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	2022-10-26: Why Did Quantum Entanglement Win the Nobel Prize in Physics? 02:36: ... to molecular scale, and the entangled property could be spin,  momentum, or any other quantum ... 06:51: Spin is the quantum version of angular momentum. 06:54: ... spin hadn’t changed in this transition, in order to conserve angular momentum the pair of photons needed to have a total spin of zero, which ...
	2022-10-19: The Equation That Explains (Nearly) Everything! 04:05: ... will reveal the existence of a conserved quantity like energy or momentum. And this is Noether's Theorem, and we also have an episode about ... 06:02: ... particles with integer spin are called bosons. They transmit energy and momentum according to the symmetries of each force. Some parts of the standard ...
	2022-10-12: The REAL Possibility of Mapping Alien Planets! 06:05: ... Just as regular sails accelerate a ship by   catching the momentum of the wind, solar sails catch the momentum of light - of photons ...
	2022-09-28: Why Is 1/137 One of the Greatest Unsolved Problems In Physics? 05:34: Those probabilities depend on many things,  like the particles’ positions and momenta, spins, charges, masses, etc.
	2022-09-14: Could the Higgs Boson Lead Us to Dark Matter? 08:39: In this case, it’s by using a 350 year old law of physics known as conservation of momentum. 08:48: ... of momentum tells us that the product of velocity times mass of all particles going ... 09:00: ... know pretty well the momentum of the particles going into our collision, and we can measure and add up ... 09:11: If total momentum seems to have decreased, this implies something invisible has sneaked that missing momentum past the detectors. 09:19: ... if we just looked at the total momentum, there’d be a lot of uncertainty due to the fact that there’s variation ... 09:28: ... another part to this trick that makes it very precise. We can do our momentum audit in a way that ensures that in-going momentum is known completely ... 09:42: Total moment in a collision is conserved, but also the momentum in each separate direction is conserved independently of the other directions. 09:51: ... momentum perpendicular to the direction of the particle beams is called the ... 10:01: ... forwards, back or sideways. But any of that sideways or transverse momentum has to add up to ... 10:30: ... of momentum tells us that there should be more stuff firing out in the opposite ... 10:56: And that lepton will be detected, meaning we can account for the momentum lost to neutrinos. 11:33: ... the same direction as the beam, making the calculation of the transverse momentum very ... 11:44: Physicists at the Large Hadron Collider’s ATLAS experiment have been adding up the outgoing transverse momenta for many, many events like this. 09:28: ... another part to this trick that makes it very precise. We can do our momentum audit in a way that ensures that in-going momentum is known completely ... 10:56: And that lepton will be detected, meaning we can account for the momentum lost to neutrinos. 09:51: ... momentum perpendicular to the direction of the particle beams is called the transverse ... 08:48: ... of momentum tells us that the product of velocity times mass of all particles going into a ... 10:30: ... of momentum tells us that there should be more stuff firing out in the opposite direction ...
	2022-06-30: Could We Decode Alien Physics? 07:38: ... everywhere in physics, for example in calculating torque, angular momentum,   and through Maxwell’s equations.  The right hand rule is another ... 16:39: ... problem is worse than that actually. Without an external source of momentum   exchange like with a light sail, you need to to carry your entire ...
	2022-06-01: What If Physics IS NOT Describing Reality? 08:49: ... of the measurement error   in a particle’s position and momentum has to be  greater than the Planck constant divided by ...
	2022-03-23: Where Is The Center of The Universe? 17:22: ... observers reference frame, given that it’s defined in reference to the momentum vector of the ... 17:49: The answer is that chirality isn’t as simple as a projection of spin onto the momentum vector. 17:22: ... observers reference frame, given that it’s defined in reference to the momentum vector of the ... 17:49: The answer is that chirality isn’t as simple as a projection of spin onto the momentum vector.
	2022-03-16: What If Charge is NOT Fundamental? 02:23: For example electrons have this thing called spin - a quantum analogy to angular momentum. 09:52: ... have right-handed chirality if their spin is clockwise relative to their momentum vector and left-handed chirality if it's ...
	2022-02-16: Is The Wave Function The Building Block of Reality? 13:19: ... or subjective fiction? Did I measure position precisely or was it momentum? Who put my cat in that funny box, and why isn’t he purring any more? But ...
	2022-01-12: How To Simulate The Universe With DFT 15:23: The the fast-moving black hole slows-down inside the Earth because exchanges momentum with or eats stationary material on its way through.
	2021-12-10: 2021 End of Year AMA! 00:02: ... actually be attracted given that the photon is expected to exchange momentum with the proton and that photon is moving in a particular direction ...
	2021-11-17: Are Black Holes Actually Fuzzballs? 01:14: ... from outside a black hole are its mass, electric charge, and angular momentum. ... 02:27: But these few numbers emerge from the motion of every air molecule — and to describe that we’d need the positions and momenta of 10^27ish particles.
	2021-11-10: What If Our Understanding of Gravity Is Wrong? 06:06: It doesn’t respect conservation of energy or momentum or angular momentum.
	2021-11-02: Is ACTION The Most Fundamental Property in Physics? 01:22: ... were some efforts - for example Euler considered properties involving momentum and kinetic energy - but to no avail. In the meantime Isaac Newton came ... 12:16: ... space could mean phase space - the space of possible positions and momenta - or it could be more general state space, representing all the quantum ...
	2021-08-10: How to Communicate Across the Quantum Multiverse 07:14: ... wavefunction. The normal linear observables are things like position, momentum, spin - the physical stuff that makes up our world. Extra observables ... 14:02: ... - first is that a white dwarf could potentially gain a lot of angular momentum or spin by absorbing material from another star, hence perhaps ... 07:14: ... wavefunction. The normal linear observables are things like position, momentum, spin - the physical stuff that makes up our world. Extra observables would be ...
	2021-08-03: How An Extreme New Star Could Change All Cosmology 02:13: ... under its own gravitational crush due to conservation of angular momentum. But typical white dwarfs take from a few hours to a few days to rotate. ... 09:51: ... be spinning really really fast because it doesn’t just have the angular momentum from its spinning parent stars - it has the angular momentum from the ...
