The connection between symmetries and conservation laws is one of the great discoveries of twentieth century physics . But I think very few non-experts will have heard either of it or its maker[:] Emily Noether, a great German mathematician. But it is as essential to twentieth century physics as famous ideas like the impossibility of exceeding the speed of light. It is not difficult to teach Noether’s theorem, as it is called; there is a beautiful and intuitive idea behind it. I’ve explained it every time I’ve taught introductory physics. But no textbook at this level mentions it. And
Relativity
cosmology / Discrete Math / Geometry / etc.
Quantum Geometry: Causal Dynamical Triangulations
A “quantum gravity expert” is presumably someone well acquainted with the details of our immense ignorance of the subject. I suppose I count. ~John Baez I long ago promised that I would discuss some of my own research. Here’s the first post that makes good on that promise. Today I’ll discuss a theory of quantum gravity. Why Quantum Gravity? Without a doubt, the two greatest advances in physics in the last 120 years were the advent of general relativity and quantum mechanics. These two amazing theories have totally changed the way we see the world. Quantum mechanics describes the
Analysis / Mathematics / Physics / etc.
Between Being and Non-Being: Imaginary Numbers
Imaginary numbers are a fine and wonderful refuge of the divine spirit almost an amphibian between being and non-being ~Gottfried Wilhelm Liebnitz One of the first things we learn how to do is multiply numbers. . That sort of thing. But what if we multiply a number by itself? This is the familiar operation, which we call squaring a number. and . That sort of thing. You can take a number to a power by multiplying it by itself some number of times equal to the power. So if you square a number, you’ve taken it to the second power.
cosmology / Physics / Relativity / etc.
Fixing the Early Universe: Cosmic Inflation
Expansion means complexity and complexity decay. ~Cyril Northcote Parkinson This is part three of a series on the early universe. In the first article, I described the history of the Big Bang theory and why we believe the universe started in a colossal explosion. In the second article, I described some inconsistencies in the Big Bang theory that need correcting. Now I’ll explain how the theory of cosmic inflation addresses these inconsistencies and why we might believe it in inflation. This explanation will use ideas from quantum mechanics and general relativity; you can find my articles on these subjects
cosmology / Geometry / Mathematics / etc.
A Mess of Cosmic Coincidences: Problems With the Big Bang Theory
The furthest bodies To which man sends his Speculation, Beyond which God is; The cosmic motes Of yawning lenses. ~Robert Frost, I Will Sing You One-0 I apologize for the long time of silence! I graduated from the University of Colorado about a month ago and was immediately assaulted by a huge amount of family affairs… and then caught up in moving. Sorry about this, everyone! My regular Sunday update schedule should resume next week. Last time, I described the theory of the Big Bang. I gave some history of the theory, and some reasons for why we believe
cosmology / Physics / Relativity / etc.
Always Walk Away From An Explosion—The Story of the Big Bang
We were fortunate to be there a day or two before ‘the big bang’ and then we got the heck out of town. ~Scotty Moore A few weeks ago, +Matthew Villaneuva asked the following question on Google+: Does anybody else find the Big Bang (the scientific explanation on how the universe got created) weird? Actually, yes! Just a century ago, everyone believed that the universe was static—i.e., that it had always existed and that it would always continue to exist. Even Albert Einstein held this view. I previously explained why we know the universe is expanding, so I’m going
Geometry / Mathematics / Physics / etc.
An Update On Kaluza-Klein Theory
I recently posted an article on Kaluza-Klein theory. This was partly because I was working a paper on it as a final project in my second semester of general relativity. The paper is finished, and I thought I’d upload it for the more mathematically inclined of my readers. If you’re interested, you can find it here.
Geometry / Mathematics / Physics / etc.
Stuff From Shape — Kaluza-Klein Theory
There is geometry in the humming of the strings. There is music in the spacing of the spheres. ~Pythagoras When Albert Einstein and David Hilbert published the theory of general relativity, they weren’t just proposing a new theory of gravity. They were proposing a new way of thinking. In general relativity, gravity isn’t a force. Instead, it’s a natural consequence of the shape of the universe. Force comes from stuff. Matter pushes and pulls on other matter. A proton may need to use its electric field to attract an electron, but the field is a property of the proton.
Physics / Relativity / Science And Math
More on General and Special Relativity
Last time, I answered some questions from readers Ms. C and Mr. A on special and general relativity. Mr. A asked some very deep follow-up questions, so I thought I’d share them. Mr. A asks: I believe you already answered what I had intended to be my follow-up question: spacetime curvature accounts for the acceleration of an object already in motion; but why does a body at rest being to move (e.g. why doesn’t a stationary object hover in the air until someone touches it)? If I understand you’re post correctly, Einstein would say that there is no such thing as being at absolute rest —
Physics / Relativity / Science And Math
Rock Me, Einstein — Some Questions on Special and General Relativity
In 1905 Albert discovered Relativity, in 1906 he invented Rock and Roll ~Yahoo Serious In the last week or two, I’ve gotten several excellent questions on special and general relativity. I’d like to devote this week’s post to presenting and answering those questions. For the sake of anonymity, I will call the people who asked the questions Ms. C and Mr. A. I hope you enjoy! A Question on Special Relativity The first question is by Ms. C, who asked: I’ve read your article “The Speed of Light is Constant.” I’ve… got a question on the speed of light