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

  • 15:11: ... back to the 1920’s and debate interpretations of quantum mechanics with Einstein and Schrödinger!” – well, then you’d need to learn ...

2022-11-23: How To See Black Holes By Catching Neutrinos

  • 10:17: This leads to massive amplification of the jet’s light due to Einstein stuff.

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

  • 17:08: ... Yavor Tch and zomgthisisawesomelol point out that Einstein was referring to wavefunction collapse when he said "spooky action at a ...
  • 17:23: ... Einstein was referring to general wavefunction collapse, in which the ...
  • 17:37: ... Einstein then got together with Boris Podolsky and Nathan Rosen and basically ...

2022-10-26: Why Did Quantum Entanglement Win the Nobel Prize in Physics?

  • 00:34: ... the prediction that Einstein refused to accept - the idea that two quantum systems can be entangled - ...
  • 00:47: ... “spooky action at a distance” as Einstein called it, is in seeming violation of his own theory of relativity, ...
  • 00:58: ... and Aspect achieved the rarest of feats - they proved Einstein wrong, while Zeilinger greatly advanced our understanding and ...
  • 03:46: ... Einstein thought that such hidden information must exist, while others like ...
  • 03:56: In almost every scientific debate,  physicists side with Einstein.
  • 10:35: There are two ways that the Bell inequalities could be violated without quantum entanglement being as spooky as Einstein feared.
  • 12:18: Any violation of locality still means that some sort of influence travels faster than light - the sort of spookiness that Einstein hated.
  • 13:32: This is a rare episode of Space Time in  which both Einstein and Feynman were wrong.
  • 13:38: Einstein because, one way or another,  the quantum world is indeed quite spooky.
  • 00:47: ... “spooky action at a distance” as Einstein called it, is in seeming violation of his own theory of relativity, which tells ...
  • 10:35: There are two ways that the Bell inequalities could be violated without quantum entanglement being as spooky as Einstein feared.
  • 12:18: Any violation of locality still means that some sort of influence travels faster than light - the sort of spookiness that Einstein hated.
  • 00:34: ... the prediction that Einstein refused to accept - the idea that two quantum systems can be entangled - bound ...
  • 03:46: ... Einstein thought that such hidden information must exist, while others like Neils ...
  • 00:58: ... and Aspect achieved the rarest of feats - they proved Einstein wrong, while Zeilinger greatly advanced our understanding and practical ...

2022-10-12: The REAL Possibility of Mapping Alien Planets!

  • 04:12: ... first let’s review gravitational  lensing. Einstein’s general theory of relativity   tells us that gravity is due to ...
  • 04:36: ... galaxy cluster. If the alignment is close enough, we can see an Einstein Ring, like this   galaxy being lensed by an intervening ...
  • 10:07: ... 550 astronomical units,   and extending indefinitely, with the Einstein ring getting wider and more diffuse the further you go.   ...
  • 04:36: ... galaxy cluster. If the alignment is close enough, we can see an Einstein Ring, like this   galaxy being lensed by an intervening galaxy. The ...
  • 10:07: ... point back at the Sun and take an image  of the faint einstein ring surrounding it.   You might note an issue here. The last thing ...
  • 04:12: ... first let’s review gravitational  lensing. Einstein’s general theory of relativity   tells us that gravity is due to ...

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

  • 02:36: ... who managed to explain  the discrepancy by including the effects of Einstein’s still-new relativity, as well as the fact that the energy levels of ...
  • 11:20: ... relativity; it’s also the relationship  between mass and energy in Einstein’s famous ...
  • 02:36: ... who managed to explain  the discrepancy by including the effects of Einstein’s still-new relativity, as well as the fact that the energy levels of ...
  • 11:20: ... relativity; it’s also the relationship  between mass and energy in Einstein’s famous ...
  • 02:36: ... who managed to explain  the discrepancy by including the effects of Einstein’s still-new relativity, as well as the fact that the energy levels of electrons with ...

2022-08-17: What If Dark Energy is a New Quantum Field?

  • 01:25: ... cosmological constant. This is just a static number that you can add to Einstein’s equations of general relativity to represent the fabric of space having ...

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

  • 01:55: Albert Einstein also came up with a scenario in which he tried to refute the non-realist implications of pure quantum mechanics.
  • 03:27: Measurement of one electron would influence the other in a very real way - something Einstein referred to as spooky action at a distance.
  • 05:11: This type of effect that made Einstein and company so uncomfortable.
  • 07:03: Countless Bell-type tests have been performed since, all with the same result: apparently entanglement is real and is as spooky as Einstein feared.
  • 07:52: There are ways to save realism in quantum mechanics by crossing Einstein and abandoning locality.
  • 07:03: Countless Bell-type tests have been performed since, all with the same result: apparently entanglement is real and is as spooky as Einstein feared.
  • 03:27: Measurement of one electron would influence the other in a very real way - something Einstein referred to as spooky action at a distance.

2022-06-15: Can Wormholes Solve The Black Hole Information Paradox?

  • 00:26: ... electromagnetism didn’t square with Galileo’s relativity led Einstein to his special   theory of relativity, from which followed ...

2022-06-01: What If Physics IS NOT Describing Reality?

  • 12:09: ... Wheeler: “whose information?”   This same question haunted Einstein. Einstein  famously once asked whether proponents of ...

2022-05-04: Space DOES NOT Expand Everywhere

  • 00:19: ... are all racing away from us, and interpreted through the lens of Einstein’s general theory of relativity, this only makes sense if all distances ...
  • 01:59: ... moving THROUGH space, but there’s a cleaner picture. Soon after Einstein finished general relativity, four scientists independently solved its ...
  • 00:19: ... are all racing away from us, and interpreted through the lens of Einstein’s general theory of relativity, this only makes sense if all distances ...

2022-04-20: Does the Universe Create Itself?

  • 00:59: ... desperate to maintain a physical and realist universe, including Albert Einstein himself. We’ve talked about this debate between the founders of quantum ...

2022-03-30: Could The Universe Be Inside A Black Hole?

  • 00:19: Einstein’s ridiculously successful general theory of relativity has never failed.
  • 00:36: Well it turns out that black holes and the Big Bang have more in common than vexing Einstein.
  • 06:05: It’s a white hole, and it’s a valid a solution to the Einstein equations.
  • 09:06: ... was the same that Alexander Friedmann made when he first solved the Einstein equations for the whole universe, and it’s the assumption behind the ...
  • 06:05: It’s a white hole, and it’s a valid a solution to the Einstein equations.
  • 09:06: ... was the same that Alexander Friedmann made when he first solved the Einstein equations for the whole universe, and it’s the assumption behind the FLRW ...
  • 00:19: Einstein’s ridiculously successful general theory of relativity has never failed.

2022-03-23: Where Is The Center of The Universe?

  • 02:55: As with much, it starts with Einstein.
  • 03:19: It wasn’t actually Einstein who worked this out.
  • 11:45: And you can do it without breaking Einstein’s general relativity.
  • 12:02: He sought solutions to the Einstein equation for a universe that is lumpy on the largest scales.
  • 11:45: And you can do it without breaking Einstein’s general relativity.

2022-02-10: The Nature of Space and Time AMA

  • 00:03: ... updated due to due to all of our beautiful newtonian mechanics then einstein came and changed all of it space and time became space-time due to the ...

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

  • 00:35: ... 1915 Einstein presented to the world the equations behind his general theory of ...
  • 00:48: Einstein’s theory predicted the existence of the ultimate gravitational object: the black hole.
  • 01:01: ... to Einstein’s theory, any object that reaches such a density has to collapse to a ...
  • 01:21: ... Einstein built the equations of GR Equation: G_{\mu\nu} + \Lambda g_{\mu\nu} = ...
  • 03:17: First we’ll see what Einstein has to say on the matter, and then we’ll go deeper, into the speculative realm of quantum gravity.
  • 08:39: ... and this one works whether we’re talking about the classical gravity of Einstein or some deeper theory of quantum ...
  • 01:21: ... Einstein built the equations of GR Equation: G_{\mu\nu} + \Lambda g_{\mu\nu} = \kappa ...
  • 00:35: ... 1915 Einstein presented to the world the equations behind his general theory of relativity, ...
  • 00:48: Einstein’s theory predicted the existence of the ultimate gravitational object: the black hole.
  • 01:01: ... to Einstein’s theory, any object that reaches such a density has to collapse to a ...
  • 00:48: Einstein’s theory predicted the existence of the ultimate gravitational object: the black hole.
  • 01:01: ... to Einstein’s theory, any object that reaches such a density has to collapse to a point-like ...
  • 00:48: Einstein’s theory predicted the existence of the ultimate gravitational object: the black hole.

2022-01-19: How To Build The Universe in a Computer

  • 09:34: ... started about the complexity  of including magnetic fields, or of Einstein’s general relativity when the gravitational field becomes very ...

2021-12-20: What Happens If A Black Hole Hits Earth?

  • 14:26: ... fields to GR so that our theory fits the data.” Well to that I’ll let Einstein respond: “It can scarcely be denied that the supreme goal of all theory ...

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

  • 00:02: ... the fact that massive bodies bend the paths of light according to einstein's theory of general relativity so when you look out there you see you ...

2021-11-17: Are Black Holes Actually Fuzzballs?

  • 00:20: ... theory - fuzzballs - are perhaps even weirder than the regular type Einstein’s general theory of relativity tells us that if the density of matter is ...

2021-11-10: What If Our Understanding of Gravity Is Wrong?

  • 00:09: New work is taking another  shot at that Einstein guy.
  • 02:52: ... Einstein found that Newtonian gravity  breaks down when the gravitational ...
  • 03:15: But what if Einstein missed something?
  • 08:35: ... Einstein’s description, the gravitational  field is what we call a ...
  • 00:09: New work is taking another  shot at that Einstein guy.
  • 03:15: But what if Einstein missed something?
  • 03:08: But Einsteinian gravity looks exactly like Newtonian gravity when gravitational fields get weak.
  • 08:35: ... Einstein’s description, the gravitational  field is what we call a ...

2021-11-02: Is ACTION The Most Fundamental Property in Physics?

  • 05:52: ... start with Einstein’s General Theory of Relativity, which, as we’ve discussed before, ...
  • 07:09: ... gives equations of motion that are valid even in the shifting frames of Einstein’s relativity. And we also start to learn something about the nature of the ...
  • 05:52: ... predict the orbit of Mercury. If you calculate that orbit using the Einstein equations in their full glory and full gory detail, you get the right answer. But ...
  • 07:09: ... gives equations of motion that are valid even in the shifting frames of Einstein’s relativity. And we also start to learn something about the nature of the ...
  • 05:52: ... start with Einstein’s General Theory of Relativity, which, as we’ve discussed before, describes the ...
  • 07:09: ... gives equations of motion that are valid even in the shifting frames of Einstein’s relativity. And we also start to learn something about the nature of the Action. ...

2021-10-20: Will Constructor Theory REWRITE Physics?

  • 00:00: ... people behind the greatest leaps in physics - Einstein, Newton, Heisenberg, all had the uncanny ability to see the fundamentals ...
  • 01:43: ... and so on from two master theories: quantum mechanics and Einstein’s general ...
  • 10:42: ... Einstein’s general theory of relativity came from asking what were the inevitable ...
  • 00:00: ... people behind the greatest leaps in physics - Einstein, Newton, Heisenberg, all had the uncanny ability to see the fundamentals - see ...
  • 01:43: ... and so on from two master theories: quantum mechanics and Einstein’s general ...
  • 10:42: ... Einstein’s general theory of relativity came from asking what were the inevitable ...
  • 01:43: ... and so on from two master theories: quantum mechanics and Einstein’s general ...
  • 10:42: ... Einstein’s general theory of relativity came from asking what were the inevitable ...
  • 01:43: ... and so on from two master theories: quantum mechanics and Einstein’s general relativity. ...
  • 10:42: ... Einstein’s general theory of relativity came from asking what were the inevitable implications of ...

2021-10-13: New Results in Quantum Tunneling vs. The Speed of Light

  • 05:22: Now, our old pal Professor Einstein is not a fan of faster-than-light motion.
  • 07:45: ... time relied on the Schrodinger equation, which doesn’t incorporate Einsteins’s special theory of relativity and so has no speed limit baked into ...

2021-09-07: First Detection of Light from Behind a Black Hole

  • 11:33: ... measuring the mass of the black hole - 30 million Suns - to verifying Einstein’s general theory of ...

