Relativity

cosmology / Geometry / Mathematics / etc.

Receding Horizons: Dark Energy and the Expanding Universe

jonah 21
Einstein and Hubble

Astronomy compels the soul to look upwards and lead us from this world to another. ~Plato The history of astronomy is a history of receding horizons. ~Edwin Powell Hubble Last week, I discussed the possible shapes our universe could take. I offhandedly mentioned that not only is the universe expanding, but that that expansion is accelerating. We attribute this expansion to a mysterious phenomenon we call dark energy. This week, I want to explore the history of this idea and the beautiful experiments that tell us all is not as it seems. The Static Universe and Einstein’s Greatest Blunder

cosmology / Geometry / Mathematics / etc.

For There We Are Captured—The Geometry of Spacetime

jonah 9

All about me there are angles— strange angles that have no counterparts on the earth. I am desperately afraid. ~Frank Belknap Long, The Hounds of Tindalos Whoever…proves his point and demonstrates the prime truth geometrically should be believed by all the world, for there we are captured. ~Albrecht Durer I was recently asked: What does it mean when we say spacetime is “curved” or “flat?” The answer lies in the interface between differential geometry and physics. This is the latest in many articles I’ve written on Einstein’s relativity, so you might want to check out my series on faster-than-light

Geometry / Mathematics / Physics / etc.

A Space-Time Cocktail: Minkowski Space and Special Relativity

jonah 26

Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality. ~Hermann Minkowski Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore. ~Albert Einstein In my previous discussions of how we know the speed of light is constant and how this results in special relativity, I used Albert Einstein’s thought experiments to derive the time-dilating, length-contracting results. There’s another way to describe special relativity, though, invented by the Polish mathematician Hermann Minkowski. It

Geometry / Mathematics / Physics / etc.

You Can’t Get There From Here: Dimension, Fractional Dimension, and the Quantum Universe

jonah 2

You can’t get there from here. ~Maine saying My father once quoted a saying from Maine, where he spent some of his youth: “You can’t get there from here.” It refers to Maine’s winding road system, which often prevents a traveller from taking a direct route between two places. In physics and math terms, we might say that Maine’s road system is of fractional dimension: Less than two-dimensional, but more than one-dimensional. Integer Dimensionality Traditionally, we define the dimensionality of a space as the number of directions one can move in. For instance, a ski lift lives in a

Geometry / Mathematics / Physics / etc.

FTL Part 3: General Relativity Lets us Take Shortcuts

jonah 10

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

Physics / Relativity / Science And Math

FTL Part 2: The Universal Speed Limit

jonah 29
Woody Allen

It is impossible to travel faster than the speed of light, and certainly not desirable, as one’s hat keeps blowing off. ~Woody Allen This is Part Two of a multipart series on faster-than-light travel. This time, I’ll describe why it’s difficult to travel faster than lightspeed. At the end of my last article, I told you that the speed of light is constant, independent of the speed of the observer or the source. If I drive past you at half the speed of light with my headlights blazing, the photons of my headlights will be going past you at

Physics / Relativity / Science And Math

FTL Part 1: The Speed of Light is Constant

jonah 18
Cover to The Hitchhiker's Guide to the Galaxy

Nothing travels faster than the speed of light, with the possible exception of bad news, which obeys its own special laws. ~Douglass Adams, Mostly Harmless This is part 1 of a many-part series on faster-than-light travel. Before we can discuss how to travel faster than light, we need to understand why this is a problem in the first place. Why is the speed of light the universal speed limit? The answer starts with the invariance of the speed of light. By this point, everyone knows that the speed of light is constant, but it is not at all obvious