
20220803: What Happens Inside a Proton?
 11:28: ... each time step results a complexvalued phase shift at each spatial point. Those complex numbers are fine in the Feynman ...


20220615: Can Wormholes Solve The Black Hole Information Paradox?
 06:01: ... that reveals that a particular type of universe with three spatial dimensions is encoded on its own 2D surface. The power of ...


20220504: Space DOES NOT Expand Everywhere
 02:24: ... a metric in GR is the coordinate system of a chunk of spacetime with 3 spatial and 1 temporal ...
 02:38: ... Earth, the FLRW metric gives the geometry or shape of the universe. The spatial part of that geometry could be the 3D analog of our surface of a ...


20220420: Does the Universe Create Itself?
 15:24: ... energy. If you just consider the positive effect of gravity, then the spatial geometry dictates the final fate. But dark energy screws everything up. ...


20220323: Where Is The Center of The Universe?
 06:02: Those three spatial dimensions just loop back on themselves.


20220210: The Nature of Space and Time AMA
 00:03: ... the big difference is that it became impossible to define a single spatial stage a single slice of space as some kind of definite now or ...


20220112: How To Simulate The Universe With DFT
 03:05: Of course the real universe has 3 spatial dimensions, so for most real applications we’d want Psi(x,y,z).


20211220: What Happens If A Black Hole Hits Earth?
 16:33: ... of the string vibrations. It’s holographically projected into 2 spatial dimensions, and in its experience it keeps falling. Meanwhile from the ...


20211117: Are Black Holes Actually Fuzzballs?
 07:13: ... this for the somewhat unrealistic case of a black hole horizon with 4 spatial dimensions, but it was a decisive step and it gave us a compelling ...
 11:54: Instead of the 4 spatial dimensions of a StromingerVafa or the 3 dimensions of regular black holes, let’s think about a 1D black hole.
 12:20: In string theory we have extra compact dimensions  spatial dimensions that are coiled up on the Planck scale so we can’t see them.
 12:43: The extra compact dimensions contract and pinch off, so all spatial dimensions end in that direction.


20211020: Will Constructor Theory REWRITE Physics?
 09:27: And she argues that only a "superinformation medium"  aka a quantum field  could mediate the entanglement of two spatially separated qubits.


20210713: Where Are The Worlds In Many Worlds?
 11:02: Well, sort of  in the sense that the position wavefunctions of the two yous can be mapped to these spatial locations.


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


20210316: The NEW Crisis in Cosmology
 13:38: ... It's the minus the sum of squares of the x, y, and z spatial intervals, plus the square of time interval times the speed of ...


20210309: How Does Gravity Affect Light?
 06:40: That temporal component is rotated into the downward spatial direction, which translates into falling.


20210224: Does Time Cause Gravity?
 07:39: If photons are already fully rotated into the spatial direction, how is it that they’re also affected by gravitational fields?


20210119: Can We Break the Universe?
 10:03: ... ladder also has a certain length in the spatial direction  initially longer than the barn, but when the ladder starts ...


20201215: The Supernova At The End of Time
 13:15: "You could say the forwardness of memory is a spatial phenomenon.
 13:37: ... information of a future collision is spread out, spatially, before the collision: to "remember" the future collision you have to ...


20201208: Why Do You Remember The Past But Not The Future?
 09:54: ... universe started in a state of extremely low entropy  spatially separated regions were definitely uncorrelated with each other, and even ...


20201020: Is The Future Predetermined By Quantum Mechanics?
 14:59: ... it would need to be the instantaneous state of the brain, the momentary spatial configuration of its particles at that instant that gives rise to our ...


20200630: Dissolving an Event Horizon
 12:00: Then the third dimension is just a way to represent the strength of the spatial curvature and the connections between different regions.


20200527: Does Gravity Require Extra Dimensions?
 03:24: In general, gravity drops off as 1/r to some power  and that power is the number of spatial dimensions minus one.
 03:36: Newton’s inverse square law for gravity tells us there are 2+1 = 3 spatial dimensions.
 04:20: Now we perceive the 3rd dimension, but perhaps our 3 spatial dimensions are similarly embedded in a higher dimensional space that we can’t perceive.
 04:32: ... wave detection from LIGO seemed to rule out the possibility of extra spatial ...
 04:48: And by large I mean they stretch out over astronomical scales like the familiar 3 spatial dimensions.
 05:45: And that’s the sense in which there may be more than 3 spatial dimensions in this universe.
 05:57: ... string theory, and in modern superstring theory there are 6 additional spatial dimensions, coiledup tight at every point in the extended 3D ...