2021-08-10: How to Communicate Across the Quantum Multiverse

  • 17:57: ... rabbit holes. Which apparently I’m never going to learn. Of course as Einstein said, "The definition of insanity is doing the same thing over and over ...

2021-07-07: Electrons DO NOT Spin

  • 02:25: ... experiment with the iron cylinder is called  the Einstein de-Haas effect, first performed by, well, Einstein and de-Haas in 1915. ...
  • 04:40: ... that plays into the conservation of angular momentum like  in the Einstein de-Haas effect, and it also gives electrons a magnetic field. An ...
  • 08:28: ... fix of the Schrodinger equation - in this case to make it work with Einstein’s special theory of relativity - something we’ve discussed  before. ...
  • 02:25: ... experiment with the iron cylinder is called  the Einstein de-Haas effect, first performed by, well, Einstein and de-Haas in 1915. It ...
  • 04:40: ... that plays into the conservation of angular momentum like  in the Einstein de-Haas effect, and it also gives electrons a magnetic field. An ...
  • 02:25: ... experiment with the iron cylinder is called  the Einstein de-Haas effect, first performed by, well, Einstein and de-Haas in 1915. It wasn’t the ...
  • 04:40: ... that plays into the conservation of angular momentum like  in the Einstein de-Haas effect, and it also gives electrons a magnetic field. An electron’s  spin ...
  • 08:28: ... fix of the Schrodinger equation - in this case to make it work with Einstein’s special theory of relativity - something we’ve discussed  before. ...

2021-06-23: How Quantum Entanglement Creates Entropy

  • 05:55: ... - this mysterious connection between quantum particles that Einstein called   “spooky action at a distance”. As a bit of a  ...

2021-06-16: Can Space Be Infinitely Divided?

  • 06:02: ... creates what we call effective mass, according to Einstein’s famous equation. The resulting   gravitational field changes ...
  • 10:55: ... space on this scale. The nature of   space is defined by Einstein’s general relativity, and GR breaks down at the Planck scale ...
  • 05:45: ... continue our gerdankenexperiment,  now adding two key ideas from Einstein:   first that mass and energy are equivalent, as expressed by the most ...
  • 06:02: ... creates what we call effective mass, according to Einstein’s famous equation. The resulting   gravitational field changes ...
  • 10:55: ... space on this scale. The nature of   space is defined by Einstein’s general relativity, and GR breaks down at the Planck scale ...
  • 06:02: ... creates what we call effective mass, according to Einstein’s famous equation. The resulting   gravitational field changes the ...
  • 10:55: ... space on this scale. The nature of   space is defined by Einstein’s general relativity, and GR breaks down at the Planck scale ...

2021-05-25: What If (Tiny) Black Holes Are Everywhere?

  • 00:41: At least, that’s the black hole as it appears in the mathematics of Einstein’s general theory of relativity.

2021-05-11: How To Know If It's Aliens

  • 16:32: ... WIMP - namely wearing interacting, massive, and particle-like. Fun fact: Einstein, along with Nathan Rosen, tried to explain particles as gravitational ...

2021-04-21: The NEW Warp Drive Possibilities

  • 00:00: That Einstein guy was a real bummer for our hopes of a star-hopping, science-fiction-y future.
  • 00:12: But Einstein also gave us a glimmer of hope.
  • 00:31: In 1915, Albert Einstein’s general theory of relativity revealed that the fabric of space and time is mutable and dynamic.
  • 01:27: Space-warp drives, time-warp drives, and eventually just warp drives became an increasingly popular way of breaking Einstein’s rules.
  • 01:34: ... - and Star Trek inspired the very first real warp field solution to the Einstein field ...
  • 02:25: Einstein’s speed limit doesn’t directly say that nothing can travel faster than light.
  • 03:29: It’s a sp acetime geometry that is a valid solution to the equations general theory of relativity. The Einstein Field Equation.
  • 03:54: The Alcubierre warp field may be a valid solution to the Einstein field equations, but that doesn’t mean it’s physically possible.
  • 04:31: ... combat this, we have a set of energy conditions that go alongside the Einstein field equations that are meant to restrict the allowable energy ...
  • 06:51: These guys propose a general definition for warp fields not tied to a particular solution to the Einstein field equations.
  • 09:19: He does this by exploring a broader family of solutions to the Einstein field equations than previous studies.
  • 12:18: Einstein and the universe appear to be trolling us - alternately inspiring and crushing our hopes for a star-hopping future.
  • 12:37: They’ll continue to try to “make it so” by exploring Einstein’s theory - hoping to build starship, but in the process learning how our universe works.
  • 01:34: ... - and Star Trek inspired the very first real warp field solution to the Einstein field ...
  • 03:29: It’s a sp acetime geometry that is a valid solution to the equations general theory of relativity. The Einstein Field Equation.
  • 03:54: The Alcubierre warp field may be a valid solution to the Einstein field equations, but that doesn’t mean it’s physically possible.
  • 04:31: ... combat this, we have a set of energy conditions that go alongside the Einstein field equations that are meant to restrict the allowable energy distributions ...
  • 06:51: These guys propose a general definition for warp fields not tied to a particular solution to the Einstein field equations.
  • 09:19: He does this by exploring a broader family of solutions to the Einstein field equations than previous studies.
  • 03:29: It’s a sp acetime geometry that is a valid solution to the equations general theory of relativity. The Einstein Field Equation.
  • 01:34: ... - and Star Trek inspired the very first real warp field solution to the Einstein field equations. ...
  • 03:54: The Alcubierre warp field may be a valid solution to the Einstein field equations, but that doesn’t mean it’s physically possible.
  • 04:31: ... combat this, we have a set of energy conditions that go alongside the Einstein field equations that are meant to restrict the allowable energy distributions to what is ...
  • 06:51: These guys propose a general definition for warp fields not tied to a particular solution to the Einstein field equations.
  • 09:19: He does this by exploring a broader family of solutions to the Einstein field equations than previous studies.
  • 00:00: That Einstein guy was a real bummer for our hopes of a star-hopping, science-fiction-y future.
  • 08:54: OK, let’s move on to the second paper by Erik Lentz: “Breaking the Warp Barrier: Hyper-Fast Solitons in Einstein-Maxwell-Plasma Theory”.
  • 00:31: In 1915, Albert Einstein’s general theory of relativity revealed that the fabric of space and time is mutable and dynamic.
  • 01:27: Space-warp drives, time-warp drives, and eventually just warp drives became an increasingly popular way of breaking Einstein’s rules.
  • 02:25: Einstein’s speed limit doesn’t directly say that nothing can travel faster than light.
  • 12:37: They’ll continue to try to “make it so” by exploring Einstein’s theory - hoping to build starship, but in the process learning how our universe works.
  • 00:31: In 1915, Albert Einstein’s general theory of relativity revealed that the fabric of space and time is mutable and dynamic.
  • 01:27: Space-warp drives, time-warp drives, and eventually just warp drives became an increasingly popular way of breaking Einstein’s rules.
  • 02:25: Einstein’s speed limit doesn’t directly say that nothing can travel faster than light.
  • 12:37: They’ll continue to try to “make it so” by exploring Einstein’s theory - hoping to build starship, but in the process learning how our universe works.

2021-04-13: What If Dark Matter Is Just Black Holes?

  • 00:44: ... are trying to find holes in Einstein’s theory of gravity - the general theory of relativity - that might ...

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

  • 00:47: In fact, it doesn't play nice with Einstein's entire theory of gravity, which itself is clearly right in its own way.

2021-03-09: How Does Gravity Affect Light?

  • 00:28: That fact is guaranteed by Einstein’s general theory of relativity.
  • 02:14: ... is Einstein’s great insight that there’s no experiment that can distinguish between ...
  • 05:02: ... let’s tackle an even trickier problem - the solving of which shot Einstein to his international fame - the deflection of the path of light by ...
  • 07:16: Einstein was in the business of overturning the ideas of Newton, so it’s not surprising that he turns to one of Newton’s great rivals.
  • 09:34: But this is exactly what Einstein did.
  • 11:21: Einstein used this approach to calculate the deflection expected when light passes a massive object.
  • 11:35: And Einstein’s deflection angle was famously verified by Sir Arthur Eddington, who voyaged to the west coast of Africa to watch a solar eclipse.
  • 11:52: So I guess the question I’d be asking at this point is why did Einstein’s calculation even work.
  • 12:08: ... you solve Einstein’s equations in a different way, you can show that gravity is due to a ...
  • 00:28: That fact is guaranteed by Einstein’s general theory of relativity.
  • 02:14: ... is Einstein’s great insight that there’s no experiment that can distinguish between ...
  • 11:35: And Einstein’s deflection angle was famously verified by Sir Arthur Eddington, who voyaged to the west coast of Africa to watch a solar eclipse.
  • 11:52: So I guess the question I’d be asking at this point is why did Einstein’s calculation even work.
  • 12:08: ... you solve Einstein’s equations in a different way, you can show that gravity is due to a ...
  • 11:52: So I guess the question I’d be asking at this point is why did Einstein’s calculation even work.
  • 11:35: And Einstein’s deflection angle was famously verified by Sir Arthur Eddington, who voyaged to the west coast of Africa to watch a solar eclipse.
  • 12:08: ... you solve Einstein’s equations in a different way, you can show that gravity is due to a free-falling ...
  • 00:28: That fact is guaranteed by Einstein’s general theory of relativity.
  • 02:14: ... is Einstein’s great insight that there’s no experiment that can distinguish between the ...

2021-02-24: Does Time Cause Gravity?

  • 00:34: ... - it follows as surely as 1+1=2 if we accept the two axioms of Einstein’s relativity theory: that the speed of light is constant for all ...
  • 03:49: In Einstein’s relativity you have to remember that time and space are not independent of each other.
  • 06:29: ... the same favorable exchange when we try to convert mass into energy via Einstein’s most famous equation, E=mc^2 - the speed of light is the exchange rate, ...
  • 07:56: In fact, the imaginary paths of light rays were one the most important tools that helped Einstein develop both special and general relativity.
  • 00:34: ... - it follows as surely as 1+1=2 if we accept the two axioms of Einstein’s relativity theory: that the speed of light is constant for all ...
  • 03:49: In Einstein’s relativity you have to remember that time and space are not independent of each other.
  • 06:29: ... the same favorable exchange when we try to convert mass into energy via Einstein’s most famous equation, E=mc^2 - the speed of light is the exchange rate, ...
  • 00:34: ... - it follows as surely as 1+1=2 if we accept the two axioms of Einstein’s relativity theory: that the speed of light is constant for all observers, and that ...
  • 03:49: In Einstein’s relativity you have to remember that time and space are not independent of each other.
  • 00:34: ... - it follows as surely as 1+1=2 if we accept the two axioms of Einstein’s relativity theory: that the speed of light is constant for all observers, and that the ...

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

  • 00:21: Albert Einstein really enjoyed imagining people falling off buildings.
  • 01:13: Einstein had his happy thought in 1907, a couple of years after he started his scientific revolution with the special theory of relativity.
  • 03:35: Einstein also had help and built on prior and contemporary wisdom to develop it.
  • 03:48: Einstein’s thought laboratory - his gedankenlab - was filled with many incredible imaginary devices, but one of his favorites was the photon clock.

2021-01-26: Is Dark Matter Made of Particles?

  • 15:11: ... to decelerate and then accelerate again to turn around, and according to Einstein’s equivalence principle, acceleration is fundamentally the same as ...
  • 16:23: And a final thought from Sebastian Elytron, who expresses surprise that apparently Einstein was a real person.
  • 15:11: ... to decelerate and then accelerate again to turn around, and according to Einstein’s equivalence principle, acceleration is fundamentally the same as ...

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

  • 00:00: That Einstein guy had some pretty wacky ideas.
  • 00:09: ... back in 1905, when Einstein was just getting started - he was already rocking our understanding of ...
  • 12:05: ... sense of this deeply strange, but unfailingly self-consistent theory of Einstein’s ...
  • 00:00: That Einstein guy had some pretty wacky ideas.
  • 12:05: ... sense of this deeply strange, but unfailingly self-consistent theory of Einstein’s ...

2021-01-12: What Happens During a Quantum Jump?

  • 04:27: The most famous quote on the not-Copenhagen side was from Albert Einstein - “God does not play dice with nature”.
  • 10:33: I suspect both Schrodinger and Einstein would agree.
  • 04:27: The most famous quote on the not-Copenhagen side was from Albert Einstein - “God does not play dice with nature”.

