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	2022-08-03: What Happens Inside a Proton? 11:28: ... each time step results a complex-valued  phase shift at each spatial point. Those   complex numbers are fine in the Feynman ...
	2022-06-15: 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 2-D surface.   The power of ...
	2022-05-04: 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 3-D analog of our surface of a ...
	2022-04-20: 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. ...
	2022-03-23: Where Is The Center of The Universe? 06:02: Those three spatial dimensions just loop back on themselves.
	2022-02-10: 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 ...
	2022-01-12: 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).
	2021-12-20: 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 ...
	2021-11-17: 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 Strominger-Vafa or the 3 dimensions of regular black holes, let’s think about a 1-D 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. 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 reason to think ... 11:54: Instead of the 4 spatial dimensions of a Strominger-Vafa or the 3 dimensions of regular black holes, let’s think about a 1-D 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.
	2021-10-20: 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.
	2021-07-13: 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.
	2021-04-21: The NEW Warp Drive Possibilities 03:37: It includes a comfortable, flat region of space surrounded by a region of extreme spatial curvature.
	2021-03-16: 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 ...
	2021-03-09: How Does Gravity Affect Light? 06:40: That temporal component is rotated into the downward spatial direction, which translates into falling.
	2021-02-24: 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?
	2021-01-19: 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 ...
	2020-12-15: 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 ... 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 ...
	2020-12-08: 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 ...
	2020-10-20: 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 ...
	2020-06-30: 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.
	2020-05-27: 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, coiled-up tight at every point in the extended 3-D ... 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 dimensions. ... 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, coiled-up tight at every point in the extended 3-D ... 03:24: In general, gravity drops off as 1/r to some power - and that power is the number of spatial dimensions minus one.
	2020-04-22: Will Wormholes Allow Fast Interstellar Travel? 03:33: ... instant in time. The technical name is an embedding diagram - a 2-D spatial sheet sliced out of 4-D ... 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 ... 03:33: ... instant in time. The technical name is an embedding diagram - a 2-D spatial sheet sliced out of 4-D ...
	2020-04-07: 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 ...
	2020-02-18: Does Consciousness Influence Quantum Mechanics? 15:19: So by the mathematical definition, a spatially-farying constant would be a field.
	2020-02-11: 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 ...
	2019-11-04: 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.
	2019-10-15: 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 - 3-D spatial metrics, 3-D space slices cut out of 4-D spacetime. 09:04: ... they could fully solve the Wheeler-deWitt equation by representing spatial metrics using Ashketar's spin ... 11:37: ... LQG has background independence in terms of different 3-D spatial geometries, it’s not actually clear that this independence extends to ... 04:30: ... and momentum of quantum mechanics literally describes location on a spatial coordinate system and the change in that location over ... 11:37: ... LQG has background independence in terms of different 3-D spatial geometries, it’s not actually clear that this independence extends to 4-D ... 06:07: ADM starts by defining this abstract space of spaces - 3-D spatial metrics, 3-D space slices cut out of 4-D spacetime. 09:04: ... they could fully solve the Wheeler-deWitt equation by representing spatial metrics using Ashketar's spin ...
	2019-07-18: 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 ... 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 ...
	2019-04-24: 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 ...
	2019-04-10: The Holographic Universe Explained 11:04: In good string-theorist 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 3-D 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 "3-D" ... 11:04: In good string-theorist style, Maldacena defined incorporated that scale factor into be a new spatial dimension. 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 "3-D" ... 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 3-D surface.
	2019-04-03: The Edge of an Infinite Universe 05:49: ... while the vertical-ish lines are set locations in space in only one spatial ... 11:40: So this disk can represent an infinite anti-de 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. 05:49: ... while the vertical-ish lines are set locations in space in only one spatial dimension. ... 11:40: So this disk can represent an infinite anti-de Sitter universe with 2 spatial dimensions at a single instant in time.
	2019-01-09: 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 ... 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 ... 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 ...
	2018-12-20: 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 Calabi-Yau manifolds. 15:37: ... last week we peered into the looking-glass and saw how a universe that's spatially reflected in a mirror has fundamentally different laws of physics to our ... 07:25: ... theory, or at least at the simplicity of just one extra circular spatial dimension. ... 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 Calabi-Yau manifolds. 15:37: ... last week we peered into the looking-glass and saw how a universe that's spatially reflected in a mirror has fundamentally different laws of physics to our ...
	2018-12-12: 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 ...
	2018-11-14: Supersymmetric Particle Found? 15:43: It may have implications for the single extra extended spatial dimension of M-theory, but I need to research that more.
	2018-11-07: 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. 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.
	2018-10-18: What are the Strings in String Theory? 05:05: ... single framework of m-theory, all for the low price of adding only one spatial dimension for an 11-dimensional ... 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. 05:05: ... single framework of m-theory, all for the low price of adding only one spatial dimension for an 11-dimensional ... 11:40: Modern M theory proposes an additional large spatial dimension. 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.
	2018-10-10: 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 ...