20200422: Will Wormholes Allow Fast Interstellar Travel?
 03:33: ... instant in time. The technical name is an embedding diagram  a 2D spatial sheet sliced out of 4D ...
 03:45: ... keep time frozen for the moment and add back the 3rd spatial dimension. The ring of the wormhole is actually a sphere the size of the ...


20200407: How We Know The Earth Is Ancient
 00:00: ... call deep time is very recent  as recent as our discovery of the true spatial vastness of our universe. And it came as scientists tried to measure the ...


20200218: Does Consciousness Influence Quantum Mechanics?
 15:19: So by the mathematical definition, a spatiallyfarying constant would be a field.


20200211: Are Axions Dark Matter?
 14:39: ... inflation. Of course all of this is assuming that the universe is spatially finite. The simplest interpetation of the cosmological equations derived ...


20191104: Why We Might Be Alone in the Universe
 14:32: Some One asks if a circle in 2 spatial dimensions would allow for closed time like curves.


20191015: Loop Quantum Gravity Explained
 04:30: ... and momentum of quantum mechanics literally describes location on a spatial coordinate system and the change in that location over ...
 06:07: ADM starts by defining this abstract space of spaces  3D spatial metrics, 3D space slices cut out of 4D spacetime.
 09:04: ... they could fully solve the WheelerdeWitt equation by representing spatial metrics using Ashketar's spin ...
 11:37: ... LQG has background independence in terms of different 3D spatial geometries, it’s not actually clear that this independence extends to ...


20190718: Did Time Start at the Big Bang?
 04:38: ... 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 ...
 05:15: ... in any one place because a point is zero dimensional there weren't spatial dimensions for it to happen in At the same time we say the Big Bang ...


20190424: No Dark Matter = Proof of Dark Matter?
 00:03: ... cook for 20 informs is that while we may feel that we live in a three spatial dimension universe serve up down left right forward back we're actually ...


20190410: The Holographic Universe Explained
 11:04: In good stringtheorist style, Maldacena defined incorporated that scale factor into be a new spatial dimension.
 13:41: ... doesn’t appear to be negatively curved AdS space, nor does it have 4 spatial dimensions as in Maldecena’s ...
 15:41: Part of the confusion comes from the fact that Maldacena's derivation is for a volume with 4 spatial dimensions, which would have a 3D surface.
 16:12: So first  the "surface" in current AdS/CFT spacetime is 3+1. 3 spatial, one temporal dimensions.
 16:27: ... of AdS/CFT is that gravity arises naturally when you add an extra spatial dimension, which ends up looking like the volume contained by the "3D" ...


20190403: The Edge of an Infinite Universe
 05:49: ... while the verticalish lines are set locations in space in only one spatial ...
 11:40: So this disk can represent an infinite antide Sitter universe with 2 spatial dimensions at a single instant in time.
 12:43: They give you a cylinder and representing an AdS spacetime with 2 spatial and one temporal dimensions – let’s call that 2+1 dimension.


20190109: Are Dark Matter And Dark Energy The Same?
 11:39: Just quickly, the density fluctuations seen in the afterglow of the Big Bang reveal a universe that is spatially flat.
 11:47: ... the energy of both regular and dark matter, are needed to explain this spatially flat ...


20181220: Why String Theory is Wrong
 07:25: ... theory, or at least at the simplicity of just one extra circular spatial ...
 07:41: Imagine only one extended and one compactified spatial dimension.
 12:43: In all superstring theories the extra spatial dimensions are wrapped, not in simple loops, but in complicated geometries called CalabiYau manifolds.
 15:37: ... last week we peered into the lookingglass and saw how a universe that's spatially reflected in a mirror has fundamentally different laws of physics to our ...


20181212: Quantum Physics in a Mirror Universe
 00:02: ... to save us in the end parity transformations involve the flipping of spatial axis if we define the mirror to be in the XY plane reflection sin z2 ...


