a strong patriarch and present a little different image about fathers um um which are very important in this whole equation I think it's a good thing speaking of the Father Figure thing the this sort of tangential but the show wasoriginally created by Mitchell burus and Robin green who are probably more well known for creating The Sopranos well
things together and we've got a recipe for some problems and the big thing here in this equation is glucose so glucose is your brain's main fuel source and what they also discovered is that there's a 6%decrease in glucose reaching your brain when you're sleep deprived all right but all of that's not even equal there 14%
and I wanted to get it done ideally in a day so I hacked together this little equation which is 33 people giving $3 and 33 cents a day for three months addsup to $10,000 so a friend of mine and I put together this little website um I filmed a bunch of videos so my video for Cliff
And gravity, as Einstein told us in 1915 with the discovery of the general theory of relativity, all of this can be written down in one simple, elegant equation , which is this, Einstein's equation .It's a beautiful equation , again very elegant, very dense, very compact in a sense.
And yet typically, when you see physics in high school, when you see physics in college, even if you take advanced courses in graduate school, it's very equation -driven. The idea of what it is that underlies our assumptions about the universe, how it is we got to where we are, why itis that physics is sort of held up as this paragon of a beautiful academic discipline, why is it the universe itself
issues and some number of them have never even heard of the singer probably a smaller number I'm just equation too but um and it is with other crowdsourced information Enterprises
influences that there are stressors out there that provoke stress in us what's missing in that equation yes our and perception right this can so what's happening is we see atiger we think and we have the thought tiger and we experience stress even if there's no tiger we experience stress
wouldn't die with stress we would just die right so so so the the the the the equation here that we've been taught the one two punch of stressor creating stress misses something really importantthere's an intermediary step and if you look at the way that we teach people how to handle stress and the way that we've
poor? How can we how can we do this in a sustainable way that's going to ensure the dignity of both sides of the equation both of people helping as well as the dignity of the poor themselves who are going to be using the bed nets.So um I really appreciate that about Jacqueline. So we are lucky to have her here today to talk to us about her book.
at which these waves move is the speed of light. And so people said, "Wow, the speed of light comes out of those equations ." And that had to be, I think, very persuasive. And of course, electromagnetism also plays a really significant role in chemistry because after all,atoms are held together by electromagnetic forces. There's more to how atoms work. There is all the quantum mechanics stuff.
And I know that this might not be what you signed up for. Equations are not usually what are focused on in popular level talks about physics, but don't worry about it.This is going to be OK.
So you can have a bunch of equations , but without some data to actually back it up, you don't really know if those equations are particularly predictive.And on the flip side of the pile of data, without any equations or model to kind of explain what the general thing
My friend Anne-Marie Slaughter, a wonderful scholar at Princeton and former State Department official under Barack Obama, speaks of every profession's having to adapt to these new equations of power and influence."The leader," she says, "must become a catalyst.
Multiply by j again, and by definition you get negative one. The equation 's pretty simple.
This was radically new. - The equation solution, called the wave function, psi, does not describe a particle with a precise position and momentum as classical laws would. But instead, the modular squared can give us the probability of finding the particle in a specific location at a specific time.
But in any case, she planted it in his mind. - "An equation for me has no meaning unless it expresses a thought of God." Ramanujan never really learned how to provide proof to his theorems. So Hardy urges him to come to Cambridge to explain them in more detail.
algebraic equation over the integers, those are known as algebraic numbers. It was an open question for a long time whether that was
An equation perhaps no more than one inch long that will allow us to quote read the mind of God. These are
But this is not what professional physicists refer to as Einstein's equation . That equation is this one. This one you probably have not heard of, again, depending on what your physics background is.
That's going to be something, that idea that we can embed multiple relationships into a single equation , it's going to be very, very useful very, very soon. Another equation we need if we want to get things off the ground and another thing that was done by Isaac Newton in his masterwork, "Principia Mathematica," is to give a specific example of a force.
