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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 ... 08:58: ... for a single Feynman diagram   you’re actually adding infinite possible  trajectories using Feynman path ...
	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 ... 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 ... 12:56: ... there’s your answer. The infinite scalability of space means the universe can and probably will expand ... 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 ... 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 hole. As ... 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 slices ... 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 chain ... 12:56: ... there’s your answer. The infinite scalability of space means the universe can and probably will expand forever with no ... 09:16: ... general relativity, space can be infinitely divided. That means we can start with a universe that’s small and grid ... 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 ... 13:16: ... horizon, in which case we never would have even known that we live in an infinitely expanding ... 09:16: ... general relativity, space can be infinitely divided. That means we can start with a universe that’s small and grid it up and ... 10:33: ... all works if space is infinitely divisible. But we know that at the smallest scales, general relativity comes into ... 10:52: ... which must expand out of the old Planck lengths. That implies an infinitely divisible space emerging from within each Planck ... 13:16: ... horizon, in which case we never would have even known that we live in an infinitely expanding ...
	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 ... 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 density ... 01:01: In general relativity, that looks like a point of infinite density surrounded by an event horizon. 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 and ... 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 ... 08:09: ... 2-D analog of the flat universe is an infinite flat plane, while the open universe corresponds to a sort of saddle shape - ... 10:13: But at the same time there are infinite points. 10:01: But what about an infinite universe? 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 ... 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 be relative ... 17:28: ... by escape I mean reach YOU at your “infinite distance”. And it’s the surface from which light is infinitely redshifted - sapped ... 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 be relative ... 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 means ... 17:28: ... at your “infinite distance”. And it’s the surface from which light is infinitely redshifted - sapped of all energy - before it reaches that infinite ...
	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. 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 ... 11:37: To get a consistent definition for mass you need to integrate - add up - the contributions to infinite distance from the black hole. 09:46: ... collapsing star continue to make their way out into the universe over infinite time. ... 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. 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. 00:39: ... matter should contract to a single point of infinite density - the singularity - which is surrounded by a surface from which even ... 06:12: Lose that pesky infinite density and we can start making sense of physics again. 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. 00:39: ... matter should contract to a single point of infinite density - the singularity - which is surrounded by a surface from which even light ... 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.
	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. 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. 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. 16:52: Light does travel a straight line if you look at an infinitesimally small patch of space.
	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. 16:37: But possibly still infinite, though that’s still being debated. 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. 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. 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.
	2021-06-16: Can Space Be Infinitely Divided? 05:08: ... space down to any conceivable precision,   perhaps even infinite precision - as long as  we’re happy to have infinite uncertainty ... 01:16: ... the energy of light in this heat-glow was   not infinitely divisible. Rather came in quanta - chunks of energy that we now ...
	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. 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. 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 particle around ...
	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 ... 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 ...
	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: ... holes tend to be associated with infinite spacetime curvature - infinite gravity. In other   words, singularities. Penrose didn’t ... 01:17: ... At that so-called singularity, the  gravitational field becomes infinite. But   physicists tend to be dubious about infinities - more often than ... 00:00: ... every black hole contains a place of   infinite gravity - a singularity. But the true  impact of Penrose’s singularity ... 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: ... holes tend to be associated with infinite spacetime curvature - infinite gravity. In other   words, singularities. Penrose didn’t ... 00:00: ... every black hole contains a place of   infinite gravity - a singularity. But the true  impact of Penrose’s singularity ... 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 ... 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 big ... 08:49: ... have holes in it.   These holes tend to be associated with infinite spacetime curvature - infinite gravity. In other   words, singularities. ...
