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2022-12-14: How Can Matter Be BOTH Liquid AND Gas?

  • 01:29: The relationship between temperature, pressure, and phase is mapped on a phase diagram.
  • 02:55: And beyond it is an entirely new state of matter - the here-be-dragons of the phase diagram.
  • 05:48: We know what we need to know, to take a journey to that strange new land of the phase diagram.
  • 06:36: ... causes pressure to rise, taking us into the realm of the phase diagram where liquid CO2 is ...
  • 06:57: To reach supercriticality, we need to get to this part of the diagram, so both pressure and temperature need to increase.
  • 07:27: ... has no effect because liquids are incompressible, but look at the phase diagram: At higher pressures the boiling point of CO2 increases, which means all ...
  • 08:01: But we’re approaching our strange new region of the phase diagram, where the rules are going to change Let's talk about density for a moment.

2022-11-09: What If Humanity Is Among The First Spacefaring Civilizations?

  • 08:58: By throwing many combinations of these two parameters into their model, the researchers generated this diagram.

2022-09-28: Why Is 1/137 One of the Greatest Unsolved Problems In Physics?

  • 05:14: ... can interact in many different ways, which we can visualize with Feynman Diagrams. ...
  • 05:27: ... diagrams are used to  add up the probabilities   of particles ...
  • 06:02: ... or in the case of two electrons interacting by,  say Feynman diagrams - it’s the base probability at each vertex, each interaction between ...

2022-09-14: Could the Higgs Boson Lead Us to Dark Matter?

  • 02:10: We can bundle the different methods into three broad categories, each represented by a different Feynman diagram.
  • 02:17: ... Feynman diagram is just a way to represent the interactions of particles, plotting time ...
  • 02:37: This particular diagram shows a dark matter particle scattering off a standard model particle in some way.
  • 03:35: The second family of experiments, indirect detection, can be represented by rotating our Feynman diagram.
  • 03:42: A cool thing about these diagrams is that if one orientation is possible, then all other orientations are possible.
  • 04:41: OK, let’s try rotating our Feynman diagram one more time.

2022-08-03: What Happens Inside a Proton?

  • 03:12: ... Each family of interaction types is represented by a Feynman diagram, and quantum electrodynamics   gives us a recipe book for ...
  • 04:17: ... their probabilities get smaller and smaller.  Diagrams with more than a few twists and turns   add almost nothing to ...
  • 05:31: ... photons of the electromagnetic field.   We can draw Feynman diagrams of these  interactions, now with curly gluon lines.   ...
  • 06:02: ... luxury of throwing away all but the simplest   Feynman diagrams when you’re calculating the interaction probability for your pair ...
  • 06:37: ... In fact it’s extremely challenging to  do QCD with the Feynman diagram approach   even with computers. Now Before any ...
  • 07:07: ... how can we even test the theory?  Well, we need to abandon Feynman diagrams.   In fact, we need to abandon the idea of particles altogether. See, ...
  • 07:53: ... course of a strong force interaction.   Similar to how Feynman diagrams work, to do this you need to account for all possible paths ...
  • 08:30: ... that even given the entire life of  the universe. For QED, Feynman diagrams let   us reduce the number of field configurations by ...
  • 08:58: ... covered. Before Richard   Feyman came up with his famous diagrams, he devised a way to calculate quantum probabilities   ...

2022-07-27: How Many States Of Matter Are There?

  • 02:48: We call this a phase diagram.
  • 03:12: The two numbers related on the phase diagram - temperature and pressure - are statistical properties of a large collection of particles.
  • 07:09: To fully convince you that quark matter has its own states of matter, behold its phase diagram.
  • 07:34: If you want to see what it’s like to move to right on this diagram, just burrow into a neutron star.

2022-07-20: What If We Live in a Superdeterministic Universe?

  • 08:18: Let’s play out the Bell test on something called a space-time diagram - with one dimension of space only on the x axis and time on the y.

2022-01-27: How Does Gravity Escape A Black Hole?

  • 10:19: ... for those of you who love their Penrose diagrams, just think about the source of the gravitational field as always being ...

2021-12-29: How to Find ALIEN Dyson Spheres

  • 08:38: If we graph temperature against luminosity we get something called a Hertzsprung-Russell diagram.
  • 09:14: Let’s see what a Dyson sphere would actually do to a star on the HR diagram.

