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	2022-12-14: How Can Matter Be BOTH Liquid AND Gas? 09:22: That means the supercritical equation of state is much more complex than the ideal gas law.
	2022-10-26: Why Did Quantum Entanglement Win the Nobel Prize in Physics? 03:07: Quantum systems are described by a mathematical object called the wavefunction, which evolves according to the Schrodinger equation. 15:54: And then the one were were went through the entire Lagrangian equation of the standard model of particle physics. 18:10: ... absolutely no way to explain an equation this complex in 10 minutes - it takes several years of coursework to get ... 19:28: The equations then work perfectly, which suggest   that the infinities don't belong there  or don't represent anything physical. 19:41: 05TE informs us that if you recite the full  Lagrangian equation three times in front of a mirror, the particle ghosts will appear. 19:28: The equations then work perfectly, which suggest   that the infinities don't belong there  or don't represent anything physical.
	2022-10-19: The Equation That Explains (Nearly) Everything! 00:00: ... it does so almost unfailingly. The theory is encapsulated in a single equation known as The Standard Model Lagrangian. It's probably the second most ... 01:33: ... unmeasurable, then we need to add a term to the Schrodinger equation to make that the case. That term turns out to be the electromagnetic ... 02:51: ... how do you go from that to actual equations describing how the forces behave? And how do you wrap it all up in a ... 03:54: ... we plug the Lagrangian of a system into the Euler-Lagrange equation and the result will be equations describing how that system will move ... 04:05: ... are other ways to get these equations of motion, but Lagrangian is especially powerful because of how it ... 09:45: ... with the EM field is equivalent to the piece added to the Schrodinger equation to ensure phase invariance. And now we have to add the pieces for the ... 11:28: ... without ghosts and perhaps we will. But until then this process gives an equation that describes Nature very well. By the way, the h.c. stands for ... 12:23: ... is a matrix with the square of the mass of each different fermion. This equation doesn’t actually predict the particle masses - that’s still an unsolved ... 14:00: ... other things. And it is a bit of a mess. Many physicists feel that the equation that truly underlies everything, if it exists, should be at least as ... 14:43: ... the predictions of the standard model lagrangian that could lead to an equation that is easier to fit on a coffee mug, and to a deeper description of ... 12:23: ... is a matrix with the square of the mass of each different fermion. This equation doesn’t actually predict the particle masses - that’s still an unsolved problem. ... 02:51: ... how do you go from that to actual equations describing how the forces behave? And how do you wrap it all up in a ... 03:54: ... of a system into the Euler-Lagrange equation and the result will be equations describing how that system will move and change over ... 04:05: ... are other ways to get these equations of motion, but Lagrangian is especially powerful because of how it ... 02:51: ... how do you go from that to actual equations describing how the forces behave? And how do you wrap it all up in a single ... 03:54: ... of a system into the Euler-Lagrange equation and the result will be equations describing how that system will move and change over ...
	2022-10-12: The REAL Possibility of Mapping Alien Planets! 19:23: ... the strength of electromagnetism, and the classical   equation for electrostatic force - coulomb’s law - has charge squared over ...
	2022-09-28: Why Is 1/137 One of the Greatest Unsolved Problems In Physics? 00:19: This is the fine structure constant, and it appears everywhere in our equations of quantum physics, and we’re still trying to figure out why. 02:04: ... the Bohr model explaining hydrogen lines, then the Schrodinger equation for heavier ... 11:20: ... also the relationship  between mass and energy in Einstein’s famous equation. ... 00:19: This is the fine structure constant, and it appears everywhere in our equations of quantum physics, and we’re still trying to figure out why.
	2022-08-24: What Makes The Strong Force Strong? 09:36: Maybe they didn’t teach you this equation in school, but it turns out that red + blue + green = 0.
	2022-08-17: What If Dark Energy is a New Quantum Field? 01:25: ... constant. This is just a static number that you can add to Einstein’s equations of general relativity to represent the fabric of space having a ... 02:31: ... candidate by taking the ratio of pressure to density. This gives us the equation of state of dark energy, with the ratio equated to the equation of state ... 04:41: If we can measure the energy density, can’t we also measure omega, the equation of state? 06:25: ... constant from the early universe measurements, we also need to assume an equation of state to see how the expansion rate should have evolved into the late ... 09:13: ... a simple numerical value - a field strength - everywhere in space. The equation of state depends on this field strength and the kinetic energy of the ... 10:55: ... density of the universe. For example, in so-called k-essence models, the equation of state is connected to the density of matter. And it only becomes ... 11:51: ... behaves. As I mentioned, the behavior of dark energy is driven by its equation of state. Any value of omega less than -⅓ means accelerating expansion, ... 14:41: ... story short - measuring the equation of state of the universe with increasing precision will teach us about ... 01:25: ... constant. This is just a static number that you can add to Einstein’s equations of general relativity to represent the fabric of space having a ...
	2022-08-03: What Happens Inside a Proton? 00:22: ... mathematical.   By writing down the laws of physics as  equations, we can make predictions about   how the universe should behave ... 00:45: ... our wizarding only works  if we can solve the equations,   and it's impossible to calculate perfectly the evolution of all but ...
	2022-07-27: How Many States Of Matter Are There? 03:34: It defines what we call the equation of state. 03:44: Different states of matter have different equations of state.
	2022-06-30: Could We Decode Alien Physics? 00:00: ... what amounts to all physics known by the aliens - including the equations of   their laws of physics and a list of all ... 04:59: ... of   electromagnetism - the Maxwell’s equations. Those equations tell us how particles with    electric charges respond to ... 05:20: ... is bad news for our fictional scenario because we can’t rely on the equations describing   the laws of physics to determine the  alien ... 07:38: ... this switch in convention does seem to change the actual equations of the laws of physics. To make   a LEFT-hand-rule work you ... 00:00: ... what amounts to all physics known by the aliens - including the equations of   their laws of physics and a list of all ... 04:59: ... of   electromagnetism - the Maxwell’s equations. Those equations tell us how particles with    electric charges respond to ... 05:20: ... is bad news for our fictional scenario because we can’t rely on the equations describing   the laws of physics to determine the  alien ... 07:38: ... this switch in convention does seem to change the actual equations of the laws of physics. To make   a LEFT-hand-rule work you ... 05:20: ... is bad news for our fictional scenario because we can’t rely on the equations describing   the laws of physics to determine the  alien sign convention for ... 00:00: ... what amounts to all physics known by the aliens - including the equations of   their laws of physics and a list of all elementary particles and ... 07:38: ... calculating torque, angular momentum,   and through Maxwell’s equations.  The right hand rule is another arbitrary  convention, and its ... 01:25: ... make such a blunder? Surely, a quick glance at the alien Maxwell’s equations   which govern the interactions of charged  particles will reveal ... 10:41: ... of charge and parity  transformation - appears to bring our equations   back to where they started. This is CP symmetry. A ... 04:59: ... difference to the laws of   electromagnetism - the Maxwell’s equations. Those equations tell us how particles with    electric charges ...
	2022-06-15: Can Wormholes Solve The Black Hole Information Paradox? 11:13: ... set n equal to 1 single black hole,   you end up with a new equation for  the entropy of the Hawking ... 11:25: ... is enough to leave an imprint on the entropy. This results in a new equation for the entropy of the   radiation, which has been called the ... 11:13: ... set n equal to 1 single black hole,   you end up with a new equation for  the entropy of the Hawking ...
	2022-06-01: What If Physics IS NOT Describing Reality? 00:25: ... Not quite - no one has to solve the Schrodinger  equation in order for an electron to be able to do   its thing. Our ... 05:53: ... even managed to derive the   equivalent of the Schrodinger equation by asking  how quantum information should evolve over ...
	2022-05-04: Space DOES NOT Expand Everywhere 01:59: ... finished general relativity, four scientists independently solved its equation for the entire universe, giving us the ...
	2022-04-27: How the Higgs Mechanism Give Things Mass 02:50: ... that we have to add a new quantum field to   the Schrodinger equation that lets the  universe counteract these phase shifts.   ... 05:38: ... magnetic interaction and they end up all aligning.  The equations of magnetism don’t start out with a   preferred orientation, ... 11:28: ... can be in a state of broken symmetry   even though the overall equations  of magnetism have not ... 06:32: ... analogy. Consider a ball rolling  back and forth in a valley. The equations   describing its motion are symmetric between  left and right because ...
	2022-03-30: Could The Universe Be Inside A Black Hole? 06:05: It’s a white hole, and it’s a valid a solution to the Einstein equations. 09:06: ... the same that Alexander Friedmann made when he first solved the Einstein equations for the whole universe, and it’s the assumption behind the FLRW ... 06:05: It’s a white hole, and it’s a valid a solution to the Einstein equations. 09:06: ... the same that Alexander Friedmann made when he first solved the Einstein equations for the whole universe, and it’s the assumption behind the FLRW ...
	2022-03-23: Where Is The Center of The Universe? 03:35: That gave him equations of motion that described how the universe must evolve. 10:03: The math of the FLWR metric and the Friedman equations tell us that as time approaches zero, the distance between any two points approaches zero. 12:02: He sought solutions to the Einstein equation for a universe that is lumpy on the largest scales. 03:35: That gave him equations of motion that described how the universe must evolve. 10:03: The math of the FLWR metric and the Friedman equations tell us that as time approaches zero, the distance between any two points approaches zero.
	2022-03-16: What If Charge is NOT Fundamental? 00:50: And neither Maxwell’s equations nor QED say a thing about what electric charge really is. 00:37: The math that describes it - Maxwell's equations  or quantum electrodynamics - seem to wrap it up nicely.
	2022-02-16: Is The Wave Function The Building Block of Reality? 05:00: The behavior of the wave function is described by the Schrodinger equation, which tracks its evolution through space and over time. 05:09: ... we’ve discussed previously, the Schrodinger equation is a linear equation - which just means that if you add together ... 05:44: ... and it’s non-reversible. It’s not part of the math of the Schrodinger equation. ... 09:25: ... possible. The instability introduces a nonlinear term in the Schrödinger equation, causing the wave function to rapidly and randomly choose to make the ... 10:19: ... these objective collapse models involve modifications to the Schrödinger equation, they are not mere interpretations of quantum mechanics — they are ... 05:09: ... we’ve discussed previously, the Schrodinger equation is a linear equation - which just means that if you add together solutions to this equation, ... 09:25: ... possible. The instability introduces a nonlinear term in the Schrödinger equation, causing the wave function to rapidly and randomly choose to make the object ...
	2022-02-10: The Nature of Space and Time AMA 00:03: ... the same thing the expansion of the universe described by friedman equations um is it's described mathematically as the growth of something called ...
	2022-01-27: How Does Gravity Escape A Black Hole? 00:35: ... 1915 Einstein presented to the world the equations behind his general theory of relativity, which describe gravity not as a ... 01:21: ... built the equations of GR Equation: G_{\mu\nu} + \Lambda g_{\mu\nu} = \kappa T_{\mu\nu} so ... 01:49: Naturally enough, the “c” of the speed of light made its way into the equations of general relativity. 01:55: When you use those equations to calculate the speed of various gravitational effects, they also turn out to be the speed of light. 00:35: ... 1915 Einstein presented to the world the equations behind his general theory of relativity, which describe gravity not as a ... 01:21: ... built the equations of GR Equation: G_{\mu\nu} + \Lambda g_{\mu\nu} = \kappa T_{\mu\nu} so ... 01:49: Naturally enough, the “c” of the speed of light made its way into the equations of general relativity. 01:55: When you use those equations to calculate the speed of various gravitational effects, they also turn out to be the speed of light.
