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	2022-10-26: Why Did Quantum Entanglement Win the Nobel Prize in Physics? 18:49: ... spurious spaces that appear when you choose a coordinate system whose dimensions extend  beyond the physical ...
	2022-10-19: The Equation That Explains (Nearly) Everything! 07:51: ... whatever was written has to be repeated several times depending on the dimensions of spacetime, the number of charges, the number of different particles, ...
	2022-09-28: Why Is 1/137 One of the Greatest Unsolved Problems In Physics? 11:20: ... example, the speed of light is the translation  factor between the dimensions of space and time in relativity; it’s also the relationship  ... 09:15: The weirdest thing is that it’s dimensionless. 11:20: ... example, the speed of light is the translation  factor between the dimensions of space and time in relativity; it’s also the relationship  ...
	2022-08-03: What Happens Inside a Proton? 11:28: ... ingenious yet. We’re going to pretend that time is just another dimension of space.   This operation is called the Wick rotation and ...
	2022-07-20: What If We Live in a Superdeterministic Universe? 08:18: Let’s play out the Bell test on something called a space-time diagram - with one dimension of space only on the x axis and time on the y.
	2022-06-15: Can Wormholes Solve The Black Hole Information Paradox? 06:01: ... that a   particular type of universe with three spatial  dimensions is encoded on its own 2-D surface.   The power of AdS/CFT ...
	2022-05-04: Space DOES NOT Expand Everywhere 02:24: ... coordinate system of a chunk of spacetime with 3 spatial and 1 temporal dimensions. ... 03:48: ... points is the sum of the squares of x, y & z, but here adding the dimension of time. And this thing is the scale factor, which represents the ... 07:12: ... try something else. Lose another dimension of space so the universe becomes an expanding ring instead of a ,sphere, ... 02:24: ... coordinate system of a chunk of spacetime with 3 spatial and 1 temporal dimensions. ...
	2022-03-23: Where Is The Center of The Universe? 04:43: In order to do that we need to lose a dimension. 04:54: But for a 2-D being living on that surface, those two dimensions are all that exists. 05:37: So could it be that there’s a higher dimensional space in which our 4-D hypersphere lives? 06:02: Those three spatial dimensions just loop back on themselves. 06:16: So far we’ve ignored the dimension of time. 06:29: So, very crudely, we can think of the radial direction as the dimension of time. 06:34: ... would be more accurate to say that the radial dimension of this expanding hypersphere is represented in the math by the scale ... 08:20: In both of these cases there is no geometrical center, even in a fictional higher dimension. 05:37: So could it be that there’s a higher dimensional space in which our 4-D hypersphere lives? 05:43: Could there be an equivalent of “down” in that space that we are just too dimensionally-challenged to point to? 04:54: But for a 2-D being living on that surface, those two dimensions are all that exists. 06:02: Those three spatial dimensions just loop back on themselves.
	2022-03-08: Is the Proxima System Our Best Hope For Another Earth? 17:58: ... framework, upon which all the quantum weirdness can play - those are the dimensions of space and ...
	2022-02-10: The Nature of Space and Time AMA 00:03: ... start in this description with newtonian physics in which they're the dimensions that form the stage on which the play of the universe takes place in ...
	2022-01-12: How To Simulate The Universe With DFT 02:46: Our Schrodinger equation just dealt with one dimension of space, x. 03:05: Of course the real universe has 3 spatial dimensions, so for most real applications we’d want Psi(x,y,z). 03:50: Every new electron adds 3 new entire dimensions. 03:53: So 26 electrons means 78 dimensions, which for our 10-point grid is 10^78 numbers. 04:52: ... adding dice to this system- every time we add a particle we increase the dimensionality of the ... 06:14: We don’t need a 3-cubed or 9 dimensional equation. 07:25: An equation is separable if the solution along one axis - in one dimension - doesn’t depend on the solutions on any other axis. 07:33: ... we can take an equation for N particles in 3D and reduce it from a 3^N dimensional equation to simply N coupled equations each in ... 08:15: And we can’t reduce the dimensionality by treating particles separately because the Schrodinger equation can’t be made “separable”. 08:49: ... and it’s perhaps the most successful approach to tackling the extreme dimensionality problem when solving realistic quantum ... 13:35: ... by understanding how the universal wavefunction with its insane hyper dimensionality is connected to the narrow sliver of that wavefunction that represents ... 13:51: Our computationally tractable reality, due to its very few dimensions of spacetime. 14:25: Peter, the infinite dimensional universal wavefunction barely contains enough information to describe your generosity. 07:25: An equation is separable if the solution along one axis - in one dimension - doesn’t depend on the solutions on any other axis. 06:14: We don’t need a 3-cubed or 9 dimensional equation. 07:33: ... we can take an equation for N particles in 3D and reduce it from a 3^N dimensional equation to simply N coupled equations each in ... 14:25: Peter, the infinite dimensional universal wavefunction barely contains enough information to describe your generosity. 06:14: We don’t need a 3-cubed or 9 dimensional equation. 07:33: ... we can take an equation for N particles in 3D and reduce it from a 3^N dimensional equation to simply N coupled equations each in ... 14:25: Peter, the infinite dimensional universal wavefunction barely contains enough information to describe your generosity. 04:52: ... adding dice to this system- every time we add a particle we increase the dimensionality of the ... 08:15: And we can’t reduce the dimensionality by treating particles separately because the Schrodinger equation can’t be made “separable”. 08:49: ... and it’s perhaps the most successful approach to tackling the extreme dimensionality problem when solving realistic quantum ... 13:35: ... by understanding how the universal wavefunction with its insane hyper dimensionality is connected to the narrow sliver of that wavefunction that represents ... 08:49: ... and it’s perhaps the most successful approach to tackling the extreme dimensionality problem when solving realistic quantum ... 03:05: Of course the real universe has 3 spatial dimensions, so for most real applications we’d want Psi(x,y,z). 03:50: Every new electron adds 3 new entire dimensions. 03:53: So 26 electrons means 78 dimensions, which for our 10-point grid is 10^78 numbers. 13:51: Our computationally tractable reality, due to its very few dimensions of spacetime.
	2021-12-20: What Happens If A Black Hole Hits Earth? 00:00: ... everything. They're not really like that. I imagined wormholes to other dimensions. ... 16:33: ... of the string vibrations. It’s holographically projected into 2 spatial dimensions, and in its experience it keeps falling. Meanwhile from the perspective ... 00:00: ... everything. They're not really like that. I imagined wormholes to other dimensions. ... 16:33: ... of the string vibrations. It’s holographically projected into 2 spatial dimensions, and in its experience it keeps falling. Meanwhile from the perspective ...
	2021-12-10: 2021 End of Year AMA! 00:02: ... it as many times where branching is just movement in a second time dimension has there been any thought on interpreting it that way and would it ...