	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 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: ... actually to the “conformal infinity” of the previous - so all the future infinite time of the previous added ... 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 endless chain ... 13:27: ... actually to the “conformal infinity” of the previous - so all the future infinite time of the previous added ... 01:12: Without it, the infinitely dense singularity and its surrounding madness is exposed to the outside universe. 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: ... every black hole and particle has decayed into faint radiation .... that infinite stretch of space and time is identically the SAME THING as the ... 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 ... 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 ... 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 the 45 ... 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 ... 09:48: The edges of this map represent “conformal infinity” - where infinite space and time are compressed onto an edge. 00:45: ... every black hole and particle has decayed into faint radiation .... that infinite stretch of space and time is identically the SAME THING as the infinitesimal and ... 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? 00:45: ... goes like this: the infinitely far future, when the universe has expanded exponentially to to an ... 10:12: Similarly, the infinitesimal or “zero-sized” point of the Big Bang can be rescaled into a finite space. 00:45: ... infinite stretch of space and time is identically the SAME THING as the infinitesimal and instantaneous big bang of a new universe, and our universe is just ... 10:12: Similarly, the infinitesimal or “zero-sized” point of the Big Bang can be rescaled into a finite space.
	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 ... 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 led our ...
	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. 04:54: The singular, central point has been spun out into a ring of infinite density. 16:36: The universe approaches infinite density in the limit as time approaches zero. 07:58: Surrounding the ring on this side is a toroidal region in which it’s possible to accelerate to infinite speed. 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. 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.
	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. ... 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 that age ... 14:06: ... started from a singularity. How do you go from infinitessimally small to infinitely ... 14:42: ... galaxies we can see were compacted into a tiny point. There were just infinitely many of those tiny ... 14:06: ... started from a singularity. How do you go from infinitessimally small to infinitely large? ... 14:42: ... galaxies we can see were compacted into a tiny point. There were just infinitely many of those tiny ... 14:06: ... age" if the universe started from a singularity. How do you go from infinitessimally small to infinitely ...
	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 ... 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 ... 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 whole ... 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 lost. ... 00:37: ... - and a single swivel at a pole carries you through the longitudes at an infinite rate. The coordinate singularity of the poles can be banished by shifting the ... 07:32: ... imagine you could travel at infinite speed - then you could take these horizontal which would dip beneath the event ... 03:14: ... compact approaching the horizon. That compactification cancels out the infinite stretching of time so that gridlines pass smoothly across the event ... 08:44: ... as an inevitable crushing future, in which the space around you becomes infinitely ... 03:14: ... after Zeno’s paradox. It’s a measure of distance that becomes infinitesimally compact approaching the horizon. That compactification cancels out the ...
	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 ... 14:39: ... from general relativity tell us that it it may be truly spatially infinite - in which case 10^10^90 is a piece of ... 12:33: ... contain infinite repetitions of everything it contains, including you. Infinite comments ensued, of which I'll now answer a finite ... 03:59: ... in QCD, where there isn’t just one lowest energy state - there are infinite lowest energy ... 12:33: ... to figure out whether a universe that is infinite in size should contain infinite repetitions of everything it contains, including you. Infinite comments ensued, of ... 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 ... totally ... 14:39: ... actually 13.5 billion years would be pretty close the beginning of an infinitely-long-lasting eternal inflation. Of course all of this is assuming that the universe ...
