
20221214: 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.


20221026: 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.


20221019: 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 EulerLagrange 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 ...


20221012: 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 ...


20220928: 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. ...


20220824: 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.


20220817: 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 socalled kessence 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 ...


20220803: 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 ...


20220727: 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.


20220630: 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 ...
 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 ...
 04:59: ... difference to the laws of electromagnetism  the Maxwell’s equations. Those equations tell us how particles with electric charges ...
 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: ... calculating torque, angular momentum, and through Maxwell’s equations. The right hand rule is another arbitrary convention, and its ...
 10:41: ... of charge and parity transformation  appears to bring our equations back to where they started. This is CP symmetry. A ...


20220615: 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 ...


20220601: 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 ...


20220504: Space DOES NOT Expand Everywhere
 01:59: ... finished general relativity, four scientists independently solved its equation for the entire universe, giving us the ...


20220427: 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, ...
 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 ...
 11:28: ... can be in a state of broken symmetry even though the overall equations of magnetism have not ...


20220330: 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 ...


20220323: 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.


20220316: What If Charge is NOT Fundamental?
 00:37: The math that describes it  Maxwell's equations or quantum electrodynamics  seem to wrap it up nicely.
 00:50: And neither Maxwell’s equations nor QED say a thing about what electric charge really is.


20220216: 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 nonreversible. 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 ...


20220210: 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 ...


20220127: 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.


20220119: 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.
 03:17: For 3 or more bodies there is no simple set of equations describing their future evolution under gravity.
 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.


20220112: 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 threebody problem, we can solve the equations for each of the 3 particles separately.
 06:14: We don’t need a 3cubed 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 KohnSham equations.
 11:13: These equations basically let you translate between a realistic interacting system and the fictitious noninteracting 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 selfconsistent  basically, it has to obey the Schrodinger equation  and the cheat is finding a way to inch your way to that ...


20211210: 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 ...


20211110: 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 ...


20211102: Is ACTION The Most Fundamental Property in Physics?
 04:29: ... Euler already did most of the work for us by finding the EulerLagrange 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 EulerLagrange 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 spin½ 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  ...


20211020: 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.


20211013: 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.


20211005: 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, ...


20210921: 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 spin½ ...
 13:49: ... equation by itself doesn’t force you to use symmetric or antisymmetric ...


20210907: 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 nonlinearity of the schrodinger equation allows these paradoxgenerating phenomena, then we can take that as ...


20210810: 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 nonlinear observables to the wavefunction. The normal ...
 08:08: ... Polchinski showed that almost any nonlinear 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 nonlinear Schrodinger equation that avoids the causalitybreaking prospect of fasterthanlight ...


20210803: 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 ...


20210713: 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.


20210707: 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 ...


20210623: 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 ...


20210616: 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 ...


20210525: 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 ...


20210421: 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.


20210407: Why the Muon g2 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.


20210309: 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 freefalling ...


20210224: 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 ...


20201208: 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.


20201118: 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 ...


20201104: Electroweak Theory and the Origin of the Fundamental Forces
 02:56: QED is what we call a gauge theory  its forcecarrying 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.


20201027: 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 ...


20201020: 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 ...


20200908: 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.


20200810: 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 ...


20200728: 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 ...


20200622: 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 ...


20200518: 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 ...


20200511: 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 ...


20200504: 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 ...


20200428: 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 ...


20200422: 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 smoothlyvarying 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 ...


20200331: 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 ...


20200324: 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, ...


20200224: 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.


20200218: Does Consciousness Influence Quantum Mechanics?
 00:52: ... quantum mechanics and physicists are still debating how to interpret its equations and the weirdness they ...


20200211: 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 ...


20200203: 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 ...


20200127: 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 ...


20200120: 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 erraticseeming 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 shapesphere, 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 ...


20191202: 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 ...


20191111: 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.


20191021: 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.


20191015: 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 WheelerdeWitt 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 WheelerdeWitt equation quantizes these  turns them into quantum operators.
 06:48: The result is a quantum equation for the fabric of space.
 06:57: The WheelerdeWitt equation was promising, but turned out to be … unsolvable.
 09:04: ... and Carlo Rovelli realized they could fully solve the WheelerdeWitt 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, nonquantum scales  in the ...
 16:29: ... the answer lies in the Einstein field equation of general relativity That equation says that the amount stretching of ...


20190819: 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 ...


20190806: 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 ...


20190718: 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 ...


20190617: 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 ...


20190501: 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 ...


