PSW 2478 Einstein's Real Equation | Sean Carroll

Lecture Starts at 13:53
PSW 2478
June 2, 2023
Einstein's Real Equation: Mass, Energy, and the Curvature of Space-Time
Sean Carroll
Homewood Professor of Natural Philosophy
Bloomberg Center for Physics and Astronomy
Johns Hopkins University

Albert Einstein is indelibly associated with a famous equation: E=mc2, relating the mass of an object to its energy. But that is not what physicists have in mind when they say “Einstein’s Equation.” The “real” Einstein’s Equation – the one physicists have in mind – is part of general relativity, which relates the curvature of spacetime to the mass and energy distributed within it. This lecture will explain why the geometry of spacetime has anything to do with gravity, and how the Einstein Equation expresses how spacetime curves.

Sean Carroll is Homewood Professor of Natural Philosophy in the Department of Philosophy and Professor in the Department of Physics and Astronomy at Johns Hopkins University, and he is a member of the Fractal Faculty at the Santa Fe Institute. Previously he was Research Professor at Caltech and before that he was on the faculty at the University of Chicago.

Sean is well known for his work in theoretical physics and the philosophy of science. His theoretical work focuses on the foundations of physics, including issues in quantum mechanics and spacetime, and on cosmology. His research publications include work on Lorentz invariance, closed time-like curves in general relativity, topological defects in field theory; extra spacetime dimensions, dark energy and its interactions with ordinary matter and dark matter, and on modifications of general relativity and aspects of quantum mechanics, including the many-worlds interpretation and a derivation of the Born rule for probabilities.

Sean is an author on many technical and general publications and books, including the well-received textbook Spacetime and Geometry, An Introduction to General Relativity and his most recent book is The Biggest Ideas in the Universe, Vol. 1: Space, Time, and Motion. Sean also has made two lecture series on physics on Wondrium/The Great Courses. And he hosts Mindscape, a weekly podcast.

Among many other honors and awards, Sean has been awarded prizes and fellowships by the National Science Foundation, NASA, the Sloan Foundation, the Packard Foundation, the American Physical Society, the American Institute of Physics, the Royal Society of London, the Guggenheim Foundation, and the American Association for the Advancement of Science.

Sean earned a BS in Astronomy and Astrophysics with a minor in Philosophy at Villanova University and a PhD in Astronomy at Harvard University.

[Native_love]

That was BEAUTIFUL! No one has brought all the details together in a easy to understand way like Sean did.

[wayneyadams]

It's been over 30 years since I got my M.S. in Physics, and during that time I have been teaching high school Physics, which can become mind numbingly mundane, even the A.P. classes. The upshot is that I have gotten rusty on advanced topics like Einstein's equation. His book, "The Biggest ideas in the Universe, Space, Time, and Motion" was a great review, and I can honestly say I learned some very useful Physics. In fact, it has inspired me to pull my intimidating 1, 280-page book, "Gravitation" by Misner, Thorne, and Wheeler off the bookshelf and dive into it. However, even if you do not plan to go into the subject this deeply, you will benefit greatly from his approach.

Having taught Physics for 33 years, let me give you some advice on how to approach this book to get the most benefit.

1) While the book is available as an Audible book from Amazon, you really need to buy the hardcover or Kindle versions. If you are an auditory learner, you can benefit from both, but do not rely solely on the audible version. I also recommend you have pencil and paper handy, and actually write down equations and study them until you feel you truly understand what they are saying (yes, I said "saying" because they tell a story). Doing this gives you two modes of learning, and if you also get the Audible version, you will have three modes of learning (auditory, visual, tactile).

2) Do not move on to the next concept until you are sure you understand the concept you are reading. This is not like reading a novel, missing something early on will affect your ability to learn and understand later concepts.

3) Take your time. It has been widely accepted that you will forget more than 50% of what you learn in the first hour after learning it. In fact, it is worse than that, you will forget 40% within the first twenty minutes. The way to combat this is to read and study a section on some concept, stop and come back to it an hour or two, a few hours, or even a day later and reread it. you will be surprised at how much you forgot. Don't believe this is true? Try answering this, how much do you remember from his talk? I mean truly remember to the point where you can explain it to another person, or even yourself. See what I mean?

If you approach his book using these techniques, you will end up with a firm understanding that will stay with you for a lifetime. This is a great book so you should do your best to get as much out of it as he put into it.

Wayne Y. Adams
B.S. Chemistry
M.S. Physics
R&D Chemist (9 yrs.)
Physics Teacher (33 yrs.)

[BabuSathyanarayana]

Sean, this one of your best lectures. Q & A session is awesome too! Well informed educated audience so the quality of the event is great!!!

[Erik-ggvb]

Sean Carroll and Kevin Rudd are some of my favorite speakers for their fluid verbal continuity of a topic.