	2018-10-03: 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 three-dimensional brane, a 3-brane, embedded in a space-time 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. 05:36: One fun way to do that is to throw in an extra spatial dimension. 08:14: ... observable universe exists, can actually expand into the extra fourth spatial dimension. ... 08:41: ... the gravitational field can extend into this hypothetical extra spatial dimension, then gravitational waves should lose energy to that extra dimension as ... 02:26: ... adding the extra spatial dimensions beyond the usual three could actually explain a lot, from the difference ... 04:21: But even there, Einstein's general relativity describes gravity perfectly with three spatial dimensions. 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 three-dimensional brane, a 3-brane, embedded in a space-time 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 ... 07:48: 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 ... 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. 07:48: In our hypothetical universe with four spatial dimensions, gravity is already weak on the scale of the solar system and the galaxy. 10:49: There was no observable leakage of gravity into extra spatial dimensions, pretty much ruling this out as an explanation for dark energy. 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.
	2018-08-23: 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.
	2018-05-16: 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. 02:45: For example, a long road in the middle of nowhere is continuously symmetric under spatial translations in the direction of the road.
	2018-03-15: Hawking Radiation 04:11: But spatial curvature can mess with the balance of the underlying quantum field modes by introducing horizons.
	2018-02-14: What is Energy? 10:06: For example, the law of conservation of momentum is due to spatial translation symmetry.
	2018-01-17: 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. 07:37: But why exchange a single spatial equation for infinite equations in momentum space? 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. 06:24: Now, each one of these momentum modes exists at all spatial points in the universe. 05:56: So let's take our spatial quantum field-- our drum skin, with its single, localized particle, and transform to 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.
	2017-12-06: 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 ...
	2017-11-08: Zero-Point 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.
	2017-11-02: The Vacuum Catastrophe 05:26: It should also massively increase the spatial curvature of the universe.
	2017-10-25: The Missing Mass Mystery 11:29: Yet, it would still push the universe towards positive spatial curvature.
	2017-10-04: 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.
	2017-09-28: 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. 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.
	2017-08-02: 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.
	2017-03-29: 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. 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. 12:20: It doesn't also have to be a regular crystal that has a repeating spatial pattern. 09:47: Below the event horizon, there's still a sense of spatial upness and downness.
	2017-01-25: 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 ...
	2017-01-19: 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.
	2017-01-04: 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.
	2016-12-21: Have They Seen Us? 06:24: That is to increase the spatial resolution of your observations.
	2016-11-16: Strange Stars 11:07: It's definitely spatially three-dimensional.
	2016-09-21: Quantum Entanglement and the Great Bohr-Einstein Debate 10:41: ... bridges, wormholes that allows instantaneous contact even between great spatial ...
	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. 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 positive-curvature 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. 02:35: k is, in a sense, the shape of the universe-- its spatial curvature, as well as its spatial extent, finite or infinite. 02:44: Notice I said "spatial" curvature. 04:13: Zero spatial curvature, at any given time. 04:16: Geometry works just as you learned in school, and a flat universe is still infinite-- open-- in all three spatial dimensions. 02:35: k is, in a sense, the shape of the universe-- its spatial curvature, as well as its spatial extent, finite or infinite. 02:53: But the spatial geometry of the universe at a fixed instant in time can be flat or curved. 03:05: "k equals plus 1" means the universe has a positive-curvature spatial geometry. 03:12: 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.
	2016-04-13: Will the Universe Expand Forever? 08:35: It describes the shape of the universe-- its spatial curvature.
	2016-04-06: 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 ... 11:10: So constant time spatial curvature, which is different to the curvature of spacetime. 11:39: ... spatial curvature refers to the fact of the geometry of space on the largest scales in the ...
	2016-03-16: Why is the Earth Round and the Milky Way Flat? 02:48: Gravity exerts itself equally along the three spatial dimensions.
	2016-01-27: The Origin of Matter and Time 01:37: So we define a thing as its complete spatial and temporal existence.
	2015-12-09: 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. 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.
	2015-08-19: 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 ... 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.
	2015-08-05: 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.
	2015-07-29: 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 ... 06:48: ... or even the pictures we sometimes use on this show, they all suggests spatial curvature only, so they're somewhat ... 07:50: ... straight, radially inward trajectories along which you would see spatial speed increase, or pretty much anything else that you would otherwise ... 01:54: ... lines of other inertial observers are straight, indicating constant spatial velocity. ... 02:08: ... other force, that would cause some world lines to become curved, i.e, spatially ... 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: ... into 3D spatial and temporal terms, what you find is planetary orbits or spatially straight, radially inward trajectories along which you would see spatial ... 02:08: ... other force, that would cause some world lines to become curved, i.e, spatially accelerated. ... 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: ... into 3D spatial and temporal terms, what you find is planetary orbits or spatially straight, radially inward trajectories along which you would see spatial speed ...
	2015-07-22: SPECIAL ANNOUNCEMENT + Flat Spacetime Geometry Comments 04:41: They're moving at constant spatial velocity.
	2015-04-22: Are Space and Time An Illusion? 06:32: So why do we perceive reality in such a vividly spatial and temporal way?

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