the physics mill

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

History / Physics / Quantum Mechanics / etc.

Spin and the Stern-Gerlach Experiment

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The word “quantum” means a single share or portion. In quantum mechanics, this means that energy comes in discrete chunks, or quanta, rather than a continuous flow. But it also means that particles have other properties that are discrete in a way that’s deeply counterintuitive. Today I want to tell you about one such property, called spin, and the experiment that discovered it: the Stern-Gerlach experiment. (The goal of the original experiment was actually to test something else. But it was revealed later, after the discovery of spin by Wolfgang Pauli, that this is in fact what Stern and Gerlach were

Computer Related / logic / Mathematics / etc.

The Turing Machine

jonah

This is the sixth part in my multi-part series on computing. In the previous parts, we learned about Boolean logic, the language computers think in. We then learned how to implement this logic electronically. And finally, we learned how to make computer memory, so that computers can record results of calculations. Now before we conclude the series, we’re going to take a quick detour into computational theory and the Turing machine. Alan Turing’s Machine of the Mind In 1936, mathematician, WWII codebreaker, and all around awesome guy Alan Turing wanted to investigate a problem in formal logic. Specifically, he

Electronics / Physics / Science And Math

Flip-Flops and the Art of Computer Memory

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It’s a poor sort of memory that only works backwards. ~The White Queen to Alice (Lewis Carroll, Through the Looking Glass) This is the fifth part in my multi-part series on how computers work. Computers are thinking machines, and the first four parts of my series have been on how we teach computers to think.  But all of this logic, electronic or otherwise, is useless unless our computers can remember what they did. After logicking something out, a computer needs to remember the result of all that logicking! In this post, I describe how to use the logic gates

Computer Related / Science And Math

Corrections to Vinyl Records Vs Digital Files

jonah 1

In my previous post, it seems I’ve made some serious errors when discussing the technicalities of music recording, both digital and vinyl. This is not my area of expertise and I apparently did not do nearly enough research. Thanks to Gregor Robinson and Jonathan Griffitts for correcting me. Here are Gregor Robinson’s and Jonathan Griffitts’ corrections verbatum. Thanks to both of you. Gregor Robinson said: There is actually a big difference between lossy formats and lossless digital audio formats (which may be in fact compressed; see FLAC). It’s not just that the sample rate is lower. Lossy compression makes

Physics / Quantum Mechanics / Science And Math

Unreal Truths: Matter Waves and the Bohr Model of the Atom

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Everything we call real is made of things that cannot be regarded as real ~Niels Bohr This is the second part of a multi-part series on quantum mechanics. In part one,  I described and motivated particle-wave duality for light. I demonstrated that light waves are also particles (photons). But does this duality go the other way? Are particles like electrons also waves? As I hinted last time, the answer is yes. These are called matter waves, and their story is very interesting. The Mystery of the Emission Spectrum Last time, I discussed the emission spectrum of hydrogen, and the

Mathematics / Science And Math

Panning For Primes With the Sieve of Eratosthenes

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They consider me to have sharp and penetrating vision because I see them through the mesh of a sieve. ~Kahlil Gibran I know that last time I promised to talk more about quantum mechanics. Unfortunately, finals hit me with all the force of a great typhoon; I don’t feel like I have the time to write an article on quantum I’d be happy with. So here’s some filler on prime numbers. Our regular programming returns next week. A prime number is a counting number that is greater than one and only divisible by one and itself. For example, 2

Physics / Quantum Mechanics / Science And Math

The Charming Doubleness: Particle-Wave Duality

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But the beauty here lay in the duality, in the charming doubleness… ~ Thomas Mann (Felix Krull) I apologize to those of you who have requested a topic. The current requests are all pretty in-depth and I want some time to think about how to explain them properly. So, in a bid to buy time, I’m going to do a multi-part series on quantum mechanics. In this part, I’ll describe some of the experimental results motivating the fundamental principle of quantum mechanics: particle wave duality. As amazing as it may seem, quantum mechanics tells us that every particle is

Analysis / Mathematics / Science And Math

Taming Infinity: infinite sums, infinite primes and the sizes of infinity

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The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents. We live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far. ~Howard Phillips Lovecraft To infinity, and beyond! ~Buzz Lightyear Infinity: The Early Years When I was about ten, I had the following conversation with my friend: Me: I want Pokemon Yellow the most of anyone! My Friend: No, I do! I want it twice as much as you! Me: I want it