20190410: 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 ...


20190403: The Edge of an Infinite Universe
 07:25: ... we write the equations of these fields in Penrose’s compactified coordinates then we can do ...


20190328: 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 ...


20190207: Sound Waves from the Beginning of Time
 16:08: In socalled bimetric gravity, you can have positive and negative masses, but each is described by its own set of Einstein field equations.


20190130: 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 ...


20190124: The Crisis in Cosmology
 05:27: Riess's Supernovae H0 for the Equation of State project,  SHOES ,...


20190109: 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 ...


20181220: Why String Theory is Wrong
 02:43: ... right sort of 5D spacetime, you can separate the resulting Einstein equations into a 4D 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 spacetime Now before I get to ...


20181212: 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 ...


20181107: 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 slowmoving, pointlike 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.


20181031: 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.


20181025: 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.


20181018: 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.


20180920: 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 oldfashioned Newtonian way.
 02:58: We already talked about how Paul Dirac fixed part of the problem with a relativistic wave equation for the electron.


20180905: 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 blackhole 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 blackhole mass for internal energy and figured out the total ...


20180823: How Will the Universe End?
 14:44: This, in essence, is because his equation has the charge and mass distributed differently.


20180815: 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 ...


20180725: 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 ...


20180718: The Misunderstood Nature of Entropy
 07:47: ... Boltzmann equation tells us that entropy is the logarithm of the number of microstates ...


20180711: 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.


20180613: 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.


20180523: 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 timereversal 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 ...


20180516: 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 ...


20180509: How Gaia Changed Astronomy Forever
 10:17: Actually, Eldon Tyrell had a decent grasp of hydrostatic equilibrium and the continuity equation.


20180228: 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 ...


20180214: 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 ...


20180117: 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.


20180110: 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.


20171213: 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.


20171206: 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.


20171129: Citizen Science + ZeroPoint 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.


20171102: 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.


20171011: 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.


20170928: 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 ...


20170830: 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 ...


20170726: 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 massenergy equation.
 05:51: They sit on the shell structure you get when you plot Einstein's equation of energy, momentum, and mass.


20170719: The Real Star Wars
 14:40: ... from last week when we talked about tricks for solving the impossible equations of quantum field ...


20170712: 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 selfenergy 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.


20170707: Feynman's Infinite Quantum Paths
 05:06: For the largescale 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.


20170628: 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.


20170621: AntiMatter 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 slowmoving 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 fourcomponent particlewave 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 antimatter electron, was spotted in cosmic rays by Carl Anderson.
 09:39: Antimatter's existence is fundamentally tied to these weird fourcomponent electrons that Dirac invented to make his equation work.


20170329: 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.


20170308: 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.


20170202: 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.


20170119: 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.


20161130: Pilot Wave Theory and Quantum Realism
 04:05: Importantly, the wave function in pilotwave 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.


20161109: 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 antigravitational 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.


20161102: 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 ...


20161005: 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? ...


20160914: SelfReplicating Robots and Galactic Domination
 00:33: Stars for the most part act very starlike, their brightnesses and colors slavishly following the equations of stellar physics.


20160706: 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.


20160629: Nuclear Physics Challenge
 02:56: And you can calculate the velocity using the equation for kinetic energy and the mass of the alpha particle.


20160622: 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.


20160608: 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.


20160525: Is an Ice Age Coming?
 10:50: Human influence on the climate messes with the whole equation.


20160518: Antigravity 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 antigravitational 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, outwardpushing antigravity 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.


20160511: 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.


20160427: 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 farfuture universe, we can write the first Friedmann equation like this.
 08:25: See, it's not the expansion rate the Adot 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 ...


20160420: 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.


20160413: 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 lefthand side of the equation for the moment.
 05:25: In fact, this Friedmann equation is an energy equation.
 06:27: In that case, the lefthand 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 ...


20160330: 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.


20160323: 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 ...


20160106: 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 ...


20151216: The Higgs Mechanism Explained
 02:14: The basic QFT equations of all the components of the atom leave them massless.


20151125: 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.


20151111: 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 ...


20151028: 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 ...


20151022: 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 ...


20151015: 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.


20151007: 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 ...


20150930: 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.


20150827: 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 ...


20150819: Do Events Inside Black Holes Happen?
 10:05: ... Einstein equations also allow for an empty universe that has an eternal black hole that ...


20150812: 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 ...


20150805: 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.


20150729: 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.


20150520: 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 ...


20150415: 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.


20150218: 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.