	2022-01-19: How To Build The Universe in a Computer 02:56: ... the time of Isaac Newton it had been possible to write down equations describing the trajectories of a pair of massive bodies moving in each ... 03:06: And then to solve those equations to find their positions at any time in the future. 03:28: ... problem doesn’t have an analytical  solution - no simple master equations - which is why Holmberg had to solve  the problem with light ... 08:17: Now we call these hydrodynamic simulations - they simulate the flow of gas using the equations of fluid dynamics. 02:56: ... the time of Isaac Newton it had been possible to write down equations describing the trajectories of a pair of massive bodies moving in each ... 03:06: And then to solve those equations to find their positions at any time in the future. 03:28: ... problem doesn’t have an analytical  solution - no simple master equations - which is why Holmberg had to solve  the problem with light ... 08:17: Now we call these hydrodynamic simulations - they simulate the flow of gas using the equations of fluid dynamics. 03:28: ... problem doesn’t have an analytical  solution - no simple master equations - which is why Holmberg had to solve  the problem with light ... 02:56: ... the time of Isaac Newton it had been possible to write down equations describing the trajectories of a pair of massive bodies moving in each other’s ... 03:17: For 3 or more bodies there  is no simple set of equations   describing their future evolution under gravity.
	2022-01-12: How To Simulate The Universe With DFT 00:00: ... used every particle in the observable universe to solve the schrodinger equation and do full quantum simulation of some chunk of the universe, how big ... 00:54: ... just scratch the good ol’ Schrodinger equation on the blackboard and solve it to learn the probability distribution of ... 01:39: To understand how, first up, let’s take a look at the Schrodinger equation. 02:10: ... atom, the different possible values of E that form solutions to this equation define the energy levels of the ... 02:19: ... can also solve the Schrodinger equation to find the wavefunction, and the square of that wavefunction gives the ... 02:30: ... time independent Schrodinger equation isn’t the be all and end all of quantum mechanics - it’s an ... 02:46: Our Schrodinger equation just dealt with one dimension of space, x. 04:52: ... particles to the Schrodinger equation is like adding dice to this system- every time we add a particle we ... 06:06: When we use Newton to solve, say, the three-body problem, we can solve the equations for each of the 3 particles separately. 06:14: We don’t need a 3-cubed or 9 dimensional equation. 07:15: In the Newtonian case, particles only interact locally, and that means the Newtonian equations of motion are what we call separable. 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: ... this is true then we can take an equation for N particles in 3D and reduce it from a 3^N dimensional equation to ... 07:46: ... fact in Newtonian mechanics we can not only write down the equations of motion for each particle separately, we can write the x, y, and z ... 07:56: That gives us a sufficiently sane number of coupled equations that we can actually solve. 08:15: And we can’t reduce the dimensionality by treating particles separately because the Schrodinger equation can’t be made “separable”. 08:26: ... yet despite the apparent impossibility of solving the Schrodinger equation for more than a few particles, researchers still manage to do quantum ... 10:54: Because they aren’t interacting, the equations of motion for these electrons are separable, just like in Newtonian mechanics. 11:02: Instead of using the Schrodinger equation, you use an analog called the Kohn-Sham equations. 11:13: These equations basically let you translate between a realistic interacting system and the fictitious non-interacting case. 11:23: Solving those equations becomes possible, and it gets you the ground state energy for your guess at the charge density. 12:37: ... must be self-consistent - basically, it has to obey the Schrodinger equation - and the cheat is finding a way to inch your way to that ... 02:10: ... atom, the different possible values of E that form solutions to this equation define the energy levels of the ... 02:30: ... time independent Schrodinger equation isn’t the be all and end all of quantum mechanics - it’s an approximation that ... 06:06: When we use Newton to solve, say, the three-body problem, we can solve the equations for each of the 3 particles separately. 07:15: In the Newtonian case, particles only interact locally, and that means the Newtonian equations of motion are what we call separable. 07:33: ... in 3D and reduce it from a 3^N dimensional equation to simply N coupled equations each in ... 07:46: ... fact in Newtonian mechanics we can not only write down the equations of motion for each particle separately, we can write the x, y, and z ... 07:56: That gives us a sufficiently sane number of coupled equations that we can actually solve. 10:54: Because they aren’t interacting, the equations of motion for these electrons are separable, just like in Newtonian mechanics. 11:02: Instead of using the Schrodinger equation, you use an analog called the Kohn-Sham equations. 11:13: These equations basically let you translate between a realistic interacting system and the fictitious non-interacting case. 11:23: Solving those equations becomes possible, and it gets you the ground state energy for your guess at the charge density. 11:13: These equations basically let you translate between a realistic interacting system and the fictitious non-interacting case.
	2021-12-10: 2021 End of Year AMA! 00:02: ... mexican physicist found this metric in a solution to einstein's equations that that that produces a field which is capable of traveling faster ...
	2021-11-10: What If Our Understanding of Gravity Is Wrong? 08:15: ... we saw that the principle of least action  allows equations of motion to be extracted in a way that automatically obeys all of our ... 11:45: ... managed to tweak their equations so that  in the early universe, that field behaved a bit like a ... 08:15: ... we saw that the principle of least action  allows equations of motion to be extracted in a way that automatically obeys all of our ... 11:45: ... managed to tweak their equations so that  in the early universe, that field behaved a bit like a ...
	2021-11-02: Is ACTION The Most Fundamental Property in Physics? 04:29: ... Euler already did most of the work for us by finding the Euler-Lagrange equations, allowing both physics students and nature to minimize their action. The ... 05:00: ... mechanics, it seems almost like a miracle. The hellishly complex equations needed to solve problems using pure Newton seem to just melt away into ... 05:52: ... the orbit of Mercury. If you calculate that orbit using the Einstein equations in their full glory and full gory detail, you get the right answer. But ... 06:47: ... frame. If you plug the relativistic Lagrangian into the Euler-Lagrange equation, you get equations of motion correctly describing the orbit of Mercury ... 07:09: ... based on this principle can be made to be “Lorentz invariant” - it gives equations of motion that are valid even in the shifting frames of Einstein’s ... 12:59: ... quantum theory. Back to Paul Dirac just for a moment. His eponymous equation was derived to describe the quantum evolution of the ... 13:16: Well it turns out that this equation is just the Lagrangian for a spin-½ quantum field. 14:57: ... have a Lagrangian of the highest order, and we're delighted that our equations of motion have joined ... 18:13: ... put Joe - so rather than digging for the particular equation that describes the precise details of a given observed phenomenon - ... 04:29: ... Euler already did most of the work for us by finding the Euler-Lagrange equations, allowing both physics students and nature to minimize their action. The ... 05:00: ... mechanics, it seems almost like a miracle. The hellishly complex equations needed to solve problems using pure Newton seem to just melt away into ... 05:52: ... the orbit of Mercury. If you calculate that orbit using the Einstein equations in their full glory and full gory detail, you get the right answer. But ... 06:47: ... the relativistic Lagrangian into the Euler-Lagrange equation, you get equations of motion correctly describing the orbit of Mercury around the ... 07:09: ... based on this principle can be made to be “Lorentz invariant” - it gives equations of motion that are valid even in the shifting frames of Einstein’s ... 14:57: ... have a Lagrangian of the highest order, and we're delighted that our equations of motion have joined ... 04:29: ... Euler already did most of the work for us by finding the Euler-Lagrange equations, allowing both physics students and nature to minimize their action. The Principle ... 05:00: ... mechanics, it seems almost like a miracle. The hellishly complex equations needed to solve problems using pure Newton seem to just melt away into much ...
	2021-10-20: Will Constructor Theory REWRITE Physics? 00:42: Come up with a set of equations that predict how those numbers change over time - e.g. 01:30: ... nice to have a set of equations for each separate aspect of the world - but if these theories are really ... 04:21: The power of constructor theory is that it allows us to explore physics without having to solve the detailed equations of motion. 00:42: Come up with a set of equations that predict how those numbers change over time - e.g. 01:30: ... nice to have a set of equations for each separate aspect of the world - but if these theories are really ... 04:21: The power of constructor theory is that it allows us to explore physics without having to solve the detailed equations of motion.
	2021-10-13: New Results in Quantum Tunneling vs. The Speed of Light 03:01: ... need to see how its wavefunction evolves according the the Schrodinger equation - which is just the equation of motion of ... 03:13: This equation tells us that the wavefunction is mostly reflected or scattered back by the wall of the nucleus. 03:20: But the Schrodinger equation is very clear that this isn’t the only thing that can happen. 07:45: ... previous work on tunneling time relied on the Schrodinger equation, which doesn’t incorporate Einsteins’s special theory of relativity and ... 07:57: These new guys use the Dirac equation, which properly incorporates special relativity and so we can take any emerging FTL motion more seriously. 08:43: That’s just what Hartman calculated using arguably the wrong equation back in 1962. 03:01: ... need to see how its wavefunction evolves according the the Schrodinger equation - which is just the equation of motion of ... 03:13: This equation tells us that the wavefunction is mostly reflected or scattered back by the wall of the nucleus.
	2021-10-05: Why Magnetic Monopoles SHOULD Exist 02:27: In particular, Gauss’s law for magnetism, one of the four Maxwell’s equations. 03:19: Let’s take a quick gander at Maxwell’s equations. 03:40: You could also have symmetry between these equations if there was such a thing as magnetic charge. 03:46: If you add magnetic charges to these equations then you get a magnetic force that looks exactly like the electrostatic force. 04:05: ... nothing in Maxwell’s equations that really says magnetic monopoles can’t exist except for the fact that ... 04:37: ... how electromagnetism arose automatically from requiring that the equations of quantum mechanics had a particular symmetry - the measurements they ... 04:54: ... pops into the equations as soon as we require this - but in that version of electromagnetism, ... 02:27: In particular, Gauss’s law for magnetism, one of the four Maxwell’s equations. 03:19: Let’s take a quick gander at Maxwell’s equations. 03:40: You could also have symmetry between these equations if there was such a thing as magnetic charge. 03:46: If you add magnetic charges to these equations then you get a magnetic force that looks exactly like the electrostatic force. 04:05: ... nothing in Maxwell’s equations that really says magnetic monopoles can’t exist except for the fact that ... 04:37: ... how electromagnetism arose automatically from requiring that the equations of quantum mechanics had a particular symmetry - the measurements they ... 04:54: ... pops into the equations as soon as we require this - but in that version of electromagnetism, ...
	2021-09-21: How Electron Spin Makes Matter Possible 13:25: ... It boils down to the fact that you need to use spinors in the Dirac equation - which is the quantum equation of motion for electrons and other spin-½ ... 13:49: ... equation by itself doesn’t force you to use symmetric or anti-symmetric ... 13:25: ... It boils down to the fact that you need to use spinors in the Dirac equation - which is the quantum equation of motion for electrons and other spin-½ ...
	2021-09-07: First Detection of Light from Behind a Black Hole 13:56: Karina makes a similar style of argument - saying that this crazy idea just makes it even more convincing that Schrodinger's equation is linear. 14:07: ... other words, if the non-linearity of the schrodinger equation allows these paradox-generating phenomena, then we can take that as ...
	2021-08-10: How to Communicate Across the Quantum Multiverse 02:56: ... happening behind the math - what “physical” mechanisms give rise to the equations of quantum mechanics. And the fact is, every prominent interpretation of ... 03:30: ... Schrodinger equation describes how the wavefunction of a quantum system changes over space ... 03:55: ... turns out there might be a way - but only if the Schrodinger equation is wrong. Well, not wrong but incomplete. There are certain additional ... 05:54: ... treated independently. A linear restoring force leads to a linear wave equation - and a linear wave equation is what you need for the superposition ... 06:28: ... the Schrodinger equation as we usually write it is a perfectly linear equation, and in quantum ... 07:14: ... He realized that even a tiny deviation from linearity in the Schrodinger equation would add extra non-linear observables to the wavefunction. The normal ... 08:08: ... Polchinski showed that almost any non-linear addition to the Schrodinger equation would mean that information could be sent between entangled pairs of ... 08:55: ... delicate. Almost ANY deviation from perfect linearity in the Schrodinger equation would make it possible to send real information between entangled pairs ... 09:23: ... He follows up by finding a way to write one non-linear Schrodinger equation that avoids the causality-breaking prospect of faster-than-light ... 05:54: ... treated independently. A linear restoring force leads to a linear wave equation - and a linear wave equation is what you need for the superposition ... 03:30: ... Schrodinger equation describes how the wavefunction of a quantum system changes over space and time - ... 02:56: ... happening behind the math - what “physical” mechanisms give rise to the equations of quantum mechanics. And the fact is, every prominent interpretation of ...
	2021-08-03: How An Extreme New Star Could Change All Cosmology 05:01: ... the only thing we’re missing from this equation for size is the distance to this star - and of all of these things ...