2021-12-10: 2021 End of Year AMA!

  • 00:02: ... the case of say an electron and a proton the uh we draw these little diagrams where the electron and the proton are moving together and a little ...

2021-04-07: Why the Muon g-2 Results Are So Exciting!

  • 05:02: We depict these interactions in Feynman diagrams.
  • 05:05: Each Feynman diagram represents one family of ways that the interaction could proceed.
  • 05:10: And the sum of all possible Feynman diagrams, gives you the interaction strength.
  • 05:14: For a deeper dive in Feynman diagrams, virtual particles, and quantum electrodynamics, we have you covered, episode list in the description.
  • 05:23: We can represent an electron interacting with a magnetic field, with the simplest possible Feynman diagram.
  • 05:29: Really not even a full Feynman diagram.
  • 06:12: Each layer of complication involve many more Feynman diagrams, but also added less and less to the interaction.
  • 06:19: The latest calculations rely on powerful computers to add many thousands of Feynman diagrams, and get us our g-factor to 12 significant figures.
  • 07:36: So you add up all of the Feynman diagram to all possible electromagnetic interactions of the muon, but you don't stop there.

2021-02-24: Does Time Cause Gravity?

  • 02:09: We can show this with our old friend the spacetime diagram.

2021-02-10: How Does Gravity Warp the Flow of Time?

  • 07:36: We can see that when we use a spacetime diagram to show how the traveler tracks the passage of time back on Earth.
  • 07:52: Here’s the spacetime diagram for our rotating lab.

2021-01-19: Can We Break the Universe?

  • 04:07: The best way to see this is on a space-time diagram.
  • 04:33: ... the spacetime diagram, the set of simultaneous events for a motionless observer lie on a ...
  • 05:12: ... the spacetime diagram, that’s whenever one of these lines of constant time extending from ...
  • 06:20: But to see why we need a much weirder version of the spacetime diagram.
  • 09:46: Again, the best way to see this is on a spacetime diagram.
  • 09:53: The doors of the barn are a certain separation apart in space - solid lines in the diagram.
  • 11:12: The answer is in our looped spacetime diagram.

2020-12-08: Why Do You Remember The Past But Not The Future?

  • 04:34: We’re showing this in the style of a Feynman diagram.
  • 05:48: We can see that when we flip the Feynman diagram on its head - it's symmetric.
  • 06:02: ... “Feynman diagram” of our asteroid looks like countless particles coming together in many ...

2020-11-18: The Arrow of Time and How to Reverse It

  • 02:31: ... how the electrons’ positions change over time. But if we flip this diagram on its head - reverse the flow of time, it still looks like two ...
  • 06:52: The real-world situation represented by this diagram is called an entropy fluctuation.
  • 11:16: ... Diagrams dropped a lot of wisdom as always. I’m going to try to restate one point ...

2020-07-28: What is a Theory of Everything: Livestream

  • 00:00: ... know somebody mentioned wheeler earlier and i you know there's this diagram that i think a lot of people have been haunted by you know ever since ...

2020-06-30: Dissolving an Event Horizon

  • 12:45: These representations are called embedding diagrams, and we went through them in detial in our recent episode on Wormholes.

2020-06-15: What Happens After the Universe Ends?

  • 04:41: This is a spacetime diagram.
  • 09:34: ... of the other things Roger Penrose is famous for is his Penrose diagrams - these are ways of mathematically transforming our grid of spacetime to ...

2020-05-18: Mapping the Multiverse

  • 00:02: Or in physics-ese, it’s the maximally extended Penrose diagram of a Kerr spacetime.
  • 02:56: ... remember how to read our multiverse map - our Penrose, or Carter-Penrose diagram - maybe it’ll help us find our way out ...
  • 03:41: As we take this journey we’re also going to plot our path on the Penrose diagram.
  • 11:21: The complete Penrose diagram for the Kerr spacetime has not one, but two inner event horizons leading to two parallel wormholes.
  • 13:57: Never travel the multiverse without a Carter-Penrose diagram of the maximally extended Kerr spacetime.

2020-05-04: How We Know The Universe is Ancient

  • 15:09: ... somewhere else. The tube Lucid refers to is in the so-called embedding diagram of the wormhole. It's really a 2-D slice out of 4-D spacetime, with time ...