2020-12-15: The Supernova At The End of Time

  • 05:27: ... failed to incorporate the effects of Albert Einstein’s relativity theory, which predicted that the world looks very different ...

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

  • 00:24: ... from the subatomic realm of quantum mechanics to the cosmic realm of Einstein’s general relativity. But if time doesn’t have a preferred direction in ...

2020-11-11: Can Free Will be Saved in a Deterministic Universe?

  • 00:25: ... determinism in the context of the block universe idea that we get from Einstein's ...

2020-10-27: How The Penrose Singularity Theorem Predicts The End of Space Time

  • 00:34: ... told us.   In 1915, Newtonian gravity was superseded by Einstein’s general theory of relativity.   But that wasn’t the end of ...
  • 01:17: ... Schwarzschild solved the equations of general relativity soon after Einstein published them,   revealing that a sufficiently dense ball of ...
  • 03:18: ... figured out how to describe a rotating black   hole in Einstein’s theory. In it, the central point of infinite gravity is spun out ...
  • 01:17: ... Schwarzschild solved the equations of general relativity soon after Einstein published them,   revealing that a sufficiently dense ball of ...
  • 00:34: ... told us.   In 1915, Newtonian gravity was superseded by Einstein’s general theory of relativity.   But that wasn’t the end of ...
  • 03:18: ... figured out how to describe a rotating black   hole in Einstein’s theory. In it, the central point of infinite gravity is spun out ...
  • 00:34: ... told us.   In 1915, Newtonian gravity was superseded by Einstein’s general theory of relativity.   But that wasn’t the end of black ...
  • 03:18: ... figured out how to describe a rotating black   hole in Einstein’s theory. In it, the central point of infinite gravity is spun out into ...
  • 00:00: ... theorem   is much deeper - it leads us to the limits Einstein’s  great theory and to the origin of the ...
  • 03:38: ... that black hole singularities   were utterly unavoidable in Einstein’s theory. Penrose’s singularity paper is   deceptively short - just a ...
  • 04:35: ... of minutes. Basically,   Penrose showed that according to Einstein’s theory plus a couple of assumptions,   black holes must contain ...
  • 03:38: ... that black hole singularities   were utterly unavoidable in Einstein’s theory. Penrose’s singularity paper is   deceptively short - just a ...
  • 04:35: ... of minutes. Basically,   Penrose showed that according to Einstein’s theory plus a couple of assumptions,   black holes must contain ...
  • 03:38: ... that black hole singularities   were utterly unavoidable in Einstein’s theory. Penrose’s singularity paper is   deceptively short - just a ...

2020-10-20: Is The Future Predetermined By Quantum Mechanics?

  • 00:00: - Einstein's Special Theory of Relativity combines space and time into one dynamic unified entity, spacetime.
  • 00:31: In a block universe of Einstein's relativity, there's no way to cleanly define the present and so no way to cleanly separate the future from the past.
  • 12:42: In Einstein's relativity, the definition of simultaneous events is well, relative.
  • 15:32: Guilherme Marquesani takes issue with my characterization of Einstein as the smartest man in the block universe.
  • 15:44: Also, I'm pretty sure Einstein was another Renegade from the Citadel of Rick's.
  • 00:00: - Einstein's Special Theory of Relativity combines space and time into one dynamic unified entity, spacetime.
  • 00:31: In a block universe of Einstein's relativity, there's no way to cleanly define the present and so no way to cleanly separate the future from the past.
  • 12:42: In Einstein's relativity, the definition of simultaneous events is well, relative.
  • 00:31: In a block universe of Einstein's relativity, there's no way to cleanly define the present and so no way to cleanly separate the future from the past.
  • 12:42: In Einstein's relativity, the definition of simultaneous events is well, relative.
  • 00:00: - Einstein's Special Theory of Relativity combines space and time into one dynamic unified entity, spacetime.

2020-10-13: Do the Past and Future Exist?

  • 05:51: Einstein says otherwise.
  • 05:53: ... his special theory of relativity, Einstein showed that there’s no absolute way to define whether two events happen ...
  • 08:29: ... that’s the effect of Einstein’s special relativity - space and time tilt into each other, so that ...

2020-09-21: Could Life Evolve Inside Stars?

  • 12:50: ... century were in part driven by the simple intuitions of the likes of Einstein and Dirac that physical law should be mathematically ...

2020-09-08: The Truth About Beauty in Physics

  • 02:41: Einstein’s equations of general relativity give even better precision than Newton’s law - perhaps perfect precision - in their description of gravity.
  • 03:13: Ptolemy, Copernicus, Kepler, Newton, Einstein - each followed their own sense of mathematical beauty in this long quest to understand gravity.
  • 06:35: The step from Kepler to Newton suggests so, but then why does complexity seem to increase when you go one level deeper from Newton to Einstein?
  • 06:45: ... is probably a good time for a quote from Einstein himself: “The supreme goal of all theory is to make the irreducible ...
  • 07:12: One of Einstein’s contemporaries, and one of the very few that might be considered his intellectual peer, seems to have disagreed.
  • 07:49: He sought to develop a quantum mechanical wave equation that agreed with Einstein’s special relativity.
  • 09:39: And then there’s Einstein’s field equations of general relativity.
  • 10:01: ... couple of years after Einstein presented his general theory of relativity - Weyl found a simple, ...
  • 10:46: The first compellingly beautiful aspect of string theory is that gravity, in the form of the Einstein field equations - automatically emerged from it.
  • 03:13: Ptolemy, Copernicus, Kepler, Newton, Einstein - each followed their own sense of mathematical beauty in this long quest to understand gravity.
  • 10:46: The first compellingly beautiful aspect of string theory is that gravity, in the form of the Einstein field equations - automatically emerged from it.
  • 10:01: ... couple of years after Einstein presented his general theory of relativity - Weyl found a simple, elegant way to ...
  • 02:41: Einstein’s equations of general relativity give even better precision than Newton’s law - perhaps perfect precision - in their description of gravity.
  • 07:12: One of Einstein’s contemporaries, and one of the very few that might be considered his intellectual peer, seems to have disagreed.
  • 07:49: He sought to develop a quantum mechanical wave equation that agreed with Einstein’s special relativity.
  • 09:39: And then there’s Einstein’s field equations of general relativity.
  • 07:12: One of Einstein’s contemporaries, and one of the very few that might be considered his intellectual peer, seems to have disagreed.
  • 02:41: Einstein’s equations of general relativity give even better precision than Newton’s law - perhaps perfect precision - in their description of gravity.
  • 09:39: And then there’s Einstein’s field equations of general relativity.
  • 07:49: He sought to develop a quantum mechanical wave equation that agreed with Einstein’s special relativity.

2020-09-01: How Do We Know What Stars Are Made Of?

  • 00:39: A hundred years ago, we were starting to plumb the deepest mysteries of the universe with Einstein’s relativity and with quantum theory.
  • 01:43: ... who recounted his recent solar eclipse expedition in which he verified Einstein’s new general theory of ...
  • 00:39: A hundred years ago, we were starting to plumb the deepest mysteries of the universe with Einstein’s relativity and with quantum theory.
  • 01:43: ... who recounted his recent solar eclipse expedition in which he verified Einstein’s new general theory of ...
  • 00:39: A hundred years ago, we were starting to plumb the deepest mysteries of the universe with Einstein’s relativity and with quantum theory.

2020-08-17: How Stars Destroy Each Other

  • 14:41: Well, as Einstein said: The eternal mystery of the world is its comprehensibility.
  • 14:46: So if you’re comprehending Space Time does that make you Einstein?

2020-08-10: Theory of Everything Controversies: Livestream

  • 00:00: ... copy right here it's um my favorite beach reading and more recently einstein's unfinished revolution the search for what lies beyond the quantum lee ...

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

  • 00:00: ... in the universe and that's a fantastic theory of course developed by einstein and you know the mathematical properties developed by some other ...

2020-07-20: The Boundary Between Black Holes & Neutron Stars

  • 01:04: ... the shape of the gravitational waveform, and based on calculations using Einstein’s general theory of relativity, the masses of those bodies were ...

2020-06-30: Dissolving an Event Horizon

  • 10:12: As Einstein taught us, mass and energy are equivalent.

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

  • 04:54: Now in Einstein’s universe it’s not quite that simple.

2020-05-27: Does Gravity Require Extra Dimensions?

  • 01:28: ... Einstein's general theory of relativity has a perfect track record predicting the ...
  • 01:42: And deviations from Newton’s description may point the way to an understanding deeper than Einstein’s.
  • 01:28: ... Einstein's general theory of relativity has a perfect track record predicting the ...
  • 01:42: And deviations from Newton’s description may point the way to an understanding deeper than Einstein’s.
  • 01:28: ... Einstein's general theory of relativity has a perfect track record predicting the behavior ...

2020-05-18: Mapping the Multiverse

  • 00:09: ... in english: when you solve Einstein’s equations of general relativity for a rotating black hole, the universe ...
  • 14:05: ... luminiferous aether, and so doing paved the way for the acceptance of Einstein's ...
  • 00:09: ... in english: when you solve Einstein’s equations of general relativity for a rotating black hole, the universe ...
  • 14:05: ... luminiferous aether, and so doing paved the way for the acceptance of Einstein's ...
  • 00:09: ... in english: when you solve Einstein’s equations of general relativity for a rotating black hole, the universe does not ...
  • 14:05: ... luminiferous aether, and so doing paved the way for the acceptance of Einstein's relativity. ...

2020-05-11: How Luminiferous Aether Led to Relativity

  • 01:09: ... The death of the aether helped open the way for the acceptance of Einstein’s theory of ...
  • 11:42: ... that brings us to Einstein. The constancy of the speed of light and the Lorentz transformation are ...
  • 12:25: ... However the general concept of the aether sort of has an afterlife. Einstein talked about the “new aether” as the medium of the gravitational field, ...
  • 13:18: ... appears to have believed in the luminiferous aether until the end. When Einstein visited Michelson on his deathbed in 1931 Michelson's daughter begged ...
  • 12:25: ... However the general concept of the aether sort of has an afterlife. Einstein talked about the “new aether” as the medium of the gravitational field, and ...
  • 13:18: ... appears to have believed in the luminiferous aether until the end. When Einstein visited Michelson on his deathbed in 1931 Michelson's daughter begged Einstein ...
  • 01:09: ... The death of the aether helped open the way for the acceptance of Einstein’s theory of ...
  • 11:42: ... which was published 8 years after the Michelson-Morley experiment. Now Einstein’s starting motivation seems to have been the fact that the Maxwell ...
  • 01:09: ... The death of the aether helped open the way for the acceptance of Einstein’s theory of ...

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

  • 03:09: ... The recession of the galaxies makes perfect sense in the context of Einstein’s then-new general theory of ...
  • 03:24: ... Russian cosmologist Alexander Friedmann solved Einstein’s equations and found the possibility of a universe that could change in ...
  • 16:15: ... can write down a solution to the Einstein equations in which the wormhole throat is short, and it has no ...
  • 03:09: ... The recession of the galaxies makes perfect sense in the context of Einstein’s then-new general theory of ...
  • 03:24: ... Russian cosmologist Alexander Friedmann solved Einstein’s equations and found the possibility of a universe that could change in ...
  • 03:09: ... The recession of the galaxies makes perfect sense in the context of Einstein’s then-new general theory of ...

2020-04-28: Space Time Livestream: Ask Matt Anything

  • 00:00: ... theory yeah yeah he's amazing the theorists theorists they call him Einstein would always carry around his version of Paul Dirac's textbook on ...