	2021-07-21: How Magnetism Shapes The Universe 09:53: Magnetic fields generated by collapsing gas clouds help to slow the rotation of those clouds - expel angular momentum.
	2021-07-13: Where Are The Worlds In Many Worlds? 04:23: ... particle position and momentum and orientation is chosen from a vast array of possibilities, a ...
	2021-07-07: Electrons DO NOT Spin 00:22: ... on the  chair. It’s a demonstration of the conservation of angular momentum. The angular momentum  of the wheel is changed in one direction, so ... 00:47: ... speed. At first glance this appears to violate conservation of angular momentum because there was nothing spinning  to start with. Except there was ... 01:26: ... And yet they do seem to possess  a very strange type of angular momentum that somehow exists without classical rotation. In fact the spin of an ... 03:48: ... would have to be moving faster than light to give the required angular momentum. And that’s assuming that electrons even have a size - as far as we know ... 04:40: ... aren’t spinning, but somehow  they act like they have angular momentum. And this is how we think about quantum spin now. It’s  an intrinsic ... 07:02: ... without rotation, but the direction of the underlying magnetic  momentum is fundamentally quantum.   The direction of this "spin" ... 10:22: To get some insight into what spin really is,   think not about angular momentum,  but regular or linear momentum. 10:30: A particle's momentum is fundamentally  connected to its position. 10:33: ... in coordinate location gives us the law of the  conservation of momentum. For related reasons in quantum mechanics position and  momentum are ... 10:58: If position is the companion variable of momentum,  what's the companion of angular momentum? 11:09: ... one way to think about the  angular momentum of an electron is not from classical rotation,   but rather ... 11:21: They have undefined orientation, but  perfectly defined angular momentum. 11:34: ... that you can derive the right values of the  electron spin angular momentum and magnetic moment by looking at the energy and charge  currents ... 11:44: ... imply that even if the electron is point like, it's angular momentum can arise  from an extended though still tiny ... 12:13: ... intrinsic angular momenta can only be observed as plus or minus a half times the reduced Planck ... 04:40: ... intrinsic angular momentum that plays into the conservation of angular momentum like  in the Einstein de-Haas effect, and it also gives electrons a magnetic ... 00:22: ... a demonstration of the conservation of angular momentum. The angular momentum  of the wheel is changed in one direction, so the angular momentum of the ... 10:22: To get some insight into what spin really is,   think not about angular momentum,  but regular or linear momentum. 10:58: If position is the companion variable of momentum,  what's the companion of angular momentum?
	2021-06-23: How Quantum Entanglement Creates Entropy 16:39: ... preferred angle. That’s the basis for the conservation of angular momentum, which we know   is obeyed. Another issue with the simple ... 17:55: ... to measure position, I said that the uncertainty in the final momentum of   the particle is roughly equal to the momentum of the ...
	2021-06-16: Can Space Be Infinitely Divided? 03:47: ... now you have a new problem. Light carries energy and momentum - and the shorter the   wavelength, the more it carries. If ... 04:30: ... photon’s momentum is the Planck  constant divided by its wavelength.   So ... 04:49: ... It also applies to other pairs of variables besides position and momentum. ... 05:08: ... as long as  we’re happy to have infinite uncertainty in   momentum. But it turns out that the Planck constant defines a new source of ... 06:02: ... distance  with perfect precision, and who cares about   momentum. We keep decreasing the wavelength of our measuring photon - ... 08:37: ... that when we do that we increase the uncertainty   in momentum of that bundle of electron-ness. That also means increasing the ... 03:47: ... now you have a new problem. Light carries energy and momentum - and the shorter the   wavelength, the more it carries. If you ...
	2021-05-25: What If (Tiny) Black Holes Are Everywhere? 14:16: Those photons are entangled with each other because various properties are correlated - in particular phase, polarization, and momentum.
	2021-05-19: Breaking The Heisenberg Uncertainty Principle 01:31: Perfect knowledge of a particle’s position means its momentum is undefined. 02:37: ... reasoned that the photon would give the particle a momentum kick, which would account for a greater uncertainty in its momentum ... 02:47: ... kick the object even harder, causing an even greater uncertainty in the momentum. ... 04:30: ... to extreme precision as long as we’re happy to have no knowledge of its momentum. ... 06:56: In this case, the complementary variables in question are not position and momentum, but rather phase and amplitude. 02:37: ... reasoned that the photon would give the particle a momentum kick, which would account for a greater uncertainty in its momentum after the ...
	2021-04-21: The NEW Warp Drive Possibilities 16:45: Momentum, which incorporates velocity, is as fundamental as position.
	2021-04-07: Why the Muon g-2 Results Are So Exciting! 03:43: For a rotating charge, that depends on the objects rate of rotation, or angular momentum, it's charge and it's mass.
	2020-11-04: Electroweak Theory and the Origin of the Fundamental Forces 04:50: ... outcomes being measured for observables like particle position and momentum. ...
	2020-07-08: Does Antimatter Explain Why There's Something Rather Than Nothing? 09:19: ... the precise mass and charge of the particles, their orbital angular momentum, their magnetic and electric dipole moments, and even the strength of the ...
	2020-06-30: Dissolving an Event Horizon 04:57: In both cases, the amount of angular momentum or charge you can fit into a black hole before it becomes extremal depends on the mass. 06:06: This can’t happen with rotating black holes because they leak away their angular momentum as well as their mass. 07:11: Rotating black holes gain their angular momentum from things they swallow. 07:20: It’s that orbital angular momentum that is fed to the black hole. 07:24: But in order for an object orbiting a black hole to fall into it, it actually has to lose at least some of that angular momentum. 07:31: ... hole like in a quasar, then the gas only spirals inwards because angular momentum is carried outwards by ... 07:42: By the time the gas reaches the black hole it has lost much of the angular momentum it started with. 07:49: The faster a black hole is rotating, the more angular momentum that gas has to lose in order to fall in. 07:55: ... of boost so it can still orbit even with very little of its own angular momentum. ... 08:06: ... riding on the carousel of frame-dragged state, and has no angular momentum of its ... 08:30: More generally, there is no trajectory into an extremal black hole that can add angular momentum from the trajectory or the “orbit” itself. 08:43: An alternative is to throw in something that’s actually spinning itself - so it has intrinsic angular momentum.
