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
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 / 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
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.
FTL Part 3: General Relativity Lets us Take Shortcuts
People assume that time is a strict progression of cause to effect, but actually, from a non-linear non-subjective viewpoint,it’s more like a big ball of wibbly-wobbly, timey-wimey… stuff. ~The Tenth Doctor (David Tennant) This is part three of a multipart series on faster-than-light travel. In the first part of the series, I explained why the speed of light is constant, no matter the observer. In part two, I explained why this invariance prevents us from going faster than light. This time, I’ll explain how we might use general relativity to get around this restriction. Fair warning: although general relativity