	2021-07-13: Where Are The Worlds In Many Worlds? 04:38: To calculate this we use the Schrodinger equation, which tells us how the amplitude of the wavefunction changes over time and space. 05:42: ... causes this random selection is not the Schrodinger equation - it’s something extra, and Copenhagen doesn’t explain why or when this ... 05:53: It says that the wavefunction never collapses - it evolves forever by the Schrodinger equation. 05:42: ... causes this random selection is not the Schrodinger equation - it’s something extra, and Copenhagen doesn’t explain why or when this ...
	2021-07-07: Electrons DO NOT Spin 07:30: ... excited about a brand new tool they’d been given - the Schrodinger equation. This equation  describes how quantum objects behave as evolving ... 08:28: ... Paul Dirac found his own even more complete fix of the Schrodinger equation - in this case to make it work with Einstein’s special theory of ... 07:30: ... a brand new tool they’d been given - the Schrodinger equation. This equation  describes how quantum objects behave as evolving distributions of ...
	2021-06-23: How Quantum Entanglement Creates Entropy 04:50: ... should call it entropy for 2 reasons: 1. it looks exactly like the equation   for thermodynamic entropy, and 2. nobody knows what entropy is, so ...
	2021-06-16: Can Space Be Infinitely Divided? 01:16: ... Planck’s discovery hinges on a single  number that appears in his equation - the   Planck constant. It represents the  chunkiness of ... 05:45: ... mass and energy are equivalent, as expressed by the most famous equation ever, E=mc2;   and second, that mass and energy warp the ... 06:02: ... creates what we call effective mass, according to Einstein’s famous equation. The resulting   gravitational field changes the distance to ... 01:16: ... Planck’s discovery hinges on a single  number that appears in his equation - the   Planck constant. It represents the  chunkiness of ...
	2021-05-25: What If (Tiny) Black Holes Are Everywhere? 00:50: ... Stephen Hawking showed that if you bring quantum mechanics into the equation, quite literally, then the black hole is neither black nor ...
	2021-04-21: The NEW Warp Drive Possibilities 01:34: ... inspired the very first real warp field solution to the Einstein field equations. ... 03:29: It’s a sp acetime geometry that is a valid solution to the equations general theory of relativity. The Einstein Field Equation. 03:54: The Alcubierre warp field may be a valid solution to the Einstein field equations, but that doesn’t mean it’s physically possible. 04:01: ... to solve these equations we input a physically possible distribution of mass, energy, on the ... 04:11: ... instead solved the equations backwards - he figured out the geometry of a warp bubble, and then ran ... 04:31: ... we have a set of energy conditions that go alongside the Einstein field equations that are meant to restrict the allowable energy distributions to what is ... 06:51: These guys propose a general definition for warp fields not tied to a particular solution to the Einstein field equations. 08:20: The velocity of the bubble is baked into the equation for the field geometry, but it’s not clear how you change that velocity. 09:19: He does this by exploring a broader family of solutions to the Einstein field equations than previous studies. 01:34: ... inspired the very first real warp field solution to the Einstein field equations. ... 03:29: It’s a sp acetime geometry that is a valid solution to the equations general theory of relativity. The Einstein Field Equation. 03:54: The Alcubierre warp field may be a valid solution to the Einstein field equations, but that doesn’t mean it’s physically possible. 04:01: ... to solve these equations we input a physically possible distribution of mass, energy, on the ... 04:11: ... instead solved the equations backwards - he figured out the geometry of a warp bubble, and then ran ... 04:31: ... we have a set of energy conditions that go alongside the Einstein field equations that are meant to restrict the allowable energy distributions to what is ... 06:51: These guys propose a general definition for warp fields not tied to a particular solution to the Einstein field equations. 09:19: He does this by exploring a broader family of solutions to the Einstein field equations than previous studies. 04:11: ... instead solved the equations backwards - he figured out the geometry of a warp bubble, and then ran it ... 03:29: It’s a sp acetime geometry that is a valid solution to the equations general theory of relativity. The Einstein Field Equation.
	2021-04-07: Why the Muon g-2 Results Are So Exciting! 03:50: Here's the equation for the classical dipole moment for a nonquantum rotating charge. 05:41: Paul Dirac first calculated g equals two from his eponymous equation.
	2021-03-09: How Does Gravity Affect Light? 12:08: ... you solve Einstein’s equations in a different way, you can show that gravity is due to a free-falling ...
	2021-02-24: Does Time Cause Gravity? 06:29: ... when we try to convert mass into energy via Einstein’s most famous equation, E=mc^2 - the speed of light is the exchange rate, and the speed of light ...
	2020-12-08: Why Do You Remember The Past But Not The Future? 00:06: The equations we use to describe how things evolve forward in time also perfectly describe their evolution backwards in time.
	2020-11-18: The Arrow of Time and How to Reverse It 00:24: ... between the future and the past. Reverse the flow of time and their equations work exactly the same to describe a universe in rewind. That’s true from ... 02:31: ... it still looks like two electrons bouncing off each other. The same equations perfectly describe the bounce in both directions, and those equations ... 00:24: ... between the future and the past. Reverse the flow of time and their equations work exactly the same to describe a universe in rewind. That’s true from ... 02:31: ... it still looks like two electrons bouncing off each other. The same equations perfectly describe the bounce in both directions, and those equations ... 00:24: ... between the future and the past. Reverse the flow of time and their equations work exactly the same to describe a universe in rewind. That’s true from the ...
	2020-11-04: Electroweak Theory and the Origin of the Fundamental Forces 02:56: QED is what we call a gauge theory - its force-carrying fields and particles arise from the symmetries of the quantum equations of motion. 05:01: Quantum mechanical equations of motion like the Schrodinger equation describe how the wavefunction evolves through space and time. 05:27: For that to be the case, we need to add some stuff to the Schrodinger equation. 05:42: So there we go - we insisted on a symmetry - that the Schrodinger equation is invariant to changes in the local phase of the wavefunction. 05:54: So that is gauge theory in a nutshell: it explains a force by imposing symmetries on the equations of motion. 06:57: ... by just one function, like our single wavefunction from the Schrodinger equation. ... 07:08: Imposing this U(1) symmetry on our equations of motion led us to something very real and physical - electromagnetism. 07:46: If we require our equations of motion to respect SU(2) we have to introduce a new field with 3 degrees of freedom. 08:50: ... an extra term to the electromagnetic field stuff in the Schrodinger equation so that it would no longer be invariant to local phase ... 09:16: ... possible for the equations of motion describing a system to have a particular symmetry - to not ... 09:42: ... equations of motion governing the overall magnetisation of this material aren’t ... 09:53: This represents the symmetry in our equations. 10:30: Even though the equations of motion say one direction is not preferred to the other, the ground state has randomly picked out a single direction. 10:48: ... the equations of motion respect the symmetries that give us the necessary gauge field, ... 12:33: We just asked what would happen if the equations of motion governing nature had certain symmetries. 02:56: QED is what we call a gauge theory - its force-carrying fields and particles arise from the symmetries of the quantum equations of motion. 05:01: Quantum mechanical equations of motion like the Schrodinger equation describe how the wavefunction evolves through space and time. 05:54: So that is gauge theory in a nutshell: it explains a force by imposing symmetries on the equations of motion. 07:08: Imposing this U(1) symmetry on our equations of motion led us to something very real and physical - electromagnetism. 07:46: If we require our equations of motion to respect SU(2) we have to introduce a new field with 3 degrees of freedom. 09:16: ... possible for the equations of motion describing a system to have a particular symmetry - to not ... 09:42: ... equations of motion governing the overall magnetisation of this material aren’t ... 09:53: This represents the symmetry in our equations. 10:30: Even though the equations of motion say one direction is not preferred to the other, the ground state has randomly picked out a single direction. 10:48: ... the equations of motion respect the symmetries that give us the necessary gauge field, ... 12:33: We just asked what would happen if the equations of motion governing nature had certain symmetries.
	2020-10-27: How The Penrose Singularity Theorem Predicts The End of Space Time 01:17: ... Schwarzschild solved the equations of general relativity soon after Einstein published ... 13:38: ... nothing but the evolution of the wavefunction under the Schrodinger equation. Other   interpretations - Copenhagen, pilot wave ... 01:17: ... Schwarzschild solved the equations of general relativity soon after Einstein published ...
	2020-10-20: Is The Future Predetermined By Quantum Mechanics? 04:23: ... wave function evolves in a precise way, perfectly defined by the equations of quantum mechanics but at the moment of measurement, a single reality ...
	2020-09-08: The Truth About Beauty in Physics 00:20: ... is a powerful guiding force towards truth - the more beautiful the equations of a proposed law of physics, the more likely it is to truly represent ... 02:41: Einstein’s equations of general relativity give even better precision than Newton’s law - perhaps perfect precision - in their description of gravity. 02:57: Yet the equations of general relativity are notoriously complex. 03:02: ... who’ve studied the field equations deeply find it supremely elegant - but it’s not straightforward to ... 04:36: ... to derive our laws of physics, and so perhaps it’s not surprising these equations possess some of the beauty of the underlying ... 07:19: ... of quantum mechanics, said “It is more important to have beauty in one's equation than to have them fit experiment.” By which he meant that an experiment ... 07:49: He sought to develop a quantum mechanical wave equation that agreed with Einstein’s special relativity. 08:11: The resulting Dirac equation is the entirely correct relativistic quantum description of the behavior of the electron. 08:45: ... was discovered only a couple of years after the 1929 publication of his equation. ... 09:09: The equations of physical law are beautiful if you get out more than you put in. 09:21: The Dirac equation is a good example. 09:30: And Maxwell’s equations, which parsimoniously unite electricity and magnetism but also predict the existence of electromagnetic waves - of light. 09:39: And then there’s Einstein’s field equations of general relativity. 10:46: The first compellingly beautiful aspect of string theory is that gravity, in the form of the Einstein field equations - automatically emerged from it. 00:20: ... is a powerful guiding force towards truth - the more beautiful the equations of a proposed law of physics, the more likely it is to truly represent ... 02:41: Einstein’s equations of general relativity give even better precision than Newton’s law - perhaps perfect precision - in their description of gravity. 02:57: Yet the equations of general relativity are notoriously complex. 03:02: ... who’ve studied the field equations deeply find it supremely elegant - but it’s not straightforward to ... 04:36: ... to derive our laws of physics, and so perhaps it’s not surprising these equations possess some of the beauty of the underlying ... 09:09: The equations of physical law are beautiful if you get out more than you put in. 09:30: And Maxwell’s equations, which parsimoniously unite electricity and magnetism but also predict the existence of electromagnetic waves - of light. 09:39: And then there’s Einstein’s field equations of general relativity. 10:46: The first compellingly beautiful aspect of string theory is that gravity, in the form of the Einstein field equations - automatically emerged from it. 03:02: ... who’ve studied the field equations deeply find it supremely elegant - but it’s not straightforward to define where ... 04:36: ... to derive our laws of physics, and so perhaps it’s not surprising these equations possess some of the beauty of the underlying ...
	2020-08-10: Theory of Everything Controversies: Livestream 00:00: ... the keys under the lamppost because that's how they know to solve the equations the the other part of the question is the one that i think is is not ...
	2020-07-28: What is a Theory of Everything: Livestream 00:00: ... the assumptions you made about quantum mechanics pops out of the equations out of that equation gravity quote unquote albeit and 10 dimensions ...
	2020-06-22: Building Black Holes in a Lab 03:26: ... had much more in common, mathematically speaking. It turns out that the equations of fluid dynamics can be expressed in a form that is a close analogy to ...
	2020-05-18: Mapping the Multiverse 00:09: ... in english: when you solve Einstein’s equations of general relativity for a rotating black hole, the universe does not ... 05:33: ... order to create these maps of spacetime, physicists use the equations of general relativity to trace what we call geodesics - these are the ... 00:09: ... in english: when you solve Einstein’s equations of general relativity for a rotating black hole, the universe does not ... 05:33: ... order to create these maps of spacetime, physicists use the equations of general relativity to trace what we call geodesics - these are the ...
