infinite. 04:06: More technically, you start to get runaway self-interactions, infinite feedback effects between the graviton and its own field. 15:26: More accurately, the conducting plates create a horizon in what would otherwise be a perfect infinite vacuum.
	2018-10-31: Are Virtual Particles A New Layer of Reality? 00:29: And every time two particles interact, an infinite number of virtual particles mediate infinite versions of that one interaction. 07:09: ... one of these infinite possible virtual particles represents a quantum of energy in a single ...
	2018-10-18: What are the Strings in String Theory? 15:54: There's no infinite set of nested simulators.
	2018-10-10: Computing a Universe Simulation 14:39: An extra dimension would add infinite layers to the current universe, while a parallel universe would just add a single separate 3D universe.
	2018-10-03: How to Detect Extra Dimensions 04:56: The only reason we see so much gravity is that its range is infinite-- and unlike the nuclear forces. 13:45: So when you use perturbation theory to calculate an interaction in field theories, feedback effects give infinite loops of interactions. 14:14: For the simplest attempts at quantum gravity, you need infinite measurements.
	2018-09-20: Quantum Gravity and the Hardest Problem in Physics 02:25: It describes particles as waves of infinite possibility whose observed properties are intrinsically uncertain. 10:11: ... and/or, two, even in the case where the corrections appear large or even infinite, they can be ... 11:00: In fact, you would need infinite measurements to do so.
	2018-09-12: How Much Information is in the Universe? 15:41: ... bang by pure chance, or do you mean that while we're waiting through the infinite future for a new big bang, quantum fluctuations will produce all sorts ...
	2018-08-23: How Will the Universe End? 01:05: In fact, our universe will spend almost all of its infinite time in darkness, slowly crawling towards maximum entropy and ultimate heat death. 09:09: ... diffuse and dim as the accelerating expansion of space continues and the infinitely long progression to absolute heat death is all that ... 09:44: Over infinite time, nothing is truly stable. 14:24: If, by contrast, you have an infinitely thin shell of charge surrounding a mass, your g equals 5/3. 15:20: Epsilon Jay asks why electrons are thought of as infinitesimal points.
	2018-08-15: Quantum Theory's Most Incredible Prediction 03:57: And it doesn't really make sense to think of an infinitesimal point as rotating. 06:35: It seethes with a faint quantum buzz, infinite phantom oscillations that add infinite complication to any electromagnetic interaction. 07:51: And the sum of the infinite possible interactions defines the strength of the one real interaction. 09:50: ... there really are infinite ways the electron can interact with the EM field, with crazy networks of ...
	2018-08-01: How Close To The Sun Can Humanity Get? 07:17: Venus will end up traveling infinitesimally faster as it absorbs Parker's orbital energy.
	2018-07-25: Reversing Entropy with Maxwell's Demon 12:55: On the other hand, if the universe lasts for infinite time, then principal entropy drops of all sizes should eventually happen.
	2018-06-20: The Black Hole Information Paradox 14:11: Virtual particles in general are just a way to mathematically account for the infinite ways a quantum field can communicate its influence.
	2018-06-13: What Survives Inside A Black Hole? 00:16: ... gravitational collapse of a massive body, a point of hypothetical infinite density surrounded by an event ... 07:15: They are infinite in range and they arise from conserved quantities, namely mass and charge. 07:34: ... so the gravitational and electromagnetic forces have infinite range, and so Gauss's law demands that the mass and charge content of ... 09:43: It's because these properties are conserved and are communicated by gravity and electromagnetism, which have infinite range.
	2018-04-11: The Physics of Life (ft. It's Okay to be Smart & PBS Eons!) 01:24: ... or all the matter in the observable universe being crunched into an infinitely dense point are low ...
	2018-04-04: The Unruh Effect 04:28: In reality, eternal constant acceleration would take infinite energy.
	2018-03-15: Hawking Radiation 03:25: They're really just a tool for calculating the infinite ways in which a fluctuating quantum field can behave.
	2018-02-21: The Death of the Sun 11:27: ... point, but we could equally make it the center of the Earth or a point infinitely far ...
	2018-01-24: The End of the Habitable Zone 13:03: ... really nice Gabe level work, you should check out our sister channel PBS "Infinite Series." It's a math channel when we're covering topics from topology to ... 13:30: "Infinite Series" is pretty awesome and pretty hardcore. 13:39: I mean, it sounds like you want to invite yourself over to "Infinite Series" to hang out where we have the good challenge questions.