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

  • 00:23: ... 1915, Karl Schwarzschild discovered a solution to Einstein’s brand new equations of general relativity - a solution that we now ...
  • 01:09: ... 1935, Albert Einstein, along with Nathan Rosen, expanded on Flamm’s idea - but not into a ...
  • 02:08: ... Archibald Wheeler, along with his ex-student Bob Fuller, realized that Einstein & Rosen’s bridge did not necessarily have to connect parallel layers ...
  • 04:50: ... paths are always at a steeper angle. The strange extra layer that Einstein and Rosen discovered is represented as a mirror reflection to our ...
  • 09:17: ... that are placed on allowable distributions of mass and energy in Einstein’s equation in order for those equations to make physical sense. But these ...
  • 13:26: ... bridge may explain quantum entanglement - itself first described by Einstein and Rosen, along with Boris Podolsky. The ER=EPR conjecture links ...
  • 02:08: ... Archibald Wheeler, along with his ex-student Bob Fuller, realized that Einstein & Rosen’s bridge did not necessarily have to connect parallel layers of ...
  • 01:52: ... turns out that this is almost certainly NOT what particles are, but the Einstein-Rosen paper inspired others to take the wormhole seriously - and inspired the ...
  • 13:26: ... example, Leonard Susskind and Juan Maldecina have speculated that the Einstein-Rosen bridge may explain quantum entanglement - itself first described by ...
  • 01:52: ... - and inspired the name for these Schwarzschild wormholes - the Einstein-Rosen bridge. ...
  • 13:26: ... example, Leonard Susskind and Juan Maldecina have speculated that the Einstein-Rosen bridge may explain quantum entanglement - itself first described by Einstein ...
  • 01:52: ... turns out that this is almost certainly NOT what particles are, but the Einstein-Rosen paper inspired others to take the wormhole seriously - and inspired the name ...
  • 00:23: ... 1915, Karl Schwarzschild discovered a solution to Einstein’s brand new equations of general relativity - a solution that we now ...
  • 09:17: ... that are placed on allowable distributions of mass and energy in Einstein’s equation in order for those equations to make physical sense. But these ...
  • 00:23: ... 1915, Karl Schwarzschild discovered a solution to Einstein’s brand new equations of general relativity - a solution that we now understand ...
  • 09:17: ... that are placed on allowable distributions of mass and energy in Einstein’s equation in order for those equations to make physical sense. But these energy ...

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

  • 01:53: ... of algebra derived by Karl Schwarzschild just a couple of months after Einstein published his general theory of relativity. It allows us to calculate ...
  • 07:32: ... horizons and emerge in the mirror universe. You’ve just traversed an Einstein-Rosen bridge - a wormhole. We’ll come back to the detailed physics of ...
  • 10:58: ... hole isn’t likely to be real, there are intriguing possibilities. That Einstein-Rosen bridge can potentially be made to lead to different parts of THIS ...
  • 07:32: ... horizons and emerge in the mirror universe. You’ve just traversed an Einstein-Rosen bridge - a wormhole. We’ll come back to the detailed physics of wormholes ...
  • 10:58: ... hole isn’t likely to be real, there are intriguing possibilities. That Einstein-Rosen bridge can potentially be made to lead to different parts of THIS universe, and ...
  • 07:32: ... horizons and emerge in the mirror universe. You’ve just traversed an Einstein-Rosen bridge - a wormhole. We’ll come back to the detailed physics of wormholes another ...

2020-03-24: How Black Holes Spin Space Time

  • 00:21: ... months after Einstein presented his complete general theory of relativity in 1915, a young ...
  • 02:36: ... importance of spin in black holes, it took nearly half a century before Einstein’s equations were solved for the rotating case. That was by Roy Kerr in ...
  • 05:14: ... Probe B measured the Earth’s frame dragging and it was exactly as Einstein’s theory predicted - incredibly weak in Earth’s case. But in the case of a ...
  • 00:21: ... months after Einstein presented his complete general theory of relativity in 1915, a young German ...
  • 02:36: ... importance of spin in black holes, it took nearly half a century before Einstein’s equations were solved for the rotating case. That was by Roy Kerr in ...
  • 05:14: ... Probe B measured the Earth’s frame dragging and it was exactly as Einstein’s theory predicted - incredibly weak in Earth’s case. But in the case of a ...
  • 02:36: ... importance of spin in black holes, it took nearly half a century before Einstein’s equations were solved for the rotating case. That was by Roy Kerr in 1963, ...
  • 05:14: ... Probe B measured the Earth’s frame dragging and it was exactly as Einstein’s theory predicted - incredibly weak in Earth’s case. But in the case of a Kerr ...

2020-03-16: How Do Quantum States Manifest In The Classical World?

  • 04:28: ... most famous entanglement experiment is the one that Einstein came up with to demonstrate an apparent absurdity predicted by pure ...
  • 05:32: ... influence is transferred potentially faster than light. This is what Einstein called spooky action at a distance, and we now know that this is a very ...
  • 04:28: ... absurdity predicted by pure quantum mechanics. This is the so-called Einstein-Podolsky-Rosen, or EPR paradox. A high energy photon decays into an electron and a ...

2020-02-18: Does Consciousness Influence Quantum Mechanics?

  • 08:20: ... role of the conscious mind - and vigorously defended himself after Einstein accused him of introducing mysticism into ...

2020-02-03: Are there Infinite Versions of You?

  • 12:29: Ilavenya rightly points out that no nice analytical solutions to the 3-body problem exist in general relativity - Einstein's modern theory of gravity.

2020-01-13: How To Capture Black Holes

  • 00:59: ... black hole mergers themselves were not so surprising. Einstein’s general relativity predicted gravitational waves and astrophysics ...

2019-12-17: Do Black Holes Create New Universes?

  • 12:42: ... subjects like relativity. In this course you’ll begin by understanding Einstein’s postulates and the Lorentz transformations, and as your knowledge ...

2019-12-09: The Doomsday Argument

  • 16:05: ... these are valid geometries for spacetimes that can be constructed within Einstein's general relativity, it's not clear how such a universe would form, and ...

2019-12-02: Is The Universe Finite?

  • 02:59: Albert Einstein’s general theory of relativity allows for three simple geometries for our universe.

2019-10-21: Is Time Travel Impossible?

  • 00:38: Or so we thought until Einstein came along.
  • 07:05: One example is the Tipler cylinder, conceived by Frank Tipler based on a solution to the Einstein equations by Willem van Stockum.

2019-10-15: Loop Quantum Gravity Explained

  • 00:28: To connect quantum physics with Einstein’s general theory of relativity.
  • 08:07: In the 1950s Einstein himself tried to rewrite general relativity in terms of these parallel transport vector connections, but the result was a mess.
  • 16:29: ... the answer lies in the Einstein field equation of general relativity That equation says that the amount ...
  • 00:28: To connect quantum physics with Einstein’s general theory of relativity.

2019-10-07: Black Hole Harmonics

  • 09:38: And that brings us to the last, and perhaps coolest application of this technique – testing Einstein.
  • 10:19: ... and the time for the decay of those oscillations agrees perfectly with Einstein’s ...
  • 11:00: But for now, Einstein reigns supreme.
  • 10:19: ... and the time for the decay of those oscillations agrees perfectly with Einstein’s ...

2019-08-19: What Happened Before the Big Bang?

  • 00:04: That is as long as you define 'The Big Bang' as the universe's early hot dense expanding state that's well described by Einstein's equations.
  • 10:51: ... receding galaxies could be explained by an expanding universe and solved Einstein's equations to show ...
  • 00:04: That is as long as you define 'The Big Bang' as the universe's early hot dense expanding state that's well described by Einstein's equations.
  • 10:51: ... receding galaxies could be explained by an expanding universe and solved Einstein's equations to show ...
  • 00:04: That is as long as you define 'The Big Bang' as the universe's early hot dense expanding state that's well described by Einstein's equations.
  • 10:51: ... receding galaxies could be explained by an expanding universe and solved Einstein's equations to show ...

2019-08-06: What Caused the Big Bang?

  • 02:26: First up, the equations of Einstein's general theory of relativity.
  • 03:23: ... is that if the vacuum of space has a constant energy density, then Einstein's equations end up having a term that we call the cosmological constant - ...
  • 04:38: To see how this could happen we need to move beyond Einstein's general relativity.
  • 02:26: First up, the equations of Einstein's general theory of relativity.
  • 03:23: ... is that if the vacuum of space has a constant energy density, then Einstein's equations end up having a term that we call the cosmological constant - ...
  • 04:38: To see how this could happen we need to move beyond Einstein's general relativity.
  • 03:23: ... is that if the vacuum of space has a constant energy density, then Einstein's equations end up having a term that we call the cosmological constant - A positive ...
  • 02:26: First up, the equations of Einstein's general theory of relativity.
  • 04:38: To see how this could happen we need to move beyond Einstein's general relativity.
  • 02:26: First up, the equations of Einstein's general theory of relativity.

2019-07-18: Did Time Start at the Big Bang?

  • 00:25: ... the retreating galaxies by Edwin Hubble and Vesto Slipher, combined with Einstein's - then - brand-new general theory of relativity, revealed that our ...
  • 01:56: ... existence In fact, There's powerful evidence that we should not rewind Einstein's equations that far, at least without introducing some very new physics ...
  • 06:02: ... if you're going forward No, you have to think about time in the way Einstein Intended there is no universal clock time is relative Clocks are ...
  • 07:22: ... the forward direction The analogy with the North Pole is a good one and Einstein himself used ...
  • 06:02: ... if you're going forward No, you have to think about time in the way Einstein Intended there is no universal clock time is relative Clocks are attached to each ...
  • 07:22: ... on how you want to think about it The point is that in the pure Einsteinian picture There is no before the Big Bang because no time line in this ...
  • 08:04: from the pure Einsteinian point of view It's meaningless to ask what happened before the Big Bang or after reaching the black hole Center?
  • 07:22: ... on how you want to think about it The point is that in the pure Einsteinian picture There is no before the Big Bang because no time line in this universe ...
  • 08:04: from the pure Einsteinian point of view It's meaningless to ask what happened before the Big Bang or after reaching the black hole Center?
  • 00:25: ... the retreating galaxies by Edwin Hubble and Vesto Slipher, combined with Einstein's - then - brand-new general theory of relativity, revealed that our ...
  • 01:56: ... existence In fact, There's powerful evidence that we should not rewind Einstein's equations that far, at least without introducing some very new physics ...
  • 00:25: ... the retreating galaxies by Edwin Hubble and Vesto Slipher, combined with Einstein's - then - brand-new general theory of relativity, revealed that our ...
  • 01:56: ... existence In fact, There's powerful evidence that we should not rewind Einstein's equations that far, at least without introducing some very new physics For one ...

2019-05-09: Why Quantum Computing Requires Quantum Cryptography

  • 16:30: The Inebriati logs the following: Day 37,736: Einstein still appears to be right about general relativity.

2019-05-01: The Real Science of the EHT Black Hole

  • 08:55: ... case with the addition of the warped spacetime of a black hole using Einstein’s theory of general ...
  • 10:17: ... couple of years ago, the black hole looks just like we predict based on Einstein’s general theory of ...
  • 10:33: ... then when black holes emerged from Karl Schwarzschild’s solution to the Einstein equations, they seemed like a deep abstraction – a prediction that ...
  • 10:54: ... team – finally hits us with visceral reality of the black hole, Einstein’s wildest prediction and the strangest object in all of space ...
  • 10:33: ... then when black holes emerged from Karl Schwarzschild’s solution to the Einstein equations, they seemed like a deep abstraction – a prediction that seemed too ...
  • 08:55: ... case with the addition of the warped spacetime of a black hole using Einstein’s theory of general ...
  • 10:17: ... couple of years ago, the black hole looks just like we predict based on Einstein’s general theory of ...
  • 10:54: ... team – finally hits us with visceral reality of the black hole, Einstein’s wildest prediction and the strangest object in all of space ...
  • 10:17: ... couple of years ago, the black hole looks just like we predict based on Einstein’s general theory of ...
  • 08:55: ... case with the addition of the warped spacetime of a black hole using Einstein’s theory of general ...
  • 10:54: ... team – finally hits us with visceral reality of the black hole, Einstein’s wildest prediction and the strangest object in all of space ...

2019-04-24: No Dark Matter = Proof of Dark Matter?

  • 00:03: ... doesn't just modify Newton's gravity but also requires modification of Einstein's general relativity over the years various efforts have been made to ...

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

  • 02:29: At least the three basic types described by Einstein’s general theory of relativity.
  • 03:17: In GR this is Minkowski space, after Hermann Minkowski, teacher and colleague of Albert Einstein’s.
  • 02:29: At least the three basic types described by Einstein’s general theory of relativity.
  • 03:17: In GR this is Minkowski space, after Hermann Minkowski, teacher and colleague of Albert Einstein’s.
  • 02:29: At least the three basic types described by Einstein’s general theory of relativity.

2019-03-28: Could the Universe End by Tearing Apart Every Atom?

