What is quantum entanglement? Part 2: Randomness and measurement

This is part 2 in a lengthy series of posts attempting to explain the idea of quantum entanglement to a non-physics audience.  Part 1 can be read here.

So, by the mid 1920s, physicists had made significant progress in developing the new quantum theory.  It had been shown that light and matter each possess a dual nature as waves and particles, and Schrödinger had derived a mathematical equation that accurately described how the wave part of matter evolves in space and time.

But it was not clear what, exactly, was doing the “waving” in a matter wave.   Water waves arise from the oscillation (waving) of water, sound waves arise from the oscillation of molecules in the air, but what is oscillating in a matter wave?  Or, to put it another way, what does such a wave represent?

We will try and answer this question by looking at how a matter wave manifests in an actual experiment.  It turns out that the best example for demonstrating the wave properties of matter is also the best example for demonstrating the wave properties of light: Young’s classic double slit experiment!  However, the double slit experiment was not done with electrons until decades after the foundation of quantum mechanics, so we must briefly step away from our historical discussion to investigate it.

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Posted in History of science, Physics | 4 Comments

What is Quantum Entanglement? Part 1: Waves and particles

If you follow science, or science fiction, to any degree, great or small, you’ve probably heard the term “quantum entanglement” before.  You may also have heard it referred to as “spooky action at a distance,” and understand that it somehow involves a weird connection between separated quantum particles that can “communicate,” in a sense, over long distances instantaneously.  You may have read that quantum entanglement is a key aspect in proposed technologies that could transform society, namely quantum cryptography and quantum computing.

But it is difficult for a non-physicist to learn more about quantum entanglement than this, because even understanding it in a non-technical sense requires a reasonably thorough knowledge of how quantum mechanics works.

In writing my recently-published textbook on Singular Optics, however, I had to write a summary of the relevant physics for a chapter on the quantum aspects of optical vortices. I realized that, with some modification, this summary could serve as an outline for a series of non-technical blog posts on the subject; so here we are!

It will take a bit of work to really get at the heart of the problem; in this first post, I attempt to outline the early history of quantum physics, which will be necessary to understand what quantum entanglement is, why it is important, and why it has caused so much mischief for nearly 100 years!

Small disclaimer: though I am a physicist, I am not an expert on the weirder aspects of quantum physics, which have many pitfalls in understanding for the unwary! There is the possibility that I may flub some of the subtle parts of the explanation. This post is, in fact, an exercise for me to test my understanding and ability to explain things. I will revise anything that I find is horribly wrong.

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Posted in History of science, Physics | 18 Comments

The Southern Reach trilogy, by Jeff VanderMeer

I’m not entirely sure why it took me three years to read Jeff VanderMeer’s Southern Reach trilogy.  One of his earlier novels, Finch, is on a very short list of “best books I’ve ever read.”  I suspect that I simply read the name “Southern Reach” and it somehow evoked images of the Southern United States in a weird way that didn’t appeal to me, and I just never got around to looking at the books.  Until, that is, I read the first description of the upcoming movie version of the first book, which instantly intrigued me.  Over the course of about 5 days, I read all three books of the trilogy.  They’re that good.

It is hard to find the right words to describe these novels.  Bewildering, intricate, confusing, surreal, thoughtful, haunting, poetic, horrific, terrifying, beautiful?  It is all these things, and more.

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Posted in Horror, Science fiction, Weird fiction | 1 Comment

Chills, by Mary SanGiovanni

I’ve been in a bit of a funk the past few weeks and haven’t been reading much.  What I needed to get myself back on track was a nice solid bit of horror fiction, and fortunately I had on hand the most recent novel by Mary SanGiovanni, Chills.

As is made clear from the cover image and the title, Chills centers on a danger that originates in the coldest weather.  A team of detectives and investigators race, in the midst of a blizzard, to solve a series of grisly murders and prevent future ones from occurring.  However, they soon learn that even worse things are happening, and that there are unnatural things in the whiteout…

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The geometry of weird-shaped dice

I’ve been enjoying a bit of reminiscing about my childhood lately, hunting down old copies of role-playing games I enjoyed in my youth as well as exploring newer games that have come out since then.  One thing that has changed dramatically since my gaming days is the proliferation of types of dice.  Most human beings never go beyond ordinary 6-sided dice, which we in the gaming world call a “d6.” Classic Dungeons & Dragons players, however, are familiar with the d4, d6, d8, d10, d12, and d20.

But these days, there are even more imaginative varieties!  I’ve starting collecting dice of every shape and size, and my current collection is shown below, in order¹:

This is a really amazing variety of dice! This is my “special dice” collection in its entirety, and includes some duplicates (don’t ask how I got 4 identical d60s), but in some cases, such as the d7, d12 and d24, there are varieties in shapes even with the same number of faces!

This variety got me wondering: how does one design dice with a weird number of faces? What mathematical strategies does one use to make them? What other types of dice are possible? And, perhaps most important: are these dice “fair”?

I thought it would be fun to answer these questions with a blog post, in which we discuss the geometry of dice!

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Posted in Mathematics, role-playing games | 7 Comments

Optics basics: reflection

It’s been some 5 years since I wrote my last “Optics basics” post!  The goal of that series of posts was to introduce some of the most fundamental concepts in optics in a non-technical way, in part so I wouldn’t have to constantly reexplain them in more advanced posts.

I’ve covered most of the topics that I would truly call “basic” — hence the long time since the last post — but I realized that I missed one concept that is truly fundamental: the law of reflection!

It may not seem like there’s much to say about reflection, but we’ll see that isn’t the case.  Many interesting things can happen when light reflects off of a surface — the challenge will be to include as many as possible while keeping this post short!

So what is the law of reflection?  Well, the classic law of reflection states that the angle that a ray of light reflects off of a smooth, flat surface (the angle of reflection \theta_r) is equal to the angle at which the light is incident upon the surface (the angle of incidence \theta_i).


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The Left Hand of Darkness, by Ursula K. Le Guin

After reading the epic Foundation series of novels by Asimov, I was in the mood for a change of pace in science fiction.  I turned to another brilliant author, Ursula K. Le Guin, and her classic 1969 novel The Left Hand of Darkness.


I vaguely remember being told about this novel when I was in college, though I didn’t read it then. At the time, the description that I was given was more or less “a book entirely about linguistic, social and cultural details.”  This description isn’t completely inaccurate, but The Left Hand of Darkness is so much more — it is a fascinating study of a culture that is completely alien to our own, thanks to one, single, fundamental, biological difference in its humans.

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Posted in Science fiction | 3 Comments