	2018-01-17: Horizon Radiation 04:26: Or even better, an infinite, extremely flexible drum skin. 06:04: That momentum field also has infinite oscillators, but now each one represents a different possible momentum for the particle. 06:13: ... perfectly localized position oscillation can also be described as an infinite number of unlocalized momentum ... 06:40: The superposition of infinite universe size momentum oscillators-- momentum particles can represent a single spatial oscillator. 06:54: Let's go back to the slightly less abstract infinite drum skin. 07:21: ... same oscillation by simultaneously hitting the drum everywhere with an infinite drumstick, adding global vibrations with different frequencies that ... 07:37: But why exchange a single spatial equation for infinite equations in momentum space? 08:28: ... oscillations can be reconfigured with our infinite drumstick to add new particles or remove old ones, for example, to ... 08:46: It's called the field operator, and it is our infinite drumstick. 09:29: In momentum space, we can think of it as a superposition of infinitely many momentum modes. 09:35: Infinite spatially undefined particles with defined momenta, and these just happen to cancel each other out, leaving 0 particles or a vacuum. 09:46: OK, so what happens when we add a horizon to our infinite quantum field? 10:26: ... means we have to reconfigure our old field operator, our infinite drumstick, in order to create and annihilate the same particles as we ... 11:04: So you can be that horizon's drum skin to produce oscillations that are consistent with the infinite, un-horizoned skin.
	2018-01-10: What Do Stars Sound Like? 02:07: While the distance stars are infinitesimal points of light to even our best telescopes, the surface of the sun can be resolved in incredible detail.
	2017-12-13: The Origin of 'Oumuamua, Our First Interstellar Visitor 11:14: [INAUDIBLE] 777 asks, if you try to do a Fourier transform of PBS Space Time, do you get PBS infinite series? 11:23: Actually, I think you need an infinite series of PBS Space Time to get a Space Time localization of PBS infinite series.
	2017-12-06: Understanding the Uncertainty Principle with Quantum Fourier Series 01:19: The vacuum itself can be thought of as constructed from the sum of infinite possible particles. 05:01: Is it even possible to make an instantaneous spike at one point in time out of a bunch of sine waves that themselves extend infinitely through time? 05:12: ... to get a spike at one point in time, you need to use infinitely many different frequency sine waves, each of which exists at all points ... 05:30: ... a perfectly known frequency is a simple traveling sine wave that extends infinitely in time so the time of its existence is ... 10:26: ... perfectly localized at one spot in space, can so be described as infinite oscillations in momentum space, spanning all possible ... 10:51: So a perfectly specially localized particle is equally an infinite number of momentum particles that themselves occupy all locations in the universe. 11:01: ... in this strange momentum space, by adding and removing these spatially infinite particles, that we can describe how the quantum vacuum changes to give ... 14:27: Well, Jaden, the trick is to assume geckos with infinitely high tensile strength. 14:32: ... had zero mass, so who's to say those rare, zero-mass geckos don't have infinite tensile ...
	2017-11-22: Suicide Space Robots 14:44: There's one way that the universe is and infinite ways that it isn't. 14:57: Those false powers sometimes sound pretty cool because they imply things like infinite free energy or fast space travel.
	2017-11-08: Zero-Point Energy Demystified 02:10: Why can't we pull infinite free energy out of nothing?
	2017-11-02: The Vacuum Catastrophe 02:23: To calculate the density of energy of the vacuum, we should add this tiny energy over an infinite range of frequency modes for all fields. 02:33: Now, multiply a finite energy density no matter how small by infinity, and you get infinite energy density. 02:42: We'll get back to whether the idea of an infinite vacuum energy is actually possible. 03:49: ... if vacuum energy did have a value this high-- in fact, even if it were infinite-- we may not notice, at least according to quantum ... 04:39: Long story short-- a crazily high, even infinite, vacuum energy doesn't affect the predictions of quantum field theory.
	2017-10-25: The Missing Mass Mystery 11:34: So enough vacuum energy could result in a closed, rather than infinite, universe.
	2017-09-28: Are the Fundamental Constants Changing? 13:41: ... whether it would be feasible to build something like an aragoscope with infinitely many concentric rings by using some sort of advanced diffracting ...