	2020-06-22: Building Black Holes in a Lab 07:24: ... vortex black hole analog. In fact, both the analog of energy and angular momentum seems to be sapped by this Hawking-like ...
	2020-04-28: Space Time Livestream: Ask Matt Anything 00:00: ... they grow in mass when they swallow things they conserve angular momentum and charge because they acquire those properties when they swallow ...
	2020-03-24: How Black Holes Spin Space Time 01:44: ... be rotating. The spin of a black hole comes from the combined angular momentum of everything that went into forming it. That includes the rotation of ... 02:26: ... black holes might not have MUCH spin - because angular momentum can cancel out if objects fall in with different spins or in different ...
	2020-03-16: How Do Quantum States Manifest In The Classical World? 00:57: ... for example a particle’s position can be expressed as a superposition of momentum states. I’ll come back to another example of this in a second. But this ... 04:28: ... to be in opposite directions in order to cancel out and conserve angular momentum. But besides being opposite to each other they can be aligned in any ... 00:57: ... for example a particle’s position can be expressed as a superposition of momentum states. I’ll come back to another example of this in a second. But this raises ...
	2020-01-27: Hacking the Nature of Reality 07:12: ... conditions include things like conservation of energy and momentum, the behavior of quantum properties like spin, and the assumption of a ... 07:56: Two go in, and two go out - the out particles could be the different to the in particles, or they could be the same just with different momenta. 14:29: ... some places it gives up angular momentum - it's orbital energy - to the gas, causing it to migrate inwards, while ... 14:41: And between these inward and outward migration regions are places where no angular momentum is exchanged. And, well, the black hole is trapped. 14:29: ... some places it gives up angular momentum - it's orbital energy - to the gas, causing it to migrate inwards, while ...
	2020-01-20: Solving the Three Body Problem 10:30: ... consistent with some basic properties like the energy and angular momentum of the system. The system explores what we call a phase space - a space ...
	2020-01-13: How To Capture Black Holes 04:50: ... dragged out of the disk, tugged by the black hole’s gravitational field. Momentum is transferred from black hole to gas, slowing the black hole down a bit ... 06:15: ... of the disk, that can cause the object to either gain or lose angular momentum. If it gains angular momentum the size of its orbit increases, so it ...
	2019-10-15: Loop Quantum Gravity Explained 03:33: ... classical physics, we have variables like position, time, momentum, energy - mathematical expressions that represent the observable ... 04:06: In the first formulations of quantum mechanics, that wavefunction describes the distribution of possible positions and momenta of, say, a particle. 04:16: These can then be resolved into concrete, measured values by acting on the wavefunction with so-called position and momentum operators. 04:30: ... all, the position and momentum of quantum mechanics literally describes location on a spatial ... 05:19: ... you calculate changing properties of a particle- - like its position or momentum - relative to the background coordinate ... 05:35: So maybe instead of thinking about the quantum fuzziness of position and momentum we can think about the quantum fuzziness of the metric itself. 06:37: You can also imagine analogies of the position and momentum in this space of metrics. 08:20: ... a spinor - a vector-like thing that also represents a quantum of angular momentum - or ... 05:19: ... you calculate changing properties of a particle- - like its position or momentum - relative to the background coordinate ... 08:20: ... a spinor - a vector-like thing that also represents a quantum of angular momentum - or ... 05:19: ... you calculate changing properties of a particle- - like its position or momentum - relative to the background coordinate ... 03:33: ... classical physics, we have variables like position, time, momentum, energy - mathematical expressions that represent the observable properties of ... 04:16: These can then be resolved into concrete, measured values by acting on the wavefunction with so-called position and momentum operators.
	2019-10-07: Black Hole Harmonics 09:05: .69 means this is a rapidly rotating black hole, which is unsurprising seeing as it just absorbed the orbital angular momentum of two black holes.
	2019-07-01: Thorium and the Future of Nuclear Energy 02:49: ... nuclei in H2O are around the same mass as neutrons they absorb a lot of momentum in Neutron collisions and Conveniently that same water can also work as ...
	2019-05-09: Why Quantum Computing Requires Quantum Cryptography 04:38: ... of certain pairs of properties – for example, a particle’s position and momentum. ...
	2019-01-30: Perpetual Motion From Negative Mass? 06:36: ... presence of active gravitational mass, and of energy, momentum, pressure, and more, change the geometry of spacetime and that new ... 09:00: At first glance that sounds like it breaks conservation of momentum and energy. 09:06: ... positive mass apple gains positive momentum and energy as it speeds up, while the negative mass apple balances that ... 06:36: ... presence of active gravitational mass, and of energy, momentum, pressure, and more, change the geometry of spacetime and that new geometry defines ...
	2019-01-24: The Crisis in Cosmology 15:31: ...both linear and angular momentum.
	2019-01-16: Our Antimatter, Mirrored, Time-Reversed Universe 01:48: ... of cobalt-60 atoms in a magnetic field, the cobalt nuclei have angular momenta that will align with a magnetic field let's say upwards so the decay ... 03:02: ... in the opposite direction to regular matter relative to their angular momentum the magnetic field in our clock will align antimatter nuclei in the ... 10:54: ... you're not converting matter to antimatter - you're just reversing all momentum and spin. Essentially you're taking all particles in the universe and ...
	2018-12-20: Why String Theory is Wrong 04:07: Momentum in that loop dimension has the exact behavior of electric charge, with the direction of rotation determining the sign of the charge. 08:55: ... times radius, or mode number divided by radius can be used to define the momentum of a particle produced by this ... 09:07: ... you can construct a theory in which momentum increases with the size of the compact dimension, or where momentum ...