  • 00:25: ... energy density with the cosmological constant in the equations of Einstein's general theory of relativity but what if dark energy is not constant ...
  • 01:55: ... let's do a quick refresher on how dark energy works in the language of Einstein's general relativity I say refresher because we spent a whole playlist ...
  • 03:05: ... which depends on how much stuff there is in the universe because this is Einstein's gravity not Newton's, gravity is influenced by mass and energy density ...
  • 00:25: ... energy density with the cosmological constant in the equations of Einstein's general theory of relativity but what if dark energy is not constant ...
  • 01:55: ... let's do a quick refresher on how dark energy works in the language of Einstein's general relativity I say refresher because we spent a whole playlist ...
  • 03:05: ... which depends on how much stuff there is in the universe because this is Einstein's gravity not Newton's, gravity is influenced by mass and energy density ...
  • 00:25: ... energy density with the cosmological constant in the equations of Einstein's general theory of relativity but what if dark energy is not constant what if the ...
  • 01:55: ... let's do a quick refresher on how dark energy works in the language of Einstein's general relativity I say refresher because we spent a whole playlist delving ...
  • 00:25: ... energy density with the cosmological constant in the equations of Einstein's general theory of relativity but what if dark energy is not constant what if the energy ...
  • 03:05: ... which depends on how much stuff there is in the universe because this is Einstein's gravity not Newton's, gravity is influenced by mass and energy density but also ...

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

  • 02:13: Mathematically we represent a constant vacuum energy with Einstein’s cosmological constant – or Lambda.

2019-02-07: Sound Waves from the Beginning of Time

  • 12:20: They also confirm the dark energy behaves just as is predicted by Einsteins cosmological constant.
  • 16:08: In so-called bimetric gravity, you can have positive and negative masses, but each is described by its own set of Einstein field equations.
  • 12:20: They also confirm the dark energy behaves just as is predicted by Einsteins cosmological constant.

2019-01-30: Perpetual Motion From Negative Mass?

  • 05:47: ... only approximation of a much more complete description of gravity: Einstein’s general theory of ...
  • 10:58: ... geodesics of general relativity – the paths carved into the geometry of Einstein’s spacetime – are the GR analogs of Newton’s second law and give the ...
  • 05:47: ... only approximation of a much more complete description of gravity: Einstein’s general theory of ...
  • 10:58: ... geodesics of general relativity – the paths carved into the geometry of Einstein’s spacetime – are the GR analogs of Newton’s second law and give the ...
  • 05:47: ... only approximation of a much more complete description of gravity: Einstein’s general theory of ...
  • 10:58: ... geodesics of general relativity – the paths carved into the geometry of Einstein’s spacetime – are the GR analogs of Newton’s second law and give the equations of ...

2019-01-09: Are Dark Matter And Dark Energy The Same?

  • 02:25: According to Einstein’s general theory of relativity, any such positive energy produces an inward-pulling gravity.
  • 02:47: That’s the solution to the Einstein equations that tells you the rate of acceleration of the expansion of the universe.
  • 03:34: In Einstein’s equations and the Friedmann equations, that constant energy density is represented by the cosmological constant, or Lambda.
  • 02:47: That’s the solution to the Einstein equations that tells you the rate of acceleration of the expansion of the universe.
  • 02:25: According to Einstein’s general theory of relativity, any such positive energy produces an inward-pulling gravity.
  • 03:34: In Einstein’s equations and the Friedmann equations, that constant energy density is represented by the cosmological constant, or Lambda.
  • 02:25: According to Einstein’s general theory of relativity, any such positive energy produces an inward-pulling gravity.

2018-12-20: Why String Theory is Wrong

  • 00:21: [intro music] Hermann Weyl once said, "If I have to choose between beauty and truth, I choose beauty." It was in reaction to a rebuke by Einstein.
  • 00:35: Weyl had tried to explain electromagnetism by imposing on Einstein's general theory of relativity.
  • 00:41: ... very first gauge symmetry -- Weyl invariance Einstein pointed out that the proposal led to some absurd results, and so the ...
  • 02:27: In 1919, not long after Einstein published his great theory of gravity, Theodor Kaluza discovered something strange.
  • 02:43: ... that in the right sort of 5-D space-time, you can separate the resulting Einstein equations into a 4-D component that looks exactly like the familiar ...
  • 03:18: Einstein himself was supposedly jubilant at the idea -- a rather better reaction than was received for the electromagnetism of poor old Hermann Weyl.
  • 02:43: ... that in the right sort of 5-D space-time, you can separate the resulting Einstein equations into a 4-D component that looks exactly like the familiar general ...
  • 00:41: ... very first gauge symmetry -- Weyl invariance Einstein pointed out that the proposal led to some absurd results, and so the idea went ...
  • 02:27: In 1919, not long after Einstein published his great theory of gravity, Theodor Kaluza discovered something strange.
  • 00:35: Weyl had tried to explain electromagnetism by imposing on Einstein's general theory of relativity.

2018-11-07: Why String Theory is Right

  • 06:36: A while ago, we talked about Paul Dirac developed a wave equation for the electron that took into account Einstein's special theory of relativity.
  • 09:43: Hermann Weyl actually came up with this symmetry right after Einstein proposed his general theory of relativity.
  • 11:44: ... of a black hole, then it looks just like the gravitational field in Einstein's ...
  • 09:43: Hermann Weyl actually came up with this symmetry right after Einstein proposed his general theory of relativity.
  • 06:36: A while ago, we talked about Paul Dirac developed a wave equation for the electron that took into account Einstein's special theory of relativity.
  • 11:44: ... of a black hole, then it looks just like the gravitational field in Einstein's ...
  • 06:36: A while ago, we talked about Paul Dirac developed a wave equation for the electron that took into account Einstein's special theory of relativity.
  • 11:44: ... of a black hole, then it looks just like the gravitational field in Einstein's theory. ...

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

  • 05:18: ... quantum numbers like charge and spin, but they don't need to obey Einstein's relationship between energy mass and ...

2018-10-03: How to Detect Extra Dimensions

  • 04:21: But even there, Einstein's general relativity describes gravity perfectly with three spatial dimensions.

2018-09-20: Quantum Gravity and the Hardest Problem in Physics

  • 00:34: First, Einstein's relativity utterly changed the way we think about space, time, motion, and gravity.
  • 01:41: General relativity, GR, is Einstein's great theory of gravity.
  • 11:27: Generations of physicists, starting with Einstein himself, spent their lives trying to fix this to unite quantum mechanics and general relativity.
  • 00:34: First, Einstein's relativity utterly changed the way we think about space, time, motion, and gravity.
  • 01:41: General relativity, GR, is Einstein's great theory of gravity.
  • 00:34: First, Einstein's relativity utterly changed the way we think about space, time, motion, and gravity.

2018-09-05: The Black Hole Entropy Enigma

  • 00:40: At least they are inevitable according to the equations of Einstein's general theory of relativity.

2018-07-18: The Misunderstood Nature of Entropy

  • 00:54: ... Einstein said that "the thermodynamics that encapsulates the second law is the ...
  • 09:56: The inevitability of the rise of entropy is as fundamental as counting, that's why Einstein and Eddington were so sure of it.

2018-07-11: Quantum Invariance & The Origin of The Standard Model

  • 02:03: Newton's laws of motion and gravity, Maxwell's equations for electromagnetism, Einstein's general relativity, and of course, the standard model.
  • 09:03: First, we need to upgrade the Schrodinger equation to the Dirac equation so it works with Einstein's special relativity.
  • 02:03: Newton's laws of motion and gravity, Maxwell's equations for electromagnetism, Einstein's general relativity, and of course, the standard model.
  • 09:03: First, we need to upgrade the Schrodinger equation to the Dirac equation so it works with Einstein's special relativity.
  • 02:03: Newton's laws of motion and gravity, Maxwell's equations for electromagnetism, Einstein's general relativity, and of course, the standard model.
  • 09:03: First, we need to upgrade the Schrodinger equation to the Dirac equation so it works with Einstein's special relativity.

2018-07-04: Will A New Neutrino Change The Standard Model?

  • 13:24: One minute I'm learning the constellations or Einstein quotes to impress my friends, and next, well, it's a long, sad down spiral to where I am today.

2018-06-20: The Black Hole Information Paradox

  • 11:44: Einstein's general theory of relativity reveals them to be regions of frozen time and cascading space.
  • 11:50: But the first hint of the existence of black holes appeared long before Einstein.
  • 05:27: ... a slight modification of general relativity called Einstein-Cartan theory, it's predicted that the formation of a rotating black hole gives ...
  • 11:44: Einstein's general theory of relativity reveals them to be regions of frozen time and cascading space.

2018-06-13: What Survives Inside A Black Hole?

  • 03:24: In Einstein's general theory of relativity, we think of the gravitational field as curvature in the fabric of spacetime.
  • 08:52: In Einstein's general relativity, a spinning mass drags the fabric of space time around with it in a phenomenon known as frame dragging.
  • 03:24: In Einstein's general theory of relativity, we think of the gravitational field as curvature in the fabric of spacetime.
  • 08:52: In Einstein's general relativity, a spinning mass drags the fabric of space time around with it in a phenomenon known as frame dragging.
  • 03:24: In Einstein's general theory of relativity, we think of the gravitational field as curvature in the fabric of spacetime.
  • 08:52: In Einstein's general relativity, a spinning mass drags the fabric of space time around with it in a phenomenon known as frame dragging.
  • 03:24: In Einstein's general theory of relativity, we think of the gravitational field as curvature in the fabric of spacetime.

2018-05-23: Why Quantum Information is Never Destroyed

  • 12:59: When she did publish it, Einstein supposedly remarked that he had no idea that anyone could think about gravity in such general ways.

2018-05-16: Noether's Theorem and The Symmetries of Reality

  • 01:03: When it was published in 1915, Einstein's general theory of relativity opened as many questions as it answered.
  • 04:35: See, Einstein's description of gravity reveals the dimensions of space and time to be dynamic and changeable.
  • 05:08: But in Einstein's universe, energy conservation is only valid as a special case.
  • 09:18: Einstein also called her a genius.
  • 01:03: When it was published in 1915, Einstein's general theory of relativity opened as many questions as it answered.
  • 04:35: See, Einstein's description of gravity reveals the dimensions of space and time to be dynamic and changeable.
  • 05:08: But in Einstein's universe, energy conservation is only valid as a special case.
  • 04:35: See, Einstein's description of gravity reveals the dimensions of space and time to be dynamic and changeable.
  • 01:03: When it was published in 1915, Einstein's general theory of relativity opened as many questions as it answered.
  • 05:08: But in Einstein's universe, energy conservation is only valid as a special case.

2018-04-18: Using Stars to See Gravitational Waves

  • 02:09: Perhaps these gravitational waves signals were amplified by another phenomenon predicted by Einstein's general relativity, gravitational lensing.
  • 08:40: ... Einstein was able to derive his general theory of relativity, which predicted the ...
  • 08:56: ... mastering Newtonian gravity is also your next step toward understanding Einstein's view of ...
  • 02:09: Perhaps these gravitational waves signals were amplified by another phenomenon predicted by Einstein's general relativity, gravitational lensing.
  • 08:56: ... mastering Newtonian gravity is also your next step toward understanding Einstein's view of ...
  • 02:09: Perhaps these gravitational waves signals were amplified by another phenomenon predicted by Einstein's general relativity, gravitational lensing.
  • 08:56: ... mastering Newtonian gravity is also your next step toward understanding Einstein's view of ...

2018-04-04: The Unruh Effect

  • 01:57: Einstein taught us that an object without mass, like a photon, can only travel at the speed of light and no slower.
  • 09:58: According to Einstein's equivalence principle, remaining stationary in a gravitational field is equivalent to acceleration in free space.
  • 01:57: Einstein taught us that an object without mass, like a photon, can only travel at the speed of light and no slower.
  • 09:58: According to Einstein's equivalence principle, remaining stationary in a gravitational field is equivalent to acceleration in free space.

2018-03-15: Hawking Radiation

  • 00:34: ... PLAYING] Soon after Einstein revealed his great general theory of relativity in 1915, physicists ...

2018-02-14: What is Energy?

  • 10:53: ... actually, conservation of energy is generally invalid in the context of Einstein's general theory of relativity due to the potential time evolution of ...

2017-11-29: Citizen Science + Zero-Point Challenge Answer

  • 05:15: But there's also Einstein at Home, which searches for LIGO gravitational wave data for signals produced by rotating neutron stars.

