geometry

Astrophysics / Physics / Relativity / etc.

The Black Holes that Created LIGO’s Gravitational Waves

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LIGO merger Bohn

A little over a week ago, the LIGO collaboration detected gravitational waves emitted during the in-spiral and merger of two black holes. And the world’s scientists, myself included, collectively went bananas. Last week, I attempted to summarize the event and capture some of the science, and poetry, that has us so excited. In short, gravitational waves provide us a totally new way to look at the universe. LIGO’s one detection has already provided us with a wealth of information about gravity and astrophysics. Today, I summarize some of what we’ve learned. Black Holes As We Knew Them In the

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”

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,

Astrophysics / Physics / Relativity

The Curvature of Spacetime

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Abell 2218

Spacetime is curved. We’ve all heard the line. But what does it mean? Well on the largest scales, the curvature of spacetime is abundantly clear as the warped fabric of the universe distorts images of distant objects. The image below is of the Abell 2218 galaxy cluster, taken by the Hubble Space Telescope. The cluster is very massive so it warps the spacetime around it. This warped spacetime acts as a lens so that light light coming from galaxies behind Abell 2218 is spread out much more than it should be. The result is that images of galaxies behind

Electronics / Geometry / Mathematics / etc.

Lightning Detection

Michael T. Schmidt

Since I’ve been very busy lately my good friend Michael Schmidt agreed to do another guest post! Mike has a masters degree in physics from the University of Colorado at Boulder. You can check out Mike’s own blog at duality.io or his personal website Mike’s Personal Website. Without further ado, here’s Mike: Lightning Detection   Currently, in the mid-west of the United States the first thunderstorms of the year have begun. Because I am a giant geek, I love lightning and I think tracking lightning is quite interesting. My personal favorite site is LightningMaps. On LightningMaps website you’ll see

Condensed Matter / cosmology / Physics / etc.

BICEP2, Primordial Gravity Waves, and Cosmic Inflation

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“Like the microscopic strands of DNA that predetermine the identity of a macroscopic species and the unique properties of its members, the modern look and feel of the cosmos was writ in the fabric of its earliest moments, and carried relentlessly through time and space. We feel it when we look up. We feel it when we look down. We feel it when we look within.” ~Niel Degrasse Tyson There was some very big news today! If you haven’t already heard, the BICEP2 research group at Harvard has found evidence of ancient gravitational waves in the sky. A lot

abstract algebra / History / Mathematics / etc.

International Women’s Day Spotlight: Emmy Noether

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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

Geometry / Mathematics / Physics / etc.

An Update On Kaluza-Klein Theory

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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.