20181114: Supersymmetric Particle Found?
 15:43: It may have implications for the single extra extended spatial dimension of Mtheory, but I need to research that more.


20181107: Why String Theory is Right
 01:14: And, by the way, these strings exist in six compact spatial dimensions on top of the familiar three.
 11:57: ... and the photon, out of string theory for a very specific number of spatial dimensions, nine to be ...
 12:23: Our universe has three spatial dimensions.


20181018: What are the Strings in String Theory?
 05:05: ... single framework of mtheory, all for the low price of adding only one spatial dimension for an 11dimensional ...
 10:13: In fact, the theory only works in precisely nine spatial dimensions, plus one for time, plus one for M theory, which we'll come back to.
 11:40: Modern M theory proposes an additional large spatial dimension.


20181010: Computing a Universe Simulation
 12:07: ... waves were used to search for and rule out the existence of an extra spatial dimension beyond our familiar ...


20181003: How to Detect Extra Dimensions
 02:26: ... adding the extra spatial dimensions beyond the usual three could actually explain a lot, from the ...
 04:21: But even there, Einstein's general relativity describes gravity perfectly with three spatial dimensions.
 05:36: One fun way to do that is to throw in an extra spatial dimension.
 05:48: But you restrict all the other stuff in the universe matter, radiation, astronomers to only three spatial dimensions.
 06:20: But in string theory, all but three spatial dimensions of the brane are inaccessible.
 06:25: They're finite and coiled up on themselves, compactified, allowing us to cram them into three spatial dimensions.
 06:35: ... a threedimensional brane, a 3brane, embedded in a spacetime with four spatial dimensions, where the extra dimension of space is extended rather than ...
 06:55: ... just right, and you get normal physics for matter and radiation in three spatial dimensions for example, the usual inverse square law for ...
 07:05: On some spatial scales, you even get the inverse square law for gravity.
 07:10: But on other spatial scales, gravity can behave very differently.
 07:48: In our hypothetical universe with four spatial dimensions, gravity is already weak on the scale of the solar system and the galaxy.
 07:59: ... square law on galactic scales, where it's sort of coupled to the three spatial dimensions of the ...
 08:14: ... observable universe exists, can actually expand into the extra fourth spatial ...
 08:41: ... the gravitational field can extend into this hypothetical extra spatial dimension, then gravitational waves should lose energy to that extra ...
 09:29: Does that match what you expect in a universe with three spatial dimensions?
 10:49: There was no observable leakage of gravity into extra spatial dimensions, pretty much ruling this out as an explanation for dark energy.


20180823: How Will the Universe End?
 15:56: But that spatial sprint really just tells us the probability of finding the electron, say, here or here or here.


20180516: Noether's Theorem and The Symmetries of Reality
 02:45: For example, a long road in the middle of nowhere is continuously symmetric under spatial translations in the direction of the road.
 03:17: We have symmetry to spatial translation.


20180315: Hawking Radiation
 04:11: But spatial curvature can mess with the balance of the underlying quantum field modes by introducing horizons.


20180214: What is Energy?
 10:06: For example, the law of conservation of momentum is due to spatial translation symmetry.


20180117: Horizon Radiation
 05:56: So let's take our spatial quantum field our drum skin, with its single, localized particle, and transform to momentum space.
 06:24: Now, each one of these momentum modes exists at all spatial points in the universe.
 06:31: ... with the right weightings, they cancel out everywhere except at the spatial location of the original ...
 06:40: The superposition of infinite universe size momentum oscillators momentum particles can represent a single spatial oscillator.
 07:37: But why exchange a single spatial equation for infinite equations in momentum space?
 09:35: Infinite spatially undefined particles with defined momenta, and these just happen to cancel each other out, leaving 0 particles or a vacuum.


20171206: Understanding the Uncertainty Principle with Quantum Fourier Series
 11:01: ... fields in this strange momentum space, by adding and removing these spatially infinite particles, that we can describe how the quantum vacuum changes ...


20171108: ZeroPoint Energy Demystified
 05:36: That means the vacuum energy between Casimir plates still produces positive spatial curvature, not the negative curvature required for warp drives.


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


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


20171004: When Quasars Collide STJC
 04:12: In fact, the spatial resolution is equivalent to what you would get with a telescope equal in size to the separation of the radio antenna.