	2021-11-17: Are Black Holes Actually Fuzzballs? 07:13: ... 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 ... 11:46: This last thing is the weirdest and coolest thing about fuzzballs, so let’s explore a bit further by dropping a few dimensions. 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. 12:04: 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. 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. 12:29: Adding a single coiled dimension to our 1-D black hole turns our line into a drinking straw. 12:35: The extra dimension is the distance around the straw. 12:43: The extra compact dimensions contract and pinch off, so all spatial dimensions end in that direction. 07:13: ... 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 ... 11:46: This last thing is the weirdest and coolest thing about fuzzballs, so let’s explore a bit further by dropping a few dimensions. 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. 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.
	2021-07-13: Where Are The Worlds In Many Worlds? 02:25: The weirdness of this is clearer if we watch two waves cross each other in one dimension.
	2021-05-19: Breaking The Heisenberg Uncertainty Principle 08:03: ... phase space, this amounts to a shrinking of the uncertainty in one dimension, and a corresponding stretching in the opposite dimension, so that the ...
	2021-05-11: How To Know If It's Aliens 16:32: ... particles as gravitational singularities - wormholes between adjacent dimensions threaded by electromagnetic fields. Turns out particles aren’t that, but ...
	2021-03-16: The NEW Crisis in Cosmology 13:38: ... asks how can we be traveling at the light speed in the time dimension? I'm glad you   asked, because this notion gets stated ... 14:47: ... matter - or whether they're really   the same type of thing - dimensionally speaking. We would also need to justify why the c in ...
	2021-02-24: Does Time Cause Gravity? 00:04: If even a tiny bit of your breakneck temporal velocity leaks into one of the dimensions of space. 02:02: At least, it stays motionless with respect to the three dimensions of space. 02:07: Everything is moving through the dimension of time. 02:13: Let’s have just two dimensions of space and so we have space … for time. 05:31: But if we interpret time as a dimension like space, then a stationary mass really is moving at the fastest possible speed in the temporal direction. 00:04: If even a tiny bit of your breakneck temporal velocity leaks into one of the dimensions of space. 02:02: At least, it stays motionless with respect to the three dimensions of space. 02:13: Let’s have just two dimensions of space and so we have space … for time.
	2021-02-10: How Does Gravity Warp the Flow of Time? 07:56: Now 2 dimensions of space instead of one. 08:07: It’s easier to see if we just take a slice out of this - one dimension of space again. 07:56: Now 2 dimensions of space instead of one.
	2021-01-19: Can We Break the Universe? 04:12: We have time on the y-axis and just one dimension of space on the x. 06:24: We’re still just doing one dimension of space, but now that dimension loops back on itself.
	2020-11-18: The Arrow of Time and How to Reverse It 01:58: ... block universe picture, where we have 2-dimensions of space and one dimension of time, with time flowing ... 02:53: ... And those laws don’t even require time to “flow” - it’s just another dimension like ... 09:39: ... of time to space, but it’s timely to spend time on that fascinating dimension that deserves more space: ...
	2020-11-11: Can Free Will be Saved in a Deterministic Universe? 03:05: Two dimensions of space and one of time, the slices of the block universe represent the causal ordering of the universe.
	2020-10-13: Do the Past and Future Exist? 02:31: Let’s cut out one dimension of space - space then becomes a 2-D slice at a given instant in time. 02:38: Now let’s stack successive instants so that time becomes the 3rd dimension. 03:17: Time is just a dimension like space, and we only observe a flow of time if we play the slices in sequence like a flip-book.
	2020-08-10: Theory of Everything Controversies: Livestream 00:00: ... where it was only about strings because they had reasons why higher dimensional objects didn't exist to brain theory it went from a finite number of ...
	2020-07-28: What is a Theory of Everything: Livestream 00:00: ... equations out of that equation gravity quote unquote albeit and 10 dimensions and supersymmetric pops out general relativity in that guys pops out ...
	2020-06-30: Dissolving an Event Horizon 11:42: Is it, for example, some extra dimension that the black hole leads into? 11:46: ... in those representations take a 3-dimensional space and take a two dimensional slice out of it, so the black hole or wormhole ends are circular instead ... 12:00: Then the third dimension is just a way to represent the strength of the spatial curvature and the connections between different regions. 13:46: Inyobill asks if we’re assuming that the lightest particles are without dimension, so they have an undefined size relative to the universe. 11:46: ... in those representations take a 3-dimensional space and take a two dimensional slice out of it, so the black hole or wormhole ends are circular instead ...
	2020-06-15: What Happens After the Universe Ends? 02:01: This is perhaps the simplest conformal transformation - just multiplying or dividing all dimensions by the same scaling factor. 04:15: ... simplify things by gridding up an imaginary universe with only one dimension of space on the x-axis and one dimension of time on the y, and we choose ... 09:56: That’s for one dimension of space and one dimension of time. 02:01: This is perhaps the simplest conformal transformation - just multiplying or dividing all dimensions by the same scaling factor.
	2020-06-08: Can Viruses Travel Between Planets? 13:42: ... time we explored the possibility that the existence of hidden extra dimensions might change the law of gravity on the smallest scales, and we saw how ...