	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. 07:24: ... 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. 06:53: We can’t tune the starting conditions to an infinite degree and still get different results - and that’s the key point. 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 definitely ... 04:06: ... and so with infinite regions of the universe - infinite trials, the infinite monkey theorem tells us it’s got to happen ... 11:39: ... just long strings of S’s underscored with fecal smears - and where the infinite monkey theorem has been experimentally ... 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 definitely happen ... 04:06: ... and so with infinite regions of the universe - infinite trials, the infinite monkey theorem tells us it’s got to happen ... 11:39: ... just long strings of S’s underscored with fecal smears - and where the infinite monkey theorem has been experimentally ... 01:12: In fact, we need infinite monkeys. 04:48: ... Infinite monkeys with standard English typewriters will eventually reproduce all of ... 00:50: An infinite universe may literally contain every possible thing allowable by the laws of physics - each in infinite multitude. 01:15: ... may have heard the old thought experiment - if an infinite number of monkeys tap randomly on an infinite number of typewriters, eventually ... 08:48: ... that still doesn’t give us an infinite number of distinguishable histories because the number of possible ... 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 that ... 04:06: ... it’s not a zero probability, and so with infinite regions of the universe - infinite trials, the infinite monkey theorem tells us ... 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. 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. 04:17: In fact, it’s got to happen infinite times and with infinite variations. 05:14: OK, so refining our question: in an infinite universe, does every POSSIBLE thing happen infinite times? 05:32: But if there are finite starting points then at least SOME of those starting configurations have to be repeated infinite times. 07:24: ... in most cases we expect these values to repeat themselves infinite times in an infinite universe - eventually leading to an exact-enough ... 10:10: ... understand, an infinite universe probably does duplicates its parts infinite times. ... 04:06: ... not a zero probability, and so with infinite regions of the universe - infinite trials, the infinite monkey theorem tells us it’s got to happen ... 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. 03:13: Perhaps you can start to see how this applies to there being infinite yous in an infinite universe. 04:36: ... up, in such an infinite universe we wouldn’t find everything - only everything that COULD happen from the ... 05:14: OK, so refining our question: in an infinite universe, does every POSSIBLE thing happen infinite times? 07:24: ... cases we expect these values to repeat themselves infinite times in an infinite universe - eventually leading to an exact-enough repetition of both the laws of ... 10:10: ... weird hiding in the laws of physics that we don’t understand, an infinite universe probably does duplicates its parts infinite ... 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? 12:04: Now I think it’s hard to avoid that conclusion ... assuming an infinite universe. 07:24: ... cases we expect these values to repeat themselves infinite times in an infinite universe - eventually leading to an exact-enough repetition of both the laws of ... 08:27: In fact that’s essentially the eternal inflation picture - one of the most popular ways to produce infinite universes. 04:17: In fact, it’s got to happen infinite times and with infinite variations. 00:00: If the universe goes on forever, does that mean there are infinite versions of you? 00:59: And that includes infinite versions of you. 04:22: So infinite yous and infinite versions of you. 11:54: As for whether there are infinite versions and variations of you. 03:13: Perhaps you can start to see how this applies to there being infinite yous in an infinite universe. 04:22: So infinite yous and infinite versions of you. 10:47: ... it’s very hard to avoid an infinite universe, or at least one that’s infinite-enough to duplicate ... 07:04: That means at least some regions must be repeated infinitely.
	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 ... 02:48: And how do you avoid the infinite interaction strengths produced by some of those infinite sums? 02:41: Early quantum theory was plagued by problems - for example, how do you compute infinite interactions? 02:16: ... and all interactions are calculated by adding up the exchanges of infinite number of virtual ... 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 description of ... 02:48: And how do you avoid the infinite interaction strengths produced by some of those infinite sums?
	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? 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 ... 03:26: ... black hole collapses, its mass doesn’t all end up stuck in the central, infinitely dense ...
	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 ... 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.
	2019-12-02: Is The Universe Finite? 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 ... 03:36: Then there’s 2) the negatively curved universe, analogous to a hyperbolic plane - an infinite saddle shape. 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 ... 07:33: That curvature was slight - meaning the universe is still unthinkably vast, but if this is right then it’s not infinitely large. 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 ... 07:33: That curvature was slight - meaning the universe is still unthinkably vast, but if this is right then it’s not infinitely large. 00:11: Although according to a new paper, it may literally be infinitely smaller than we previously thought.
	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. 10:54: ... mechanics, in which every possible universe exists, splitting off in an infinite ... 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. 10:54: ... mechanics, in which every possible universe exists, splitting off in an infinite tree. ... 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. 11:17: ... prohibits it - for example, the quantum vacuum may be unstable in the infinitely iterating loops of a closed timelike ... 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. 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.