2020-04-22: Will Wormholes Allow Fast Interstellar Travel?

  • 03:33: ... of space at a single instant in time. The technical name is an embedding diagram - a 2-D spatial sheet sliced out of 4-D ...
  • 04:08: ... we saw in our parallel universe episode. This is the Kruskal-Szekeres diagram. Now I don’t want to go into the complexities of this right now - check ...
  • 05:43: ... Kruskal-Szekeres diagram shows that faster than light travel is needed to cross the wormhole, but ...

2020-04-14: Was the Milky Way a Quasar?

  • 14:22: Theo RixLux wants to know more about how cracks in a crystal can lead to a linear correlation in the concordance diagram.

2020-04-07: How We Know The Earth Is Ancient

  • 10:03: ... But the comparison of the two ratios one something called a Concordia Diagram. Allows you to correct for any lead ...

2020-03-31: What’s On The Other Side Of A Black Hole?

  • 03:46: ... light always be at a 45 degree angle. In the resulting Kruskal–Szekeres diagram, the event horizon becomes is also a 45 degree line, even though it ...
  • 04:31: ... are even more popular for intergalactic travelers. On Penrose diagrams, space and time also bunch up at infinite distance so tha t the entire ...
  • 05:00: ... true singularities, like at the center of the black hole. On our Penrose diagram, we see that light rays can either travel away from the black hole to ...
  • 05:49: ... say this Penrose diagram is geodesically incomplete because there are light rays with undefined ...

2020-01-27: Hacking the Nature of Reality

  • 07:23: But in order to avoid those sums of Feynman diagrams, S-matrix theory also relies on symmetries between those virtual interactions.
  • 07:36: ... traveling backwards in time - that folds together large sets of Feynman diagram and helps us ignore the actual causal structure within the interaction ...

2019-08-26: How To Become an Astrophysicist + Challenge Question!

  • 11:51: ... write up your answers Neatly show all of your work and draw some nice diagrams if you can Submit answers within two weeks of release of this episode to ...

2019-04-03: The Edge of an Infinite Universe

  • 05:19: ... the early 60s he developed his Penrose coordinates and Penrose diagrams – also known as Penrose-Carter diagrams, for Brandon Carter who came up ...
  • 05:40: As a quick review: start with a graph of space versus time – a spacetime diagram – then compactify.
  • 06:16: ... amazing thing about the Penrose diagram is that the transformation preserves all internal angles – all angles ...
  • 07:44: ... diagrams represent a universe that is “asymptotically flat” – it may have some ...
  • 09:09: Penrose diagrams define the infinite boundary of a flat universe as a useful tool in calculation.
  • 09:29: Just like the Penrose diagram we’ll do a conformal transformation – all internal angles preserved, and will compactify layers towards the edge.

2019-03-20: Is Dark Energy Getting Stronger?

  • 00:45: ... new paper in Nature Astronomy, “Cosmological constraints from the Hubble diagram of quasars at high redshifts” by Risaliti and ...
  • 10:23: It’s what we call a Hubble diagram.

2019-01-16: Our Antimatter, Mirrored, Time-Reversed Universe

  • 10:26: ... to his path integral approach to quantum mechanics and to Feynman diagrams maybe that's why he was so into building antimatter clocks. So, yeah the ...

2018-11-07: Why String Theory is Right

  • 03:34: On a spacetime diagram, time versus one dimension of space, this is called its world line.
  • 04:32: When strings move on a spacetime diagram, they trace out sheets or columns.

2018-10-31: Are Virtual Particles A New Layer of Reality?

  • 04:33: Maybe you recognize these things-- Feynman diagrams.
  • 04:48: Particles that either enter or leave these diagrams are our real particles.
  • 04:53: All those that both start and end within the diagram are virtual particles.
  • 04:58: ... diagrams are an absolutely essential tool in most modern quantum field theory ...
  • 06:17: Let's look at the fine and diagram of a single virtual photon passing from electron to positron.
  • 08:22: In fact, you only see that force in the sum of all possible virtual photons over all possible Feynman diagrams.

2018-10-25: Will We Ever Find Alien Life?