	2020-05-11: How Luminiferous Aether Led to Relativity 05:53: ... like a wave. Add to that the fact that in the 1860s, Maxwell’s equations predicted that electromagnetic waves should travel at exactly the speed ... 11:42: ... starting motivation seems to have been the fact that the Maxwell equations are also a little broken under Galilean relativity. But the death of the ... 05:53: ... like a wave. Add to that the fact that in the 1860s, Maxwell’s equations predicted that electromagnetic waves should travel at exactly the speed ... 11:42: ... starting motivation seems to have been the fact that the Maxwell equations are also a little broken under Galilean relativity. But the death of the ... 05:53: ... like a wave. Add to that the fact that in the 1860s, Maxwell’s equations predicted that electromagnetic waves should travel at exactly the speed of … wait ...
	2020-05-04: How We Know The Universe is Ancient 03:24: ... Russian cosmologist Alexander Friedmann solved Einstein’s equations and found the possibility of a universe that could change in size - a ... 04:40: ... So if we can predict that the big bang by rewinding the Friedman equations, surely we can also predict how long ago it happened. Think of it this ... 11:07: ... effect of dark energy speeding it up. Those can be put into the Friedman equations and a bit of calculus later gets you an age. The real hard part is ... 12:59: ... of other quantities. Quantities important for plugging into the Friedman equations, which define the way the universe would expand in the many billions of ... 16:15: ... can write down a solution to the Einstein equations in which the wormhole throat is short, and it has no relationship to the ... 03:24: ... Russian cosmologist Alexander Friedmann solved Einstein’s equations and found the possibility of a universe that could change in size - a ... 04:40: ... So if we can predict that the big bang by rewinding the Friedman equations, surely we can also predict how long ago it happened. Think of it this ... 11:07: ... effect of dark energy speeding it up. Those can be put into the Friedman equations and a bit of calculus later gets you an age. The real hard part is ... 12:59: ... of other quantities. Quantities important for plugging into the Friedman equations, which define the way the universe would expand in the many billions of ... 16:15: ... can write down a solution to the Einstein equations in which the wormhole throat is short, and it has no relationship to the ... 12:59: ... other approaches to getting the necessary numbers to fuel the Friedman equations - and despite some intriguing conflicts - different methods are mostly in ... 04:40: ... So if we can predict that the big bang by rewinding the Friedman equations, surely we can also predict how long ago it happened. Think of it this way - if ...
	2020-04-28: Space Time Livestream: Ask Matt Anything 00:00: ... awkward silence awkward silence and then Paul Dirac says I have an equation do you have one - yeah so Paul Dirac had the direct equation which ...
	2020-04-22: Will Wormholes Allow Fast Interstellar Travel? 00:23: ... 1915, Karl Schwarzschild discovered a solution to Einstein’s brand new equations of general relativity - a solution that we now understand describes a ... 07:31: ... knew that too, and so quickly derived the equations describing an actual traversable wormhole. As the story goes, scribbling ... 07:52: ... just how do you design a traversable wormhole? Well, the equations of general relativity permit any smoothly-varying shape for the fabric ... 09:17: ... are placed on allowable distributions of mass and energy in Einstein’s equation in order for those equations to make physical sense. But these energy ... 00:23: ... 1915, Karl Schwarzschild discovered a solution to Einstein’s brand new equations of general relativity - a solution that we now understand describes a ... 07:31: ... knew that too, and so quickly derived the equations describing an actual traversable wormhole. As the story goes, scribbling ... 07:52: ... just how do you design a traversable wormhole? Well, the equations of general relativity permit any smoothly-varying shape for the fabric ... 09:17: ... of mass and energy in Einstein’s equation in order for those equations to make physical sense. But these energy conditions are more guidelines ... 07:31: ... knew that too, and so quickly derived the equations describing an actual traversable wormhole. As the story goes, scribbling in the ...
	2020-03-31: What’s On The Other Side Of A Black Hole? 00:37: ... coordinate singularities. A singularity is where a variable in the equation becomes infinite - and a single swivel at a pole carries you through the ...
	2020-03-24: How Black Holes Spin Space Time 00:21: ... physicist named Karl Schwarzschild was the first to fully solve its equations for a realistic situation. Schwarzschild’s eponymous metric describes ... 02:36: ... of spin in black holes, it took nearly half a century before Einstein’s equations were solved for the rotating case. That was by Roy Kerr in 1963, ... 00:21: ... physicist named Karl Schwarzschild was the first to fully solve its equations for a realistic situation. Schwarzschild’s eponymous metric describes ... 02:36: ... of spin in black holes, it took nearly half a century before Einstein’s equations were solved for the rotating case. That was by Roy Kerr in 1963, ...
	2020-02-24: How Decoherence Splits The Quantum Multiverse 02:04: Wavefunctions evolve over time according to the Schrodinger equation, and that evolution tracks how the system’s properties might change.
	2020-02-18: Does Consciousness Influence Quantum Mechanics? 00:52: ... quantum mechanics and physicists are still debating how to interpret its equations and the weirdness they ...
	2020-02-11: Are Axions Dark Matter? 01:05: ... be symmetric with respect to certain properties of the universe. If the equations describing a given physical process do not change when you transform a ... 02:35: ... get its own episode before long. For now it’s enough to know that the equations of motion of the strong force, derived with QCD, actually allow ... 04:33: ... those states at once. This bizarre structure for the vacuum alters the equations of motion that come from QCD, new terms get added and the strength of ... 14:39: ... is spatially finite. The simplest interpetation of the cosmological equations derived from general relativity tell us that it it may be truly ... 01:05: ... be symmetric with respect to certain properties of the universe. If the equations describing a given physical process do not change when you transform a ... 02:35: ... get its own episode before long. For now it’s enough to know that the equations of motion of the strong force, derived with QCD, actually allow ... 04:33: ... those states at once. This bizarre structure for the vacuum alters the equations of motion that come from QCD, new terms get added and the strength of ... 14:39: ... is spatially finite. The simplest interpetation of the cosmological equations derived from general relativity tell us that it it may be truly ... 01:05: ... be symmetric with respect to certain properties of the universe. If the equations describing a given physical process do not change when you transform a particular ...
	2020-02-03: Are there Infinite Versions of You? 00:14: ... cosmological equations that so beautifully describe our universe make an uncomfortable ... 00:26: ... be finite, or perhaps the simplest interpretation of the cosmological equations is too ... 10:31: ... still have to hope that it’s reasonable to extrapolate our cosmological equations ... 13:03: It's hard to write down a simple equation of motion when the coordinate system is changing. 13:09: ... much heavier than the other then the Schwarzschild solution gives simple equations for orbits which work pretty well as long as the bodies aren't too close ... 00:14: ... cosmological equations that so beautifully describe our universe make an uncomfortable ... 00:26: ... be finite, or perhaps the simplest interpretation of the cosmological equations is too ... 10:31: ... still have to hope that it’s reasonable to extrapolate our cosmological equations ... 13:09: ... much heavier than the other then the Schwarzschild solution gives simple equations for orbits which work pretty well as long as the bodies aren't too close ... 10:31: ... still have to hope that it’s reasonable to extrapolate our cosmological equations forever. ...
	2020-01-27: Hacking the Nature of Reality 01:08: ... followed - for example, the wave mechanics driven by the Schrodinger equation and Paul Dirac’s notation representing evolution in a space of quantum ...
	2020-01-20: Solving the Three Body Problem 00:20: ... in 1687 when Isaac Newton published his Principia. Within it were equations of motion and gravity that transformed our erratic-seeming cosmos into a ... 01:24: ... and his law of universal gravitation give us a set of differential equations. In some cases these can be solved with Newton’s other great invention - ... 01:49: ... equations will then give you the state of the system at that time, no matter how ... 02:06: ... of two gravitating bodies, the solutions to Newton’s laws are just the equations for the path traveled by the bodies - be it the parabola of a thrown ... 06:09: ... method of solving differential equations one step at a time is called numerical integration, and when applied to ... 06:43: ... 5 additional orbits for a third body that can be described with simple equations. These are the only perfectly analytical solutions to the three body ... 08:46: ... came up with a fascinating way to depict them in the absence of simple equations. It’s called the shape-sphere, and it works like this. Imagine the bodies ... 12:21: ... successive terms diminished to effectively nothing, so in principle the equation could be written out on paper. However the convergence of Sundman’s ... 01:24: ... solved with Newton’s other great invention - calculus - to give a simple equation. Plug numbers into that equation and its solved. Those numbers are the ... 00:20: ... in 1687 when Isaac Newton published his Principia. Within it were equations of motion and gravity that transformed our erratic-seeming cosmos into a ... 01:24: ... and his law of universal gravitation give us a set of differential equations. In some cases these can be solved with Newton’s other great invention - ... 01:49: ... equations will then give you the state of the system at that time, no matter how ... 02:06: ... of two gravitating bodies, the solutions to Newton’s laws are just the equations for the path traveled by the bodies - be it the parabola of a thrown ... 06:09: ... method of solving differential equations one step at a time is called numerical integration, and when applied to ... 06:43: ... 5 additional orbits for a third body that can be described with simple equations. These are the only perfectly analytical solutions to the three body ... 08:46: ... came up with a fascinating way to depict them in the absence of simple equations. It’s called the shape-sphere, and it works like this. Imagine the bodies ...
	2019-12-02: Is The Universe Finite? 12:30: ... explore the experiments of quantum mechanics and use them to construct equations of motion, laws of physics, and systems of measurement based on the ...
	2019-11-11: Does Life Need a Multiverse to Exist? 00:26: Our universe seems to operate according to a set of fundamental rules that we try to understand and model with the equations of our laws of physics. 00:35: Those equations always include one or more fundamental constants - simple numbers that set the scale for the equation. 00:26: Our universe seems to operate according to a set of fundamental rules that we try to understand and model with the equations of our laws of physics. 00:35: Those equations always include one or more fundamental constants - simple numbers that set the scale for the equation.
	2019-10-21: Is Time Travel Impossible? 00:41: ... the way we think about time forever, and believe it or not, their raw equations permit time ... 02:23: ... notice I said “regular mass.” We can hack the equations of special relativity by allowing mass to take values in the weird realm ... 03:00: This is an example where the equations of a theory technically allow something to be true, but there’s still no good reason to believe that it is. 05:00: The equations of GR do permit large wormholes, but they are definitely not stable. 06:25: While the actual equations of general relativity themselves don’t prohibit it, there are a set of secondary rules in GR that do. 07:05: One example is the Tipler cylinder, conceived by Frank Tipler based on a solution to the Einstein equations by Willem van Stockum. 00:41: ... the way we think about time forever, and believe it or not, their raw equations permit time ... 02:23: ... notice I said “regular mass.” We can hack the equations of special relativity by allowing mass to take values in the weird realm ... 03:00: This is an example where the equations of a theory technically allow something to be true, but there’s still no good reason to believe that it is. 05:00: The equations of GR do permit large wormholes, but they are definitely not stable. 06:25: While the actual equations of general relativity themselves don’t prohibit it, there are a set of secondary rules in GR that do. 07:05: One example is the Tipler cylinder, conceived by Frank Tipler based on a solution to the Einstein equations by Willem van Stockum. 00:41: ... the way we think about time forever, and believe it or not, their raw equations permit time ...