	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? 09:40: The exponential nature of the process will take over and the speck becomes infinite universes. 09:06: ... stunning; inflation never stops, but rather forms a fractal structure of infinitely expanding space in dispersed with bubble universes of all different ... 09:56: Can eternal inflation last infinitely into the past as well as the future? 09:06: ... stunning; inflation never stops, but rather forms a fractal structure of infinitely expanding space in dispersed with bubble universes of all different ...
	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? 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 ... 03:27: ... may or may not be infinite but if we can understand this for the infinite case Then getting all of this for the finite case is baby stuff at least by ... 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? well, ... 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 Bang of a ... 05:15: ... because even the tiniest fraction of a second later The universe has infinite size and everywhere is expanding equally Even if the universe is not infinite ... 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 number ... 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 ... 03:27: ... stuff at least by comparison It's tricky to talk about the size of an infinite universe Instead of the overall volume or radius we talk about the size of an ... 05:15: ... the infinite universe becomes infinitesimal all points become the same point and ... 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 ... 05:15: ... the infinite universe becomes infinitesimal all points become the same point and three-dimensional space becomes ... 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 ...
	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 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. 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. 12:49: That’s tough to imagine – so let’s go back to our depiction of an infinite hyperbolic space from the last episode. 06:36: This adds a degree of freedom everywhere – like a new infinite number line at each of the 2-D grid points. 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. 00:24: ... spacetime one dimension lower – like a hologram projected from a surface infinitely far ... 05:43: We see scale invariance in fractal patterns, where the rules defining the structures repeat to infinitely large or small scales. 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. 05:43: We see scale invariance in fractal patterns, where the rules defining the structures repeat to infinitely large or small scales. 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 ...
	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. 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: ... 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 ... 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 ... 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. 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. 11:40: So this disk can represent an infinite anti-de Sitter universe with 2 spatial dimensions at a single instant in time. 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 holographic ... 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. 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. 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. 06:10: The boundaries themselves represent infinite distance and infinite past and future. 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 quantum ... 07:05: ... must also converge to this point which represents all of space in the infinite future. ... 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 shorter and ... 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. 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 horizon of a ... 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. 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. 04:20: ... tried to find ways to map infinite spacetime –to the edge of an infinite universe or across the event horizon of a black ... 03:57: ... all these types exist, there should be infinitely more people in infinite universes compared to people in non-infinite ... 11:27: ... space is fascinating because there are literally infinite ways it can be tessellated with regular polygons, while spheres and flat ... 00:50: Beyond it there exists at a minimum of thousands and possibly infinitely more regions just as large. 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 ... 05:03: ... singularity) It was Roger Penrose who defeated the true infinity of an infinitely large ... 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. 11:56: The boundary is infinitely far away and looks the same no matter where we travel. 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. 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. 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. 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. 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. 14:49: Every particle, every gravitational effect in the bulk is represented by quantum fields on an infinitely distant surface. 05:03: ... singularity) It was Roger Penrose who defeated the true infinity of an infinitely large ...
	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 ... 00:05: ... cats and dogs living together and then tragically separated by the infinitely accelerating expansion of space on subatomic ... 12:53: ... all be over much sooner when the universe is ripped to shreds by the infinitely accelerating subatomic structure of ... 00:05: ... cats and dogs living together and then tragically separated by the infinitely accelerating expansion of space on subatomic ... 12:53: ... all be over much sooner when the universe is ripped to shreds by the infinitely accelerating subatomic structure of ... 10:03: ... be nothing but hopelessly isolated elementary particles separated by infinitely expanding space. That's a hell of a ...
	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? 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? 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 ... 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 ... 05:08: A negative mass apple would still fall to the Earth, and you wouldn’t notice Earth’s infinitesimal repulsion from the apple.
	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. 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 ... 00:29: And every time two particles interact, an infinite number of virtual particles mediate infinite versions of that one interaction.
	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. 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. 02:25: It describes particles as waves of infinite possibility whose observed properties are intrinsically uncertain.