	2018-12-12: Quantum Physics in a Mirror Universe 00:02: ... vectors point in the opposite direction same with the velocity / momentum through our board the mirror away from yourself and its reflection looks ...
	2018-10-31: Are Virtual Particles A New Layer of Reality? 03:25: ... interacts once with the EM field, transferring between them energy momentum and one photon worth of quantum properties in a single packet that we ... 05:18: ... they don't need to obey Einstein's relationship between energy mass and momentum. ... 06:39: Their momenta are pointing from positron to electron rather than electron to positron. 07:20: In a way, a virtual particle represents a pure excitation of the field, an idealized case of perfectly defined momentum. 07:29: The Heisenberg uncertainty principle tells us that the perfectly defined momenta of virtual particles means completely undefined position. 07:39: In contrast, real particles are mixed up combinations of many excitations, many different momentum modes. 07:46: And that uncertain momentum gives them real locations, real trajectories through space. 07:57: It can move between our electron and positron even if its momentum is pointing in the wrong direction. 07:39: In contrast, real particles are mixed up combinations of many excitations, many different momentum modes.
	2018-10-18: What are the Strings in String Theory? 02:09: ... pairs of mesons, as well as an odd relationship between their angular momenta and masses suggested that the quarks in mesons are connected by-- you ...
	2018-09-20: Quantum Gravity and the Hardest Problem in Physics 06:28: Steady viewers will remember that the uncertainty principle talks about the trade-off between position and momentum. 06:34: But large momentum also means large energy. 07:01: ... its position wave function needs to be constructed from a wide range of momentum wave functions that include extremely high frequencies or extremely high ... 07:18: And so large momenta are possible. 07:24: And then momentum becomes extremely uncertain and includes the possibility of ridiculously high values. 14:25: As they lose spin, angular momentum, they become more spherical. 07:01: ... its position wave function needs to be constructed from a wide range of momentum wave functions that include extremely high frequencies or extremely high ...
	2018-09-12: How Much Information is in the Universe? 04:21: ... space, which includes position, but also other degrees of freedom, like momentum, spin direction, et ...
	2018-08-23: How Will the Universe End? 15:43: All they have is their quantum wave function, which tells the probability of the particle's location, momentum, spin, direction, et cetera.
	2018-08-15: Quantum Theory's Most Incredible Prediction 04:02: Nonetheless, electrons do have a sort of intrinsic, angular momentum, a fundamental quantum spin that is as intrinsic as mass and charge. 05:09: ... expect for a tiny classical sphere with the same charge and angular momentum as an ...
	2018-07-18: The Misunderstood Nature of Entropy 06:32: ... an analogy for all possible combinations of all properties-- position, momentum, spin, vibration, really any degree of freedom that the system can ...
	2018-07-11: Quantum Invariance & The Origin of The Standard Model 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. 02:49: The best we can do is make a measurement of physical observables, like position or momentum. 06:08: Among other things, messing with local phase really screws up our prediction for the particle's momentum. 06:15: See, momentum is related to the average steepness of the wave function. 06:19: Change the shape of that wave function with local phase shifts and you actually break conservation of momentum. 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. 06:54: After all, momentum is what got screwed up. 06:57: ... turns out that we can add a mathematical term to the momentum operator that's specially designed to undo any mess we make to the phase ... 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. 06:57: ... turns out that we can add a mathematical term to the momentum operator that's specially designed to undo any mess we make to the phase of the ...
	2018-06-20: The Black Hole Information Paradox 01:54: It states that black holes can only exhibit three properties-- mass, electric charge, and angular momentum. 08:11: ... pairs of quantum-observable complimentary observables, like position and momentum, that can't both be perfectly measured at the same ...
	2018-06-13: What Survives Inside A Black Hole? 01:09: ... properties are mass, electric charge, and angular momentum, or at least this is the proposition behind the famous no-hair conjecture ... 01:45: ... that no other properties besides mass, electric charge, and angular momentum should emerge from beneath the event ... 02:28: ... the black hole are its mass-energy content, electric charge, and angular momentum. ... 03:06: So how does mass, electric charge, and angular momentum communicate their influence across the uncrossable horizon? 08:30: But what about the magnetic part of electromagnetism, and what about angular momentum? 09:19: ... material with angular momentum falls into a black hole, whether it's a spinning star or a whirlpool of ... 09:30: Its angular momentum is remembered in the frame dragging as though the entire black hole was spinning. 09:36: I hope I've given you a sense of why mass, charge, and angular momentum are remembered by the space outside a black hole. 03:06: So how does mass, electric charge, and angular momentum communicate their influence across the uncrossable horizon? 09:19: ... material with angular momentum falls into a black hole, whether it's a spinning star or a whirlpool of gas, ...
	2018-05-16: Noether's Theorem and The Symmetries of Reality 03:24: That quantity is momentum. 03:26: If two cars collide on that road, the sum of their combined momentum stays the same. 03:34: Momentum doesn't appear to be conserved. 04:07: ... then, Noether's theorem predicts another conserved quantity, angular momentum. ... 03:34: Momentum doesn't appear to be conserved. 03:26: If two cars collide on that road, the sum of their combined momentum stays the same.
	2018-04-25: Black Hole Swarms 03:07: The black hole can also slingshot stars outwards, losing momentum in that process, too. 03:12: The key is that the more massive object-- usually, the black hole-- tends to donate its momentum to the less massive object.
	2018-03-28: The Andromeda-Milky Way Collision 06:16: Meanwhile, the black holes lose angular momentum and fall towards the center.
	2018-03-15: Hawking Radiation 10:32: ... example, uncertainty in position or momentum can lead to particle pairs that we'll want in the same location or modes ...
	2018-02-14: What is Energy? 01:43: Besides the whole co-inventing calculus thing, Leibniz's vis viva seen as a competition to Newton's idea of conservation of momentum. 02:01: Besides, this vis viva thing wasn't conserved in the event of friction, while momentum was. 02:20: When she introduced the idea of gravitational potential energy, she put the laws of conservation of energy and momentum on equal footing. 10:06: For example, the law of conservation of momentum is due to spatial translation symmetry.