  • 14:52: Well, I'm going to quote Vacuum Diagrams on this one.
  • 15:20: ... actually we've always used the word theory to mean-- again, quoting Dr. Diagrams-- some framework that, loosely described, allows you to understand some ...

2018-10-03: How to Detect Extra Dimensions

  • 15:30: [INAUDIBLE] Vacuum Diagrams, Gareth [INAUDIBLE] complaining-- they just keep at it.

2018-08-15: Quantum Theory's Most Incredible Prediction

  • 05:02: So that electron diagram you did in middle school, it's time to kill that idea just like you kill your tamagotchi.
  • 08:08: In particular, we've been at Feynman diagrams, which are our best tool for dealing with the absurd complexity of quantum fields.
  • 08:30: A basic interaction of an electron with an EM field is illustrated by this partial Feynman diagram.
  • 10:18: For each new degree of precision, the number of Feynman diagrams needed explodes.

2018-06-20: The Black Hole Information Paradox

  • 12:52: EpsilonJ asked, what would happen if you fired a continuous beam of electrons at a black hole and how would the charge affect the Penrose diagram?
  • 13:11: And it turns out that a charged black hole has a pretty weird Penrose diagram.
  • 14:28: Check out our episode on the path integral and Feynman diagrams for more info on this wackiness.

2018-05-09: How Gaia Changed Astronomy Forever

  • 02:44: We often plot these properties against each other in a Hertzsprung-Russell or HR diagram.
  • 02:50: Location on this diagram can tell us about a star's mass, size, fusion activity, and even its past and future evolution.
  • 03:13: So let's take a look at the Gaia HR diagram, it's pretty incredible.
  • 03:17: ... population far beyond the neighborhood of the sun, compared to the HR diagram of ...
  • 04:09: We can even watch variable stars dance along the HR diagram as their brightness' change.

2018-04-11: The Physics of Life (ft. It's Okay to be Smart & PBS Eons!)

  • 11:07: ... Diagrams points out that from the point of view of an inertial observer, an ...

2018-04-04: The Unruh Effect

  • 01:26: We just need a little special relativity and a space-time diagram.
  • 01:34: A space-time diagram has two axes, time and, well, space, with time on the vertical axis.
  • 01:40: We can show an object's path through space and time using world lines on the diagram.
  • 02:04: On the space-time diagram, this is a line with a 45-degree angle from the vertical axis.

2018-02-28: The Trebuchet Challenge

  • 07:57: Draw diagrams if you need to.

2017-11-22: Suicide Space Robots

  • 11:30: And just quickly regarding the objections of vacuum diagrams to some of my statements in this whole quantum vacuum series-- doctor diagrams, vacuum.
  • 11:41: Doctor diagrams, I cede most of your points.

2017-10-19: The Nature of Nothing

  • 04:41: Virtual particles are the links governing all particle interactions in the famous Feynman diagrams.

2017-08-30: White Holes

  • 04:34: To really understand what this eternal black hole looks like, we're going to need to use a tool that we've already played with, that Penrose diagram.
  • 04:42: To refresh your memory, in a Penrose diagram, the x and y-axes are redefined from space and time to merge space and time into new coordinates.
  • 05:12: We are hanging out here and now at the center of the diagram.
  • 06:44: We can make some sense of the behavior of this strange region by using the Penrose diagram.
  • 07:30: ... to entry, but also light rays within that region must move up on the diagram. ...
  • 11:25: But speaking of other universes, it turns out that we haven't finished building our Penrose diagram yet.

2017-08-16: Extraterrestrial Superstorms

  • 11:50: Last week, we talked about John Archibald Wheeler's one electron universe idea as well as gave the solution to the Feynman diagram challenge.
  • 12:41: To prove this to yourself, try drawing a space-time diagram, time on the y-axis and space on the x-axis.
  • 13:13: Vacuum Diagrams points out that two diagrams are missing from the challenge answer.
  • 13:17: There should be diagrams with photons connecting across the vertices of the two-vertex photon deflection diagram, like this.
  • 13:27: I incorrectly considered these to be self-energy diagrams.

