Will you understand what I’m going to tell you? …No, you’re not going to be able to understand it. … I don’t understand it. Nobody does. ~Richard Feynman on the Path Integral The “paradox” is only a conflict between reality and your feeling of what reality “ought to be.” ~Richard Feynman, in his lectures on physics Quantum mechanics is a very strange beast. Things tunnel and ooze. You can’t know both position and momentum at the same time. These strange properties come from the amazing realization that particles are waves. Not only that, but the amplitude of the wave
Quantum Mechanics
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
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
Condensed Matter / Physics / Quantum Mechanics / etc.
I’m With the (Valence) Band: Band Structure and the Science of Conduction
It was not so very long ago that people thought that semiconductors were part-time orchestra leaders and microchips were very, very small snack foods. ~Geraldine A. Ferraro More is different. ~Philip Warren Anderson Metals conduct electricity. Nonmetals don’t. That’s the conventional wisdom, anyway. In truth, there is a third class of material, called semiconductors. A semiconductor sometimes conducts electricity and sometimes doesn’t. This week, we’ll learn precisely what a semiconductor is and how the forces of quantum mechanics determine whether a material is a conductor, an insulator, or a semiconductor. More is Different Nobel laureate Philip Warren Anderson said
Physics / Quantum Mechanics / Science And Math
Binary Unity: The Pauli Exclusion Principle
Sameness leaves us in peace but it is contradiction that makes us productive. ~Johann Wolfgang Von Goethe In previous entries, I’ve discussed the wave nature of particles and some consequences of that wave nature, how electrons occupy specific energy states in atoms, and how particles obey the laws of probability. This is all pretty weird stuff. However, there’s another strange phenomenon in quantum mechanics that I haven’t discussed. That phenomenon is the Pauli exclusion principle. The Mystery of Stability An atom is made of protons, neutrons, and electrons. A good (but not quite right) model of the atom is
Geometry / Mathematics / Physics / etc.
You Can’t Get There From Here: Dimension, Fractional Dimension, and the Quantum Universe
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
Mathematics / Physics / Quantum Mechanics / etc.
Resolution, Fourier Analysis, and The Heisenberg Uncertainty Principle
All the effects of nature are only mathematical results of a small number of immutable laws. ~Pierre-Simon Laplace In my discussion last time (corrections here), I discussed how there is a physical limit to how good a recording can sound, whether vinyl or digital. There is a more fundamental limit, however, that I glossed over—a limit that depends not on atoms or compression techniques, but on pure mathematics. This limit was partially discovered by Jean Baptiste Joseph Fourier, and the method we will discuss bears his name. The Superposition Principle Before we discuss Fourier’s discovery, let’s take a brief
Physics / Quantum Mechanics / Science And Math
The Dice Are Loaded: Probability Waves
God does not play dice ~Albert Einstein Einstein, stop telling God what to do! ~Niels Bohr This is part three of a multi-part series on quantum mechanics. In part one, I discussed how we discovered that light is both a wave and a particle. The dual nature of light suggests that massive particles like electrons might be waves too. In part two, I gave a theoretical underpinning to the dual nature of electrons: treating electrons as waves completes the Bohr Model of the atom and explains the Rydberg Formula. However, legendary physicist Richard Feynman once said: It doesn’t matter
Physics / Quantum Mechanics / Science And Math
Unreal Truths: Matter Waves and the Bohr Model of the Atom
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
Physics / Quantum Mechanics / Science And Math
The Charming Doubleness: Particle-Wave Duality
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