	2018-01-31: Kronos: Devourer Of Worlds 09:05: It tugs on the Earth gravitationally, increasing our angular momentum. 09:10: The asteroid loses angular momentum in the process, but it regains it as it flies by Jupiter. 09:15: Essentially, we steal angular momentum from Jupiter via the asteroid, which increases our orbit.
	2018-01-17: Horizon Radiation 05:35: Quantum wave functions and quantum fields can be described in terms of variation with position or variations with momentum. 05:44: So instead of writing the field as having a value at every possible position in space, we can write it as having a value for every possible momentum. 05:56: So let's take our spatial quantum field-- our drum skin, with its single, localized particle, and transform to momentum space. 06:04: That momentum field also has infinite oscillators, but now each one represents a different possible momentum for the particle. 06:13: ... in momentum space, that single, perfectly localized position oscillation can also be ... 06:24: Now, each one of these momentum modes exists at all spatial points in the universe. 06:31: ... we add these momentum oscillations together with the right weightings, they cancel out ... 06:40: The superposition of infinite universe size momentum oscillators-- momentum particles can represent a single spatial oscillator. 07:37: But why exchange a single spatial equation for infinite equations in momentum space? 07:48: Those momentum oscillations have two important qualities. 08:00: The field at each momentum spot oscillates independently from its neighboring momenta. 08:05: Dealing with uncoupled equations allows you to add and subtract oscillations without affecting the neighboring momenta. 08:12: However, changing the momentum modes does affect the superposition-- the sum of all oscillations, for example, by creating or destroying particles. 08:22: OK, so a single particle can be described as many oscillations in momentum space. 08:51: ... at a time, by changing the number of particles or oscillations in each momentum ... 09:29: In momentum space, we can think of it as a superposition of infinitely many momentum modes. 09:35: Infinite spatially undefined particles with defined momenta, and these just happen to cancel each other out, leaving 0 particles or a vacuum. 10:18: If we introduce an event horizon, then we lose access to some momentum modes, while other modes behave very differently. 10:51: Now when you use the new, rejigged field operator to describe the vacuum, some momentum modes that once canceled out no longer cancel out. 06:04: That momentum field also has infinite oscillators, but now each one represents a different possible momentum for the particle. 08:51: ... at a time, by changing the number of particles or oscillations in each momentum mode. ... 06:24: Now, each one of these momentum modes exists at all spatial points in the universe. 08:12: However, changing the momentum modes does affect the superposition-- the sum of all oscillations, for example, by creating or destroying particles. 09:29: In momentum space, we can think of it as a superposition of infinitely many momentum modes. 10:18: If we introduce an event horizon, then we lose access to some momentum modes, while other modes behave very differently. 10:51: Now when you use the new, rejigged field operator to describe the vacuum, some momentum modes that once canceled out no longer cancel out. 06:24: Now, each one of these momentum modes exists at all spatial points in the universe. 06:13: ... oscillation can also be described as an infinite number of unlocalized momentum oscillations. ... 06:31: ... we add these momentum oscillations together with the right weightings, they cancel out everywhere except at ... 07:48: Those momentum oscillations have two important qualities. 06:40: The superposition of infinite universe size momentum oscillators-- momentum particles can represent a single spatial oscillator. 05:56: So let's take our spatial quantum field-- our drum skin, with its single, localized particle, and transform to momentum space. 06:13: ... in momentum space, that single, perfectly localized position oscillation can also be ... 07:37: But why exchange a single spatial equation for infinite equations in momentum space? 08:22: OK, so a single particle can be described as many oscillations in momentum space. 09:29: In momentum space, we can think of it as a superposition of infinitely many momentum modes. 08:00: The field at each momentum spot oscillates independently from its neighboring momenta.
	2017-12-13: The Origin of 'Oumuamua, Our First Interstellar Visitor 09:50: [INAUDIBLE] Leonard asks whether a particle can have momentum higher than its mass times the speed of light. 09:56: In other words, shouldn't there be an upper limit to momentum if the speed of light is limited? 10:00: Well actually, momentum can be arbitrarily high, even when speed is limited to the speed of light. 10:05: The equation for momentum, P = M times V, only works at low speeds approaching the speed of light. 10:22: That means momentum approaches infinity for any object with mass that's approaching the speed of light. 10:30: How can a photon's frequency be generalized as momentum? 10:36: Well we generalize frequency as momentum because the Heisenberg uncertainty principle applies to momentum in general. 10:42: In the case of matter, uncertainty in momentum can manifest in both velocity and mass. 11:03: ... the photon passing through the slit, we increase the uncertainty in its momentum and hence, its direction of motion after it exits the ... 10:22: That means momentum approaches infinity for any object with mass that's approaching the speed of light. 09:50: [INAUDIBLE] Leonard asks whether a particle can have momentum higher than its mass times the speed of light.