2017-08-10: The One-Electron Universe

  • 06:22: ... calculations, because it massively cuts down the number of Feynman diagrams you ...
  • 06:34: ... example, this one diagram for electron and photon scattering represents both the double deflection ...
  • 07:18: ... we draw a Feynman diagram for the whole universe, we can have only one electron undergo countless ...
  • 07:30: At some point in the middle of the diagram, we see many, many electrons.
  • 09:13: ... of anti-matter, let's go back and look at the solution to the Feynman diagram challenge ...
  • 09:22: ... asked you to draw all of the two-vertex and four-vertex diagrams for the interaction where electrons and positrons scatter off each other ...
  • 09:35: Well, here are the two-vertex diagrams.
  • 10:12: And the four-vertex diagrams look like this.

2017-08-02: Dark Flow

  • 09:54: Last week, we talked about the actual rules by which Feynman diagrams can be used to describe real interactions in quantum electrodynamics.
  • 10:04: ... couple of you pointed out that the Feynman diagram vertex, representing interactions between an electron, positron, and ...
  • 10:20: In fact, vertices are really just building blocks for Feynman diagrams.
  • 10:43: ... in Bhabha scattering have to remain on their respective sides of the diagram, or whether they can cross ...
  • 10:53: Well, actually, the spatial positions and even directions of motions of particles in the diagrams don't mean much at all.
  • 11:06: And we don't need to worry about drawing the diagrams accurately to represent those.
  • 11:57: ... after the electron undergoes an interaction, represented by a Feynman diagram, then we need to think of that retro-causal influence as also propagating ...
  • 12:14: Squid Master started studying physics and got a tattoo of a Feynman diagram, then switched majors to economics.

2017-07-26: The Secrets of Feynman Diagrams

  • 00:03: ... Feynman diagrams revolutionized particle physics by providing a simple system to sort out ...
  • 01:12: ... we discussed in our episode on solving impossible equations, the Feynman diagrams allow physicists to quickly figure out which of the infinite ...
  • 01:27: ... diagram represents a family of interactions and tells us the equation needed to ...
  • 01:38: The miracle of Feynman diagrams is that an absurdly simple set of rules allows you to easily find all of the important interactions.
  • 02:19: In Feynman diagrams, we depict the electron as an arrow pointing forwards in time, while the positron is an arrow pointing backwards in time.
  • 02:40: Throw these on a plot of space versus time, and we have a Feynman diagram-- a useless one.
  • 03:25: And it can be used to construct infinite Feynman diagrams.
  • 05:25: The overall interaction described by a set of Feynman diagrams is defined by the particles going in and the particles going out.
  • 06:06: Each possible diagram that results in the same ingoing and outgoing particles is a valid part of the possibility space for that interaction.
  • 06:15: The particles that have their entire existence between vertices within the diagram but don't enter or leave are called virtual particles.
  • 07:37: Part of the beauty of Feynman diagrams is that each of these diagrams themselves represents an infinite number of specific interactions.
  • 09:43: These may seem like wildly different processes, but in the math represented by Feynman diagrams, they're exactly the same.
  • 09:54: All we care about is the topology of the diagram.
  • 10:02: ... fact makes Feynman diagrams an incredibly powerful tool in simplifying quantum field theory ...
  • 10:27: But for now, I want to give you a chance to play with Feynman diagrams yourselves.
  • 10:41: The most important Feynman diagrams for Bhabha scattering are the two cases involving a single virtual photon.
  • 10:50: Those diagrams seem to describe very, very different events.
  • 10:57: ... the rules I described in this episode to draw both of the two-vertex diagrams for Bhabha scattering, and describe what's happening in each of these ...
  • 11:07: Then, I want you to try to draw all of the possible four-vertex diagrams.
  • 11:12: For the latter, don't bother with what we call the self-energy diagrams, in which electrons or positrons emit and then reabsorb a photon.
  • 11:21: Send your neatly drawn Feynman diagrams to within one week of the release of this episode.
  • 11:29: Include in the subject line the words Feynman diagram challenge, because we filter by subject line.

2017-07-19: The Real Star Wars

  • 16:27: When we draw the Feynman diagrams for electron scattering, we need to include separate diagrams in which the ingoing electrons swap places.
  • 16:37: A few of you asked why it is that each additional vertex reduces the probability contribution of a given Feynman diagram by around a factor of 100.