2017-11-02: The Vacuum Catastrophe

  • 04:57: Einstein's theory tells us that any form of energy produces gravity, and what matters is the absolute amount of energy, not relative deviations.

2017-10-04: When Quasars Collide STJC

  • 13:23: Wait, we're summing over the superscript mu in gamma as per the Einstein summation convention.
  • 13:30: Is-- is Einstein out the window now?
  • 13:23: Wait, we're summing over the superscript mu in gamma as per the Einstein summation convention.

2017-08-30: White Holes

  • 00:05: Lurking in the depths of the mathematics of Einstein's general relativity is an object even stranger than the mysterious black hole.
  • 00:37: ... the idea first emerged from Einstein's general theory of relativity, physicists wondered how seriously to take ...
  • 02:31: ... a few months after Einstein published his general theory of relativity, Karl Schwarzschild solved ...
  • 12:05: ... on the other side of the black hole, accessible through what we call an Einstein-Rosen Bridge, better known as a ...
  • 00:05: Lurking in the depths of the mathematics of Einstein's general relativity is an object even stranger than the mysterious black hole.
  • 00:37: ... the idea first emerged from Einstein's general theory of relativity, physicists wondered how seriously to take ...
  • 00:05: Lurking in the depths of the mathematics of Einstein's general relativity is an object even stranger than the mysterious black hole.
  • 00:37: ... the idea first emerged from Einstein's general theory of relativity, physicists wondered how seriously to take this ...
  • 00:05: Lurking in the depths of the mathematics of Einstein's general relativity is an object even stranger than the mysterious black hole.
  • 00:37: ... the idea first emerged from Einstein's general theory of relativity, physicists wondered how seriously to take this ...

2017-08-10: The One-Electron Universe

  • 04:58: In a quantum field theory that's consistent with Einstein's special relativity, all particles must be symmetric under what we call CPT transformation.

2017-07-26: The Secrets of Feynman Diagrams

  • 05:41: And they obey Einstein's mass-energy equation.
  • 05:51: They sit on the shell structure you get when you plot Einstein's equation of energy, momentum, and mass.
  • 05:41: And they obey Einstein's mass-energy equation.
  • 05:51: They sit on the shell structure you get when you plot Einstein's equation of energy, momentum, and mass.
  • 05:41: And they obey Einstein's mass-energy equation.

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

  • 08:16: That means it treats space and time symmetrically and so works very naturally with Einstein's theory of special relativity.

2017-06-28: The First Quantum Field Theory

  • 04:08: This is exactly how light behaves, as was first realized by Max Planck and proved by Einstein.
  • 05:07: Basically, the Schrodinger equation is incompatible with Einstein's relativity.
  • 13:44: In fact, Schrodinger followed the same approach, starting with Einstein's mass energy momentum equation.
  • 05:07: Basically, the Schrodinger equation is incompatible with Einstein's relativity.
  • 13:44: In fact, Schrodinger followed the same approach, starting with Einstein's mass energy momentum equation.
  • 05:07: Basically, the Schrodinger equation is incompatible with Einstein's relativity.

2017-06-21: Anti-Matter and Quantum Relativity

  • 00:16: Einstein's theory of special and general relativity had changed forever the way we think about motion, space, and time.
  • 00:50: By the late 1920s, Einstein and Planck had already shown that light is a particle, as well as a wave.
  • 01:40: First and most obvious, the Schrodinger equation is totally incompatible with Einstein's relativity.
  • 04:54: He wrote down Einstein's famous equation, E equals mc squared, but in its full form, including momentum.
  • 00:16: Einstein's theory of special and general relativity had changed forever the way we think about motion, space, and time.
  • 01:40: First and most obvious, the Schrodinger equation is totally incompatible with Einstein's relativity.
  • 04:54: He wrote down Einstein's famous equation, E equals mc squared, but in its full form, including momentum.
  • 01:40: First and most obvious, the Schrodinger equation is totally incompatible with Einstein's relativity.
  • 00:16: Einstein's theory of special and general relativity had changed forever the way we think about motion, space, and time.

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

  • 02:56: This comes from Karl Schwarzschild's solution to the Einstein field equations, the very first accurate description of a black hole.

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

  • 02:16: Einstein showed us that there is no universal clock.

2017-02-02: The Geometry of Causality

  • 00:15: ... we peer deeper into Einstein's theory to find that the immutable ordering of cause and effect emerges ...
  • 01:04: First, let's recap a little bit of Einstein's special theory of relativity.
  • 00:15: ... we peer deeper into Einstein's theory to find that the immutable ordering of cause and effect emerges ...
  • 01:04: First, let's recap a little bit of Einstein's special theory of relativity.
  • 00:15: ... we peer deeper into Einstein's theory to find that the immutable ordering of cause and effect emerges when we ...

2017-01-19: The Phantom Singularity

  • 03:39: So you're saying Einstein is wrong?
  • 03:44: Actually, Einstein himself agreed on this point.
  • 04:16: ... star or a black hole-- Newton's law gives the wrong answers, and we need Einstein's general theory of relativity, which is the far more complete theory of ...
  • 04:45: ... what you get when you solve the delightfully complicated Einstein field equations for the simple case of a spherically symmetric mass in ...
  • 11:19: Actually, Einstein's theory and the Schwarzschild solution that is derived from it suggests it must exist.
  • 11:34: ... to better understand why the central infinity is unavoidable in Einstein's theory, we have to go back to that coordinate shift at the event ...
  • 04:45: ... what you get when you solve the delightfully complicated Einstein field equations for the simple case of a spherically symmetric mass in an ...
  • 04:16: ... star or a black hole-- Newton's law gives the wrong answers, and we need Einstein's general theory of relativity, which is the far more complete theory of ...
  • 11:19: Actually, Einstein's theory and the Schwarzschild solution that is derived from it suggests it must exist.
  • 11:34: ... to better understand why the central infinity is unavoidable in Einstein's theory, we have to go back to that coordinate shift at the event ...
  • 04:16: ... star or a black hole-- Newton's law gives the wrong answers, and we need Einstein's general theory of relativity, which is the far more complete theory of ...
  • 11:19: Actually, Einstein's theory and the Schwarzschild solution that is derived from it suggests it must exist.
  • 11:34: ... to better understand why the central infinity is unavoidable in Einstein's theory, we have to go back to that coordinate shift at the event ...

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

  • 04:41: ... studies will be powerful tests of whether they behave as predicted by Einstein's general theory of relativity or whether there are tantalizing ...
  • 10:36: In Einsteinian terms, spacetime is flat within the sphere.
  • 04:41: ... studies will be powerful tests of whether they behave as predicted by Einstein's general theory of relativity or whether there are tantalizing ...

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

  • 01:07: ... radiation or black hole rotational growth, the simplest black hole of Einstein's general theory of relativity-- purely gravitational, static, and ...
  • 12:02: It even takes you through the beginnings of Einstein's general relativity.
  • 10:47: ... to a parallel universe on the other side of untraversable wormhole, the Einstein-Rosen ...
  • 01:07: ... radiation or black hole rotational growth, the simplest black hole of Einstein's general theory of relativity-- purely gravitational, static, and ...
  • 12:02: It even takes you through the beginnings of Einstein's general relativity.
  • 01:07: ... radiation or black hole rotational growth, the simplest black hole of Einstein's general theory of relativity-- purely gravitational, static, and eternal-- is a ...
  • 12:02: It even takes you through the beginnings of Einstein's general relativity.
  • 01:07: ... radiation or black hole rotational growth, the simplest black hole of Einstein's general theory of relativity-- purely gravitational, static, and eternal-- is a subtle ...

2016-11-30: Pilot Wave Theory and Quantum Realism

  • 03:07: Einstein famously hated the idea of fundamental randomness.

2016-11-16: Strange Stars

  • 00:55: Einstein's general theory of relativity tells us that the core of a dead star must collapse under its own incredible weight.

2016-11-09: Did Dark Energy Just Disappear?

  • 04:14: ... the cosmological constant, written as lambda, is the thing you add to Einstein's equations of general relativity to give the anti-gravitational effect of ...

2016-09-21: Quantum Entanglement and the Great Bohr-Einstein Debate

  • 02:22: On the other hand, Albert Einstein insisted on an objective reality, a reality independent of our observation of it.
  • 02:40: ... an effort to demonstrate the silliness of Bohr's idea, Einstein along with Doris Podolsky and Nathan Rosen proposed a quantum scenario ...
  • 03:05: This is fundamental to Einstein's relativity, which tells us that the chain of cause and effect can't propagate any faster than the speed of light.
  • 03:13: The Einstein Podolsky Rosen, or EPR, paradox introduces one of the most mysterious ideas in quantum mechanics-- quantum entanglement.
  • 04:14: Einstein et al thought this was very silly.
  • 04:31: The argument between Bohr and Einstein felt a bit philosophical at the time.
  • 06:00: ... one, if Einstein was right, imagine the response of each particle to all possible spin ...
  • 07:07: This is exactly the spooky action at a distance that made Einstein so uncomfortable.
  • 07:13: ... so-called Bell inequalities, that we'd expect to see in the case that Einstein was right and quantum mechanics needs local hidden ...
  • 09:09: Are babies really better at quantum mechanics than Einstein?
  • 09:40: That sounds blasphemous to anyone who accepts Einstein's theory of relativity.
  • 04:31: The argument between Bohr and Einstein felt a bit philosophical at the time.
  • 02:22: On the other hand, Albert Einstein insisted on an objective reality, a reality independent of our observation of it.
  • 03:13: The Einstein Podolsky Rosen, or EPR, paradox introduces one of the most mysterious ideas in quantum mechanics-- quantum entanglement.
  • 10:41: ... example, entangled particles may be dimensionally connected by Einstein-Rosen bridges, wormholes that allows instantaneous contact even between great ...
  • 03:05: This is fundamental to Einstein's relativity, which tells us that the chain of cause and effect can't propagate any faster than the speed of light.
  • 09:40: That sounds blasphemous to anyone who accepts Einstein's theory of relativity.
  • 03:05: This is fundamental to Einstein's relativity, which tells us that the chain of cause and effect can't propagate any faster than the speed of light.
  • 09:40: That sounds blasphemous to anyone who accepts Einstein's theory of relativity.

2016-08-03: Can We Survive the Destruction of the Earth? ft. Neal Stephenson

  • 11:02: Well, Einstein would say they can't-- God, dice, nature, et cetera.

2016-07-27: The Quantum Experiment that Broke Reality

  • 02:13: ... indivisible little bundles of electromagnetic energy called "photons." Einstein demonstrated this through the photoelectric effect but his clue came ...

2016-06-22: Planck's Constant and The Origin of Quantum Mechanics

  • 09:23: As usual, it took Albert Einstein to fully understand the physics behind Planck's strange quantized vibrations.
  • 09:31: Einstein realized that it's actually light that is quantized.
  • 09:52: ... discovery was the clue Einstein needed to hypothesize the existence of the photon-- part wave, part ...
  • 10:09: Einstein proved this through the photoelectric effect.
  • 11:42: OK, a lot of you wanted to know why it is that the Einstein cross is a cross rather than a full ring.
  • 12:05: We call that an Einstein ring.
  • 13:01: Then you'll see an Einstein ring.
  • 13:03: There are some cases where you see four individual quasar images connected by an Einstein ring.
  • 13:10: That Einstein ring is actually the galaxy that hosts the quasar.
  • 11:42: OK, a lot of you wanted to know why it is that the Einstein cross is a cross rather than a full ring.
  • 09:52: ... discovery was the clue Einstein needed to hypothesize the existence of the photon-- part wave, part particle, ...
  • 10:09: Einstein proved this through the photoelectric effect.
  • 09:31: Einstein realized that it's actually light that is quantized.
  • 12:05: We call that an Einstein ring.
  • 13:01: Then you'll see an Einstein ring.
  • 13:03: There are some cases where you see four individual quasar images connected by an Einstein ring.
  • 13:10: That Einstein ring is actually the galaxy that hosts the quasar.