	2017-09-13: Neutron Stars Collide in New LIGO Signal? 15:00: What I mean by that is that the Big Bang happened everywhere at once, not at an infinitesimal point in space. 15:13: Now, we can imagine both the white hole and the earliest instant of the Big Bang as possessing infinite or at least extremely high density.
	2017-08-30: White Holes 03:24: ... events occurring at the event horizon, including folding into it, happen infinitely far in the ... 04:14: We find the singularity again lurking infinitely far in the past. 04:20: From the point of view of the outside universe, the eternal black hole singularity exists both in the infinite future and in the infinite past. 04:53: They compactify space time so that time bunches up towards the edges, and the borders correspond to infinite past and future. 05:39: ... traveling at that 45 degree angle takes infinite time to escape the event horizon, and the region beyond that line ... 07:20: The light rays from any crossing reach us infinitely far in the future, even if the black hole plunge began far in the past. 08:11: The past singularity and past event horizon are infinitely far in the past from our point of view. 08:18: Light has to traverse infinite time to reach our location. 11:42: We required that all paths be traceable through infinite past and future space, provided they don't hit the singularity.
	2017-08-02: Dark Flow 11:57: ... to think of that retro-causal influence as also propagating through the infinite possible interactions within the virtual space of the Feynman ...
	2017-07-26: The Secrets of Feynman Diagrams 00:03: ... particle physics by providing a simple system to sort out the infinite possibilities when elementary particles ... 01:06: This is impossible, because there are infinite possible intermediate states. 01:12: ... the Feynman diagrams allow physicists to quickly figure out which of the infinite possibilities need to be considered to get an answer that's good ... 03:25: And it can be used to construct infinite Feynman diagrams. 07:37: Part of the beauty of Feynman diagrams is that each of these diagrams themselves represents an infinite number of specific interactions. 07:47: To start with, each of the particle paths are actually infinite paths. 07:51: As well as infinite possibilities for particle momenta, we have to consider even impossible faster than light paths. 12:19: Mayank, thanks so much for choosing one of the infinite improbable paths that led you to join us.
	2017-07-12: Solving the Impossible in Quantum Field Theory 04:49: There are literally infinite ways that scattering could have occurred. 04:52: In fact, according to some interpretations, all infinite intermediate events that lead to the same final result actually do happen, sort of. 05:53: With infinite possible interactions behind this one simple process, a perfectly complete quantum field theoretic solution is impossible. 08:54: ... mass using quantum electrodynamics, you get that the electron has infinite extra ... 09:44: ... electrons do not have infinite mass, and we know that because we've measured that mass, although any ... 10:19: In a sense, you capture the theoretical infinite terms within an experimental finite number. 10:27: ... of the infinities that arise in quantum field theory-- for example, the infinite shielding of electric charge due to virtual particle-anti-particle pairs ...
	2017-07-07: Feynman's Infinite Quantum Paths 02:27: Feeling cocky, the student asked, what about if you cut infinite slits so there's no more screen? 02:34: And then what if you add a second screen with infinite slits? 03:27: But when something travels through empty space, it's like it's traveling through infinitely packed barriers, each with infinite slits. 03:37: There are infinite possible paths. 03:40: ... Feynman actually figured out a way to combine the infinite paths to give a very real finite probability of a particle reaching its ... 05:24: Feynman instead used quantum action to assign an importance, a weight, to each of the infinite paths that a single particle could take. 05:33: ... of calculus, he was able to add up the contributions from all of those infinite possible paths to find the probability of a particle making that simple ... 07:13: Now, when Feynman used this action quantity to figure out the probability amplitudes of his infinite paths, something amazing happened. 07:34: The familiar paths of the large-scale classical world are just the small set of infinite possible paths that don't cancel each other out. 08:56: It's not just that a particle can travel infinite physical paths. 09:00: Also, infinite things can happen to the particle on the way. 10:37: If we have to take those infinite simultaneous paths seriously, then we also have to take those infinite intervening events seriously. 10:54: However, unlike the ridiculous infinite trajectories a particle can take, those infinite events don't cancel out nearly so neatly. 11:04: In fact, they lead to rampant, uncontrolled infinite probabilities. 11:12: One powerful tool in making sense of these infinite possible events also came from Richard Feynman, specifically Feynman diagrams.
	2017-06-28: The First Quantum Field Theory 07:43: So Dirac described a space of quantum states, including position and momentum/frequency, like an infinite array of springs. 10:26: ... fermion, or electron quark, et cetera, per quantum state, rather than infinite particles in the case of the ... 11:53: That's a challenge because there are infinite ways in which anything can occur.