2017-07-12: Solving the Impossible in Quantum Field Theory

  • 00:23: The most famous of these are the incredible Feynman diagrams.
  • 01:16: Finally, the entire mess was ordered into a system that mere humans could deal with using the famous Feynman diagrams.
  • 03:04: This is a good time to introduce our first Feynman diagram.
  • 03:18: In a Feynman diagram, one direction is the time-- in this case, up.
  • 03:38: But Feynman diagrams aren't really just drawings of the interaction.
  • 03:46: Each part of the Feynman diagrams represents a chunk of the math.
  • 04:09: ... equation you string together from this one diagram represents all of the ways that two electrons can deflect involving only ...
  • 05:18: And this is where Feynman diagrams start to come in handy, because they keep track of the different families of possibilities.
  • 06:46: Here, Feynman diagrams are indispensable.
  • 06:50: It turns out that the probability amplitude of a particular interaction depends on the number of connections, or vertices, in the diagram.
  • 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.
  • 08:09: Perturbation theory, with the help of Feynman diagrams, make the calculation possible, but that doesn't mean we're done.
  • 11:08: ... diagrams successfully describe everything from particle scattering, self-energy ...
  • 11:20: We'll go further into the nuts and bolts of Feynman diagrams in an upcoming challenge episode.
  • 11:26: ... set of relatively straightforward rules governs what diagrams are possible, and these rules make Feynman's doodles an incredibly ...

2017-07-07: Feynman's Infinite Quantum Paths

  • 11:12: One powerful tool in making sense of these infinite possible events also came from Richard Feynman, specifically Feynman diagrams.

2017-06-28: The First Quantum Field Theory

  • 13:33: ... Diagrams points out that Schrodinger himself did write down a relativistic ...
  • 13:50: ... Mr. Diagrams points out, the resulting Klein Gordon equation gives negative energy ...
  • 14:26: ... we're still struggling to reconcile it with general relativity?" Vacuum Diagrams had a great response that explains the problem of infinities that both ...

2017-03-29: How Time Becomes Space Inside a Black Hole

  • 05:19: On our ever popular spacetime diagram, we see a sharp division between the two.
  • 06:26: At this point, it's time we switch diagrams.
  • 06:28: Close to and within the black hole, the Penrose diagram is much more useful.
  • 06:42: We talked about these diagrams previously.

2017-03-22: Superluminal Time Travel + Time Warp Challenge Answer

  • 01:23: We'll do this in flat space, so we need a flat or Minkowski spacetime diagram.
  • 02:08: In the olden days, the same time axis of a space time diagram would apply to everyone, but no longer.
  • 02:34: Everyone draws their space time diagram time axis parallel to their direction of motion, because that's their experience of stillness.
  • 03:48: So greater than 45 degrees on the diagram.
  • 04:43: Let's see what that looks like on the spacetime diagram.
  • 05:56: To see what the Annihilator sees, let's transform the space time diagram to their perspective.
  • 08:09: ... we transform the diagram to their perspective, we see that the Paradox really does appear to ...
  • 08:48: Let's fill in the space time diagram with all four quadrants.

2017-03-15: Time Crystals!

  • 05:35: Yao et al.'s work was theoretical, but it involved numerical calculations that allowed them to draw a phase diagram.
  • 05:43: This is sort of like the phase diagram of regular matter in which you plot pressure versus temperature.
  • 05:48: Different materials become solid, liquid, gas, or plasma at different locations on that phase diagram.
  • 05:54: The analogous phase diagram for time crystals plots interaction strength between atoms versus imperfection in the spin-flip driving signal.
  • 07:36: ... both fit the predicted phase diagram, their time asymmetry melting when subjected to too much perturbation or ...

2017-03-08: The Race to a Habitable Exoplanet - Time Warp Challenge

  • 00:51: In that episode, we talked about the spacetime diagram and how it transforms between observers traveling at different speeds.
  • 01:35: ... to x and to equal zero as contours, then we can transform the spacetime diagram into a 3D graph, in which causality must always flow ...
  • 03:29: To answer this, you'll need to draw a spacetime diagram showing the world lines of the two ships.
  • 03:40: When you transform the diagram to the perspective of the Annihilator, the paradox should suddenly appear to act like a time machine.
  • 03:49: It will be helpful to draw the hyperbolic spacetime interval contours on your diagram.
  • 04:43: Submit your answers with full explanations and spacetime diagrams within two weeks of the release of this video to be in the running.