	2020-05-27: Does Gravity Require Extra Dimensions? 00:16: That steampunk contraption may even reveal the existence of extra dimensions of space. 03:09: ... if our universe had more dimensions, say 4, then gravity would spread out over the “surface” of a 4-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. 03:32: Cool - so we have a way to test how many dimensions there are. 03:36: Newton’s inverse square law for gravity tells us there are 2+1 = 3 spatial dimensions. 03:46: ... with the other forces actually propose that there are MORE than 3 dimensions of space, and that these additional dimensions may explain the hierarchy ... 04:03: So let’s talk about dimensions a bit more. 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: ... detection from LIGO seemed to rule out the possibility of extra spatial dimensions. ... 04:42: But there’s a caveat - that experiment only ruled out extra large dimensions. 04:48: And by large I mean they stretch out over astronomical scales like the familiar 3 spatial dimensions. 04:54: But there’s another possibility - the extra dimensions could be compactified - in other words, wound up very small. 05:03: In that case, gravity would only deviate from the inverse square law on the tiny scales of these compactified dimensions. 05:37: It looks 1-dimensional from a distance, but up close you see that it’s really a 2-D surface - extended in one dimension, but looped in the other. 05:45: And that’s the sense in which there may be more than 3 spatial dimensions in this universe. 05:50: 3 extended dimension, but others that are looped - or “compactified” as we say in physics. 05:57: ... most famous example of compactified extra dimensions is in string theory, and in modern superstring theory there are 6 ... 06:10: ... the idea of compact extra dimensions is much older than string theory - first proposed by Oscar Klein in the ... 06:25: ... we’ve never detected these extra dimensions, they seem a promising potential solution to unifying gravity with the ... 06:36: There are different ways of thinking about how compactified extra dimensions can effect the strength of gravity. 06:42: One is that you can imagine the gravity trying to propagate through multiple dimensions, which would dilute it more quickly. 06:48: We can also think about it as gravity producing excitations within those extra dimensions that sap its energy. 06:55: ... the inverse square law, but would be diluted due to the hidden extra dimensions - and that could explain its relative weakness compared compared to ... 07:06: ... on small scales these extra dimensions would actually change the way gravity falls off with distance - but to ... 07:21: So, to search for these hidden dimensions, we need a way to test gravity on very small length scales. 10:53: ... that’s still quite a bit larger than any likely compactified extra dimensions, but we’d still expect a tiny and perhaps detectable deviation from the ... 11:14: So, how many dimensions are there? 11:32: ... are still nowhere near being able to probe the size-scale of the extra dimensions from string theory though, and so string theorists can keep on ... 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. 00:16: That steampunk contraption may even reveal the existence of extra dimensions of space. 03:09: ... if our universe had more dimensions, say 4, then gravity would spread out over the “surface” of a 4-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. 03:32: Cool - so we have a way to test how many dimensions there are. 03:36: Newton’s inverse square law for gravity tells us there are 2+1 = 3 spatial dimensions. 03:46: ... with the other forces actually propose that there are MORE than 3 dimensions of space, and that these additional dimensions may explain the hierarchy ... 04:03: So let’s talk about dimensions a bit more. 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: ... detection from LIGO seemed to rule out the possibility of extra spatial dimensions. ... 04:42: But there’s a caveat - that experiment only ruled out extra large dimensions. 04:48: And by large I mean they stretch out over astronomical scales like the familiar 3 spatial dimensions. 04:54: But there’s another possibility - the extra dimensions could be compactified - in other words, wound up very small. 05:03: In that case, gravity would only deviate from the inverse square law on the tiny scales of these compactified dimensions. 05:45: And that’s the sense in which there may be more than 3 spatial dimensions in this universe. 05:57: ... most famous example of compactified extra dimensions is in string theory, and in modern superstring theory there are 6 ... 06:10: ... the idea of compact extra dimensions is much older than string theory - first proposed by Oscar Klein in the ... 06:25: ... we’ve never detected these extra dimensions, they seem a promising potential solution to unifying gravity with the ... 06:36: There are different ways of thinking about how compactified extra dimensions can effect the strength of gravity. 06:42: One is that you can imagine the gravity trying to propagate through multiple dimensions, which would dilute it more quickly. 06:48: We can also think about it as gravity producing excitations within those extra dimensions that sap its energy. 06:55: ... the inverse square law, but would be diluted due to the hidden extra dimensions - and that could explain its relative weakness compared compared to ... 07:06: ... on small scales these extra dimensions would actually change the way gravity falls off with distance - but to ... 07:21: So, to search for these hidden dimensions, we need a way to test gravity on very small length scales. 10:53: ... that’s still quite a bit larger than any likely compactified extra dimensions, but we’d still expect a tiny and perhaps detectable deviation from the ... 11:14: So, how many dimensions are there? 11:32: ... are still nowhere near being able to probe the size-scale of the extra dimensions from string theory though, and so string theorists can keep on ... 06:55: ... the inverse square law, but would be diluted due to the hidden extra dimensions - and that could explain its relative weakness compared compared to other ... 10:53: ... law several orders of magnitude larger than the size-scale of those dimensions - depending on other factors - most importantly depending the strength ... 05:57: ... 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.
	2020-05-18: Mapping the Multiverse 03:11: Time flows up - for the most part - and one dimension of space is left or right.
	2020-05-04: How We Know The Universe is Ancient 15:09: ... It's really a 2-D slice out of 4-D spacetime, with time and one dimension of space discarded. But the diagram has 3 dimensions, so what is that ...
	2020-04-28: Space Time Livestream: Ask Matt Anything 00:00: ... know this particular set of rules will generate a universe of three dimensions that have this particular set of laws for gravity for particles ...
	2020-04-22: Will Wormholes Allow Fast Interstellar Travel? 03:33: ... represents the fabric of only 2 dimensions of space at a single instant in time. The technical name is an embedding ... 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 ... 04:08: ... if we unfreeze the wormhole - if we add back the dimension of time - that journey becomes impossible. Fuller and Wheeler proved ... 03:33: ... represents the fabric of only 2 dimensions of space at a single instant in time. The technical name is an embedding ...
	2020-03-31: What’s On The Other Side Of A Black Hole? 01:38: ... map the universe we need 3 dimensions of space instead of two, plus the dimension of time. And maps of the ... 07:57: ... in one direction - to your crushing demise. These lines are the old time dimension, but now traversable in both ... 01:38: ... map the universe we need 3 dimensions of space instead of two, plus the dimension of time. And maps of the ...
	2019-12-17: Do Black Holes Create New Universes? 04:27: Perhaps the configuration of the geometry string theory’s extra dimensions gets shifted - this would do the job.
	2019-12-09: The Doomsday Argument 15:37: ... - for example the 3-torus embedded which is like a donut, but with more dimensions. ...
	2019-11-11: Does Life Need a Multiverse to Exist? 11:24: ... energy, are set by the particular configuration of the extra coiled dimensions of that ...
	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.
	2019-10-21: Is Time Travel Impossible? 12:21: We remain firmly in the grip of that one dimension that we can never halt nor reverse it's pace: time.
	2019-10-15: Loop Quantum Gravity Explained 00:47: ... of conceptual baggage like tiny wiggling strings made of coiled up extra dimensions. ... 05:00: This is completely at odds with general relativity, in which time is treated as just another dimension. 11:13: And without adding big assumptions – like the existence of strings or extra dimensions or supersymmetry. 00:47: ... of conceptual baggage like tiny wiggling strings made of coiled up extra dimensions. ... 11:13: And without adding big assumptions – like the existence of strings or extra dimensions or supersymmetry.
	2019-10-07: Black Hole Harmonics 08:50: ... also get a spin for the final black hole – a so-called dimensionless spin magnitude of .69 – where the spin magnitude can vary between 0– not ...
	2019-09-30: How Many Universes Are There? 05:43: ... on standard ideas, they probably have the same number of dimensions as ours – 3 space, 1 time – but their contents and physics could be very ... 07:27: ... are countless possible minimum-energy configurations of its 6 curled up dimensions. ... 07:46: The vast space of possible configurations of these compact dimensions is referred to as the string landscape. 05:43: ... on standard ideas, they probably have the same number of dimensions as ours – 3 space, 1 time – but their contents and physics could be very ... 07:27: ... are countless possible minimum-energy configurations of its 6 curled up dimensions. ... 07:46: The vast space of possible configurations of these compact dimensions is referred to as the string landscape.