20170928: Are the Fundamental Constants Changing?
 07:57: Looking in the new direction, they found that Alpha was larger in the past, suggesting both a temporal and a spatial variation.
 08:05: The significance of the spatial variation was claimed to be 4 sigma so still tentative.


20170802: Dark Flow
 10:53: Well, actually, the spatial positions and even directions of motions of particles in the diagrams don't mean much at all.


20170329: How Time Becomes Space Inside a Black Hole
 05:46: Our future light cone stares fixedly forwards, encompassing all spatial directions equally.
 09:02: Those directions, those spatial freedoms, are now described by what was once the time coordinate.
 09:47: Below the event horizon, there's still a sense of spatial upness and downness.
 12:20: It doesn't also have to be a regular crystal that has a repeating spatial pattern.


20170125: Why Quasars are so Awesome
 01:57: ... were only blobby because those early radio antennae had some pretty bad spatial resolution, making it difficult to pinpoint exactly where on the sky ...


20170119: The Phantom Singularity
 09:17: And once inside, inward spatial movement continues to be the only way to fuel the ticking of an object's proper time clock.


20170104: How to See Black Holes + Kugelblitz Challenge Answer
 03:14: The effect is a telescope thousands of kilometers in diameter, at least in terms of its spatial resolution.


20161221: Have They Seen Us?
 06:24: That is to increase the spatial resolution of your observations.


20161116: Strange Stars
 11:07: It's definitely spatially threedimensional.


20160921: Quantum Entanglement and the Great BohrEinstein Debate
 10:41: ... bridges, wormholes that allows instantaneous contact even between great spatial ...


20160420: 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.
 02:44: Notice I said "spatial" curvature.
 02:53: But the spatial geometry of the universe at a fixed instant in time can be flat or curved.
 03:05: "k equals plus 1" means the universe has a positivecurvature spatial geometry.
 03:12: Spatial snapshots of the cosmos at an instant in time will be curved like the surface of a sphere except the 3D surface of a 4D hypersphere.
 03:39: But the total spatial volume of such a universe is finite.
 04:13: Zero spatial curvature, at any given time.
 04:16: Geometry works just as you learned in school, and a flat universe is still infinite open in all three spatial dimensions.


20160413: Will the Universe Expand Forever?
 08:35: It describes the shape of the universe its spatial curvature.


20160406: We Are Star Stuff
 11:10: So constant time spatial curvature, which is different to the curvature of spacetime.
 11:39: ... spatial curvature refers to the fact of the geometry of space on the largest ...


20160316: Why is the Earth Round and the Milky Way Flat?
 02:48: Gravity exerts itself equally along the three spatial dimensions.


20160127: The Origin of Matter and Time
 01:37: So we define a thing as its complete spatial and temporal existence.


20151209: How to Build a Black Hole
 04:16: Every spatial location and every momentum location connected to those special locations contains a neutron.
 07:06: If we can somehow add more matter to a neutron star throw another star at it, maybe it won't get spatially larger.


20150819: Do Events Inside Black Holes Happen?
 03:24: According to observers like the monkey who are at those events, those events take place at spatial locations inside that black blob we see in the sky.
 03:58: ... blob you see in the sky is just what it ends up looking like in ordinary spatial and temporal terms when you delete entire occurrences from every ...


20150805: What Physics Teachers Get Wrong About Tides!
 12:33: So you down project everything into 3D spatial and temporal terms with respect to that not inertial frame.


20150729: General Relativity & Curved Spacetime Explained!
 01:54: ... lines of other inertial observers are straight, indicating constant spatial ...
 02:08: ... other force, that would cause some world lines to become curved, i.e, spatially ...
 06:48: ... or even the pictures we sometimes use on this show, they all suggests spatial curvature only, so they're somewhat ...
 07:07: ... it's curved time that makes the free fall orbits of satellites looks spatially circular in frames of reference that cover too big a space time ...
 07:50: ... when you translate those geodesics into 3D spatial and temporal terms, what you find is planetary orbits or spatially ...


20150722: SPECIAL ANNOUNCEMENT + Flat Spacetime Geometry Comments
 04:41: They're moving at constant spatial velocity.


20150422: Are Space and Time An Illusion?
 06:32: So why do we perceive reality in such a vividly spatial and temporal way?