2017-02-15: Telescopes of Tomorrow

  • 11:39: ... about the relationship between the geometry I depicted on the space-time diagram and the geometry that comes from mass and energy-curving ...
  • 11:49: The space-time diagram I showed is for flat or Minkowski space.

2017-02-02: The Geometry of Causality

  • 02:49: To preserve our sanity, we represent this on a spacetime diagram plotting time and only one dimension of space.
  • 03:03: There is no standing still on a spacetime diagram.
  • 04:51: First, we need to draw the spacetime diagram from the perspective of one of the other travelers.
  • 04:58: To transform the diagram, we need to figure out what they see as their space and time axes.
  • 06:27: That comes from insisting that we all see the same speed of light, 45 degrees on the spacetime diagram.
  • 06:40: In fact, we grid up the diagram with a set of lines parallel to these new axes and square up everything while maintaining our intersection points.
  • 09:40: In fact, the nearest downhill contour defines the forward light cone for anyone anywhere on the spacetime diagram.
  • 10:08: ... spacetime diagram we looked at today was for a flat or Minkowski space, in which faster ...

2017-01-04: How to See Black Holes + Kugelblitz Challenge Answer

  • 05:55: I also asked you to draw a Penrose diagram to justify your choice.
  • 06:02: In the challenge question, I showed you the Penrose diagram for a star collapsing into a black hole.
  • 06:10: I'm drawing only the right part of the usual Penrose diagram here.
  • 06:41: On the Penrose diagram, that horizon extends both forwards and backwards in time.
  • 07:17: That shell takes a 45-degree path, as do all light speed things on the Penrose diagram.
  • 08:11: First, the Penrose diagram for Project Disco Ball.
  • 09:01: ... on the Penrose diagram, that's seen as the future light cone of everything below the event ...

2016-12-21: Have They Seen Us?

  • 15:54: You know, there's probably a Penrose diagram for this.

2016-12-14: Escape The Kugelblitz Challenge

  • 00:11: This is the Penrose diagram.
  • 00:14: ... of the dimensions of space and time, allowing us to fit onto the one diagram the infinitely stretched space-time in the vicinity of a black hole's ...
  • 00:27: The Penrose diagram allows us to easily understand the limits of our access to this universe.
  • 00:34: ... get to, and the speed of light is always at a 45-degree angle on this diagram. ...
  • 00:44: ... we are going to use the Penrose diagram to look at the difference between the idealized, theoretical black hole ...
  • 01:11: The Penrose diagram we looked at represents a Schwarchild black hole-- so no electric charge and no rotation, but also an eternal black hole.
  • 01:42: So what does this look like on a Penrose diagram?
  • 02:40: Outside the black hole, the event horizon becomes the new edge of the universe on our Penrose diagram.
  • 03:27: On the Penrose diagram, we should extend our effective event horizon backwards to include that space.
  • 07:19: The president is especially upset, so draw a nice Penrose diagram of the situation to show why your preferred plan has the best shot.
  • 07:29: ... your carefully explained and diagrammed answer to within two weeks of release of this ...

2016-12-08: What Happens at the Event Horizon?

  • 02:01: The tool that will answer these questions is called the Penrose diagram, sometimes also the Carter Penrose diagram.
  • 02:08: It's a special type of space-time diagram designed to clarify the nature of horizons.
  • 02:15: But first, a quick refresher on basic space-time diagrams.
  • 02:30: With the right choice of space and time units, the speed of light becomes a diagonal line on the space-time diagram.
  • 03:01: Let's drop a black hole onto our space-time diagram.
  • 03:48: The problem with the regular space-time diagram is that the path of light and the shape of the light cone changes as space-time becomes warped.
  • 04:04: And this is where the Penrose diagram comes in.
  • 04:10: It transforms the regular space-time diagram to give it two powerful features.
  • 04:42: This is the Penrose diagram for flat space-time with no black holes.
  • 04:48: ... as with a regular space-time diagram, blue verticalish lines represent fixed locations in one dimension of ...
  • 05:16: The lines also converge together towards the corners so that light travels a 45 degree path everywhere on the diagram.
  • 05:24: ... from really, really far away and coming towards us hugs the edge of the diagram and crosses an enormous number of time and space steps, only reaching us ...
  • 05:56: The future cosmic horizon on the Penrose diagram is replaced with a plunge into a black hole.
  • 07:01: Now that we've nailed the Penrose diagram, we can use it to do some serious black hole monkey physics.
  • 10:43: For example, I only showed you half of the Penrose diagram.
  • 11:19: Then our Penrose diagram blooms outwards to include potentially infinite parallel regions of space-time.
  • 16:16: Vacuum Diagrams correctly points out that to know the future trajectory of a particle, you only need position, not velocity, as I had stated.
  • 16:47: ... of it was from people who know a good deal more than I do, like Vacuum Diagrams. ...