2016-06-15: The Strange Universe of Gravitational Lensing

  • 01:27: ... Einstein's general theory of relativity describes the real universe as a flexible, ...
  • 02:33: The deflection angle was exactly what Einstein's theory predicted.
  • 02:37: This particular confirmation of general relativity was the one that shot Einstein to his great fame.
  • 03:06: And Einstein originally felt that it would be acute but subtle, and not particularly relevant phenomena.
  • 04:51: This is the Einstein Cross, an extremely luminous distant quasar powered by a supermassive black hole feeding on its surroundings.
  • 07:36: Despite Einstein's pessimism, gravitational lensing has become an important staple in the astronomer's toolkit.
  • 04:51: This is the Einstein Cross, an extremely luminous distant quasar powered by a supermassive black hole feeding on its surroundings.
  • 03:06: And Einstein originally felt that it would be acute but subtle, and not particularly relevant phenomena.
  • 01:27: ... Einstein's general theory of relativity describes the real universe as a flexible, ...
  • 02:33: The deflection angle was exactly what Einstein's theory predicted.
  • 07:36: Despite Einstein's pessimism, gravitational lensing has become an important staple in the astronomer's toolkit.
  • 01:27: ... Einstein's general theory of relativity describes the real universe as a flexible, dynamic ...
  • 07:36: Despite Einstein's pessimism, gravitational lensing has become an important staple in the astronomer's toolkit.
  • 02:33: The deflection angle was exactly what Einstein's theory predicted.

2016-05-18: Anti-gravity and the True Nature of Dark Energy

  • 00:19: ... episodes ago, I asked you to take a wild ride with me into the heart of Einstein's general theory of relativity and its description of the vaster of scales ...
  • 06:26: This was actually Einstein's motivation for adding the cosmological constant in the first place.
  • 00:19: ... episodes ago, I asked you to take a wild ride with me into the heart of Einstein's general theory of relativity and its description of the vaster of scales ...
  • 06:26: This was actually Einstein's motivation for adding the cosmological constant in the first place.
  • 00:19: ... episodes ago, I asked you to take a wild ride with me into the heart of Einstein's general theory of relativity and its description of the vaster of scales of our ...
  • 06:26: This was actually Einstein's motivation for adding the cosmological constant in the first place.

2016-05-11: The Cosmic Conspiracy of Dark Energy Challenge Question

  • 02:16: ... the Einstein field equations and in the Friedmann equations that are derived from ...

2016-04-27: What Does Dark Energy Really Do?

  • 00:16: ... we talked about how the fate of the universe can be described using Einstein's general theory of relativity via the Friedmann ...

2016-04-20: Why the Universe Needs Dark Energy

  • 00:08: ... the existence of a strange influence called "dark energy." [THEME MUSIC] Einstein's general theory of relativity allows us to describe the behavior of the ...
  • 00:35: ... To truly understand dark energy, we're glimpsing into the workings of Einstein's theory on a cosmic ...
  • 06:26: But when we tried to describe the universe by reducing the Einstein field equations into the Friedmann equations, we missed something.
  • 06:40: ... very same addition to the Einstein field equations that can describe cosmic inflation can also fix this ...
  • 06:26: But when we tried to describe the universe by reducing the Einstein field equations into the Friedmann equations, we missed something.
  • 06:40: ... very same addition to the Einstein field equations that can describe cosmic inflation can also fix this little ...
  • 06:26: But when we tried to describe the universe by reducing the Einstein field equations into the Friedmann equations, we missed something.
  • 06:40: ... very same addition to the Einstein field equations that can describe cosmic inflation can also fix this little problem with ...
  • 00:08: ... the existence of a strange influence called "dark energy." [THEME MUSIC] Einstein's general theory of relativity allows us to describe the behavior of the ...
  • 00:35: ... To truly understand dark energy, we're glimpsing into the workings of Einstein's theory on a cosmic ...
  • 00:08: ... the existence of a strange influence called "dark energy." [THEME MUSIC] Einstein's general theory of relativity allows us to describe the behavior of the cosmos on ...
  • 00:35: ... To truly understand dark energy, we're glimpsing into the workings of Einstein's theory on a cosmic ...

2016-04-13: Will the Universe Expand Forever?

  • 00:12: Yet the fact that Einstein's theory allows us to learn the answer to this question is incredible.
  • 00:19: ... MUSIC] Soon after Albert Einstein proposed his general theory of relativity, industrious physicists-- and, ...
  • 01:33: At the heart of general relativity are the Einstein field equations, which look like this.
  • 01:48: G is the Einstein tensor.
  • 02:58: Now this escape velocity comes right out of Newton's universal law of gravitation, which itself can be derived from the Einstein equations.
  • 04:09: By solving the Einstein field equations for the whole universe, of course.
  • 04:26: ... galaxies, the resulting smooth universe lets us reduce those 10 Einstein equations to only two relationships, called the Friedmann equations, ...
  • 02:58: Now this escape velocity comes right out of Newton's universal law of gravitation, which itself can be derived from the Einstein equations.
  • 04:26: ... galaxies, the resulting smooth universe lets us reduce those 10 Einstein equations to only two relationships, called the Friedmann equations, devised by ...
  • 01:33: At the heart of general relativity are the Einstein field equations, which look like this.
  • 04:09: By solving the Einstein field equations for the whole universe, of course.
  • 01:33: At the heart of general relativity are the Einstein field equations, which look like this.
  • 04:09: By solving the Einstein field equations for the whole universe, of course.
  • 00:19: ... MUSIC] Soon after Albert Einstein proposed his general theory of relativity, industrious physicists-- and, in ...
  • 01:48: G is the Einstein tensor.
  • 02:16: ... gravity from a Newtonian perspective-- as a force, rather than as an Einsteinian spacetime ...
  • 00:12: Yet the fact that Einstein's theory allows us to learn the answer to this question is incredible.

2016-03-23: How Cosmic Inflation Flattened the Universe

  • 06:48: Actually, Einstein came up with the exact mathematical description that we need-- an antigravity term called the cosmological constant.
  • 07:10: When it was later discovered that the universe is indeed expanding, Einstein retracted his constant.
  • 07:35: Einstein is right, even when he's wrong.
  • 07:10: When it was later discovered that the universe is indeed expanding, Einstein retracted his constant.

2016-03-16: Why is the Earth Round and the Milky Way Flat?

  • 02:15: Here it's fine to think about gravity Newtonianly as a force rather than as an Einsteinian warping of space time.

2016-03-02: What’s Wrong With the Big Bang Theory?

  • 01:06: ... by rewinding the laws of physics, and in particular running the math of Einstein's general theory of relativity ...

2016-02-24: Why the Big Bang Definitely Happened

  • 01:50: ... the context of Einstein's theory of general relativity, the only sensible interpretation for this ...

2016-02-11: LIGO's First Detection of Gravitational Waves!

  • 00:17: ... existence of these waves is the last major prediction of Einstein's theory of general relativity to be directly verified a century after the ...
  • 04:51: Well, everything else aside, it's a great vindication for Einstein's general relativity.
  • 05:09: So Einstein wins again.
  • 00:17: ... existence of these waves is the last major prediction of Einstein's theory of general relativity to be directly verified a century after the ...
  • 04:51: Well, everything else aside, it's a great vindication for Einstein's general relativity.
  • 00:17: ... existence of these waves is the last major prediction of Einstein's theory of general relativity to be directly verified a century after the theory ...

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

  • 00:00: [MUSIC PLAYING] Einstein's theory of special relativity has shown us mass and time are not the concrete things we imagine them to be.
  • 04:40: ... the invariance of the speed of light, the other fundamental principle of Einstein's special relativity at play here is the Galilean relativity of ...
  • 00:00: [MUSIC PLAYING] Einstein's theory of special relativity has shown us mass and time are not the concrete things we imagine them to be.
  • 04:40: ... the invariance of the speed of light, the other fundamental principle of Einstein's special relativity at play here is the Galilean relativity of ...
  • 00:00: [MUSIC PLAYING] Einstein's theory of special relativity has shown us mass and time are not the concrete things we imagine them to be.

2016-01-20: The Photon Clock Challenge

  • 00:35: And the resulting slowing of clock ticks due to motion is the time dilation of Einstein's theory of special relativity.

2016-01-13: When Time Breaks Down

  • 03:02: We're going to use a very close cousin to the photon box to explore time-- a thought experiment of Einstein's that we'll call the photon clock.
  • 04:28: This effect is the time dilation of Einstein's special relativity.
  • 05:20: But Einstein's equivalence principle tells us that a frame suspended in a gravitational field is indistinguishable from an accelerating frame.
  • 03:02: We're going to use a very close cousin to the photon box to explore time-- a thought experiment of Einstein's that we'll call the photon clock.
  • 04:28: This effect is the time dilation of Einstein's special relativity.
  • 05:20: But Einstein's equivalence principle tells us that a frame suspended in a gravitational field is indistinguishable from an accelerating frame.
  • 04:28: This effect is the time dilation of Einstein's special relativity.

2016-01-06: The True Nature of Matter and Mass

  • 00:02: NARRATOR: Einstein showed us that matter, mass, and the flow of time are intrinsically connected, but opened the question, are they even real?
  • 00:54: ... already covered Einstein's famous equation, E equals Mc squared, and showed that most of the mass ...
  • 06:23: ... we accept Einstein's description of space-time as described by general relativity, it's not ...
  • 00:54: ... already covered Einstein's famous equation, E equals Mc squared, and showed that most of the mass ...
  • 06:23: ... we accept Einstein's description of space-time as described by general relativity, it's not ...
  • 00:54: ... already covered Einstein's famous equation, E equals Mc squared, and showed that most of the mass of atoms ...

2015-12-09: How to Build a Black Hole

  • 00:56: Yet, to actually form a black hole, Einstein's descriptions of mass energy and space time are not enough.

2015-11-25: 100 Years of Relativity + Challenge Winners!

  • 00:24: ... this day in 1915, Albert Einstein first presented his complete theory of general relativity to the ...
  • 00:36: ... we cover a lot of material on this show, but Einstein's beautiful theory is an essential part of what inspires us here at "Space ...
  • 01:01: The elegance of this theory has inspired so many students of physics to follow in Einstein's path exploring the mysteries of the universe.
  • 00:36: ... we cover a lot of material on this show, but Einstein's beautiful theory is an essential part of what inspires us here at "Space ...
  • 01:01: The elegance of this theory has inspired so many students of physics to follow in Einstein's path exploring the mysteries of the universe.
  • 00:36: ... we cover a lot of material on this show, but Einstein's beautiful theory is an essential part of what inspires us here at "Space Time." ...
  • 01:01: The elegance of this theory has inspired so many students of physics to follow in Einstein's path exploring the mysteries of the universe.

2015-11-11: Challenge: Can you save Earth from a Killer Asteroid?

  • 01:45: Never mind Einstein for now.

2015-10-28: Is The Alcubierre Warp Drive Possible?

  • 00:45: ... Alcubierre constructed a warp field in the mathematical language of Einstein's theory of general relativity, a real solution to the equations of GR ...
  • 02:03: ... the spacetime around and within a black hole is predicted by solving Einstein's field equations around a point of extreme positive energy ...
  • 03:05: ... you just make up a spacetime description and then essentially solve the Einstein equations backwards to figure out what arrangement of matter and energy ...
  • 05:46: ... that we're just making up solutions to the Einstein equations, we could even shrink down the warp bubble while expanding the ...
  • 03:05: ... you just make up a spacetime description and then essentially solve the Einstein equations backwards to figure out what arrangement of matter and energy would be ...
  • 05:46: ... that we're just making up solutions to the Einstein equations, we could even shrink down the warp bubble while expanding the internal ...
  • 03:05: ... you just make up a spacetime description and then essentially solve the Einstein equations backwards to figure out what arrangement of matter and energy would be needed to ...
  • 00:45: ... Alcubierre constructed a warp field in the mathematical language of Einstein's theory of general relativity, a real solution to the equations of GR ...
  • 02:03: ... the spacetime around and within a black hole is predicted by solving Einstein's field equations around a point of extreme positive energy ...
  • 00:45: ... Alcubierre constructed a warp field in the mathematical language of Einstein's theory of general relativity, a real solution to the equations of GR that would ...

2015-10-22: Have Gravitational Waves Been Discovered?!?