	2017-12-06: Understanding the Uncertainty Principle with Quantum Fourier Series 01:40: The uncertainty principle is most often expressed in terms of position and momentum. 01:44: We cannot simultaneously know both position and momentum for a quantum system with absolute precision. 01:51: Try to perfectly nail down a particle's position, and we have complete uncertainty about its momentum. 01:59: And it's not just because our measurement of position requires us to interact with the particle, therefore changing its momentum, no. 06:39: The second of this pair is momentum, not frequency. 06:43: See, momentum is sort of the generalization of frequency for what we call a matter wave. 06:49: In the early days of quantum mechanics, it was realized that photons are electromagnetic wave packets whose momentum is given by their frequency. 06:58: ... De Broglie relation generalizes the relationship between frequency and momentum of a matter ... 07:08: ... waves wave functions, and we can describe them in terms of position or momentum, just as a traveling sound wave can be expressed in terms of time or ... 07:29: ... being smeared over possible positions or as a combination of many momenta with accompanying intensities, in which case the particle would be ... 07:41: And of course, this means that position and momentum have the same kind of uncertainty relation that time and frequency had in the sound wave. 07:50: But what does it even mean for a particle to be comprised of waves of many different positions or momenta? 08:30: If we apply the Born rule to the momentum function, then we learn the range of momenta the particle is likely to have. 08:48: ... as a superposition of waves with a very large range of different momenta via a Fourier ... 09:00: The result is a very fat momentum wave function that gives a wide range of possible momenta. 09:06: ... its position wave function, and so the less certain we become about its momentum, as that momentum wave function gets ... 09:22: ... particle by narrowing the slit, we also increase the uncertainty of its momentum as it passes the ... 09:55: Waves that can be represented in terms of either position or momentum. 10:18: Well, the key to understanding these things is to be able to switch between thinking about quantum fields in terms of position versus momentum. 10:26: ... at one spot in space, can so be described as infinite oscillations in momentum space, spanning all possible ... 10:39: But each of these oscillations in momentum space are equivalent to particles with highly specific momenta. 10:51: So a perfectly specially localized particle is equally an infinite number of momentum particles that themselves occupy all locations in the universe. 11:01: ... only by manipulating quantum fields in this strange momentum space, by adding and removing these spatially infinite particles, that ... 08:30: If we apply the Born rule to the momentum function, then we learn the range of momenta the particle is likely to have. 10:51: So a perfectly specially localized particle is equally an infinite number of momentum particles that themselves occupy all locations in the universe. 07:29: ... accompanying intensities, in which case the particle would be smeared in momentum space. ... 10:26: ... at one spot in space, can so be described as infinite oscillations in momentum space, spanning all possible ... 10:39: But each of these oscillations in momentum space are equivalent to particles with highly specific momenta. 11:01: ... only by manipulating quantum fields in this strange momentum space, by adding and removing these spatially infinite particles, that we can ... 10:26: ... at one spot in space, can so be described as infinite oscillations in momentum space, spanning all possible ... 09:00: The result is a very fat momentum wave function that gives a wide range of possible momenta. 09:06: ... function, and so the less certain we become about its momentum, as that momentum wave function gets ... 09:00: The result is a very fat momentum wave function that gives a wide range of possible momenta. 09:06: ... function, and so the less certain we become about its momentum, as that momentum wave function gets ...
	2017-11-08: Zero-Point Energy Demystified 06:02: The fact is, any acceleration of a real particle involves a transfer of momentum between real particles via virtual particles. 06:15: However, it's not possible to transfer momentum from a particle to the vacuum without getting another real particle out the other end. 06:23: That momentum must be given up by the vacuum to produce real particles again. 06:28: Those particles would become the propellant carrying momentum away. 06:41: ... particles are somehow extracting momentum from the resonant cavity, then they're giving it up again to real ...
	2017-10-19: The Nature of Nothing 01:09: ... that perfect stillness implies that a particle's position and momentum are simultaneously perfectly defined, and this is impossible according ... 01:21: Fix a particle's position, and its momentum, and so its motion, becomes a quantum blur of many possible momenta. 03:39: We saw that it's impossible to simultaneously fix position and momentum.
	2017-10-11: Absolute Cold 04:52: Well, its position relative to its neighbors would be fixed, and its momentum would be 0. 05:11: For example, the more precisely a quantum particle's position is defined, the less defined is its momentum. 05:20: A particle with a perfectly defined position has a perfectly undefined momentum. 05:26: So try to fix a particle's position perfectly, try to hold it still, and its momentum enters a state of quantum haziness. 05:34: That momentum can then fluctuate, potentially, to very high values. 08:38: ... years for this black hole binary to spiral together from losing angular momentum to gravitational ... 09:03: So they probably lose angular momentum by dragging against gas in the center of galaxies, but we don't know how long that takes. 05:26: So try to fix a particle's position perfectly, try to hold it still, and its momentum enters a state of quantum haziness.
	2017-10-04: When Quasars Collide STJC 07:35: Each time they do that they lose a bit of orbital energy or angular momentum, causing them to fall deeper into the gravitational well. 08:52: ... but it's going to take many billions of years to lose enough angular momentum to merge that ... 07:35: Each time they do that they lose a bit of orbital energy or angular momentum, causing them to fall deeper into the gravitational well.
	2017-08-10: The One-Electron Universe 09:44: ... one case, we have a positron and an electron influencing each other's momentum by exchanging a virtual photon-- similar to electron-electron ... 10:05: As long as the incoming and outgoing particles have the same momenta, these two are part of the same overall interaction.
	2017-08-02: Dark Flow 10:24: By themselves, they don't obey momentum conservation. 10:30: Incoming and outgoing particles must obey energy and momentum conservation. 10:35: For example, in order to conserve momentum, an annihilating electron and positron must produce two photons, not one. 11:01: Each incoming and outgoing particle is identified with a numerical position and momentum. 10:24: By themselves, they don't obey momentum conservation. 10:30: Incoming and outgoing particles must obey energy and momentum conservation.
	2017-07-26: The Secrets of Feynman Diagrams 03:52: The photon vanishes as its momentum is completely transferred to the electron. 04:35: ... because of conservation laws-- energy and momentum conservation requires that particles not just vanish or appear from ... 05:37: We know their properties-- for example, their energy and momentum. 05:51: They sit on the shell structure you get when you plot Einstein's equation of energy, momentum, and mass. 07:02: We know the momentum of the ingoing and outgoing electrons. 07:13: Simple examples are the exchange of a single photon to transfer momentum between electrons, or the exchange of two or more photons. 07:51: As well as infinite possibilities for particle momenta, we have to consider even impossible faster than light paths. 04:35: ... because of conservation laws-- energy and momentum conservation requires that particles not just vanish or appear from nothing, which ...
	2017-07-19: The Real Star Wars 16:24: All we know is the momenta of all of those electrons.
	2017-07-12: Solving the Impossible in Quantum Field Theory 02:35: One electron excites a photon, and that photon delivers a bit of the first electron's momentum to the second electron.