	2019-07-18: Did Time Start at the Big Bang? 05:15: ... points become the same point and three-dimensional space becomes zero dimensional That's the singularity We say that it didn't happen in any one place ... 09:52: ... the Steinhardt-Turok model suggests that our universe floats in a higher dimensional space living on geometric objects called brains collisions between those ... 05:15: ... points become the same point and three-dimensional space becomes zero dimensional That's the singularity We say that it didn't happen in any one place ... 09:52: ... the Steinhardt-Turok model suggests that our universe floats in a higher dimensional space living on geometric objects called brains collisions between those ... 05:15: ... 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 happened ...
	2019-04-24: No Dark Matter = Proof of Dark Matter? 00:03: ... 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 in a ...
	2019-04-10: The Holographic Universe Explained 00:00: We live in a universe with 3 dimensions of space and one of time. 00:08: 3+1 dimensions. 00:24: ... of the most startling possibilities is that our 3+1 dimensional universe may better described as resulting from a spacetime one ... 03:55: How does the 2-D surface store information about that extra dimension? 04:26: Let’s ignore string theory for the moment and just think about how to create an extra dimension. 06:51: If objects at different scales don’t tend to interact with each other then this new degree of freedom behaves just like another dimension. 07:05: You might say it’s not a real 3-D volume because the 3rd dimension is fake. 07:15: ... is a dimension but a number-line of possible values which a) exists alongside the other ... 07:36: Crudely, this is how an extra dimension can be coded in a holographic universe. 07:47: Even from the beginning string theory had hints of this scale invariance and dimensional weirdness. 08:15: That means you can pretend string length-slash-energy is a separate dimension as a calculation trick. 08:23: ... wave equation for the gluon strand with length expressed as a separate dimension you get the wave equation for a graviton – the quantum particle of ... 10:23: ... resulting braney structure looked just like a Minkowski spacetime of 3+1 dimensions on which their lived a field theory that arose from interactions between ... 11:04: In good string-theorist style, Maldacena defined incorporated that scale factor into be a new spatial dimension. 11:46: ... interactions in the lower dimensional field theory are extremely strong – we would say the fields are strongly ... 11:58: ... strong gravitational fields in the higher dimensional space – like in black holes – look like a solvable configuration of ... 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. 13:41: ... appear to be negatively curved AdS space, nor does it have 4 spatial dimensions as in Maldecena’s ... 13:58: ... may be holographic – or at least have a dual representation in a lower dimension. ... 15:10: A few of you asked whether our percieved universe is just the surface of a higher dimensional space. 15:16: ... our percieved universe is the volume, but it can be encoded on its lower dimensional ... 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: ... 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" ... 00:24: ... universe may better described as resulting from a spacetime one dimension lower – like a hologram projected from a surface infinitely far ... 07:47: Even from the beginning string theory had hints of this scale invariance and dimensional weirdness. 11:46: ... interactions in the lower dimensional field theory are extremely strong – we would say the fields are strongly ... 11:58: ... strong gravitational fields in the higher dimensional space – like in black holes – look like a solvable configuration of ... 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. 15:10: A few of you asked whether our percieved universe is just the surface of a higher dimensional space. 15:16: ... our percieved universe is the volume, but it can be encoded on its lower dimensional ... 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. 11:46: ... interactions in the lower dimensional field theory are extremely strong – we would say the fields are strongly ... 11:58: ... strong gravitational fields in the higher dimensional space – like in black holes – look like a solvable configuration of particles ... 15:10: A few of you asked whether our percieved universe is just the surface of a higher dimensional space. 15:16: ... our percieved universe is the volume, but it can be encoded on its lower dimensional surface. ... 00:24: ... of the most startling possibilities is that our 3+1 dimensional universe may better described as resulting from a spacetime one dimension lower – ... 07:47: Even from the beginning string theory had hints of this scale invariance and dimensional weirdness. 00:00: We live in a universe with 3 dimensions of space and one of time. 00:08: 3+1 dimensions. 07:15: ... but a number-line of possible values which a) exists alongside the other dimensions but is independent of them; b) over which the rules of physics stay the ... 10:23: ... resulting braney structure looked just like a Minkowski spacetime of 3+1 dimensions on which their lived a field theory that arose from interactions between ... 13:41: ... 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.
	2019-04-03: The Edge of an Infinite Universe 05:49: ... the vertical-ish lines are set locations in space in only one spatial dimension. ... 09:38: But this time we’re not mapping space versus time – we’ll just map two dimensions of hyperbolic space. 11:40: So this disk can represent an infinite anti-de Sitter universe with 2 spatial dimensions at a single instant in time. 12:16: ... is itself a conformally-compactified Minkowski space with one fewer dimension. ... 12:34: In fact let’s add the dimension of time to our hyperbolic projection. 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. 12:53: On the other hand the surface of the disk has only one dimension of space – the circumference – and the same one-D of time – 1+1. 13:17: You can extrapolate to any number of extra dimensions – say a 3+1 dimensional - Poincare ball. 14:31: Quantum mechanics in the form of a conformal field theory in one space is a theory of quantum gravity in a space with one higher dimension. 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. 13:17: You can extrapolate to any number of extra dimensions – say a 3+1 dimensional - Poincare ball. 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. 13:17: You can extrapolate to any number of extra dimensions – say a 3+1 dimensional - Poincare ball. 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. 09:38: But this time we’re not mapping space versus time – we’ll just map two dimensions of hyperbolic space. 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. 13:17: You can extrapolate to any number of extra dimensions – say a 3+1 dimensional - Poincare ball.
	2019-03-06: The Impossibility of Perpetual Motion Machines 15:39: Fourier analysis represents functions in one dimension with a series of sine curves.
