Category Archives: Science

Reversing Reality

“Time is out of joint.”

I’ve long puzzled over the idea that physics is reversible. That its laws, with some caveats, work the same if time runs forwards or backwards. It’s even been suggested that, except for entropy, time could run backwards just as easily as forwards.

But this seems contrary to our everyday experience. With some exceptions, we can tell if a film or video clip is shown in reverse. Objects that fall, break, or grow (such as plants or crystals), look different seen in reverse.

I think there is more going on there than just entropy.

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JWST First image!

If you follow stuff like this, you probably already know, but the James Webb Space Telescope team just released the first actual image from the telescope:

More images are expected to be released tomorrow (July 12). Visit their page for details (and the full-sized image — all 4537×4630 pixels of it). Visit their excellent “Where Is Webb?” page for the latest status and stats on the JWST.

Congrats again to everyone involved! This was an amazing (and prolonged) effort. I’m glad I get to see some of the results now!

Matter Waves

A single line from a blog post I read got me wondering if maybe (just maybe) the answer to a key quantum question has been figuratively lurking under our noses all along.

Put as simply as possible, the question is this: Why is the realm of the very tiny so different from the larger world? (There’s a cosmological question on the other end involving gravity and the realm of the very vast, but that’s another post.)

Here, the answer just might involve the wavelength of matter.

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The Power of Qubits

I’ve been working my way through The Principles of Quantum Mechanics (1930), by Paul Dirac. (It’s available as a Kindle eBook for only 6.49 USD.) It’s perhaps best known for being where he defines and describes his 〈bra|ket〉 notation (which I posted about in QM 101: Bra-Ket Notation). More significantly, Dirac shows how to build a mathematical quantum theory from the ground up.

This is not a pop-science book. Common wisdom is that including even a single equation in a science book greatly reduces reader interest. Dirac’s book, in its 82 chapters, has 785 equations! (And no diagrams, which is a pity. I like diagrams.)

What I wanted to post about is something he mentioned about qubits.

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Euler Spirals and Pi Paths

I posted a while back about the wonders of Fourier Curves, and I’ve posted many times about Euler’s Formula and other graphical wonders of the complex plane. Recently, a Numberphile video introduced me to another graphical wonder: Euler Spirals. They’re one of those very simple ideas that results in almost infinite variety (because of chaos).

As it turned out, the video (videos, actually) led to a number of fun diversions that have kept me occupied recently. (Numberphile has inspired more than a few projects over the years. Cool ideas I just had to try for myself.)

This all has to do with virtual turtles.

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Back to Plato’s Line

Last February I posted about how my friend Tina, who writes the Diotima’s Ladder blog, asked for some help with a set of diagrams for her novel. The intent was to illustrate an aspect of Plato’s Divided Line — an analogy about knowledge from his worldwide hit, the Republic. Specifically, to demonstrate that the middle two (of four) segments always have equal lengths.

The diagrams I ended up with outlined a process that works, but I was never entirely happy with the last steps. They depended on using a compass to repeat a length as well as on two points lining up — concrete requirements that depend on drawing accuracy.

Last week I had a lightbulb moment and realized I didn’t need them. Lurking right in front of my eyes is a solid proof that’s simple, clear, and fully abstract.

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Objective Collapse

In the last four posts (Quantum Measurement, Wavefunction Collapse, Quantum Decoherence, and Measurement Specifics), I’ve explored the conundrum of measurement in quantum mechanics. As always, you should read those before you read this.

Those posts covered a lot of ground, so here I want to summarize and wrap things up. The bottom line is that we use objects with classical properties to observe objects with quantum properties. Our (classical) detectors are like mousetraps with hair-triggers, using stored energy to amplify a quantum interaction to classical levels.

Also, I never got around to objective collapse. Or spin experiments.

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Measurement Specifics

In the last three posts (Quantum Measurement, Wavefunction Collapse, and Quantum Decoherence), I’ve explored one of the key conundrums of quantum mechanics, the problem of measurement. If you haven’t read those posts, I recommend doing so now.

I’ve found that, when trying to understand something, it’s very useful to think about concrete real-world examples. Much of my puzzling over measurement involves trying to figure out specific situations and here I’d like to explore some of those.

Starting with Mr. Schrödinger’s infamous cat.

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Quantum Decoherence

In the last two posts (Quantum Measurement and Wavefunction Collapse), I’ve been exploring the notorious problem of measurement in quantum mechanics. This post picks up where I left off, so if you missed those first two, you should go read them now.

Here I’m going to venture into what we mean by quantum coherence and the Yin to its Yang, quantum decoherence. I’ll start by trying to explain what they are and then what the latter has to do with the measurement problem.

The punchline: Not very much. (But not exactly nothing, either.)

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Wavefunction Collapse

The previous post began an exploration of a key conundrum in quantum physics, the question of measurement and the deeper mystery of the divide between quantum and classical mechanics. This post continues the journey, so if you missed that post, you should go read it now.

Last time, I introduced the notion that “measurement” of a quantum system causes “wavefunction collapse”. In this post I’ll dig more deeply into what that is and why it’s perceived as so disturbing to the theory.

Caveat lector: This post contains a tiny bit of simple geometry.

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