	2017-06-28: The First Quantum Field Theory 05:52: It follows the changing position and momentum and generally the physical quantum state of every individual particle but that's extremely inefficient. 07:12: Instead of quantizing particles' physical properties like position and momentum, as did Schrodinger, Dirac quantized the electromagnetic field itself. 13:44: In fact, Schrodinger followed the same approach, starting with Einstein's mass energy momentum equation. 07:43: So Dirac described a space of quantum states, including position and momentum/frequency, like an infinite array of springs.
	2017-06-21: Anti-Matter and Quantum Relativity 02:21: ... as simple wave functions, distributions of possible positions and momenta that have no internal ... 02:42: But spin does result in a sort of quantum angular momentum. 04:05: ... down degrees of freedom were the direction of pointing of the angular momentum ... 04:54: He wrote down Einstein's famous equation, E equals mc squared, but in its full form, including momentum. 05:02: He then used quantum mechanical expressions for energy and momentum. 04:05: ... down degrees of freedom were the direction of pointing of the angular momentum axis. ...
	2017-04-05: Telescopes on the Moon 08:46: But momentum is building.
	2017-03-15: Time Crystals! 04:07: These atoms have spin values, quantum mechanical angular momenta from their electrons.
	2017-02-22: The Eye of Sauron Reveals a Forming Solar System! 02:51: Conservation of angular momentum has the central star spinning rapidly.
	2017-01-11: The EM Drive: Fact or Fantasy? 02:06: ... direction, the fat end for the EmDrive, can be achieved by extracting momentum from the internal radiation field, but with no ... 02:33: The law of conservation of momentum demands this. 02:56: Which is to say, this explanation breaks the law of conservation of momentum. 03:01: ... those photons actually escape the cavity, then any momentum exchange between the cavity and radiation field gets redistributed ... 07:02: The paper invokes pilot wave theory as a way to justify treating the quantum vacuum as a sort of plasma with which it can exchange momentum. 07:28: To exchange momentum with virtual particles over a distance longer than a Planck length, those particles need to become real. 07:49: Or if they escaped, they'd be a propellant, and momentum would be exchanged with no more efficiency than a photon thruster. 02:33: The law of conservation of momentum demands this. 03:01: ... those photons actually escape the cavity, then any momentum exchange between the cavity and radiation field gets redistributed again, because ...
	2016-12-14: Escape The Kugelblitz Challenge 06:32: ... impossible EM Drive technology that allows it to ignore conservation of momentum, so the satellites don't get ricocheted back to ...
	2016-12-08: What Happens at the Event Horizon? 14:14: ... about how pilot wave theory might explain the apparent conservation of momentum-breaking ...
	2016-08-24: Should We Build a Dyson Sphere? 07:22: ... from heat generated from infalling material, or by extracting angular momentum from the black hole's ...
	2016-07-27: The Quantum Experiment that Broke Reality 05:52: In fact, several quantum properties, like momentum, energy, and spin, all display similar waviness in different situations.
	2016-07-06: Juno to Reveal Jupiter's Violent Past 04:12: A planet can lose angular momentum to the debris, causing its orbit to shrink. 04:25: The planet can even migrate outwards, stealing angular momentum from the debris. 05:27: Drag from that gas would have sapped angular momentum from Jupiter, causing it to migrate inwards until it stalled at around 1.5 AU.
	2016-06-15: The Strange Universe of Gravitational Lensing 11:28: The idea is that a physical system doesn't have the familiar classical properties like position, momentum, spin, et cetera, until it is observed. 12:39: ... wave function into the classical physical properties like position and momentum. ... 11:28: The idea is that a physical system doesn't have the familiar classical properties like position, momentum, spin, et cetera, until it is observed.
	2016-06-01: Is Quantum Tunneling Faster than Light? 02:23: See an object's de Broglie wavelength depends on its momentum, so mass times velocity. 02:31: Higher momentum means a smaller wavelength. 02:33: In fact, it's the minuscule Planck constant divided by momentum.
	2016-05-25: Is an Ice Age Coming? 14:32: But, for example, a stress energy momentum pseudo tensor isn't mathematically the same thing as classical energy.
	2016-04-13: Will the Universe Expand Forever? 01:57: And it describes all of the energy, the pressure, the momentum, and more-- all of the stuff within that spacetime.
	2016-03-23: How Cosmic Inflation Flattened the Universe 12:52: ... the rate of accretion, the viscosity of the material, the way angular momentum is lost by that material, stuff like ...
	2016-03-16: Why is the Earth Round and the Milky Way Flat? 10:26: They also give us things like the Laws of Conservation of Energy and of Linear and Angular Momentum, topics that we will get to.
	2016-01-13: When Time Breaks Down 06:38: ... particles and fields, in which the internal parts exchange energy, momentum, and other properties-- interactions which hold the atom ...
	2016-01-06: The True Nature of Matter and Mass 02:20: The photons exert a force on the box, the box also exerts a force on the photons-- Newton's Third Law, which gives us the conservation of momentum. 02:29: Momentum lost by the box is transferred to the photons. 02:33: Now, if the box stops accelerating, then everything jiggles around and momentum gets shared out evenly between the box and the photons again. 03:14: And you can derive the famous E equals Mc squared just by looking at how momentum transfers between the photons in the box under acceleration. 07:23: The presence in the flow of energy and momentum as well as pressure all have their quite different effects on the curvature of space-time. 02:29: Momentum lost by the box is transferred to the photons. 03:14: And you can derive the famous E equals Mc squared just by looking at how momentum transfers between the photons in the box under acceleration.
	2015-12-16: The Higgs Mechanism Explained 01:43: ... vibrations and fields interact with each other, transferring energy, momentum, charge, et cetera, between particles and ...