	2018-12-20: Why String Theory is Wrong 01:35: ... string theory into a single picture with a very specific number of extra dimensions. I'll talk more about that ... 02:14: ... with, to a precursor to string theory and the origin of all this extra dimension ... 02:35: He was playing around with the newfangled general relativity in five dimensions, 4 space and 1 time, because why not. 02:43: ... in our universe, plus an extra bit of math from the extra special dimension. ... 03:08: It appeared that gravity acting in this fifth dimension looks like electromagnetism to being trapped in our 4-D space-time. 03:27: The mild inconvenience of their very clearly being no extra special dimension was solved by Oskar Klein in the late 1920's. 03:37: Klein realized that you can get a sensible quantum theory if you compactify that extra dimension. 03:52: In the resulting in Kaluza–Klein theory, the fifth dimension is looped into a tiny circle. 04:07: Momentum in that loop dimension has the exact behavior of electric charge, with the direction of rotation determining the sign of the charge. 05:07: For example, adding more compact dimensions of various shapes and, of course, strings. 05:18: So, start with Kaluza-Klein, add vibrating strings and exactly the right extra special dimensions, and you have string theory. 05:47: ... along with the discovery of the right symmetries for the extra dimensions sparked the first superstring revolution of the mid 80s, roughly ... 06:20: Five different approaches to getting all of the desired particles out of the basic premise of strings wiggling in ten dimensions. 06:28: All required six compactified extra dimensions of space. 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. 07:50: Our tiny quantum strings can roam that small dimension. 08:01: ... number of times a string winds around this compactified dimension is called its winding number. The energy of such a string depends on the ... 09:07: ... a theory in which momentum increases with the size of the compact dimension, or where momentum decreases with that size and both give the same ... 10:51: ... real detail, but the important thing here is that it adds a single extra dimension, to connect all of the five super string theory types via ... 11:08: So whereas the original superstring theories were ten dimensional with six compactified, M-theory is 11D, with seven hidden dimensions. 11:24: Whoa Well, that all sounds a bit arbitrary. Your theory not working? Just add an extra dimension. 11:32: Actually, the realization that superstring theory could be 11 dimensional was a revolution. It sparked the second superstring revolution. 11:49: ... have time to get into, 11 is also the magic number for super gravity dimensions. Super gravity should be the low energy, large-scale limit to super ... 12:43: In all superstring theories the extra spatial dimensions are wrapped, not in simple loops, but in complicated geometries called Calabi-Yau manifolds. 12:53: The behavior of strings in these hyper dimensional surfaces is only understood in idealized cases. 13:08: ... higher. This is the string landscape. Each geometry for the compactified dimensions implies a different set of porperties for vibrating strings, and so a ... 13:44: ... in the string landscape, but without knowing the geometry of the extra dimensions, this can't be verified nor can we make testable predictions beyond the ... 02:14: ... with, to a precursor to string theory and the origin of all this extra dimension stuff. ... 11:08: So whereas the original superstring theories were ten dimensional with six compactified, M-theory is 11D, with seven hidden dimensions. 11:32: Actually, the realization that superstring theory could be 11 dimensional was a revolution. It sparked the second superstring revolution. 11:49: ... So it was incredibly exciting that string theory appeared to have an 11 dimensional version, M-theory, to correspond to everyone's favorite 11 D super ... 12:53: The behavior of strings in these hyper dimensional surfaces is only understood in idealized cases. 11:49: ... So it was incredibly exciting that string theory appeared to have an 11 dimensional version, M-theory, to correspond to everyone's favorite 11 D super ... 01:35: ... string theory into a single picture with a very specific number of extra dimensions. I'll talk more about that ... 02:35: He was playing around with the newfangled general relativity in five dimensions, 4 space and 1 time, because why not. 05:07: For example, adding more compact dimensions of various shapes and, of course, strings. 05:18: So, start with Kaluza-Klein, add vibrating strings and exactly the right extra special dimensions, and you have string theory. 05:47: ... along with the discovery of the right symmetries for the extra dimensions sparked the first superstring revolution of the mid 80s, roughly ... 06:20: Five different approaches to getting all of the desired particles out of the basic premise of strings wiggling in ten dimensions. 06:28: All required six compactified extra dimensions of space. 11:08: So whereas the original superstring theories were ten dimensional with six compactified, M-theory is 11D, with seven hidden dimensions. 11:49: ... have time to get into, 11 is also the magic number for super gravity dimensions. Super gravity should be the low energy, large-scale limit to super ... 12:43: In all superstring theories the extra spatial dimensions are wrapped, not in simple loops, but in complicated geometries called Calabi-Yau manifolds. 13:08: ... higher. This is the string landscape. Each geometry for the compactified dimensions implies a different set of porperties for vibrating strings, and so a ... 13:44: ... in the string landscape, but without knowing the geometry of the extra dimensions, this can't be verified nor can we make testable predictions beyond the ... 02:35: He was playing around with the newfangled general relativity in five dimensions, 4 space and 1 time, because why not. 01:35: ... string theory into a single picture with a very specific number of extra dimensions. I'll talk more about that ... 13:08: ... higher. This is the string landscape. Each geometry for the compactified dimensions implies a different set of porperties for vibrating strings, and so a different ... 05:47: ... along with the discovery of the right symmetries for the extra dimensions sparked the first superstring revolution of the mid 80s, roughly coinciding with ... 11:49: ... have time to get into, 11 is also the magic number for super gravity dimensions. Super gravity should be the low energy, large-scale limit to super string ...
	2018-11-14: Supersymmetric Particle Found? 14:17: To quote, "I thought one of the fundamental properties of the strings was that the maths only works if they are one dimensional. 14:24: So how can you get world sheets?" Yes, it is a pain keeping the number of dimensions straight in string theory. 14:32: ... invariance only works for the 2D world sheet, which has one dimension of space and one of time, this is the shape traced out by a string ... 14:54: Some of you recalled a recent episode in which we talked about a study of gravitational waves that appears to refute the idea of extra dimensions. 15:04: Actually, this study was specifically evidence against the idea of extra extended dimensions. 15:11: ... weakness of the gravitational force is that there's an extra special dimension that has the same scale as the familiar three, so a 4d space in which we ... 15:27: Gravity then leaks into the extra fourth dimension, causing it to weaken. 15:32: But this has no bearing on the compactified extra dimensions of string theory. 15:36: Those dimensions are tiny in extent and they're coiled on themselves so there is nowhere for gravity to escape into. 15:43: It may have implications for the single extra extended spatial dimension of M-theory, but I need to research that more. 15:27: Gravity then leaks into the extra fourth dimension, causing it to weaken. 14:17: To quote, "I thought one of the fundamental properties of the strings was that the maths only works if they are one dimensional. 14:24: So how can you get world sheets?" Yes, it is a pain keeping the number of dimensions straight in string theory. 14:54: Some of you recalled a recent episode in which we talked about a study of gravitational waves that appears to refute the idea of extra dimensions. 15:04: Actually, this study was specifically evidence against the idea of extra extended dimensions. 15:32: But this has no bearing on the compactified extra dimensions of string theory. 15:36: Those dimensions are tiny in extent and they're coiled on themselves so there is nowhere for gravity to escape into. 14:24: So how can you get world sheets?" Yes, it is a pain keeping the number of dimensions straight in string theory.