2016-06-29: Nuclear Physics Challenge

  • 03:04: ... info, plus drawing some of your own diagrams, plus some basic algebra is enough to get you the probability that an ...

2016-02-17: Planet X Discovered?? + Challenge Winners!

  • 04:11: The best way to illustrate this is with a spacetime diagram.
  • 04:21: So a photon clock that stationary on the spacetime diagram moves straight up.

2016-01-27: The Origin of Matter and Time

  • 01:13: A while ago, we introduced the space time diagram.
  • 01:43: You put something-- say this clock-- on this diagram.
  • 05:01: The whole space time diagram can be transformed to give the second clock's world line a constant location in space.
  • 07:04: And on our space time diagram, our object becomes an impossibly complex ensemble of light speed world lines confined in equally complex ways.
  • 07:28: We're extrapolating the validity of space time diagrams, and these tiny lifelike segments into the quantum realm.
  • 08:18: One of them-- a point on the space time diagram-- can influence another if a signal can travel between the two.

2015-08-19: Do Events Inside Black Holes Happen?

  • 00:37: ... terms like "geodesic" or "flat spacetime" and if I can draw a spacetime diagram or ...

2015-08-05: What Physics Teachers Get Wrong About Tides!

  • 00:34: Typically, they show this diagram, along with an explanation that goes something like this.

2015-07-29: General Relativity & Curved Spacetime Explained!

  • 01:54: ... think about it, on the flat spacetime diagrams of inertia observers, the world lines of other inertial observers are ...
  • 05:44: On a flat spacetime diagram the world lines of those photons should be parallel and congruent.

2015-07-22: SPECIAL ANNOUNCEMENT + Flat Spacetime Geometry Comments

  • 03:33: ... French, and also corrected an error that we had made in the space time diagrams that we showed at Minute 504 in the ...
  • 03:42: Some of the dots and we had placed in the two red guy and blue guy space time diagrams were placed inconsistently.
  • 04:32: ... notice that all the space time diagrams that I drew in the last episode were from the point of view of inertial ...

2015-07-15: Can You Trust Your Eyes in Spacetime?

  • 01:22: Our principle tool for exploring flat spacetime geometry will be something called a spacetime diagram for representing physical events.
  • 02:01: To represent this set up in a diagram, let's copy my x-axis onto a blackboard and add a vertical axis to show the time on my clock.
  • 03:53: And from his perspective the diagram looks like this.
  • 04:00: We agree about the speed of light, so its world line looks the same as in my diagram.
  • 04:11: Instead, red guy's world line and the monkey's world line are vertical in his diagram since they're both stationary from this perspective.
  • 04:18: ... on either diagram, I could also have drawn lines that are more horizontal than 45 degrees, ...
  • 04:34: ... spacetime diagrams are great for visualizing cool phenomena like time dilation, or length ...
  • 04:45: Instead, I just want to use these diagrams to establish how parallel transport works in flat spacetime.
  • 04:51: Because here's the thing, the answer is not clear a priori since you can't trust your eyes in spacetime diagrams.
  • 04:58: These highlighted points in my diagram and in the red guy's diagram correspond to the same events.
  • 05:08: Yet, between diagrams, their visual length, and the angle between them, have changed.
  • 05:19: ... spacetime diagrams preserve the spacetime interval between points with its weird minus ...
  • 05:30: So while these diagrams help quasi-visualize things, spacetime doesn't really look like this.
  • 05:41: But notice that visually parallel lines do remain visually parallel in all three diagrams.
  • 07:25: But that interpretation doesn't work on a spacetime diagram.

2015-07-02: Can a Circle Be a Straight Line?

  • 02:26: Intuitively, we know that curve number one, joining points A and B in the diagram is straight, and curve number two is not.
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