[odedbarash]

Great talk and very good questions from the audience.

[denisconstales]

Great stuff, more people should watch this!

[Dan-zqwt]

Sean is really one of the most entertaining lecturers on science for laypersons. He’s a great personality and excellent at simplifying complex ideas for us average enthusiasts. Thanks Sean!

[Twokubikmeter]

Great presentation. I am also very impressed with the editing. Probably the best edited lecture I have ever seen.

[donmilland]

I like the decorative painting/stenciling on the walls and the marbling of the columns.

[rayoflight]

Love the picture of the original Fiat 500 at 17:00. The "500" was the battle cry of a resurging Italy in the early '60s. It is admirable how the picture is showing the car in its most likely status through its lifetime, i.e. in need of some external energy input...

[gytisbaranauskasjagmort]

Jesus. Best, most comprehensive Q&A ever.

[CptTrips]

one of the best lectures that manages the balancing act between a popular scientific approach and mathematical derivation. On spot prof Carroll

[CalamitousJonathan]

When I wrote the Miguel Alcubierre papers (I never imagined someone would give a child the name before sending him to school to claim false credit for the papers) E=MC2 is the missing equation that has be prodominate in the scientific communtity for years and wasn't missing. The Alcubierre equations explain warping space infront of the ship and my Einstein equation eE=MC2 has to do with expanding matter behind the spaceship

[cnhrvvs]

Truly fantastic, brilliant and gorgeous!

[tuutuutuuttuutuutuut]

always a good feeling when you see not a single person looking at their phone

[WillieBloom]

Why couldn’t my high school math teachers explain the fundamentals like Dr Carroll does? It would have put my brain in the right place conceptually and made trig a whole lot easier and calculus attemptable.

[JanPBtest]

26:44 Not in Newtonian mechanics (its equations do not presume a preferred system at rest) but in Maxwell's electrodynamics (Maxwell's equations are true only in a certain system "at rest" (unless one changes the concepts of space and time which is what Einstein did), this was a huge conceptual problem before 1905). What Newtonian mechanics does presume is the idea of absolute simultaneity, so I think Sean misspoke here.
1:04:16 Schwarzschild was even better than that: he solved Einstein's equation already in 1915! His letter to Einstein informing him of his solution is dated 22 December 1915 and contains in it the formula shown on the slide.
1:07:00 In all fairness, this is not what they said. What Schwarzschild and Einstein thought (and many others until the early 1920s) was that the locus r=2GM merely corresponded to _the location of the central point mass._ This was an easy mistake to make in those days because Schwarzschild actually used a different coordinate system in his solution than Sean is showing on his slide, so for Schwarzschild this locus corresponded to r=0, and it seemed perfectly sensible to have an infinity there, given the fact that a spherical coordinate system is not even well-defined at the origin, as everyone remembers from high school. But this was a mistake, a particularly nasty mental trap to fall into, due to the fact that tensor calculus was still in its infancy in 1915 and nobody at the time had yet figured out that line element singularities need _not_ correspond to the _actual_ singularities of the _geometry._ They can be simply artefacts of the coordinate choice. Which is what happened here, and sometime in the 1920s (IIRC) people have finally figured out that r=2GM was not the locus of any geometry singularity, it was just one of those fake artefacts. Today we recognise r=2GM (Schwarzschild's r=0) as the location of the event horizon.
1:27:00 I believe the question was whether light _itself_ can be a source of gravity. The answer is yes because light also has its own energy-momentum tensor T which couples to spacetime curvature per Einstein's equation.
1:27:32 Strictly speaking Einstein's theory does not say that matter curves spacetime, it only says that the two are always correlated in that certain way. But correlation does not imply causation. So it may be that both are a result of something _else, _ yet undiscovered, which is the actual cause of both.
So for now the answer is: we don't know.

1:29:59 I think Sean misunderstood the (clumsily formed) question: what would happen to the theory if we let the speed of light parameter go to infinity. The questioner had the right idea: the Schwarzschild spacetime would become flat. Similarly, if in _special_ relativity one allowed c go to infinity, one would obtain Newtonian mechanics with the Galilean transformation instead of the Lorentz one.
An _excellent_ lecture, BTW.

[KarelSeeuwen]

I have so many interests that viewing your channel today was like going back in time. Thanks to all involved and a special thanks to Sean for his tireless work in bringing Physic to the masses..

[spaceinyourface]

I think I must have listened to every single Sean Carroll lecture, Interview, podcast he's ever appeared on. I'm just about to watch him at the Royal institute, , probably a similar lecture to this one.
My memory is soooo bad, ,I need to keep at it . I promise myself one day I'll go back to school & learn all this for real.

[tedgrant]

When I did "science" in school, Newton was correct and Einstein wasn't mentioned. That was obviously "old school" science.
Perhaps, in the future, Einstein will suffer the same fate as Newton.