	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. 03:34: On a spacetime diagram, time versus one dimension of space, this is called its world line. 10:25: That's on the 2D dimensional world sheet of a quantum string. 10:41: ... but only for 1D strings making a 2D world sheet, not for any other dimensional ... 11:57: ... the photon, out of string theory for a very specific number of spatial dimensions, nine to be ... 12:11: In fact, if string theory makes any predictions, it's the existence of exactly this number of extra dimensions. 12:23: Our universe has three spatial dimensions. 12:25: ... theorists hypothesize that the extra dimensions are coiled on themselves so they can't be seen, but that seems like a ... 12:37: There's also no experimental evidence of the existence of these dimensions. 10:25: That's on the 2D dimensional world sheet of a quantum string. 10:41: ... but only for 1D strings making a 2D world sheet, not for any other dimensional ... 01:14: And, by the way, these strings exist in six compact spatial dimensions on top of the familiar three. 11:57: ... the photon, out of string theory for a very specific number of spatial dimensions, nine to be ... 12:11: In fact, if string theory makes any predictions, it's the existence of exactly this number of extra dimensions. 12:23: Our universe has three spatial dimensions. 12:25: ... theorists hypothesize that the extra dimensions are coiled on themselves so they can't be seen, but that seems like a ... 12:37: There's also no experimental evidence of the existence of these dimensions.
	2018-10-25: Will We Ever Find Alien Life? 13:24: Sam Pollard asks, how does adding more particles require fewer dimensions? 13:42: Adding the symmetry gives you fermions but it also shaves off dimensions. 14:04: ... need to search through to find the geometry of our universe's extra dimensions. ... 13:24: Sam Pollard asks, how does adding more particles require fewer dimensions? 13:42: Adding the symmetry gives you fermions but it also shaves off dimensions. 14:04: ... need to search through to find the geometry of our universe's extra dimensions. ...
	2018-10-18: What are the Strings in String Theory? 00:24: And what's all this nonsense of extra dimensions? 04:15: Oh, and we needed to add 22 dimensions to the familiar four. 04:58: As an added bonus, this ambition also shaved off a bunch of dimensions. 05:05: ... framework of m-theory, all for the low price of adding only one spatial dimension for an 11-dimensional ... 10:01: ... of known particles, they need to vibrate in more than just the three dimensions of ... 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. 10:23: In short, without exactly this number of dimensions, you don't get gravitons or any other massless particle. 10:34: It's a theory that works in a universe that is clearly not our own with its measly three dimensions of space. 10:44: There's a way to add extra special dimensions that is still consistent with our perceived 3D universe. 11:08: This is a Pac-Man dimension. 11:11: Travel the tiny width of this dimension and you'll find yourself back where you started. 11:16: Very tiny objects like quantum strings could explore that extra dimension, and importantly, oscillate in it. 11:30: Three large dimensions of space and six tiny Pac-Man dimensions that only strings experience. 11:40: Modern M theory proposes an additional large spatial dimension. 11:54: ... fascinating dualities between different ways of thinking about the dimensions. ... 12:13: The exact behavior of strings depends on the shape of their compact dimensions. 12:19: In fact, the single free parameter in string theory becomes the configuration of the extra dimensions. 00:24: And what's all this nonsense of extra dimensions? 04:15: Oh, and we needed to add 22 dimensions to the familiar four. 04:58: As an added bonus, this ambition also shaved off a bunch of dimensions. 10:01: ... of known particles, they need to vibrate in more than just the three dimensions of ... 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. 10:23: In short, without exactly this number of dimensions, you don't get gravitons or any other massless particle. 10:34: It's a theory that works in a universe that is clearly not our own with its measly three dimensions of space. 10:44: There's a way to add extra special dimensions that is still consistent with our perceived 3D universe. 11:30: Three large dimensions of space and six tiny Pac-Man dimensions that only strings experience. 11:54: ... fascinating dualities between different ways of thinking about the dimensions. ... 12:13: The exact behavior of strings depends on the shape of their compact dimensions. 12:19: In fact, the single free parameter in string theory becomes the configuration of the extra dimensions.
	2018-10-10: Computing a Universe Simulation 12:07: ... were used to search for and rule out the existence of an extra spatial dimension beyond our familiar ... 14:29: Squirrel Bacon is bothered when people use the term dimension to refer to parallel universe. 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 00:07: The hunt for extra dimensions sounds like science fiction. 00:16: So how many dimensions are there? 00:43: ... particular described in a new paper, "Limits on the Number of Spacetime Dimensions from GW170817," by Pardoa, Fishbachb, Holzb, and ... 02:05: In the case of today's paper, it allows us to measure how many dimensions that space actually has. 02:17: Add one dimension of time to give us 4D space-time, which we'll also refer to as 3-plus-1-dimensional space-time. 02:26: ... adding the extra spatial dimensions beyond the usual three could actually explain a lot, from the difference ... 03:45: ... way pulses fade in brightness depends on the number of dimensions, typically proportional to 1 over the distance to the power of the number ... 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. 05:40: If you recall, intensity drops off more quickly the more dimensions you have. 05:44: So you drain gravity into an extra dimension. 05:48: But you restrict all the other stuff in the universe-- matter, radiation, astronomers-- to only three spatial dimensions. 06:07: ... can think of them as geometrical structures of potentially any number of dimensions on which the quantum field and their corresponding particles can ... 06:15: They're used in string theory, where they typically have a large number of 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: ... 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: ... and you get normal physics for matter and radiation in three spatial dimensions-- for example, the usual inverse square law for ... 07:14: If gravity spreads out in four dimensions rather than three, then it should become much weaker. 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: ... law on galactic scales, where it's sort of coupled to the three spatial dimensions of the ... 08:14: ... 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 ... 09:11: If space has four or more dimensions, then gravitational waves should drop off in intensity faster than you'd expect in three dimensions. 09:29: Does that match what you expect in a universe with three spatial dimensions? 09:34: If the dropping intensity was too much, then you have evidence for extra dimensions-- basic stuff, right? 10:36: How many extra dimensions did we discover? 10:49: There was no observable leakage of gravity into extra spatial dimensions, pretty much ruling this out as an explanation for dark energy. 10:59: There still might be compactified extra dimensions. 11:25: I mean, how cool would it have been to discover extra dimensions? 00:07: The hunt for extra dimensions sounds like science fiction. 00:16: So how many dimensions are there? 00:43: ... particular described in a new paper, "Limits on the Number of Spacetime Dimensions from GW170817," by Pardoa, Fishbachb, Holzb, and ... 02:05: In the case of today's paper, it allows us to measure how many dimensions that space actually has. 02:26: ... adding the extra spatial dimensions beyond the usual three could actually explain a lot, from the difference ... 03:45: ... way pulses fade in brightness depends on the number of dimensions, typically proportional to 1 over the distance to the power of the number ... 04:21: But even there, Einstein's general relativity describes gravity perfectly with three spatial dimensions. 05:40: If you recall, intensity drops off more quickly the more dimensions you have. 05:48: But you restrict all the other stuff in the universe-- matter, radiation, astronomers-- to only three spatial dimensions. 06:07: ... can think of them as geometrical structures of potentially any number of dimensions on which the quantum field and their corresponding particles can ... 06:15: They're used in string theory, where they typically have a large number of 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: ... 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: ... and you get normal physics for matter and radiation in three spatial dimensions-- for example, the usual inverse square law for ... 07:14: If gravity spreads out in four dimensions rather than three, then it should become much weaker. 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: ... law on galactic scales, where it's sort of coupled to the three spatial dimensions of the ... 09:11: If space has four or more dimensions, then gravitational waves should drop off in intensity faster than you'd expect in three dimensions. 09:29: Does that match what you expect in a universe with three spatial dimensions? 09:34: If the dropping intensity was too much, then you have evidence for extra dimensions-- basic stuff, right? 10:36: How many extra dimensions did we discover? 10:49: There was no observable leakage of gravity into extra spatial dimensions, pretty much ruling this out as an explanation for dark energy. 10:59: There still might be compactified extra dimensions. 11:25: I mean, how cool would it have been to discover extra dimensions? 09:34: If the dropping intensity was too much, then you have evidence for extra dimensions-- basic stuff, right? 07:48: In our hypothetical universe with four spatial dimensions, gravity is already weak on the scale of the solar system and the galaxy. 03:45: ... proportional to 1 over the distance to the power of the number of dimensions minus ... 10:49: There was no observable leakage of gravity into extra spatial dimensions, pretty much ruling this out as an explanation for dark energy. 00:07: The hunt for extra dimensions sounds like science fiction. 03:45: ... way pulses fade in brightness depends on the number of dimensions, typically proportional to 1 over the distance to the power of the number of ...