	2019-10-15: Loop Quantum Gravity Explained 01:46: ... mechanics, and indeed most theories in physics, involve a set of equations describing how stuff moves around, exerts force, etc. on some background ... 02:23: General relativity, on the other hand, has to be background independent - because that’s what its equations do - they change the background. 02:41: ... the geometry and causal structure of spacetime - evolves in the equations of GR. So those equations need to work regardless of that ... 05:19: ... equations of quantum mechanics let you calculate changing properties of a ... 05:28: The equations of general relativity let you calculate the changing shape of the coordinate system itself, encapsulated in the metric. 05:45: ... instead of an equation that describes the quantum evolution of the properties of an object in ... 06:01: It’s called the Wheeler-deWitt equation, based on something called the ADM Formalism. 06:20: It then gives a sort of equation of motion for how these metrics evolve through time. 06:43: So the Wheeler-deWitt equation quantizes these - turns them into quantum operators. 06:48: The result is a quantum equation for the fabric of space. 06:57: The Wheeler-deWitt equation was promising, but turned out to be … unsolvable. 09:04: ... and Carlo Rovelli realized they could fully solve the Wheeler-deWitt equation by representing spatial metrics using Ashketar's spin ... 11:20: ... and black hole entropy consistent with Hawking and Bekenstein’s equations. ... 11:54: ... generally, for this theory to be successful it needs give you the equations of good old general relativity on large, non-quantum scales - in the ... 16:29: ... the answer lies in the Einstein field equation of general relativity That equation says that the amount stretching of ... 06:01: It’s called the Wheeler-deWitt equation, based on something called the ADM Formalism. 06:43: So the Wheeler-deWitt equation quantizes these - turns them into quantum operators. 01:46: ... mechanics, and indeed most theories in physics, involve a set of equations describing how stuff moves around, exerts force, etc. on some background ... 02:23: General relativity, on the other hand, has to be background independent - because that’s what its equations do - they change the background. 02:41: ... the geometry and causal structure of spacetime - evolves in the equations of GR. So those equations need to work regardless of that ... 05:19: ... equations of quantum mechanics let you calculate changing properties of a ... 05:28: The equations of general relativity let you calculate the changing shape of the coordinate system itself, encapsulated in the metric. 11:20: ... and black hole entropy consistent with Hawking and Bekenstein’s equations. ... 11:54: ... generally, for this theory to be successful it needs give you the equations of good old general relativity on large, non-quantum scales - in the ... 01:46: ... mechanics, and indeed most theories in physics, involve a set of equations describing how stuff moves around, exerts force, etc. on some background coordinate ...
	2019-08-19: What Happened Before the Big Bang? 00:04: That is as long as you define 'The Big Bang' as the universe's early hot dense expanding state that's well described by Einstein's equations. 10:51: ... could be explained by an expanding universe and solved Einstein's equations to show ... 00:04: That is as long as you define 'The Big Bang' as the universe's early hot dense expanding state that's well described by Einstein's equations. 10:51: ... could be explained by an expanding universe and solved Einstein's equations to show ...
	2019-08-06: What Caused the Big Bang? 02:26: First up, the equations of Einstein's general theory of relativity. 03:23: ... if the vacuum of space has a constant energy density, then Einstein's equations end up having a term that we call the cosmological constant - A positive ... 02:26: First up, the equations of Einstein's general theory of relativity. 03:23: ... if the vacuum of space has a constant energy density, then Einstein's equations end up having a term that we call the cosmological constant - A positive ...
	2019-07-18: Did Time Start at the Big Bang? 00:25: ... expansion far enough - mathematically - purely according to Einstein's equations, it seems inevitable that all space and mass and energy should once have ... 01:56: ... In fact, There's powerful evidence that we should not rewind Einstein's equations that far, at least without introducing some very new physics For one ... 00:25: ... expansion far enough - mathematically - purely according to Einstein's equations, it seems inevitable that all space and mass and energy should once have ... 01:56: ... In fact, There's powerful evidence that we should not rewind Einstein's equations that far, at least without introducing some very new physics For one ...
	2019-06-17: How Black Holes Kill Galaxies 11:24: ... quantum physics or brush up on your complex algebra and differential equations you can learn more at Brilliant.org/spacetime Last time we talked about ...
	2019-05-01: The Real Science of the EHT Black Hole 10:33: ... black holes emerged from Karl Schwarzschild’s solution to the Einstein equations, they seemed like a deep abstraction – a prediction that seemed too ...
	2019-04-10: The Holographic Universe Explained 01:19: The story started with black holes, and with Jacob Bekenstein, who derived an equation to describe their entropy. 08:23: ... weird thing is that when you write the quantum wave equation for the gluon strand with length expressed as a separate dimension you ...
	2019-04-03: The Edge of an Infinite Universe 07:25: ... we write the equations of these fields in Penrose’s compactified coordinates then we can do ...
	2019-03-28: Could the Universe End by Tearing Apart Every Atom? 00:25: ... describe a constant energy density with the cosmological constant in the equations of Einstein's general theory of relativity but what if dark energy is ... 01:55: ... into the mysteries of dark energy we actually used math the Friedmann equations we're not going to go so deep here but we are gonna take a quick methy ... 03:05: ... beautiful thing is the second Friedman equation it's basically the equivalent of Newton's law of gravity for the whole ... 04:32: ... the pressure that it exerts but now that pressure term is important the equation of state of dark energy is pressure divided by density equals -1. That ... 05:32: ... energy is pushing outwards to increase the expansion rate. In fact, any equation of state parameter less than -1/3 would cause that effect. It would mean ... 06:03: ... episode. For today, let's push things to the limit: What if we make the equation of state parameter smaller than negative ... 08:25: ... a name, we call any dark energy that increases in strength - so with an equation of state less than -1, 'phantom ... 08:59: Any equation of state parameter smaller than -1 means a big rip. 10:45: Our efforts to understand the nature of dark energy are focused on measuring the value of this 'equation of state parameter thing'. 11:08: Combined with a few other measures these tell us that the equation of state of dark energy is very very close to -1. 12:40: ... acceleration rate measured using distant quasars hints at an equation of state parameter slightly less than negative 1 well they're not yet ... 03:05: ... energy density and no real pressure leaves the right side of the equation negative so negative acceleration matter on its own can only cause deceleration ... 04:32: ... emo - that cancels this negative sign and makes the right side of the equation positive. ... 03:05: ... density, the "equation of state" it's a simplification of the good ol equation PV Eagles NKT relating pressure volume temperature and the amount of stuff ... 00:25: ... describe a constant energy density with the cosmological constant in the equations of Einstein's general theory of relativity but what if dark energy is ... 01:55: ... into the mysteries of dark energy we actually used math the Friedmann equations we're not going to go so deep here but we are gonna take a quick methy ...
	2019-02-07: Sound Waves from the Beginning of Time 16:08: In so-called bimetric gravity, you can have positive and negative masses, but each is described by its own set of Einstein field equations.
	2019-01-30: Perpetual Motion From Negative Mass? 07:05: In fact, in pure general relativity, inertial and passive gravitational masses don’t even appear in the equations. 10:58: ... spacetime – are the GR analogs of Newton’s second law and give the equations of motion of ... 11:10: ... are calculated from the geodesic equation, which itself arises directly from the equivalence principle, or from ... 07:05: In fact, in pure general relativity, inertial and passive gravitational masses don’t even appear in the equations. 10:58: ... spacetime – are the GR analogs of Newton’s second law and give the equations of motion of ...
	2019-01-24: The Crisis in Cosmology 05:27: Riess's Supernovae H0 for the Equation of State project, - SHOES -,...
	2019-01-09: Are Dark Matter And Dark Energy The Same? 02:43: The big reveal was in this one, where we pick apart the second Friedmann equation. 02:47: That’s the solution to the Einstein equations that tells you the rate of acceleration of the expansion of the universe. 03:34: In Einstein’s equations and the Friedmann equations, that constant energy density is represented by the cosmological constant, or Lambda. 05:14: In this equation, mass is inertial mass. 05:29: For a negative mass, this equation suggests that acceleration is in the opposite direction to the applied force. 08:18: ... we look at the second Friedmann equation, which is really the analog of Newton’s law of gravity for the whole ... 09:15: ... uses the first Friedmann equation – that’s this thing - to correctly conclude that a universe with a ... 05:14: In this equation, mass is inertial mass. 05:29: For a negative mass, this equation suggests that acceleration is in the opposite direction to the applied force. 02:47: That’s the solution to the Einstein equations that tells you the rate of acceleration of the expansion of the universe. 03:34: In Einstein’s equations and the Friedmann equations, that constant energy density is represented by the cosmological constant, or Lambda.
	2018-12-20: Why String Theory is Wrong 02:43: ... right sort of 5-D space-time, you can separate the resulting Einstein equations into a 4-D component that looks exactly like the familiar general ... 03:00: Crazily, that math also looked familiar. It looked like Maxwell's equations for electromagnetism. 15:37: ... in quantum physics or brush up on your complex algebra and differential equations you can learn more at brilliant org slash space-time Now before I get to ... 02:43: ... right sort of 5-D space-time, you can separate the resulting Einstein equations into a 4-D component that looks exactly like the familiar general ... 03:00: Crazily, that math also looked familiar. It looked like Maxwell's equations for electromagnetism. 15:37: ... in quantum physics or brush up on your complex algebra and differential equations you can learn more at brilliant org slash space-time Now before I get to ...
	2018-12-12: Quantum Physics in a Mirror Universe 00:02: ... quantum physics or brush up on your complex algebra and differential equations you can learn more at brilliant org slash spacetime before we get to ...
	2018-11-07: Why String Theory is Right 06:05: ... do this, you basically take the classical equations of motion and follow a standard recipe to turn them into wave equations ... 06:21: This is a tricky process, and it only works if your equations of motion are especially friendly. 06:28: Schrodinger's equation is the first and easiest example. 06:31: It quantizes the equations of motion of slow-moving, point-like particles. 06:36: A while ago, we talked about Paul Dirac developed a wave equation for the electron that took into account Einstein's special theory of relativity. 07:02: The resulting Dirac equation is incredibly elegant, and in the pursuit of that elegance Dirac predicted the existence of antimatter. 08:28: In the raw Schrodinger equation, you can't. 08:35: ... out that you can add a very special corrective term to the Schrodinger equation that fixes these phase differences preserving local phase ... 08:47: That term looks like what you would get if you added the electromagnetic field to the Schrodinger equation. 10:41: ... out that surface mathematically and write a nice, simple quantum wave equation from the equations of motion, but only for 1D strings making a 2D world ... 11:07: ... required us to add the electromagnetic field to the Schrodinger equation, adding Weyl invariance means we need to add a new ... 11:28: So, with our quantized equations of motion in hand, you can predict the quantum oscillations of our string. 11:07: ... required us to add the electromagnetic field to the Schrodinger equation, adding Weyl invariance means we need to add a new ... 06:05: ... do this, you basically take the classical equations of motion and follow a standard recipe to turn them into wave equations ... 06:21: This is a tricky process, and it only works if your equations of motion are especially friendly. 06:31: It quantizes the equations of motion of slow-moving, point-like particles. 10:41: ... mathematically and write a nice, simple quantum wave equation from the equations of motion, but only for 1D strings making a 2D world sheet, not for any ... 11:28: So, with our quantized equations of motion in hand, you can predict the quantum oscillations of our string.
	2018-10-31: Are Virtual Particles A New Layer of Reality? 01:05: The quantization part of his math trick was meant to disappear in the final form of the equation, but it remained.
	2018-10-25: Will We Ever Find Alien Life? 07:13: ... is often done in terms of the famous Drake equation, which tries to estimate the current number of communicative ... 09:37: That is perhaps it's one of the biological factors of the Drake equation that keeps the number of aliens low.
	2018-10-18: What are the Strings in String Theory? 00:51: Its equations predict many things with stunning accuracy, but they first required us to tune many mathematical knobs and dials.
	2018-09-20: Quantum Gravity and the Hardest Problem in Physics 02:41: That math started with the Schrodinger equation, which tracks these probability waves through space and time. 02:49: But the Schrodinger equation treats space and time as fundamentally separate in the old-fashioned Newtonian way. 02:58: We already talked about how Paul Dirac fixed part of the problem with a relativistic wave equation for the electron. 02:49: But the Schrodinger equation treats space and time as fundamentally separate in the old-fashioned Newtonian way.
	2018-09-05: The Black Hole Entropy Enigma 00:40: At least they are inevitable according to the equations of Einstein's general theory of relativity. 07:10: ... also realized that the equation relating the change in black-hole surface area to the change in its mass ... 07:29: ... you extract energy from the black hole, and it looks the same as the equation for the work extracted from a thermodynamic ... 09:26: ... Hawking just plugged his Hawking temperature into that equation along with black-hole mass for internal energy and figured out the total ... 07:10: ... also realized that the equation relating the change in black-hole surface area to the change in its mass closely ... 00:40: At least they are inevitable according to the equations of Einstein's general theory of relativity.
	2018-08-23: How Will the Universe End? 14:44: This, in essence, is because his equation has the charge and mass distributed differently.