	2017-06-21: Anti-Matter and Quantum Relativity 06:38: ... moving in an electromagnetic field could keep releasing energy as light infinitely, and sink lower and lower, to infinite negative energy ... 07:00: Imagine an infinitely deep ocean of electrons that exists everywhere in the universe. 08:44: These fields are more like membranes than infinitely deep oceans. 13:12: ... "universe" to be the bounded post-inflationary pocket in a single true infinite ...
	2017-06-07: Supervoids vs Colliding Universes! 09:37: But regardless, in an infinitely inflating space time, collisions between bubble universes are eventually expected.
	2017-05-03: Are We Living in an Ancestor Simulation? ft. Neil deGrasse Tyson 08:01: ... idea is that in an infinite multiverse, it should be vastly more common for particles to randomly ...
	2017-04-26: Are You a Boltzmann Brain? 04:12: But, given infinite time, any nonimpossible arrangement will happen. 04:17: Imagine an infinitely large room-- a universe that's in perfect thermal equilibrium for infinite time. 10:12: ... out of existence in the next instant, as momentary fluctuations in the infinite chaos of a max-- maximally entropic space ...
	2017-04-05: Telescopes on the Moon 13:07: So do you get infinitely spaghettified before you are tortellinified?
	2017-03-22: Superluminal Time Travel + Time Warp Challenge Answer 00:30: Enter the warp drive, and hyperspace, and star gates, and the infinite improbability drive. 07:06: Well, you just trace the photon paths, assuming for a moment that an FTL ship doesn't produce infinitely red or blue shifted photons.
	2017-02-02: The Geometry of Causality 11:56: ... Lloyd asks, "Is the calculated infinite density of the core of a black hole an artifact of the limitations of ... 12:22: One idea is that the inside of an event horizon is composed of a ball of raw strings, a so-called fuzzball, and that no infinite density exists.
	2017-01-19: The Phantom Singularity 00:04: The point of infinite density at the core of a black hole, but also so much more. 01:03: Then the result of the equation, the force, becomes extremely large and is infinite when R becomes equal to 0. 01:14: Infinite force means infinite acceleration, which means-- well, physics breaks. 01:21: According to Newton's law, in order to fuel that infinite gravitational acceleration you need to get zero distance from an object's center of mass. 01:30: That means all of that object's mass would need to be concentrated at that center, a single point of 0 size, which means infinite density. 01:43: ... often use the word singularity to describe the hypothetically infinitely dense core of a black hole, but in math the meaning of this word is much ... 02:01: Guys, meet Kelsey Houston Edwards of the new PBS show, "Infinite Series." Hey, Kelsey. 02:54: It's possible to pass their time zones infinitely quickly, but only because of your choice of spherical coordinates. 03:09: I mean, the curvature and the density are infinite from any frame of reference. 03:47: Guys, you should check out Kelsey's show "infinite Series," where she goes into much more depth on the nature of singularities. 06:53: When you use the Schwarzschild metric to calculate the curvature at r equals 0, that curvature is infinite. 07:00: This gives us the same infinite gravitational pull as the Newtonian singularity. 07:05: And just as with the Newtonian case, this gravitational singularity can only exist if infinite densities are possible. 07:13: But unlike Newton's laws of gravity, the Schwarzschild metric actually tells us whether or not that infinite density is expected. 09:42: ... and so it can hang out at the event horizon, which also only exists at 1 infinitely stretched out ... 10:09: But what is actually infinite here? 10:13: ... the fact that even an outgoing light ray takes infinite time to move any distance, so using boring old time and distance, delta ... 11:14: But can that point of infinite density really exist? 12:18: Be sure to check out the PBS "Infinite Series" episode dealing with earthly singularities right here.
	2017-01-04: How to See Black Holes + Kugelblitz Challenge Answer 09:33: Fortunately, I said that the sphere was infinitely strong. 10:41: ... slight problem of having blocked out the sun, but hey, we just built an infinitely strong Dyson sphere and charged it with an impossible amount of ...
	2016-12-14: Escape The Kugelblitz Challenge 00:14: ... of space and time, allowing us to fit onto the one diagram the infinitely stretched space-time in the vicinity of a black hole's event ... 05:55: Plan A is to build an infinitely-strong Dyson sphere surrounding the earth just outside the moon's orbital radius.
