General Relativity

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,

Physics / Relativity / Science And Math

Galileo Almost Discovered General Relativity

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Hipster Galileo

We all know the (probably apocryphal) story. Galileo Galilei, all around physics bad-ass, went up to the top of Leaning Tower of Pisa and dropped stuff off the top. He found that objects of vastly different weights, like bowling balls and feathers for example, would fall at exactly the same rate and hit the ground at exactly the same time. Air resistance gets in the way, of course. But if you perform the experiment in vacuum, as these guys did, then you do find the bowling ball and the feather land at exactly the same time: This leads to

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

Astrophysics / Physics / Relativity / etc.

Simulating Gamma Ray Bursts

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It was the mid 1960s. The United States and the Soviet Union had recently signed the Partial Nuclear Test Ban Treaty, which forbid the detonation of nuclear weapons except underground. Since neither nation trusted the other, each was carefully monitoring the other for non-compliance. In particular, the United States feared that the soviets might be, I kid you not, testing bombs behind the moon. Vela The United States solved this problem with the Vela satellites. When a nuclear bomb goes off, it emits a short burst of gamma rays, which are rays of extremely high energy light. The Vela

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

Analysis / Mathematics / Physics / etc.

Between Being and Non-Being: Imaginary Numbers

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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.

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.

Geometry / Mathematics / Physics / etc.

Stuff From Shape — Kaluza-Klein Theory

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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.