Science And Math

explanatory articles on physics and math

Science And Math

Conference Report: SC15

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This last week, I had the privilege to attend the biggest annual supercomputing conference in north America, SC. I was one of about ten students studying high performance computing (and related fields) who were funded to go by a travel grant from the HPC topical group of the Association for Computing Machinery. It was a blast, and I learned a ton. I haven’t had much time to write up any science results, so I figured I’d give a few brief highlights of the conference, if I could. Vast Scale SC15 was by far the biggest conference I’ve ever attended.

Physics / Quantum Mechanics / Science And Math

Bruno Maddox and the Magnet: A Story of Misconceptions

jonah 9

This week the ever-inquisitive Gary Matthews pointed me to a 2008 article for Discover Magazine by Bruno Maddox, claiming that physicists cannot explain how magnetism works, and that they are in denial about it. I encourage you to read the article. Maddox is wrong—dead wrong—but his argument displays a number of common misconceptions about science. And I’d like to address some of them. The most important misconceptions Maddox displays are that of first cause, of classical intuition, and of distrust of the abstract. Let’s get started. (DISCLAIMER: The opinions in this article are my own. I will be describing

cosmology / Physics / Science And Math

The CMB Axis of Evil and the Nature of Randomness

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axis of evil planck

This Halloween, Nature News released an article titled Zombie Physics: 6 Baffling Results that Just Won’t Die. It’s a fun article describing several mysteries in physics whose solution sits in a sort of limbo. For fun, I figured, I’d explain some of these mysteries, and give my opinion about possible solutions. And first, I’m going to discuss the CMB Axis of Evil, a strange pattern in the leftover radiation from the Big Bang. A Much-Too-Short Summary of Cosmic Inflation and the CMB About 13.8 billion years ago, the universe was extremely hot, so hot that matter couldn’t form at

Mathematics / Physics / Science And Math

A Retraction: Backwards Heat is Not Chaotic

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Airplane_vortex_edit

Yesterday I wrote a post that explored the flow of heat both forwards and backwards in time. I used this as a venue to introduce the notion of entropy and to describe one extreme example of the butterfly effect—where small changes in initial data can create big changes in the final result. That’s all fine and good and I stand by that. But I said that the reverse heat equation, which runs the flow of heat backwards in time, was an example of chaos. And as this reddit user points out, this is very wrong. I have now fixed the

Mathematics / Physics / Science And Math

Heat, Chaos, and Predictability

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A funny comic about the butterfly effect

The butterfly effect, shown comically in figure 1, is the idea that a very small change in one place on Earth can cause a very big change somewhere else. In this case, a butterfly flaps its wings and causes a tornado. This metaphor illustrates the mathematical concept of chaos, in which the Earth’s atmosphere is a chaotic system. While a single butterfly probably isn’t literally responsible for a tornado, mathematical chaos is very real and important. So this week, I’m going to try giving you some intuition for the butterfly effect using one extreme example from physics. Heat Suppose

Geometry / Physics / Relativity / etc.

In-Falling Geodesics in Our Local Spacetime

jonah
spacetime!

My previous post was a description of the shape of spacetime around the Earth. I framed the discussion by asking what happens when I drop a ball from rest above the surface of the Earth. Spacetime is curved. And the ball takes the straightest possible path through spacetime. So what does that look like? Last time I generated a representation of the spacetime to illustrate. However, I generated some confusion by claiming that it “should be obvious” that the straightest possible path is curved towards or away from the Earth. When a textbook author says “the proof is trivial”

Geometry / Physics / Relativity / etc.

Our Local Spacetime

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Gravity Probe B circling Earth

General relativity tells us that mass (and energy) bend spacetime. And when people visualize the effect of a planet on spacetime, they usually imagine something like in figure 1, where the planet creates a “dip” in spacetime much like a “gravitational well.” But today I’m going to show you what spacetime actually looks like near a planet… and it doesn’t look anything like the common picture. This is the fifth part in my many-part series on general relativity. Here are the first four parts: Galileo almost discovered general relativity General relativity is the dynamics of distance General relativity is

Physics / Relativity / Science And Math

Distance Ripples: How Gravitational Waves Work

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Look at those curves!

Gravitational waves are “ripples in space time” that propagate through it like waves on water. That’s the common story and, for the most part, it’s right. But what does that mean? This is part four in my many-part series on general relativity. The first three parts introduce general relativity from the ground up. You can find them here: Galileo almost discovered general relativity General relativity is the dynamics of distance General relativity is the curvature of spacetime Okay. Without further ado, gravitational waves! Spooky Action at a Distance First, I want to help you get an intuition for why

Geometry / Mathematics / Physics / etc.

General Relativity is the Curvature of Spacetime

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Einstein rings are awesome!

Figure 1 shows light from a distant blue galaxy that is distorted into a so-called Einstein ring by the curvature of spacetime around a red galaxy. This is called gravitational lensing and today we’ll learn how it works. This is part three of my many-part series on general relativity. Last time, I told you how general relativity is the dynamics of distance, which we know is a consequence of the fact that gravity is the same as acceleration. This time, I describe the consequences of the fact gravity warps distance. And in the process, we’ll learn precisely why gravity

Physics / Relativity / Science And Math

General Relativity is the Dynamics of Distance

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kogler crazy art installation

This is part two in a many-part series on general relativity. Last time, I described how Galileo almost discovered general relativity. In particular, I told you that gravity isn’t a force. In fact, gravity is the same as acceleration. Now, this is a completely crazy idea. After all, we’re all sitting in the gravitational field of the Earth right now, but we don’t feel like we’re moving, let alone accelerating. But let’s take this crazy idea at face value and see where it leads us. (Of course, the Earth is spinning, which is an acceleration. And it’s orbiting the sun,