	2018-08-15: Quantum Theory's Most Incredible Prediction 05:38: Experiments point to this but so does the Dirac equation. 05:42: This equation is the origin of quantum electrodynamics and the first to correctly capture the notion of quantum spin. 06:09: ... even though the Dirac equation tells us how a relativistic electron would interact with an ...
	2018-07-25: Reversing Entropy with Maxwell's Demon 04:59: As well as unifying the equations of electromagnetism, James Clerk Maxwell was one of the founders of statistical mechanics. 10:34: If you take all possible results of the die roll to be equally likely, then Shannon's formula looks just like the Boltzmann equation. 12:01: Starting with this assumption gets you to the Boltzmann equation, and it's a nice, relatively simple way to understand entropy. 12:13: If different microstates can have different probabilities, then you need to include those probabilities in your equation for entropy. 12:20: ... resulting formula, the Gibbs entropy equation, was derived soon after Boltzmann's equation, and is the more general ... 04:59: As well as unifying the equations of electromagnetism, James Clerk Maxwell was one of the founders of statistical mechanics.
	2018-07-18: The Misunderstood Nature of Entropy 07:47: ... Boltzmann equation tells us that entropy is the logarithm of the number of microstates ...
	2018-07-11: Quantum Invariance & The Origin of The Standard Model 00:33: Our laws of physics are equations of motion tuned by the fundamental constants. 00:38: Previously, we've talked a bit about the symmetries of these equations and how they lead us to conserved quantities like energy and momentum. 01:35: ... bottom of the hill, sea level, even the center of the earth-- for the equations of motion of the ball, the altitude zero point is ... 01:51: And we say that the equations of motion are invariant to that parameter. 02:03: Newton's laws of motion and gravity, Maxwell's equations for electromagnetism, Einstein's general relativity, and of course, the standard model. 02:24: The standard model is ultimately based on quantum field theory, but we're going to use the Schrodinger equation. 02:31: That's the most basic equation of motion of quantum mechanics. 04:56: The equations of quantum mechanics have what we call global phase invariance. 06:03: According to the basic Schrodinger equation, we just ruined everything. 06:26: Local phase is not a gauge symmetry of the basic Schrodinger equation. 06:38: Just for funsies, maybe we can change the Schrodinger equation to find a version that really is invariant to local phase shifts. 06:45: To do that, we need to alter the part of the Schrodinger equation that gives us the momentum of a particle, the momentum operator. 08:05: By discovering how it fits into the Schrodinger equation, we've unlocked its quantum behavior. 09:03: First, we need to upgrade the Schrodinger equation to the Dirac equation so it works with Einstein's special relativity. 09:35: To understand those, we'll need to go beyond the Schrodinger equation and to explore new gauge symmetries. 08:05: By discovering how it fits into the Schrodinger equation, we've unlocked its quantum behavior. 00:33: Our laws of physics are equations of motion tuned by the fundamental constants. 00:38: Previously, we've talked a bit about the symmetries of these equations and how they lead us to conserved quantities like energy and momentum. 01:35: ... bottom of the hill, sea level, even the center of the earth-- for the equations of motion of the ball, the altitude zero point is ... 01:51: And we say that the equations of motion are invariant to that parameter. 02:03: Newton's laws of motion and gravity, Maxwell's equations for electromagnetism, Einstein's general relativity, and of course, the standard model. 04:56: The equations of quantum mechanics have what we call global phase invariance.
	2018-06-13: What Survives Inside A Black Hole? 05:41: In fact, it's one of Maxwell's equations, which together give the classical description of electromagnetism.
	2018-05-23: Why Quantum Information is Never Destroyed 00:23: [MUSIC PLAYING] The laws of physics are equations of motion. 00:36: Newton's equations for classical mechanics, Maxwell's equations for electromagnetism, and the Schrodinger equation for quantum mechanics. 01:34: ... that are conserved in a system by looking at the symmetries of the equations of ... 01:43: For example, if the equations stay the same from one point in time to the next, then energy is conserved. 02:23: ... say that a system is time-reversal symmetric if its equations of motion allow us to perfectly predict the starting point simply by ... 04:45: To get at this, let's think about the basic equation of motion of quantum mechanics. 04:50: That's the Schrodinger equation. 04:51: The time dependent Schrodinger equation describes the time evolution of this thing called the wave function. 05:19: ... Schrodinger equation perfectly predicts both the past and future evolution of a given wave ... 05:51: ... the Schrodinger equation guarantees time reversibility and so the conservation of information, as ... 04:51: The time dependent Schrodinger equation describes the time evolution of this thing called the wave function. 05:51: ... the Schrodinger equation guarantees time reversibility and so the conservation of information, as do the ... 05:19: ... Schrodinger equation perfectly predicts both the past and future evolution of a given wave function in ... 00:23: [MUSIC PLAYING] The laws of physics are equations of motion. 00:36: Newton's equations for classical mechanics, Maxwell's equations for electromagnetism, and the Schrodinger equation for quantum mechanics. 01:34: ... that are conserved in a system by looking at the symmetries of the equations of ... 01:43: For example, if the equations stay the same from one point in time to the next, then energy is conserved. 02:23: ... say that a system is time-reversal symmetric if its equations of motion allow us to perfectly predict the starting point simply by ... 01:43: For example, if the equations stay the same from one point in time to the next, then energy is conserved.
	2018-05-16: Noether's Theorem and The Symmetries of Reality 03:03: In the case of Noether's theorem, when we say the environment stays the same, we mean the equations that give the laws of motion for the system. 06:43: ... of least action can be used to derive the laws of motion from the equations of classical mechanics to Feynman's path integral formulation of quantum ... 03:03: In the case of Noether's theorem, when we say the environment stays the same, we mean the equations that give the laws of motion for the system. 06:43: ... of least action can be used to derive the laws of motion from the equations of classical mechanics to Feynman's path integral formulation of quantum ...
	2018-05-09: How Gaia Changed Astronomy Forever 10:17: Actually, Eldon Tyrell had a decent grasp of hydrostatic equilibrium and the continuity equation.
	2018-02-28: The Trebuchet Challenge 04:46: ... it's possible to figure out the equations of motion of a trebuchet in terms of Newton's laws, with a complicated ...
	2018-02-14: What is Energy? 07:35: Instead, the concept of energy allows us to write down equations describing the evolution of the entire system. 07:42: ... example, Bernoulli's equation predicts the flow of fluids by demanding the conservation of the kinetic ... 08:12: It produces the same equations of motion as Newtonian mechanics but without having to keep track of those innumerable fiddly force vectors. 08:25: ... equation describes the motion of individual particles but can also describe the ... 08:50: ... describe anything from the motion of a single particle in Schrodinger's equation to complex interactions of particles and fields in quantum field ... 08:25: ... equation describes the motion of individual particles but can also describe the evolution ... 07:42: ... example, Bernoulli's equation predicts the flow of fluids by demanding the conservation of the kinetic and ... 07:35: Instead, the concept of energy allows us to write down equations describing the evolution of the entire system. 08:12: It produces the same equations of motion as Newtonian mechanics but without having to keep track of those innumerable fiddly force vectors. 07:35: Instead, the concept of energy allows us to write down equations describing the evolution of the entire system.
	2018-01-17: Horizon Radiation 03:44: ... the equations describing the interaction transform cleanly between inertial reference ... 03:55: ... when an observer who sees a horizon tries to write down these equations, in order to preserve the laws of physics, they find they have to ... 04:57: The equations we write to describe the oscillations are coupled to each other. 05:08: But it also makes it devilishly difficult to solve those equations because the individual oscillations in space can't be solved independently. 07:37: But why exchange a single spatial equation for infinite equations in momentum space? 08:05: Dealing with uncoupled equations allows you to add and subtract oscillations without affecting the neighboring momenta. 03:44: ... the equations describing the interaction transform cleanly between inertial reference ... 03:55: ... when an observer who sees a horizon tries to write down these equations, in order to preserve the laws of physics, they find they have to ... 04:57: The equations we write to describe the oscillations are coupled to each other. 05:08: But it also makes it devilishly difficult to solve those equations because the individual oscillations in space can't be solved independently. 07:37: But why exchange a single spatial equation for infinite equations in momentum space? 08:05: Dealing with uncoupled equations allows you to add and subtract oscillations without affecting the neighboring momenta. 03:44: ... the equations describing the interaction transform cleanly between inertial reference frames in a ...
	2018-01-10: What Do Stars Sound Like? 00:49: ... equations of hydrostatic equilibrium allow us to calculate things like the density ... 01:23: You see, stars have a dynamical complexity far exceeding the simplest predictions of the equations describing stellar structure. 00:49: ... equations of hydrostatic equilibrium allow us to calculate things like the density ... 01:23: You see, stars have a dynamical complexity far exceeding the simplest predictions of the equations describing stellar structure.
	2017-12-13: The Origin of 'Oumuamua, Our First Interstellar Visitor 10:05: The equation for momentum, P = M times V, only works at low speeds approaching the speed of light.
	2017-12-06: Understanding the Uncertainty Principle with Quantum Fourier Series 06:09: The solution to the Schrodinger equation that contains all of the information about a quantum system.
	2017-11-29: Citizen Science + Zero-Point Challenge Answer 07:59: And if vacuum energy is proportional to the fourth power of cutoff frequency, then this equation gives the relationship we need.
	2017-11-02: The Vacuum Catastrophe 04:12: In fact, in both quantum mechanics and classical mechanics, a particle's equations of motion depend only on changes in energy.
	2017-10-11: Absolute Cold 10:28: Your criticism of my Lagrangian from the previous week's episode was just about my bad [INAUDIBLE],, not about the equation being wrong.
	2017-09-28: Are the Fundamental Constants Changing? 00:43: Those relationships are often expressed as equations, but they're also governed by the constants within those equations. 00:50: ... example, the standard model of particle physics is comprised of equations that predict the existence and behavior of the particle building blocks ... 00:43: Those relationships are often expressed as equations, but they're also governed by the constants within those equations. 00:50: ... example, the standard model of particle physics is comprised of equations that predict the existence and behavior of the particle building blocks ...
	2017-08-30: White Holes 02:31: ... his general theory of relativity, Karl Schwarzschild solved its equations for a very particular case-- a single point of mass in an otherwise ...
	2017-07-26: The Secrets of Feynman Diagrams 01:12: ... as we discussed in our episode on solving impossible equations, the Feynman diagrams allow physicists to quickly figure out which of the ... 01:27: ... diagram represents a family of interactions and tells us the equation needed to calculate the contribution of that family to the total ... 05:41: And they obey Einstein's mass-energy equation. 05:51: They sit on the shell structure you get when you plot Einstein's equation of energy, momentum, and mass. 01:27: ... diagram represents a family of interactions and tells us the equation needed to calculate the contribution of that family to the total ... 01:12: ... as we discussed in our episode on solving impossible equations, the Feynman diagrams allow physicists to quickly figure out which of the ...
	2017-07-19: The Real Star Wars 14:40: ... from last week when we talked about tricks for solving the impossible equations of quantum field ...
	2017-07-12: Solving the Impossible in Quantum Field Theory 00:06: Quantum field theory is stunningly successful at describing the smallest scales of reality, but its equations are also stunningly complex. 00:15: A lot of the genius in QFT's development was in finding brilliant hacks to make these equations workable. 00:27: ... PLAYING] The equations of quantum field theory allow us to calculate the behavior of subatomic ... 00:42: ... and complete formulations of quantum field theory, like the Dirac equation or Feynman's path integral, become impossibly complicated when we try to ... 01:05: First, they expressed these impossible equations in approximate, but solvable, forms. 01:09: Then they tackled the pesky infinities that kept appearing in these new approximate equations. 01:50: At least in the simplest cases, the Coulomb equation governing this subatomic billiards shot is really easy to solve. 03:43: They're actually equations in disguise. 04:09: ... equation you string together from this one diagram represents all of the ways ... 04:19: And from that equation, it's possible to perfectly calculate the effect of that simple exchange. 06:15: ... idea is that if the correct equation is unsolvable, just find a similar equation that you can solve, then ... 08:00: So with Feynman diagrams, you very quickly get an idea of which are the important additions to your equation and which you can ignore. 10:05: ... with the unmeasurable fundamental mass of the electron and solve the equations from there, you fold in a term for the self-energy corrected mass based ... 13:23: ... which is compatible with special relativity, can derive Schrodinger's equation when Schrodinger's equation is not ... 13:35: So the deal is that Schrodinger's equation is a special case of a more general formulation of quantum mechanics. 13:41: In Schrodinger's equation, all of the particles are tracked according to one universal master clock. 01:50: At least in the simplest cases, the Coulomb equation governing this subatomic billiards shot is really easy to solve. 00:06: Quantum field theory is stunningly successful at describing the smallest scales of reality, but its equations are also stunningly complex. 00:15: A lot of the genius in QFT's development was in finding brilliant hacks to make these equations workable. 00:27: ... PLAYING] The equations of quantum field theory allow us to calculate the behavior of subatomic ... 01:05: First, they expressed these impossible equations in approximate, but solvable, forms. 01:09: Then they tackled the pesky infinities that kept appearing in these new approximate equations. 03:43: They're actually equations in disguise. 10:05: ... with the unmeasurable fundamental mass of the electron and solve the equations from there, you fold in a term for the self-energy corrected mass based ... 00:15: A lot of the genius in QFT's development was in finding brilliant hacks to make these equations workable.
