cosmology / Geometry / Mathematics / etc.

Receding Horizons: Dark Energy and the Expanding Universe

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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

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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

Condensed Matter / Physics / Quantum Mechanics / etc.

How Things Work: The Field Effect Transistor

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I don’t know how to do this on a small scale in a practical way, but I do know that computing machines are very large; they fill rooms. Why can’t we make them very small, make them of little wires, little elements – and by little, I mean little. ~Richard Feynman (1959) As of 2012, the highest transistor count in a commercially available CPU is over 2.5 billion transistors. ~Wikipedia In my article on quantum tunneling, I mistakenly claimed that diodes and transistors made use of this phenomenon. In an effort to correct my mistake, I’m going to explain

Uncategorized

Delay Due to Grad School Open Houses

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Hi everyone. Sorry for yet another delay. I’m currently visiting graduate schools on the east coast (U Mass Amherst and Stony Brook University). I expected to have consistent internet access the last few days, but I have had almost no internet access and very little time to access the internet anyway. As such, my post may be delayed as late as Wednesday. I will get it up online this week though. Because I’ve spent three weekends in a row visiting various schools or going to conferences, I’m quite behind on my work. This might mean that my posts will

cosmology / Physics / Science And Math

What Is Time? A Simple Explanation

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Mastery is achieved when “telling time” becomes “telling time what to do.” ~“Telling Time” This week I’m trying something a little different. I heard about a contest where the goal was to explain time in terms an eleven-year-old could understand. While I didn’t make the contest deadline, I thought I’d share my attempt with you all. What Is Time? What is time? Scientists often think of time as a direction you can travel in. Just as we can move up, down, left, or right in space, we can move in time. Something is wrong with this comparison, though. When

Uncategorized

No Cat Returns

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Hi everyone, because I’m at a graduate school open house this weekend and next, I’m having trouble keeping up with everything I need to do. For this reason, I’m going to be posting very short things for the rest of the month. I’m also going to be delayed this week. The main post will probably be up sometime Sunday. Sorry about that. In the meantime, here’s a video of a cat barking. …and here’s a video of a very upset cat. I know, little guy. I’m sorry about the delay.  

Physics / Quantum Mechanics / Science And Math

Like Chords of Music: Quantum Tunneling

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The world is a dynamic mess Of jiggling things It’s hard to believe ~Richard Feynman The essential nature of matter Lies not in objects, but in interconnections Like chords of music, it’s beautiful ~Sophia Hoffman +Dripto Biswas recently asked me through google plus to explain why a superfluid climbs up the walls of its container. I don’t know very much about superfluids themselves. However, I can explain the basic quantum mechanics behind their behavior. (Spoiler alert: I’m going to mention quantum tunneling!) It might be helpful to reveiw some of my previous posts on quantum mechanics. The most relevant

Geometry / Mathematics / Science And Math

TexTAG Conference Report

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Hi everyone. Sorry, but I’ve been at the Texas Undergraduate Geometry and Topology conference all weekend and I haven’t had time to write my blog post yet. I will post actual content as soon as I can, probably late tomorrow afternoon. In the meantime, I gave a talk on differential geometry at the conference! It’s not much of a consolation prize, but here are my slides from the talk. To better see the families of commensurate curves on various surfaces, we can animate our numerical integral as a function of the initial conditions. Here are some of the animations:

Physics / Science And Math

Refraction: (How We See) Through the Looking Glass

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We do not see the lens through which we look. ~Ruth Benedict I was recently asked to explain refraction using quantum mechanics. To really understand this on the quantum level requires understanding a field called “quantum electrodynamics,” which was invented independently by Richard Feynman, Sin-Itiro Tomonaga, and Julian Schwinger (and for which they all shared a Nobel prize). Unfortunately, I don’t know very much about quantum electrodynamics, so I can’t explain this the way a particle physicist or condensed matter physicist might. I can however, give a “pseudoclassical” model that was invented around the turn of the twentieth century…right

Geometry / Mathematics / Physics / etc.

A Space-Time Cocktail: Minkowski Space and Special Relativity

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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