	2016-12-08: What Happens at the Event Horizon? 03:10: It has a point of infinite density, the singularity, and an event horizon a bit further out. 04:15: It crunches together, or compactifies, the grid lines to fit infinite space-time on one graph-- very useful for black holes. 09:35: ... the monkey isn't actually above the horizon for infinite time, it only appears that way to us because as long as we're outside ... 11:19: Then our Penrose diagram blooms outwards to include potentially infinite parallel regions of space-time.
	2016-11-30: Pilot Wave Theory and Quantum Realism 00:55: ... alive and dead, or even that the universe is constantly splitting into infinite alternate ...
	2016-07-06: Juno to Reveal Jupiter's Violent Past 11:41: ... I said that the assumption of infinite divisibility of space was a problem with the scenario in this paradox, ... 11:54: ... complains that to catch a tortoise, Achilles needs to complete an infinite number of tasks, closing the remaining gap every time he reaches the ... 12:06: ... it doesn't need to take an infinite amount of time to complete an infinite number of tasks, as long as the ... 12:37: That's what we call a convergent series, because it doesn't add up to infinity, even if you do an infinite number of these additions. 12:50: That's how long Achilles takes to complete the infinite steps and overtake the tortoise.
	2016-06-22: Planck's Constant and The Origin of Quantum Mechanics 00:53: To overtake a tortoise, you need to travel to its previous position infinite times. 00:59: Each of those steps is shorter than the last, but there are still an infinite number of them. 01:05: There are a few problems with this paradox, but one is that it assumes that space is infinitely divisible. 05:58: It paints the crazy picture of a universe full of infinite extreme energy gamma radiation. 06:19: The problem turned out to be that in classical physics, everything can be infinitely divided. 06:28: The Rayleigh-Jeans calculation allows particles to vibrate with any amount of energy, all the way down to infinitesimally tiny wiggles. 06:51: ... Rayleigh and Jeans were chasing Zeno's tortoise, infinitely dividing the smallest remaining energy states, and so never ever finding ... 07:09: ... spectrum, he needed some sort of math trick to count the supposedly infinite energy ...
	2016-06-08: New Fundamental Particle Discovered?? + Challenge Winners! 11:53: ... past doublings that have happened since the end of inflation, and the infinite number of doublings the will happen in the ...
	2016-06-01: Is Quantum Tunneling Faster than Light? 02:13: There's an infinitesimal chance that I'm on the moon.
	2016-05-11: The Cosmic Conspiracy of Dark Energy Challenge Question 05:01: And for the vast majority of future doublings, regular matter will have diluted away and be an infinitesimal influence compared to dark energy. 05:29: ... for how many of those infinite future doublings will regular matter and energy have any significant ...
	2016-04-27: What Does Dark Energy Really Do? 00:33: Observations show that out universe is infinitely expanding. 05:46: ... recollapsing universe and faint or more distant in a low-density, infinitely-expanding ...
	2016-04-20: Why the Universe Needs Dark Energy 02:35: k is, in a sense, the shape of the universe-- its spatial curvature, as well as its spatial extent, finite or infinite. 04:04: Such a universe is infinitely large, or "open." But "k equals 0" means the universe is flat. 04:16: Geometry works just as you learned in school, and a flat universe is still infinite-- open-- in all three spatial dimensions. 04:51: An underdense, infinitely expanding universe should be hyperbolic. 04:56: ... at exactly its escape velocity, one that will slow to a stop over infinite time, should be flat, with the both left and right sides coming out to ... 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? 03:53: ... the future expansion rate of the universe to slowly grind to a halt over infinite ... 09:20: Dark energy won't save us from infinite expansion.
	2016-04-06: We Are Star Stuff 11:34: Space is still three dimensional, and perhaps infinite in all three dimensions.
	2016-03-30: Pulsar Starquakes Make Fast Radio Bursts? + Challenge Winners! 03:33: ... cross-section, which means that even though the electrons themselves are infinitesimally small, photons don't have to get too close before they interact via the ...
	2016-03-16: Why is the Earth Round and the Milky Way Flat? 11:33: Instead, the early universe is described as a very high density over an extremely large, and possibly infinite, volume.
	2016-03-02: What’s Wrong With the Big Bang Theory? 00:10: The Big Bang Theory suggests that once the entire universe was compacted into an infinitely small speck at the beginning of time. 11:45: If our universe is infinite, then you can compact it as much as you like and it will still be infinite.