	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. 09:44: Over infinite time, nothing is truly stable. 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. 09:44: Over infinite time, nothing is truly stable. 09:09: ... diffuse and dim as the accelerating expansion of space continues and the infinitely long progression to absolute heat death is all that ... 14:24: If, by contrast, you have an infinitely thin shell of charge surrounding a mass, your g equals 5/3. 09:09: ... diffuse and dim as the accelerating expansion of space continues and the infinitely long progression to absolute heat death is all that ... 15:20: Epsilon Jay asks why electrons are thought of as infinitesimal points.
	2018-08-15: Quantum Theory's Most Incredible Prediction 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 ... 06:35: It seethes with a faint quantum buzz, infinite phantom oscillations that add infinite complication to any electromagnetic interaction. 09:50: ... there really are infinite ways the electron can interact with the EM field, with crazy networks of ... 03:57: And it doesn't really make sense to think of an infinitesimal point as rotating.
	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. 00:16: ... gravitational collapse of a massive body, a point of hypothetical infinite density surrounded by an event ... 07:34: ... so the gravitational and electromagnetic forces have infinite range, and so Gauss's law demands that the mass and charge content of any ... 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. 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. 09:35: 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. 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 cancel out ... 08:28: ... oscillations can be reconfigured with our infinite drumstick to add new particles or remove old ones, for example, to describe a ... 08:46: It's called the field operator, and it is our infinite drumstick. 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 had in an ... 07:21: ... same oscillation by simultaneously hitting the drum everywhere with an infinite drumstick, adding global vibrations with different frequencies that cancel out everywhere ... 07:37: But why exchange a single spatial equation for infinite equations in momentum space? 04:26: Or even better, an infinite, extremely flexible drum skin. 10:26: ... in order to create and annihilate the same particles as we had in an infinite, horizonless ... 06:13: ... perfectly localized position oscillation can also be described as an infinite number of unlocalized momentum ... 06:04: That momentum field also has infinite oscillators, but now each one represents a different possible momentum for the particle. 09:46: OK, so what happens when we add a horizon to our infinite quantum field? 09:35: Infinite spatially undefined particles with defined momenta, and these just happen to cancel each other out, leaving 0 particles or a vacuum. 11:04: So you can be that horizon's drum skin to produce oscillations that are consistent with the infinite, un-horizoned skin. 06:40: The superposition of infinite universe size momentum oscillators-- momentum particles can represent a single spatial oscillator. 09:29: In momentum space, we can think of it as a superposition of infinitely many momentum modes.
	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. 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. 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 ... 14:32: ... had zero mass, so who's to say those rare, zero-mass geckos don't have infinite tensile ... 10:51: So a perfectly specially localized particle is equally an infinite number of momentum particles that themselves occupy all locations in the universe. 10:26: ... perfectly localized at one spot in space, can so be described as infinite oscillations in momentum space, spanning all possible ... 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 us phenomena ... 14:32: ... had zero mass, so who's to say those rare, zero-mass geckos don't have infinite tensile ... 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 ... 14:27: Well, Jaden, the trick is to assume geckos with infinitely high tensile strength. 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 in ...
	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. 14:44: There's one way that the universe is and infinite ways that it isn't.
	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. 02:33: Now, multiply a finite energy density no matter how small by infinity, and you get infinite energy density. 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. 02:42: We'll get back to whether the idea of an infinite vacuum energy is actually possible. 04:39: Long story short-- a crazily high, even infinite, vacuum energy doesn't affect the predictions of quantum field theory. 02:42: We'll get back to whether the idea of an infinite vacuum energy is actually possible. 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? 15:13: 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. 15:00: What I mean by that is that the Big Bang happened everywhere at once, not at an infinitesimal point in space.
	2017-08-30: White Holes 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 ... 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. 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. 05:39: ... traveling at that 45 degree angle takes infinite time to escape the event horizon, and the region beyond that line represents ... 08:18: Light has to traverse infinite time to reach our location. 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. 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.