	2015-12-09: How to Build a Black Hole 03:04: For a neutron star, this is the space of both 3D position and 3D momentum. 03:52: So two fermions can apply the same physical location just fine, as long as their momenta or any other quantum property is different. 04:09: In the case of a neutron star, position momentum phase space is completely full of neutrons. 04:16: Every spatial location and every momentum location connected to those special locations contains a neutron. 06:04: ... principle tells us that particular pairs of quantities, position and momentum or time and energy, must, when taken together, contain a minimum degree ... 06:32: Therefore, the Heisenberg uncertainty principle tells us that they must have highly undefined momenta. 06:44: To put it another way, the neutrons are packed so close together in position space that their momentum space becomes gigantic. 06:55: And here's the thing-- the denser the neutron star becomes, the more momentum space you get. 07:22: The star expands in momentum space. 09:17: Well, momentum space expands accordingly, with the corresponding enormous velocities all inward pointing. 04:16: Every spatial location and every momentum location connected to those special locations contains a neutron. 04:09: In the case of a neutron star, position momentum phase space is completely full of neutrons. 06:44: To put it another way, the neutrons are packed so close together in position space that their momentum space becomes gigantic. 06:55: And here's the thing-- the denser the neutron star becomes, the more momentum space you get. 07:22: The star expands in momentum space. 09:17: Well, momentum space expands accordingly, with the corresponding enormous velocities all inward pointing.
	2015-11-18: 5 Ways to Stop a Killer Asteroid 05:10: A one ton impact gives the necessary one part to a million momentum change needed to divert city killers.
	2015-10-15: 5 REAL Possibilities for Interstellar Travel 02:10: Conservation of momentum sucks.
	2015-05-06: Should the First Mars Mission Be All Women? 08:45: It should tilt slightly to the right because of the already tangential momentum that it had. 09:14: Fortstorm asks, wouldn't a rotating stations have trouble turning because its angular momentum vector would have trouble being shifted? 09:22: ... so that there would be gravity here and gravity here but no net angular momentum, and thus no net gyroscope ... 09:14: Fortstorm asks, wouldn't a rotating stations have trouble turning because its angular momentum vector would have trouble being shifted?
	2015-04-15: Could NASA Start the Zombie Apocalypse? 05:04: And they come out from straight up momentum conservation. 05:23: ... to take that loss of mass into account and 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. 05:04: And they come out from straight up momentum conservation. 05:23: ... to take that loss of mass into account and 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. 05:23: ... to take that loss of mass into account and use a more correct version of momentum conservation called the rocket equation that compensates for ...
	2015-04-08: Could You Fart Your Way to the Moon? 02:58: Conservation of momentum. 03:00: After a propulsion event, the net momentum of you and your fuel must remain zero. 03:05: So your forward momentum must be equal and opposite to the backward momentum of the gas you expel. 03:10: So how much momentum is that? 04:57: So the net result for momentum conservation?
	2015-03-25: Cosmic Microwave Background Explained 05:50: ... trick was to cancel out all the intermediate angular momentum vectors produced as a flywheel with forward-pointing angular momentum ... 06:00: ... solution is to have two flywheels, both with forward-pointing angular momentum that you rotate into the reverse orientation in opposite ... 06:08: That way, any sideways intermediate angular momentum that gets produced is canceled out. 06:43: ... could be spun sufficiently fast, you could store up a lot of angular momentum with very little ... 05:50: ... momentum vectors produced as a flywheel with forward-pointing angular momentum rotates to end up with backward-pointing angular ...
	2015-03-18: Can A Starfox Barrel Roll Work In Space? 02:03: That tendency to keep rotating is called an objects' angular momentum, and physicists represent it by a vector or an arrow. 02:23: To do that, the shipments needs to acquire a forward-pointing angular momentum vector. 02:27: To stop, that angular momentum must be removed. 02:59: But what if you could store up the angular momentum in advance and carry it with you? 03:04: And I don't mean having the ship doing a nonstop barrel roll, I mean happy angular momentum on demand without thrusters. 03:23: By rotating the flywheel quickly, I end up transferring its angular momentum to myself, so I start spinning. 03:47: So its angular momentum vector points toward the nose of the ship, which here is the top of your screen. 03:53: ... can also think of this vector as the net angular momentum of the entire ship flywheel system, all of which currently happens to ... 04:04: When I flip the flywheel 180 degrees, its individual angular momentum starts pointing toward the rear of the ship, i.e. 04:12: But the net angular momentum of the entire ship wheel system must remain unchanged. 04:17: That can happen only if the entire fuselage acquires its own large, forward-pointing angular momentum. 04:23: That, combined with the wheel's angular momentum, nets out to the same total angular momentum vector we began with. 04:56: Space telescopes, like Hubble and Kepler, also use angular momentum conservation to turn without thrusters. 05:33: ... fast they'd have to spin in the first place to store up enough angular momentum for the barrel ... 05:50: ... unlike with thrusters, you can keep storing and reusing that angular momentum to do as many barrel rolls as you ... 06:18: In the process, both of flipping and of flipping back, its angular momentum vector sweeps through a bunch of partially-sideways directions. 06:25: To compensate, the ship would have to do some wonky rotating as the flywheel flips, in order to keep the total angular momentum vector unchanged. 04:56: Space telescopes, like Hubble and Kepler, also use angular momentum conservation to turn without thrusters. 04:23: That, combined with the wheel's angular momentum, nets out to the same total angular momentum vector we began with. 04:04: When I flip the flywheel 180 degrees, its individual angular momentum starts pointing toward the rear of the ship, i.e. 02:23: To do that, the shipments needs to acquire a forward-pointing angular momentum vector. 03:47: So its angular momentum vector points toward the nose of the ship, which here is the top of your screen. 04:23: That, combined with the wheel's angular momentum, nets out to the same total angular momentum vector we began with. 06:18: In the process, both of flipping and of flipping back, its angular momentum vector sweeps through a bunch of partially-sideways directions. 06:25: To compensate, the ship would have to do some wonky rotating as the flywheel flips, in order to keep the total angular momentum vector unchanged. 03:47: So its angular momentum vector points toward the nose of the ship, which here is the top of your screen. 06:18: In the process, both of flipping and of flipping back, its angular momentum vector sweeps through a bunch of partially-sideways directions. 06:25: To compensate, the ship would have to do some wonky rotating as the flywheel flips, in order to keep the total angular momentum vector unchanged.

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