The equation is excitement, attention.
Every equation supposedly halves the audience, or something like that has been said.
The equation that describes this trend line is really what happiness is.
This equation tells you about the statistics of the electrons, of the electron distribution, and how it evolves with time.
The equation of communism with totalitarianism, the equation of being Muslim with being a terrorist-- it's so easy to twist these and use these for--
That equation , you probably know, is Metcalfe's Law, but it shows just how fast the number of connections
This equation here-- a number to the 12th power plus another number to the 12th power equals another number to the 12th power.
This equation here, H, which is called the Hamiltonian is really the equation of everything. If I could solve this equation , I would know everything I need to know about a
The equation isn't simple in the sense that--.
Four equations , four unknowns, that makes the system solvable.
50 years and wrote his laws of electromagnetism, and they're really fascinating. If you look at the laws of electromagnetism, they are-- they're differential equations or inter- integral equations . But basically, what they say is on one side, you have a bunch of terms that have electricity in them, and then you have equals on the other side, a magnetism thing.
This is the language in which modern physics is written, equations . And equations means that you have something that is absolutely precise. This is not just a statement in words that the more you push on something, the faster it will accelerate.
and equations . They know that physics just isn't in the business of answering the question, and this is Hawking's words again,
Treat equations on the page the same way.
Linear equations and plugging in the answers and seeing that it worked out.
the equations now of a Feynman path integral without really stepping back to think of, OK, what's going on intuitively here?
No equations .
these equations , and inside the math.
The solution to this equation is called the wave function psi.
Now this equation still looks a little bit like a mess, but actually we can rearrange it into this form.
But instead, the modular squared can give us the probability of finding the particle in a specific location at a specific time. - Deriving the Schrodinger equation is actually surprisingly simple. Just start by writing down the total energy, which, for a free particle, is just its kinetic energy, 1/2 mv squared.
For example, take the element gold. The Schrodinger equation suggests that it should be a silver gray color, just like all the other metals. But it's not, I mean, it's gold.
But for particles moving at relativistic speeds close to the speed of light, that equation isn't the right one. The correct equation is the energy momentum relation from special relativity. - Schrodinger's equation is not consistent with the theory of relativity, so it's...
The correct equation is the energy momentum relation from special relativity. - Schrodinger's equation is not consistent with the theory of relativity, so it's... Technically, it's not right.
And now, back to Klein, Gordon, and Fock. The Klein-Gordon-Fock equation even made its way over to one of the fathers of quantum physics, Niels Bohr, who must have been impressed, because at the 1927 Solvay Conference, Bohr was chatting to a promising young physicist about what he was working on.
as it was for the Schrodinger equation . For the Klein-Gordon equation , a new equation was needed to describe the probability using the wave function, which takes a while to derive, so we won't get into that here, but it looks like this.
But what's even more beautiful is that if you look at this, Dirac's equation isn't just first order in time derivatives, it's also first order in spatial derivatives. Whereas the Schrodinger equation was second order in spatial derivatives. So you might wonder, "Well, why does that matter?" Well, because not only does going first order in all derivatives solve the second-order time derivative problem
So you might wonder, "Well, why does that matter?" Well, because not only does going first order in all derivatives solve the second-order time derivative problem of the Klein-Gordon equation , it now also treats time and space symmetrically. And it becomes really important if you start thinking about relativity, where time and space are not separate dimensions, they're intertwined in a four dimensional spacetime.
And it becomes really important if you start thinking about relativity, where time and space are not separate dimensions, they're intertwined in a four dimensional spacetime. And while the Schrodinger equation had just a single component wave function, to make the wave function work with these 4x4 matrices, in Dirac's case, you actually need a wave function that has four components.
And you can actually see this if you zoom into the emission spectrum for a hydrogen atom. Schrödinger's equation didn't predict that splitting since it just had one solution for each energy level. But with Dirac's four-component solution, the top two wave functions now described two different spin states with two slightly different energies.