	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. 03:25: And it can be used to construct infinite Feynman diagrams. 12:19: Mayank, thanks so much for choosing one of the infinite improbable paths that led you to join us. 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. 00:03: ... particle physics by providing a simple system to sort out the infinite possibilities when elementary particles ... 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 ... 07:51: As well as infinite possibilities for particle momenta, we have to consider even impossible faster than light paths.
	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 ... 08:54: ... mass using quantum electrodynamics, you get that the electron has infinite extra ... 04:52: In fact, according to some interpretations, all infinite intermediate events that lead to the same final result actually do happen, sort of. 09:44: ... electrons do not have infinite mass, and we know that because we've measured that mass, although any ... 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 popping ... 10:19: In a sense, you capture the theoretical infinite terms within an experimental finite number. 04:49: There are literally infinite ways that scattering could have occurred.
	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. 10:54: However, unlike the ridiculous infinite trajectories a particle can take, those infinite events don't cancel out nearly so neatly. 10:37: If we have to take those infinite simultaneous paths seriously, then we also have to take those infinite intervening events seriously. 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 final ... 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. 07:13: Now, when Feynman used this action quantity to figure out the probability amplitudes of his infinite paths, something amazing happened. 08:56: It's not just that a particle can travel infinite physical paths. 11:04: In fact, they lead to rampant, uncontrolled infinite probabilities. 10:37: If we have to take those infinite simultaneous paths seriously, then we also have to take those infinite intervening events seriously. 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. 09:00: Also, infinite things can happen to the particle on the way. 10:54: However, unlike the ridiculous infinite trajectories a particle can take, those infinite events don't cancel out nearly so neatly. 03:27: But when something travels through empty space, it's like it's traveling through infinitely packed barriers, each with infinite slits.
	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. 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: ... keep releasing energy as light infinitely, and sink lower and lower, to infinite negative energy ... 13:12: ... "universe" to be the bounded post-inflationary pocket in a single true infinite ... 06:38: ... keep releasing energy as light infinitely, and sink lower and lower, to infinite negative energy ... 13:12: ... "universe" to be the bounded post-inflationary pocket in a single true infinite universe? ... 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. 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. 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.
	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 ... 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.
	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. 11:56: ... Lloyd asks, "Is the calculated infinite density of the core of a black hole an artifact of the limitations of three ... 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. 02:01: Guys, meet Kelsey Houston Edwards of the new PBS show, "Infinite Series." Hey, Kelsey. 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. 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. 01:14: Infinite force means infinite acceleration, which means-- well, physics breaks. 07:05: And just as with the Newtonian case, this gravitational singularity can only exist if infinite densities are possible. 00:04: The point of infinite density at the core of a black hole, but also so much more. 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. 07:13: But unlike Newton's laws of gravity, the Schwarzschild metric actually tells us whether or not that infinite density is expected. 11:14: But can that point of infinite density really exist? 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. 07:00: This gives us the same infinite gravitational pull as the Newtonian singularity. 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. 07:00: This gives us the same infinite gravitational pull as the Newtonian singularity. 02:01: Guys, meet Kelsey Houston Edwards of the new PBS show, "Infinite Series." Hey, Kelsey. 03:47: Guys, you should check out Kelsey's show "infinite Series," where she goes into much more depth on the nature of singularities. 12:18: Be sure to check out the PBS "Infinite Series" episode dealing with earthly singularities right here. 02:01: Guys, meet Kelsey Houston Edwards of the new PBS show, "Infinite Series." Hey, Kelsey. 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 t and ... 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 ... 02:54: It's possible to pass their time zones infinitely quickly, but only because of your choice of spherical coordinates. 09:42: ... and so it can hang out at the event horizon, which also only exists at 1 infinitely stretched out ... 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 more ... 09:42: ... and so it can hang out at the event horizon, which also only exists at 1 infinitely stretched out ...
	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 ... 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. 03:10: It has a point of infinite density, the singularity, and an event horizon a bit further out. 11:19: Then our Penrose diagram blooms outwards to include potentially infinite parallel regions of space-time. 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 the ...
