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Tag Archives: QM101

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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8 Comments | tags: de Broglie wavelength, QM101, quantum computing, quantum mechanics, qubits | posted in Opinion, Physics

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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14 Comments | tags: Bloch sphere, bra-ket notation, Paul Dirac, QM101, quantum computing, quantum mechanics, qubits | posted in Physics

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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10 Comments | tags: measurement problem, QM101, quantum mechanics, quantum physics, wave-function | posted in Opinion, Physics

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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7 Comments | tags: measurement problem, QM101, quantum mechanics, quantum physics, Schrödinger's Cat | posted in Opinion, Physics

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 ***de*coherence. 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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7 Comments | tags: measurement problem, QM101, quantum mechanics, quantum physics | posted in Opinion, Physics

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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10 Comments | tags: measurement problem, QM101, quantum mechanics, quantum physics, Schrödinger Equation | posted in Opinion, Physics

Over the last handful of years, fueled by many dozens of books, lectures, videos, and papers, I’ve been pondering one of the biggest conundrums in quantum physics: **What is measurement?** It’s the keystone of an even deeper quantum mystery: **Why is quantum mechanics so strangely different from classical mechanics?**

I’ll say up front that I don’t have an answer. No one does. The greatest minds in science have chewed on the problem for almost 100 years, and all they’ve come up with are guesses — some of them pretty wild.

This post begins an exploration of the conundrum of measurement and the deeper mystery of quantum versus classical mechanics.

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24 Comments | tags: measurement problem, QM101, quantum mechanics, quantum physics | posted in Opinion, Physics

Last time I explored the quantum spin of photons, which manifests as the **polarization of light**. (Note that all forms of light can be polarized. That includes radio waves, microwaves, IR, UV, x-rays, and gamma rays. Spin — polarization — is a fundamental property of photons.)

I left off with some simple experiments that demonstrated the basic behavior of polarized light. They were simple enough to be done at home with pairs of sunglasses, yet they demonstrate the counter-intuitive nature of quantum mechanics.

Here I’ll dig more into those and other experiments.

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9 Comments | tags: Bell's Theorem, photons, QM101, quantum mechanics | posted in Physics

Earlier in this QM-101 series I posted about quantum spin. That post looked at spin 1/2 particles, such as electrons (and silver atoms). This post looks at spin in **photons**, which are spin 1 particles. (Bell tests have used both spin types.) In photons, spin manifests as **polarization**.

Photon spin connects the Bloch sphere to the Poincaré sphere — an optics version designed to represent different polarization states. Both involve a two-state system (a qubit) where system state is a *superposition* of two basis states.

Incidentally, photon polarization reflects light’s wave-particle duality.

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7 Comments | tags: Bell's Theorem, photons, QM101, quantum spin, wave-function, wave-particle duality | posted in Physics

When I was in high school, bras were of great interest to me — mostly in regards to trying to remove them from my girlfriends. That was my errant youth and it slightly tickles my sense of the absurd that they’ve once again become a topic of interest, although in this case it’s a whole other kind of bra.

These days it’s all about Paul Dirac’s useful **Bra-Ket notation**, which is used throughout quantum mechanics. I’ve used it a bit in this series, and I thought it was high time to dig into the details.

Understanding them is one of the many important steps to climb.

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6 Comments | tags: bra-ket notation, inner product, matrix multiplication, outer product, QM101, quantum mechanics | posted in Math, Physics