  • 00:03: Gravitational waves are the last prediction of Einstein's Theory of General Relativity.
  • 00:17: What is it about Einstein?
  • 00:51: Einstein is amazing, because every one of these predictions from his beautiful work has been physically tested and verified.
  • 00:58: We love Einstein because he's been proven right so many times.
  • 02:25: ... speed limit comes from the fact that the speed of light is built into Einstein's field equation, which is necessary for it to be invariant to the Lorentz ...
  • 09:13: But if this is real, then Einstein's last great prediction will have been directly verified.
  • 00:03: Gravitational waves are the last prediction of Einstein's Theory of General Relativity.
  • 02:25: ... speed limit comes from the fact that the speed of light is built into Einstein's field equation, which is necessary for it to be invariant to the Lorentz ...
  • 09:13: But if this is real, then Einstein's last great prediction will have been directly verified.
  • 02:25: ... speed limit comes from the fact that the speed of light is built into Einstein's field equation, which is necessary for it to be invariant to the Lorentz ...
  • 00:03: Gravitational waves are the last prediction of Einstein's Theory of General Relativity.

2015-10-15: 5 REAL Possibilities for Interstellar Travel

  • 11:58: Spooky action at a distance, as Einstein called it, on the surface does seem to mess with us.

2015-10-07: The Speed of Light is NOT About Light

  • 01:25: This is not Einstein's Relativity, but, instead, the brilliant precursor.
  • 05:14: And it was discovered even before Einstein's Relativity.
  • 05:17: ... it was Einstein who realized that the Lorentz transformation tells us how space and time ...
  • 05:26: Now, you can get to this transformation the way Lorentz and Einstein did by requiring a constant speed of light.
  • 09:19: ... Einstein's interpretation of the meaning of the Lorentz transformation gives us the ...
  • 09:36: ... space and time as described by the Lorentz transformation and we accept Einstein's interpretation of ...
  • 01:25: This is not Einstein's Relativity, but, instead, the brilliant precursor.
  • 05:14: And it was discovered even before Einstein's Relativity.
  • 09:19: ... Einstein's interpretation of the meaning of the Lorentz transformation gives us the ...
  • 09:36: ... space and time as described by the Lorentz transformation and we accept Einstein's interpretation of ...
  • 09:19: ... Einstein's interpretation of the meaning of the Lorentz transformation gives us the special theory ...
  • 09:36: ... space and time as described by the Lorentz transformation and we accept Einstein's interpretation of ...
  • 01:25: This is not Einstein's Relativity, but, instead, the brilliant precursor.
  • 05:14: And it was discovered even before Einstein's Relativity.

2015-09-30: What Happens At The Edge Of The Universe?

  • 04:09: There's no doubt that Einstein was right in setting that limit for objects moving through space.
  • 05:26: If spacetime really is perfectly flat, then, with the most simplistic application of Einstein's equations, we get that the universe is infinite.
  • 06:59: We also have to keep in mind that these geometries assume that we can just extrapolate Einstein's equations in the most simplistic way.
  • 07:36: ... Squishina and others ask whether it's contradictory or circular to use Einstein's theory of general relativity to prove ...
  • 05:26: If spacetime really is perfectly flat, then, with the most simplistic application of Einstein's equations, we get that the universe is infinite.
  • 06:59: We also have to keep in mind that these geometries assume that we can just extrapolate Einstein's equations in the most simplistic way.
  • 07:36: ... Squishina and others ask whether it's contradictory or circular to use Einstein's theory of general relativity to prove ...
  • 05:26: If spacetime really is perfectly flat, then, with the most simplistic application of Einstein's equations, we get that the universe is infinite.
  • 06:59: We also have to keep in mind that these geometries assume that we can just extrapolate Einstein's equations in the most simplistic way.
  • 07:36: ... Squishina and others ask whether it's contradictory or circular to use Einstein's theory of general relativity to prove ...

2015-09-23: Does Dark Matter BREAK Physics?

  • 03:10: Either particle physics is wrong, or at least horribly incomplete, in that we're missing 80% to 90% of the mass in the universe, or Einstein is wrong.
  • 04:21: Any replacement theory has to reproduce all, and I mean all, of the verified predictions of Einstein's theory and be able to explain dark matter.
  • 05:33: Once again, Einstein prevails.
  • 04:21: Any replacement theory has to reproduce all, and I mean all, of the verified predictions of Einstein's theory and be able to explain dark matter.

2015-08-27: Watch THIS! (New Host + Challenge Winners)

  • 00:09: There was a Newtonian and an Einsteinian version of the challenge.
  • 02:32: For the Einsteinian challenge, we had fewer than five people submit correct responses.
  • 02:43: Now explaining the answer to the Einsteinian challenge is a bit more involved because we don't know the geometry from the outset.
  • 03:50: What's the answer to the Einsteinian version of the two-particle challenge question?
  • 02:32: For the Einsteinian challenge, we had fewer than five people submit correct responses.
  • 02:43: Now explaining the answer to the Einsteinian challenge is a bit more involved because we don't know the geometry from the outset.
  • 00:09: There was a Newtonian and an Einsteinian version of the challenge.
  • 03:50: What's the answer to the Einsteinian version of the two-particle challenge question?

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

  • 10:05: ... Einstein equations also allow for an empty universe that has an eternal black ...
  • 00:37: ... treat gravity Einsteinially rather than Newtonianially from the outset, it will help a lot if I can ...

2015-08-12: Challenge: Which Particle Wins This Race?

  • 04:31: ... have to solve the Einstein equations in the presence of a spherically symmetric perfect fluid whose ...
  • 05:09: You can only enter one challenge, though, Newton or Einstein.
  • 04:31: ... have to solve the Einstein equations in the presence of a spherically symmetric perfect fluid whose energy ...
  • 04:09: Finally, I want to discuss the Einsteinian version of this question.
  • 04:58: You can submit your answers to that challenge by email with the subject line "Two-particle Einsteinian gravity challenge".
  • 05:16: ... you can enter the Einsteinian challenge at all, that means you can solve the Newtonian challenge in ...
  • 05:29: But you also have more time, and both the Newtonian and Einsteinian versions of the question are pretty fun exercises.
  • 05:16: ... you can enter the Einsteinian challenge at all, that means you can solve the Newtonian challenge in about 60 ...
  • 04:58: You can submit your answers to that challenge by email with the subject line "Two-particle Einsteinian gravity challenge".
  • 04:09: Finally, I want to discuss the Einsteinian version of this question.
  • 05:29: But you also have more time, and both the Newtonian and Einsteinian versions of the question are pretty fun exercises.

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

  • 02:04: It's not that Einstein can't explain tides.
  • 13:33: But Einstein says, hold on.
  • 14:04: Einstein says, you don't really have a choice.
  • 14:27: In other words, Einstein says the standard of non-acceleration can only be defined locally in small spacetime patches.

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

  • 00:14: [THEME MUSIC] Newton's and Einstein's dispute over gravity comes down to competing notions of what constitutes an inertial frame of reference.
  • 00:36: But Einstein says, nuh-uh, it's the apple's frame that behaves like a frame in deep space.
  • 00:55: Well, between our gravity illusion episode and your comments, we've seem that Einstein's position seems internally inconsistent.
  • 01:11: Today we're finally going to show how curved spacetime makes Einstein's model of the world just as self consistent as Newton's.
  • 01:18: ... one is to express both Newton's and Einstein's viewpoints in geometric spacetime terms, since that's the only way to ...
  • 02:19: Now for Einstein's position.
  • 03:18: OK, Einstein's position is that Newton is making the same mistake as the ant.
  • 04:32: ... according to Einstein, it happens because the apples are on initially parallel geodesics that, ...
  • 05:04: OK, so Einstein's gravity-free curved space time sounds like it's self consistent.
  • 07:32: Its curvature in geodesics are determined by how much energy is present at those events via set of rules called, no surprise, the Einstein equations.
  • 07:40: So for example, say you stick the energy distribution of the sun into the Einstein equations and turn a crank.
  • 07:32: Its curvature in geodesics are determined by how much energy is present at those events via set of rules called, no surprise, the Einstein equations.
  • 07:40: So for example, say you stick the energy distribution of the sun into the Einstein equations and turn a crank.
  • 00:14: [THEME MUSIC] Newton's and Einstein's dispute over gravity comes down to competing notions of what constitutes an inertial frame of reference.
  • 00:55: Well, between our gravity illusion episode and your comments, we've seem that Einstein's position seems internally inconsistent.
  • 01:11: Today we're finally going to show how curved spacetime makes Einstein's model of the world just as self consistent as Newton's.
  • 01:18: ... one is to express both Newton's and Einstein's viewpoints in geometric spacetime terms, since that's the only way to ...
  • 02:19: Now for Einstein's position.
  • 03:18: OK, Einstein's position is that Newton is making the same mistake as the ant.
  • 05:04: OK, so Einstein's gravity-free curved space time sounds like it's self consistent.
  • 00:14: [THEME MUSIC] Newton's and Einstein's dispute over gravity comes down to competing notions of what constitutes an inertial frame of reference.
  • 05:04: OK, so Einstein's gravity-free curved space time sounds like it's self consistent.
  • 01:11: Today we're finally going to show how curved spacetime makes Einstein's model of the world just as self consistent as Newton's.
  • 00:55: Well, between our gravity illusion episode and your comments, we've seem that Einstein's position seems internally inconsistent.
  • 02:19: Now for Einstein's position.
  • 03:18: OK, Einstein's position is that Newton is making the same mistake as the ant.
  • 01:18: ... one is to express both Newton's and Einstein's viewpoints in geometric spacetime terms, since that's the only way to compare them ...

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

  • 04:48: ... this is part of what prompted Einstein to want to develop a more general way of talking about the world that ...
  • 05:41: ... we dive into Part 3-- curved space time, and, finally, an explanation of Einstein's self-consistent view of what gravity ...

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

  • 00:00: [MUSIC PLAYING] Einstein said that gravity is not a force.
  • 00:57: In that episode we noted objections to Einstein's viewpoint, many of which you echoed in the comments.

2015-06-17: How to Signal Aliens

  • 06:55: ... in the last episode, I was just trying to give the gist of Einstein's early thinking about gravity, which evolved and to give you a general ...

2015-06-03: Is Gravity An Illusion?

  • 00:26: But according to Einstein, there's no such thing as a gravitational force.
  • 00:42: ... today I'm going to clarify what exactly this point of view means, why Einstein came to adopt it, and how it planted the seeds for what would eventually ...
  • 05:39: ... Einstein asked, hold on, what if the so-called "real" downward gravity from Earth ...
  • 06:07: Well, not so fast, says Einstein.
  • 06:53: Einstein says, look buddy, I'm just following your rules.
  • 07:21: Einstein called it the equivalence principle, and if you buy it, then maybe the falling frames really are inertial.
  • 07:59: Now Newton says, nice try, Einstein, but you forgot something-- Earth is round.
  • 08:27: Second, by your criterion, Einstein, orbiting frames of reference-- like on the space station-- should also be considered inertial.
  • 08:44: So it looks like game over for Einstein, right?
  • 08:48: It turns out that there's a loophole that makes Einstein's viewpoint self-consistent.
  • 09:12: It took Einstein about seven years to realize that.
  • 09:57: For now, just reflect on Einstein's inspired thinking and how he got there, maybe next time you get in a car or a train.
  • 05:39: ... Einstein asked, hold on, what if the so-called "real" downward gravity from Earth is ...
  • 07:21: Einstein called it the equivalence principle, and if you buy it, then maybe the falling frames really are inertial.
  • 08:27: Second, by your criterion, Einstein, orbiting frames of reference-- like on the space station-- should also be considered inertial.
  • 08:48: It turns out that there's a loophole that makes Einstein's viewpoint self-consistent.
  • 09:57: For now, just reflect on Einstein's inspired thinking and how he got there, maybe next time you get in a car or a train.
  • 08:48: It turns out that there's a loophole that makes Einstein's viewpoint self-consistent.

2015-05-20: The Real Meaning of E=mc²

  • 00:16: ... most famous equation in all of physics, but in his original 1905 paper, Einstein actually wrote it down differently, as m equals E divided by c ...
  • 01:33: According to Einstein, the watch that's running has a greater mass.
  • 02:28: That's why, according to Einstein, most of us have always incorrectly believed that mass is an indicator of the amount of matter in an object.
  • 08:15: First, Einstein's original paper on this topic is only three pages long and not that hard to read.

2015-04-29: What's the Most Realistic Artificial Gravity in Sci-Fi?

  • 00:53: Whether you want to think of gravity in the Newtonian or the Einsteinian sense, the problem persists.

2015-04-22: Are Space and Time An Illusion?

  • 00:41: This is challenging for everyone, even Einstein.
  • 04:13: ... shortly after relativity first came out, a former math professor of Einstein's named Hermann Minkowski noticed that the spacetime interval resembles a ...
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