	2016-02-24: Why the Big Bang Definitely Happened 02:36: ... we get that the entire observable universe was once compacted into an infinitesimal point, a singularity at time t equals 0, the hypothetical instant of the ...
	2016-02-03: Will Mars or Venus Kill You First? 10:00: We just don't understand the physics well enough to confidently project the size of the universe to infinitesimal smallness, to a singularity.
	2016-01-27: The Origin of Matter and Time 08:30: Two infinitesimally nearby bits of the universe can affect each other at exactly the speed of light.
	2016-01-13: When Time Breaks Down 04:45: And that distance is infinite when the clock reaches the speed of light.
	2016-01-06: The True Nature of Matter and Mass 10:06: Then, without an infinite source and sink of weak hypercharge, the weak nuclear force and the electromagnetic force were all the same force.
	2015-12-16: The Higgs Mechanism Explained 05:29: This makes the Higgs field an infinite source and sink of weak hyper-charge. 05:34: ... from all directions, giving and taking away the weak hyper-charge on infinitesimally short time ... 05:53: ... invisible and infinite ocean of some sort of charge that we've never heard of all invented so ...
	2015-12-09: How to Build a Black Hole 07:58: And yet, below the star's surface, their lurks the potential event horizon, the surface of infinite time dilation. 09:03: All paths lead to the central point of infinite curvature, the singularity. 09:29: But what happens to these as the star approaches an infinitesimal point, the Planck scale? 10:05: On our clock, the singularity forms infinitely far in the future.
	2015-10-07: The Speed of Light is NOT About Light 02:38: In fact, we now know that even Newton's mechanics were using assumptions that implied an infinite speed of light, which is really bad. 09:53: Because it would take infinite energy to make any mass. 09:56: There is only massless particles traveling at infinite speed. 09:59: Time dilation and length contraction are infinite. 10:11: The universe is an infinitesimal here-and-now This is all pretty paradoxical. 10:19: However, the paradox itself tells us that an infinite speed limit is impossible. 10:41: Denny Hiu asks how a universe that is already infinite expand? 10:52: Imagine an infinitely long ruler with markings spaced at every inch. 10:56: If we stretched the ruler so that the markings are spaced at every two inches, the ruler is still infinitely long.
	2015-09-30: What Happens At The Edge Of The Universe? 00:11: You might be thinking, wait, how is there an edge to the universe if it's infinite? 00:32: The universe is infinite because general relativity tells us that the universe is demonstrably flat and therefore the galaxies go on forever. 00:41: Are you sure you measured the universe's curvature with infinite precision? 02:44: Bad news, you'd have to travel infinitely far, even if you were in a spaceship that could travel at the speed of light. 05:18: Measurements of the distribution of galaxies and the CMB confirm this flatness with very high, but not infinite, precision. 05:26: If spacetime really is perfectly flat, then, with the most simplistic application of Einstein's equations, we get that the universe is infinite. 05:49: And there are many types of infinity, including some that involve infinitely repeating versions of this bit of the universe. 07:12: ... our universe may just be a slowly expanding bubble in an exponentially infinitely-inflating ...
	2015-09-23: Does Dark Matter BREAK Physics? 08:12: That lasts an infinitesimal fraction of a second before it crosses.
	2015-08-19: Do Events Inside Black Holes Happen? 02:43: But everyone else insisted he never does, even after an infinite amount of time on any of our clocks. 03:01: ... the black hole, those events just don't occur, even if we wait an infinite amount of ... 08:29: ... is correct, I shouldn't really have used the verb "see," because the infinite redshift keeps me from seeing him at ... 09:13: ... not what you mean by "density." Maybe you mean that all black holes are infinitely dense because all the stuff that goes into the black hole collapses to ...
	2015-07-15: Can You Trust Your Eyes in Spacetime? 01:48: And I've got an infinitely long stick with tick marks on it attached to me at the x equals zero mark, my own personal x-axis.
	2015-05-20: The Real Meaning of E=mc² 05:32: Suppose we call the potential energy of a proton and electron zero when they're infinitely far apart.
	2015-04-29: What's the Most Realistic Artificial Gravity in Sci-Fi? 09:26: There are an infinite number of self-consistent ways to arrange events according to when and where they happen.
	2015-03-25: Cosmic Microwave Background Explained 04:04: ... then just before neutralized was one last hurrah, one final flash of an infinite number of orange bulbs going off at every point in the universe more or ...

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