	2018-08-01: How Close To The Sun Can Humanity Get? 14:03: Did you think metaphorical physics demons are limited to our paltry three dimensions? 14:08: That their writing is one dimensional? 14:03: Did you think metaphorical physics demons are limited to our paltry three dimensions?
	2018-05-16: Noether's Theorem and The Symmetries of Reality 04:35: See, Einstein's description of gravity reveals the dimensions of space and time to be dynamic and changeable. 07:22: ... of the theorem means we can apply it to not just the symmetries in the dimensions of space and time, but also to more abstract ... 11:44: Yet, it pixels are only 60 milliarcseconds on their shortest dimension. 04:35: See, Einstein's description of gravity reveals the dimensions of space and time to be dynamic and changeable. 07:22: ... of the theorem means we can apply it to not just the symmetries in the dimensions of space and time, but also to more abstract ...
	2017-09-28: Are the Fundamental Constants Changing? 02:54: ... meaningful to talk about it changing independently to its underlying dimensions? ... 03:11: The dimensions behind, say, Newton's gravitational constant-- or the mass of the electron-- all have arbitrary human definitions. 03:20: ... though we've seen a change in a fundamental constant, way to study a dimensionless constant-- one that has no units, and therefore, isn't dependent on our ... 03:37: It's a dimensionless description of the strength of the electromagnetic force. 04:08: It's a dimensionless number. 10:38: ... are also looking into the variation of other dimensionless constants, such as the proton electron mass ratio, and the more obscure ... 03:20: ... though we've seen a change in a fundamental constant, way to study a dimensionless constant-- one that has no units, and therefore, isn't dependent on our definitions ... 10:38: ... are also looking into the variation of other dimensionless constants, such as the proton electron mass ratio, and the more obscure proton ... 03:37: It's a dimensionless description of the strength of the electromagnetic force. 04:08: It's a dimensionless number. 02:54: ... meaningful to talk about it changing independently to its underlying dimensions? ... 03:11: The dimensions behind, say, Newton's gravitational constant-- or the mass of the electron-- all have arbitrary human definitions.
	2017-08-30: White Holes 05:50: There the dimensions of space and time switch roles.
	2017-07-07: Feynman's Infinite Quantum Paths 15:24: These, in turn, may exist in a space of 11 or even 26 dimensions, most of which are compactified.
	2017-06-28: The First Quantum Field Theory 02:38: Guitar strings are one-dimensional, but we can expand the analogy to any number of dimensions. 02:59: Every point in space has some displacement in some imaginary extra direction-- analogous to but not the same as a fourth dimension. 02:38: Guitar strings are one-dimensional, but we can expand the analogy to any number of dimensions.
	2017-06-21: Anti-Matter and Quantum Relativity 01:47: In relativity, the dimensions of space and time are intrinsically connected and they float into each other as frames of reference change.
	2017-03-29: How Time Becomes Space Inside a Black Hole 09:53: However the old radial dimension isn't space-like, it's time-like. 10:47: ... this mysterious dimensional flip does give us some fascinating insight into how time and space blend ... 09:53: However the old radial dimension isn't space-like, it's time-like. 10:47: ... this mysterious dimensional flip does give us some fascinating insight into how time and space blend ...
	2017-02-15: Telescopes of Tomorrow 08:15: In a way, LSST focuses more on the dimension of time rather than space. 11:57: The hyperbolic geometry is just what you did when you map the space-time interval to a third dimension.
	2017-02-02: The Geometry of Causality 02:49: To preserve our sanity, we represent this on a spacetime diagram plotting time and only one dimension of space. 11:56: ... of the core of a black hole an artifact of the limitations of three dimensional mathematics?" Well, maybe, sort ... 12:07: ... in regular 4D spacetime result from oscillations within many more coiled dimensions, so-called ... 11:56: ... of the core of a black hole an artifact of the limitations of three dimensional mathematics?" Well, maybe, sort ... 12:07: ... in regular 4D spacetime result from oscillations within many more coiled dimensions, so-called ...
	2016-12-14: Escape The Kugelblitz Challenge 00:14: ... compactifies our representation of the dimensions of space and time, allowing us to fit onto the one diagram the ...
	2016-12-08: What Happens at the Event Horizon? 02:19: ... graphing time versus just one dimension in space, we can look at the limits of our access to the universe due to ... 04:48: ... diagram, blue verticalish lines represent fixed locations in one dimension of space and red horizontalish lines are fixed moments in ... 05:44: And because we only have one dimension of space, and any motion to the left brings us closer to the black hole.
	2016-11-16: Strange Stars 12:37: That arc occurs in an imaginary fourth dimension that is analogous to the radial dimension of the 3D sphere.
	2016-09-21: Quantum Entanglement and the Great Bohr-Einstein Debate 10:41: ... example, entangled particles may be dimensionally connected by Einstein-Rosen bridges, wormholes that allows instantaneous ...
	2016-06-15: The Strange Universe of Gravitational Lensing 01:27: ... theory of relativity describes the real universe as a flexible, dynamic dimensional grid that only resembles our mind's eye Euclidean lattice in the absence ...