	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. 11:41: ... I said that the assumption of infinite divisibility of space was a problem with the scenario in this paradox, that the real ... 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 tortoise's ... 12:06: ... it doesn't need to take an infinite amount of time to complete an infinite number of tasks, as long as the time taken for those tasks gets ... 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. 05:58: It paints the crazy picture of a universe full of infinite extreme energy gamma radiation. 07:09: ... spectrum, he needed some sort of math trick to count the supposedly infinite energy ... 05:58: It paints the crazy picture of a universe full of infinite extreme energy gamma radiation. 00:59: Each of those steps is shorter than the last, but there are still an infinite number of them. 00:53: To overtake a tortoise, you need to travel to its previous position infinite times. 01:05: There are a few problems with this paradox, but one is that it assumes that space is infinitely divisible. 06:19: The problem turned out to be that in classical physics, everything can be infinitely divided. 06:51: ... Rayleigh and Jeans were chasing Zeno's tortoise, infinitely dividing the smallest remaining energy states, and so never ever finding ... 06:19: The problem turned out to be that in classical physics, everything can be infinitely divided. 06:51: ... Rayleigh and Jeans were chasing Zeno's tortoise, infinitely dividing the smallest remaining energy states, and so never ever finding an end ... 01:05: There are a few problems with this paradox, but one is that it assumes that space is infinitely divisible. 06:28: The Rayleigh-Jeans calculation allows particles to vibrate with any amount of energy, all the way down to infinitesimally tiny wiggles.
	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 05:29: ... for how many of those infinite future doublings will regular matter and energy have any significant ... 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.
	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. 04:16: Geometry works just as you learned in school, and a flat universe is still infinite-- open-- in all three spatial dimensions. 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 ... 04:16: Geometry works just as you learned in school, and a flat universe is still infinite-- open-- in all three spatial dimensions. 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 ... 04:04: Such a universe is infinitely large, or "open." But "k equals 0" means the universe is flat. 04:51: An underdense, infinitely expanding universe should be hyperbolic. 06:13: This is totally inconsistent with the level of positive curvature we'd expect from an infinitely expanding universe. 04:51: An underdense, infinitely expanding universe should be hyperbolic. 06:13: This is totally inconsistent with the level of positive curvature we'd expect from an infinitely expanding universe. 04:51: An underdense, infinitely expanding universe should be hyperbolic. 06:13: This is totally inconsistent with the level of positive curvature we'd expect from an infinitely expanding universe. 04:04: Such a universe is infinitely large, or "open." But "k equals 0" means the universe is flat.
	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. 03:53: ... the future expansion rate of the universe to slowly grind to a halt over infinite time. ...
	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? 11:45: If our universe is infinite, then you can compact it as much as you like and it will still be infinite. 00:10: The Big Bang Theory suggests that once the entire universe was compacted into an infinitely small speck at the beginning of time.
	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. 05:53: ... invisible and infinite ocean of some sort of charge that we've never heard of all invented so ... 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 ...
	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. 07:58: And yet, below the star's surface, their lurks the potential event horizon, the surface of infinite time dilation. 10:05: On our clock, the singularity forms infinitely far in the future. 09:29: But what happens to these as the star approaches an infinitesimal point, the Planck scale?
	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. 10:19: 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? 09:53: Because it would take infinite energy to make any mass. 10:41: Denny Hiu asks how a universe that is already infinite expand? 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. 09:56: There is only massless particles traveling at infinite speed. 10:19: However, the paradox itself tells us that an infinite speed limit is impossible. 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. 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. 10:52: Imagine an infinitely long ruler with markings spaced at every inch. 10:11: The universe is an infinitesimal here-and-now This is all pretty paradoxical.
	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? 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. 00:41: Are you sure you measured the universe's curvature with infinite precision? 05:18: Measurements of the distribution of galaxies and the CMB confirm this flatness with very high, but not 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. 05:49: 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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