	2017-07-07: Feynman's Infinite Quantum Paths 05:06: For the large-scale classical universe, minimizing proper time lets you derive all equations of motion. 07:44: Feynman's path integral formulation allowed him to derive the Schrodinger equation from scratch. 08:23: On the other hand, the Schrodinger equation gave time a special role, so it doesn't work with relativity at all. 08:30: We already saw how Paul Dirac manage to fix this two decades earlier with his Dirac equation. 05:06: For the large-scale classical universe, minimizing proper time lets you derive all equations of motion.
	2017-06-28: The First Quantum Field Theory 01:38: The pillars of QED are the description of the behavior of the EM field and the description of the behavior of the electron via the Dirac equation. 01:49: We covered the Dirac equation last time and you really should watch that episode first if you haven't already. 04:56: However, the first full formulation of quantum mechanics was Schrodinger's equation and it couldn't account for light at all. 05:07: Basically, the Schrodinger equation is incompatible with Einstein's relativity. 05:21: We also saw how Paul Dirac managed to find an equation describing the behavior of the electron that worked with relativity-- the Dirac equation. 05:43: Let me first mention another problem with the Schrodinger equation. 13:21: Last week, we began our discussion of quantum field theory by looking at the amazing Dirac equation and how it predicts the existence of antimatter. 13:33: ... that Schrodinger himself did write down a relativistic version of his equation a few years before Dirac came up with the Dirac ... 13:44: In fact, Schrodinger followed the same approach, starting with Einstein's mass energy momentum equation. 13:50: ... Mr. Diagrams points out, the resulting Klein Gordon equation gives negative energy solutions just like the Dirac equation does, but ... 14:12: As a result, Schrodinger instead published his nonrelativistic Schrodinger equation first. 14:18: However, the Klein Gordon equation is actually the exactly right description for particles with no spin. 05:21: We also saw how Paul Dirac managed to find an equation describing the behavior of the electron that worked with relativity-- the Dirac equation.
	2017-06-21: Anti-Matter and Quantum Relativity 01:10: Then, in 1926, Erwin Schrodinger wrote down his famous equation, the Schrodinger equation, which breathed life into this emerging model. 01:40: First and most obvious, the Schrodinger equation is totally incompatible with Einstein's relativity. 01:56: ... the Schrodinger equation tracks the evolution of a particle's wave function according to one and ... 02:11: So the Schrodinger equation only works for slow-moving objects. 02:21: ... other problem with the Schrodinger equation is that it describes particles as simple wave functions, distributions ... 04:20: Now, it's OK to ignore spin in the old Schrodinger equation and get approximate answers. 04:31: So for fast moving electrons and for electrons in electromagnetic fields, the Schrodinger equation gives the wrong answers. 04:45: He wanted a fully relativistic version of the Schrodinger equation that worked for electrons. 04:54: He wrote down Einstein's famous equation, E equals mc squared, but in its full form, including momentum. 05:10: ... horrendous mathematics to collapse into an incredibly simple, beautiful equation. ... 05:39: But the resulting equation was so simple and elegant that somehow Dirac knew that he was onto something. 05:45: The resulting Dirac equation describes the spacetime evolution of this weird four-component particle-wave function, represented by the symbol psi. 06:02: The Dirac equation perfectly predicts the motion of electrons at any speed, even in an electromagnetic field. 06:22: The answer came from trying to calculate the energy of the electron using this equation. 09:19: Only a few years after Dirac wrote down his equation in 1928, the positron, the anti-matter electron, was spotted in cosmic rays by Carl Anderson. 09:39: Anti-matter's existence is fundamentally tied to these weird four-component electrons that Dirac invented to make his equation work. 05:45: The resulting Dirac equation describes the spacetime evolution of this weird four-component particle-wave function, represented by the symbol psi. 06:02: The Dirac equation perfectly predicts the motion of electrons at any speed, even in an electromagnetic field. 01:56: ... the Schrodinger equation tracks the evolution of a particle's wave function according to one and only ... 09:39: Anti-matter's existence is fundamentally tied to these weird four-component electrons that Dirac invented to make his equation work.
	2017-03-29: How Time Becomes Space Inside a Black Hole 02:56: This comes from Karl Schwarzschild's solution to the Einstein field equations, the very first accurate description of a black hole. 03:06: This equation assumes no orbital motion, only motion towards or away from the center of the black hole, which is a distance r away. 10:28: In fact the Schwarzschild metric really gives two separate spacetime maps in a single equation, one for above and one for below the event horizon. 03:06: This equation assumes no orbital motion, only motion towards or away from the center of the black hole, which is a distance r away. 02:56: This comes from Karl Schwarzschild's solution to the Einstein field equations, the very first accurate description of a black hole.
	2017-03-08: The Race to a Habitable Exoplanet - Time Warp Challenge 02:39: You don't have a faster ship, but you do have the wait equation.
	2017-02-02: The Geometry of Causality 04:29: ... of causality down which time flows, and etched into spacetime by the equations of special ... 04:47: Instead of doing that with equations, we can see it with geometry. 04:29: ... of causality down which time flows, and etched into spacetime by the equations of special ... 04:47: Instead of doing that with equations, we can see it with geometry.
	2017-01-19: The Phantom Singularity 00:39: Newton's equation gives you the gravitational force exerted between two masses, m1 and m2 that are a distance R apart. 01:03: Then the result of the equation, the force, becomes extremely large and is infinite when R becomes equal to 0. 04:45: ... what you get when you solve the delightfully complicated Einstein field equations for the simple case of a spherically symmetric mass in an otherwise ... 05:09: Actually, it's really easy to see the singularities in this equation, but let me first walk you through what it tells us. 06:34: There would have been some speed of lights through the equation, but we set them equal to 1 because we're that cool. 07:22: To see how, we need to look at the second singularity in this equation, a singularity that Newton's law does not contain. 07:40: At that point, the entire equation starts behaving very badly. 10:00: At the moment of crossing, the denominator here in the Schwarzschild metric is 0, and the whole equation leads up to infinity. 07:40: At that point, the entire equation starts behaving very badly. 04:45: ... what you get when you solve the delightfully complicated Einstein field equations for the simple case of a spherically symmetric mass in an otherwise ...
	2016-11-30: Pilot Wave Theory and Quantum Realism 04:05: Importantly, the wave function in pilot-wave theory evolves exactly according to the Schrodinger equation. 04:13: That's the equation at the heart of all quantum mechanics that tells the wave function how to change across space and time. 07:05: ... well as the Schrodinger equation that tells the wave function how to change, it also has a guiding ... 07:24: However, the guiding equation is derived directly from the wave function, so some would argue that it was there all along.
	2016-11-09: Did Dark Energy Just Disappear? 04:14: ... constant, written as lambda, is the thing you add to Einstein's equations of general relativity to give the anti-gravitational effect of dark ... 06:27: But that means we have to consider all off the things affecting that expansion when we decide whether dark energy is part of that equation. 04:14: ... constant, written as lambda, is the thing you add to Einstein's equations of general relativity to give the anti-gravitational effect of dark ...
	2016-11-02: Quantum Vortices and Superconductivity + Drake Equation Challenge Answers 03:24: ... answer this, you used Frank and Sullivan's modified version of the Drake Equation which says that the number of civilizations that will develop in any ...
	2016-10-05: Are We Alone? Galactic Civilization Challenge 00:11: The famous Drake Equation tries to estimate the number of technological civilizations currently existing in our galaxy. 00:56: When Frank Drake formulated his equation in the early '60s, most of the factors going into it were hopelessly unconstrained. 02:48: ... pretty hopeless, some researchers have decided to reframe the Drake equation. ... 03:03: ... that say about the biological and sociological factors in the Drake equation? ...
	2016-09-14: Self-Replicating Robots and Galactic Domination 00:33: Stars for the most part act very star-like, their brightnesses and colors slavishly following the equations of stellar physics.
	2016-07-06: Juno to Reveal Jupiter's Violent Past 10:28: We recently talked about the origin of quantum theory with Max Planck's derivation of an equation to describe the black body spectrum.
	2016-06-29: Nuclear Physics Challenge 02:56: And you can calculate the velocity using the equation for kinetic energy and the mass of the alpha particle.
	2016-06-22: Planck's Constant and The Origin of Quantum Mechanics 02:04: In fact, the Planck constant appears in essentially all equations that describe quantum phenomena. 02:12: ... principle and the de Broglie wavelength, but also the Schrodinger equation, the energy levels of electron orbits, and importantly, the relationship ... 08:11: Planck's new equation described the shape of the blackbody spectrum exactly, across all frequencies of light. 08:40: In that case, the Planck constant would have canceled out in the final equation, but it didn't. 02:04: In fact, the Planck constant appears in essentially all equations that describe quantum phenomena.
	2016-06-08: New Fundamental Particle Discovered?? + Challenge Winners! 09:44: So at that point in the past, we know that this equation is true. 10:57: Put all of this into our original equation and rearrange, and we get this equation for the ratio of scale factors. 12:10: Now to do that, you need to integrate the first Friedmann equation over the scale factors that you got for the main part of the question.
	2016-05-25: Is an Ice Age Coming? 10:50: Human influence on the climate messes with the whole equation.
	2016-05-18: Anti-gravity and the True Nature of Dark Energy 01:24: This dark energy is described by the cosmological constant in the equations of general relativity. 02:25: We saw that general relativity demands this when we looked at the first Friedmann equation. 02:40: Now, the Friedmann equation that we've been playing with so far just isn't going to cut it. 03:06: It's anti-gravitational effect emerges in the second Friedmann equation. 03:11: The first Friedmann equation is all about the rate of expansion of the universe. 06:34: So he added to his field equations that would give a positive outward acceleration in the second Friedmann equation. 10:47: And it's a clear, outward-pushing anti-gravity effect when we look at its role in the second Friedmann equation. 10:56: In the first Friedmann equation, we see it as an exponential change in the scale factor. 01:24: This dark energy is described by the cosmological constant in the equations of general relativity. 06:34: So he added to his field equations that would give a positive outward acceleration in the second Friedmann equation.
	2016-05-11: The Cosmic Conspiracy of Dark Energy Challenge Question 02:16: ... the Einstein field equations and in the Friedmann equations that are derived from those, dark energy ... 06:04: Or you could go ahead and solve the Friedmann equations. 02:16: ... the Einstein field equations and in the Friedmann equations that are derived from those, dark energy ... 06:04: Or you could go ahead and solve the Friedmann equations.
	2016-04-27: What Does Dark Energy Really Do? 00:16: ... using Einstein's general theory of relativity via the Friedmann equations. ... 07:22: Add the cosmological constant to the first Friedmann equation, and we reconcile the left and the right side. 08:09: For that far-future universe, we can write the first Friedmann equation like this. 08:25: See, it's not the expansion rate-- the A-dot-- that's constant in this equation. 10:32: ... the degree of curvature required by the first Friedmann equation to agree with the balance between expansion and density is much, much ... 00:16: ... using Einstein's general theory of relativity via the Friedmann equations. ...