	2016-05-18: Anti-gravity and the True Nature of Dark Energy 11:35: This law is a property of a Newtonian universe, in which space and time are fixed static dimensions.
	2016-05-11: The Cosmic Conspiracy of Dark Energy Challenge Question 04:30: That's 100 doublings of its scale factor-- so its linear dimension, not its volume.
	2016-04-20: Why the Universe Needs Dark Energy 04:16: Geometry works just as you learned in school, and a flat universe is still infinite-- open-- in all three spatial dimensions.
	2016-04-06: We Are Star Stuff 01:30: So the tapestry of our universe is woven across the dimensions of space and time and complexity. 11:34: Space is still three dimensional, and perhaps infinite in all three dimensions. 01:30: So the tapestry of our universe is woven across the dimensions of space and time and complexity. 11:34: Space is still three dimensional, and perhaps infinite in all three dimensions.
	2016-03-16: Why is the Earth Round and the Milky Way Flat? 01:43: ... and stars have spherical symmetry, meaning you can rotate them in three dimensions and the basic shape stays the ... 02:48: Gravity exerts itself equally along the three spatial dimensions. 02:53: And this type of dimensional egalitarianism is also shared by another effect, ultimately leading to the ball shapes of stars, planets, and moons. 01:43: ... and stars have spherical symmetry, meaning you can rotate them in three dimensions and the basic shape stays the ... 02:48: Gravity exerts itself equally along the three spatial dimensions.
	2016-01-27: The Origin of Matter and Time 01:17: It's just a graph of position in space-- just one special dimension for simplicity-- versus position in time. 01:31: In fact, thinking in four dimensional space time, a thing is its world line.
	2016-01-13: When Time Breaks Down 07:47: Is time even a real dimension?
	2015-12-09: How to Build a Black Hole 02:51: ... think not in regular 3D space or even 4D space time but, rather, in six dimensional quantum phase ...
	2015-11-25: 100 Years of Relativity + Challenge Winners! 02:43: We're also just going to figure this out in one dimension.
	2015-10-28: Is The Alcubierre Warp Drive Possible? 05:33: ... warp field, and you hypothetically soften the fabric of space via higher dimensional effects-- literally, a hyper space warp ...
	2015-10-07: The Speed of Light is NOT About Light 06:52: Essentially, we're just requiring basic consistency in how the dimensions work.
	2015-09-30: What Happens At The Edge Of The Universe? 07:31: Are the laws of physics, or even the number of dimensions, the same?
	2015-07-29: General Relativity & Curved Spacetime Explained! 02:21: ... to explain if I first set up an analogy using our old friend the two dimensional ant on the surface of the ... 08:32: ... just a lot easier to say the word gravity than say curvature of four dimensional ... 02:21: ... to explain if I first set up an analogy using our old friend the two dimensional ant on the surface of the ... 08:32: ... just a lot easier to say the word gravity than say curvature of four dimensional ... 02:21: ... to explain if I first set up an analogy using our old friend the two dimensional ant on the surface of the ... 08:32: ... just a lot easier to say the word gravity than say curvature of four dimensional spacetime. ...
	2015-07-08: Curvature Demonstrated + Comments 04:19: ... Shi and SamBskate were both asking how the dimensionality of the ambient space in which the surface of the sphere is embedded-- ... 05:18: ... the video, the Earth it was shown was supposed to be the physical, three dimensional Earth, and we were taking a vector and moving along a circle in orbit ... 05:27: ... you wanted to know if the three dimensional space around Earth is curved, you would follow the procedure of using ... 05:18: ... the video, the Earth it was shown was supposed to be the physical, three dimensional Earth, and we were taking a vector and moving along a circle in orbit ... 05:27: ... you wanted to know if the three dimensional space around Earth is curved, you would follow the procedure of using ... 05:18: ... the video, the Earth it was shown was supposed to be the physical, three dimensional Earth, and we were taking a vector and moving along a circle in orbit around ... 05:27: ... Earth is curved, you would follow the procedure of using Euclidean three dimensional rules to parallel transport that vector around the circle and see if you end ... 04:19: ... Shi and SamBskate were both asking how the dimensionality of the ambient space in which the surface of the sphere is embedded-- ...
	2015-07-02: Can a Circle Be a Straight Line? 03:39: From the ant's two dimensional confined perspective, curve one between A and B is straight. 03:55: ... from the ambient three dimensional perspective, you could say that those tangent vectors aren't really ... 04:08: ... parallel, tangent, and straight that it can apply solely within that two dimensional ... 04:47: By the same process you can find geodesics on a saddle or a hillside or in three dimensional spaces. 06:57: Now in a three dimensional space you can test curvature the same way we've been describing. 07:17: So is the three dimensional space around Earth curved? 07:24: And 3D curved space isn't what explains away gravity, it's four dimensional curved spacetime. 03:39: From the ant's two dimensional confined perspective, curve one between A and B is straight. 03:55: ... from the ambient three dimensional perspective, you could say that those tangent vectors aren't really ... 04:08: ... parallel, tangent, and straight that it can apply solely within that two dimensional ... 04:47: By the same process you can find geodesics on a saddle or a hillside or in three dimensional spaces. 06:57: Now in a three dimensional space you can test curvature the same way we've been describing. 07:17: So is the three dimensional space around Earth curved? 07:24: And 3D curved space isn't what explains away gravity, it's four dimensional curved spacetime. 03:39: From the ant's two dimensional confined perspective, curve one between A and B is straight. 07:24: And 3D curved space isn't what explains away gravity, it's four dimensional curved spacetime. 03:55: ... from the ambient three dimensional perspective, you could say that those tangent vectors aren't really staying parallel ... 04:08: ... parallel, tangent, and straight that it can apply solely within that two dimensional space. ... 06:57: Now in a three dimensional space you can test curvature the same way we've been describing. 07:17: So is the three dimensional space around Earth curved? 04:47: By the same process you can find geodesics on a saddle or a hillside or in three dimensional spaces. 03:55: ... is really straight, but the ant, who's very flat, can't look in three dimensions anymore than we can look in four ...
	2015-04-22: Are Space and Time An Illusion? 04:25: So he proposed the following radical idea-- maybe reality is not a three dimensional space that evolves in time. 04:33: Instead, it's a four dimensional non-Euclidean mathematical space that's just there. 04:25: So he proposed the following radical idea-- maybe reality is not a three dimensional space that evolves in time. 04:33: Instead, it's a four dimensional non-Euclidean mathematical space that's just there. 04:25: So he proposed the following radical idea-- maybe reality is not a three dimensional space that evolves in time.
	2015-04-15: Could NASA Start the Zombie Apocalypse? 03:35: ... because the bottom line is that infectious disease takes on a whole new dimension in ...

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