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.
Physics
explanatory articles on physics
Physics / Relativity / Science And Math
More on General and Special Relativity
Last time, I answered some questions from readers Ms. C and Mr. A on special and general relativity. Mr. A asked some very deep follow-up questions, so I thought I’d share them. Mr. A asks: I believe you already answered what I had intended to be my follow-up question: spacetime curvature accounts for the acceleration of an object already in motion; but why does a body at rest being to move (e.g. why doesn’t a stationary object hover in the air until someone touches it)? If I understand you’re post correctly, Einstein would say that there is no such thing as being at absolute rest —
Physics / Relativity / Science And Math
Rock Me, Einstein — Some Questions on Special and General Relativity
In 1905 Albert discovered Relativity, in 1906 he invented Rock and Roll ~Yahoo Serious In the last week or two, I’ve gotten several excellent questions on special and general relativity. I’d like to devote this week’s post to presenting and answering those questions. For the sake of anonymity, I will call the people who asked the questions Ms. C and Mr. A. I hope you enjoy! A Question on Special Relativity The first question is by Ms. C, who asked: I’ve read your article “The Speed of Light is Constant.” I’ve… got a question on the speed of light
cosmology / Geometry / Mathematics / etc.
Receding Horizons: Dark Energy and the Expanding Universe
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
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
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
cosmology / Physics / Science And Math
What Is Time? A Simple Explanation
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
Physics / Quantum Mechanics / Science And Math
Like Chords of Music: Quantum Tunneling
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
Physics / Science And Math
Refraction: (How We See) Through the Looking Glass
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
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