	2016-04-20: Why the Universe Needs Dark Energy 00:52: ... at how general relativity, expressed in the first of the two Friedmann equations, can describe the cosmic balance between the outward expansion of the ... 01:48: Today, let's look at one of these measurements-- the geometry of the universe, which points to a discrepancy in the first Friedmann equation. 01:56: We know for sure that, the left side of this equation, the sum of the expansion and density terms don't cancel out to zero. 02:16: So the left side of this equation, as we wrote it, is positive, which means the right side should be, too. 04:26: ... independently verify what we got on the left side of the first Friedmann equation, when we measured the universe's ... 04:39: So, assuming we got the equation correct, then the shape of the universe should be intrinsically tied to its fate. 06:06: The right side of the first Friedmann equation has to be very close to zero. 06:26: But when we tried to describe the universe by reducing the Einstein field equations into the Friedmann equations, we missed something. 06:40: ... very same addition to the Einstein field equations that can describe cosmic inflation can also fix this little problem with ... 06:50: ... we derive the first Friedmann equation with the cosmological constant included-- that's the lambda symbol, ... 08:46: ... along with it, the second Friedmann equation, which will give us the insight we need to understand dark energy's ... 10:20: Mychelly Goulart would like to know whether the density we use in the Friedmann equation includes dark matter. 04:39: So, assuming we got the equation correct, then the shape of the universe should be intrinsically tied to its fate. 10:20: Mychelly Goulart would like to know whether the density we use in the Friedmann equation includes dark matter. 00:52: ... at how general relativity, expressed in the first of the two Friedmann equations, can describe the cosmic balance between the outward expansion of the ... 06:26: But when we tried to describe the universe by reducing the Einstein field equations into the Friedmann equations, we missed something. 06:40: ... very same addition to the Einstein field equations that can describe cosmic inflation can also fix this little problem with ...
	2016-04-13: Will the Universe Expand Forever? 01:33: At the heart of general relativity are the Einstein field equations, which look like this. 01:39: "Equations," plural. 02:05: ... have 10 independent components, giving 10 independent field equations to describe the response of the fabric of the universe to everything it ... 02:58: Now this escape velocity comes right out of Newton's universal law of gravitation, which itself can be derived from the Einstein equations. 04:09: By solving the Einstein field equations for the whole universe, of course. 04:26: ... galaxies, the resulting smooth universe lets us reduce those 10 Einstein equations to only two relationships, called the Friedmann equations, devised by ... 04:59: Now the Friedmann equation tells us how a evolves over time. 05:14: Let's stick to the left-hand side of the equation for the moment. 05:25: In fact, this Friedmann equation is an energy equation. 06:27: In that case, the left-hand side of the equation adds to zero. 07:59: The left side of the Friedmann equation is positive. 08:23: But wait-- we never got to the right side of the equation. 08:40: ... to the first Friedmann equation, the fate of the universe-- as determined by its expansion and density-- ... 08:54: ... mismatch between the left and the right sides of the first Friedmann equation that tells us that we're missing something ... 09:08: ... show you why the Friedmann equations tell us that dark energy must exist in this universe, and what these ... 06:27: In that case, the left-hand side of the equation adds to zero. 04:59: Now the Friedmann equation tells us how a evolves over time. 01:33: At the heart of general relativity are the Einstein field equations, which look like this. 01:39: "Equations," plural. 02:05: ... have 10 independent components, giving 10 independent field equations to describe the response of the fabric of the universe to everything it ... 02:58: Now this escape velocity comes right out of Newton's universal law of gravitation, which itself can be derived from the Einstein equations. 04:09: By solving the Einstein field equations for the whole universe, of course. 04:26: ... galaxies, the resulting smooth universe lets us reduce those 10 Einstein equations to only two relationships, called the Friedmann equations, devised by ... 09:08: ... show you why the Friedmann equations tell us that dark energy must exist in this universe, and what these ... 04:26: ... 10 Einstein equations to only two relationships, called the Friedmann equations, devised by our boy ... 01:39: "Equations," plural.
	2016-03-30: Pulsar Starquakes Make Fast Radio Bursts? + Challenge Winners! 07:50: Plug our numbers into this equation and we get a mean free path of around 7,500 light years.
	2016-03-23: How Cosmic Inflation Flattened the Universe 06:57: ... the field equations of his general theory of relativity, he added this as a way to allow his ...
	2016-01-06: The True Nature of Matter and Mass 00:54: ... already covered Einstein's famous equation, E equals Mc squared, and showed that most of the mass of atoms comes ...
	2015-12-16: The Higgs Mechanism Explained 02:14: The basic QFT equations of all the components of the atom leave them massless.
	2015-11-25: 100 Years of Relativity + Challenge Winners! 02:13: ... Apophis to get the desired change in position and then the rocket equation to see how much fuel we'll need to achieve ... 03:41: ... need to use one of the basic kinematic equations, the one relating change in position, average acceleration, and time, ... 03:53: ... this equation, the average acceleration comes out to around 10 to the power of minus 9 ... 04:58: For that we need the rocket equation. 05:40: Rearranging all of this, we get this equation for the ratio of fuel mass to asteroid mass. 03:41: ... need to use one of the basic kinematic equations, the one relating change in position, average acceleration, and time, ...
	2015-11-11: Challenge: Can you save Earth from a Killer Asteroid? 01:54: ... also need the rocket equation which relates velocity change to the propellant exhaust velocity and the ...
	2015-10-28: Is The Alcubierre Warp Drive Possible? 00:45: ... of Einstein's theory of general relativity, a real solution to the equations of GR that would actually allow faster than light ... 02:03: ... around and within a black hole is predicted by solving Einstein's field equations around a point of extreme positive energy ... 02:16: But if you're cheeky, you can actually just make up a solution to the equations of GR without starting with a real mass/energy distribution. 03:05: ... make up a spacetime description and then essentially solve the Einstein equations backwards to figure out what arrangement of matter and energy would be ... 05:46: ... that we're just making up solutions to the Einstein equations, we could even shrink down the warp bubble while expanding the internal ... 00:45: ... of Einstein's theory of general relativity, a real solution to the equations of GR that would actually allow faster than light ... 02:03: ... around and within a black hole is predicted by solving Einstein's field equations around a point of extreme positive energy ... 02:16: But if you're cheeky, you can actually just make up a solution to the equations of GR without starting with a real mass/energy distribution. 03:05: ... make up a spacetime description and then essentially solve the Einstein equations backwards to figure out what arrangement of matter and energy would be ... 05:46: ... that we're just making up solutions to the Einstein equations, we could even shrink down the warp bubble while expanding the internal ... 03:05: ... make up a spacetime description and then essentially solve the Einstein equations backwards to figure out what arrangement of matter and energy would be needed to ...
	2015-10-22: Have Gravitational Waves Been Discovered?!? 02:25: ... from the fact that the speed of light is built into Einstein's field equation, which is necessary for it to be invariant to the Lorentz ...
	2015-10-15: 5 REAL Possibilities for Interstellar Travel 02:18: The rocket equation tells us that maximum speed is based on exhaust velocity, fuel mass, and spacecraft mass.
	2015-10-07: The Speed of Light is NOT About Light 02:00: ... Maxwell, scientific maestro, who weaves these laws into his eponymous equations, describing the entire electromagnetic phenomenon with such ... 02:11: By the late 1800s, we have Maxwell's equations, Newton's mechanics, various other awesome theories. 02:31: And more importantly for this episode, Maxwell's equations had cast confusion on the sacred Galilean Relativity. 02:51: First, let me explain the issue with Maxwell's equations. 03:08: And I can figure out the field strength from Maxwell's equations based on what I see is the monkey's total velocity. 03:23: But what if this very clever pony also solves Maxwell's equations? 04:06: ... going to be encoded in the transformation that will allow Maxwell's equations to jump seamlessly between reference frames-- the transformation that ... 04:38: And we just applied it to Maxwell's equations to get total monkey speed. 04:43: But it turns out that there's no way to write out Maxwell's equations so that they give consistent results under the Galilean transformation. 07:52: See, the Lorentz transformation finally allows us to write down a version of Maxwell's equation that is invariant to transformation. 08:14: That value has to be a combination of the fundamental constants of Maxwell's equations. 09:19: ... and, of course, mass to energy equivalence, as described by the famous equation, E equals mc ... 02:00: ... Maxwell, scientific maestro, who weaves these laws into his eponymous equations, describing the entire electromagnetic phenomenon with such ... 02:11: By the late 1800s, we have Maxwell's equations, Newton's mechanics, various other awesome theories. 02:31: And more importantly for this episode, Maxwell's equations had cast confusion on the sacred Galilean Relativity. 02:51: First, let me explain the issue with Maxwell's equations. 03:08: And I can figure out the field strength from Maxwell's equations based on what I see is the monkey's total velocity. 03:23: But what if this very clever pony also solves Maxwell's equations? 04:06: ... going to be encoded in the transformation that will allow Maxwell's equations to jump seamlessly between reference frames-- the transformation that ... 04:38: And we just applied it to Maxwell's equations to get total monkey speed. 04:43: But it turns out that there's no way to write out Maxwell's equations so that they give consistent results under the Galilean transformation. 08:14: That value has to be a combination of the fundamental constants of Maxwell's equations. 03:08: And I can figure out the field strength from Maxwell's equations based on what I see is the monkey's total velocity. 02:00: ... Maxwell, scientific maestro, who weaves these laws into his eponymous equations, describing the entire electromagnetic phenomenon with such ... 02:11: By the late 1800s, we have Maxwell's equations, Newton's mechanics, various other awesome theories.
	2015-09-30: What Happens At The Edge Of The Universe? 05:26: If spacetime really is perfectly flat, then, with the most simplistic application of Einstein's equations, we get that the universe is infinite. 06:59: We also have to keep in mind that these geometries assume that we can just extrapolate Einstein's equations in the most simplistic way. 05:26: If spacetime really is perfectly flat, then, with the most simplistic application of Einstein's equations, we get that the universe is infinite. 06:59: We also have to keep in mind that these geometries assume that we can just extrapolate Einstein's equations in the most simplistic way.
	2015-08-27: Watch THIS! (New Host + Challenge Winners) 00:50: ... by drawing a formal algebraic analogy between the gravitational equation on the one hand, and the spring equation on the other, you can find ...
	2015-08-19: Do Events Inside Black Holes Happen? 10:05: ... Einstein equations also allow for an empty universe that has an eternal black hole that ...
	2015-08-12: Challenge: Which Particle Wins This Race? 04:31: ... have to solve the Einstein equations in the presence of a spherically symmetric perfect fluid whose energy ...
	2015-08-05: What Physics Teachers Get Wrong About Tides! 12:21: ... that frame's not going to be inertial-- and then you work out what the equations of general relativity say the geodesics should be around the Earth and ... 12:39: ... turns out that the pieces of the geodesic equation-- the things the tell you what the geodesics should be-- that resemble-- ... 13:02: Go up to equation 4.22 in the link that you see below. 12:21: ... that frame's not going to be inertial-- and then you work out what the equations of general relativity say the geodesics should be around the Earth and ...
	2015-07-29: General Relativity & Curved Spacetime Explained! 07:32: Its curvature in geodesics are determined by how much energy is present at those events via set of rules called, no surprise, the Einstein equations. 07:40: So for example, say you stick the energy distribution of the sun into the Einstein equations and turn a crank. 07:32: Its curvature in geodesics are determined by how much energy is present at those events via set of rules called, no surprise, the Einstein equations. 07:40: So for example, say you stick the energy distribution of the sun into the Einstein equations and turn a crank.
	2015-05-20: The Real Meaning of E=mc² 00:12: And today, we're going to clarify what the most famous equation in physics really says. 00:16: ... PLAYING] E equals mc squared is probably the most famous equation in all of physics, but in his original 1905 paper, Einstein actually ...
	2015-04-15: Could NASA Start the Zombie Apocalypse? 05:23: ... use a more correct version of momentum conservation called the rocket equation that compensates for ... 05:32: Dariodario alluded to the rocket equation in that form of calculating momentum conservation in his comment.
	2015-02-18: Is It Irrational to Believe in Aliens? 01:15: What I've just described is similar in spirit to what's called the Drake equation.

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