Tag Archives: Schrödinger Equation

QM 101: Diffusion in 2D

Last time I began exploring the similarity between the Schrödinger equation and a classical heat diffusion equation. In both cases, valid solutions push the high curvature parts of their respective functions towards flatness. The effect is generally an averaging out in whatever space the function occupies.

Both equations involve partial derivatives, and I ignored that in our simple one-dimensional case. Regular derivatives were sufficient. But math in two dimensions, let alone in three, requires partial derivatives.

Which were yet another hill I faced trying to understand physics math. If they are as opaque to you as they were to me, read on…

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QM 101: Heat Diffusion

This is the first of a series of posts exploring the mysterious Schrödinger Equation — a central player of quantum mechanics. Previous QM-101 posts have covered important foundational topics. Now it’s time to begin exploring that infamous, and perhaps intimidating, equation.

We’ll start with something similar, a classical equation that, among other things, governs how heat diffuses through a material. For simplicity, we’ll first consider a one-dimensional example — a thin metal rod. (Not truly one-dimensional, but reasonably close.)

Traveller’s Advisory: Math and graphs ahead!

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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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BB #73: Wavefunction Collapse

I’m two-thirds through my second Paul Halpern book this month. Earlier I read his book about cosmology, Edge of the Universe: A Voyage to the Cosmic Horizon and Beyond (2012), which was okay. Now I’m reading The Quantum Labyrinth: How Richard Feynman and John Wheeler Revolutionized Time and Reality (2017), which I’m enjoying a bit more. In part because cosmology has changed more since 2012 than quantum physics has since 2017. (Arguably, the latter hasn’t changed much since the 1960s.)

I wrote about Halpern’s book, Einstein’s Dice and Schrödinger’s Cat (2015), last year. As the title implies, it focuses on two great names from physics. Quantum Labyrinth (as its title also implies) also focuses on two great physics names.

But today’s Brain Bubble (as the title implies) is about wavefunction collapse.

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MWI: Questions, part 3

This is the third part of a series examining the Many Worlds Interpretation of Quantum Mechanics (the MWI of QM). The popularity of the MWI in books, blogs, and science videos, especially among the science-minded, tends to keep in present in some corner of my mind. Blog posts are a way to shoo it out.

The first part introduced the topic and talked about cats. The second part discussed the Schrödinger equation, wavefunctions, decoherence, and the question of how multiple instances of matter can coincide. That question, to me, is a central issue I have with MWI.

This time I dig into quantum superposition and touch on a few other topics.

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MWI: Questions, part 2

Last time I started exploring questions I have about the Many Worlds Interpretation of Quantum Mechanics (the MWI of QM). Obviously I’m not a fan; quite the opposite. It presents as parsimonious, hung on the single hook of a universal wavefunction, but I think it gets more complicated and cumbersome when examined. I can’t say it’s broken, but I don’t find it very attractive.

I suspect most people, even in physics, don’t care. A few have invested themselves in books or papers, but these interpretations don’t matter to real physics work. The math is the math. But among the philosophical, especially the ontological, it’s food for debate.

Being both philosophical and ontological, I do smell what’s cooking!

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Old School Viral

Remember when “going viral” didn’t mean hospitalization and possible death? (Obviously if we go back even further to the original meaning, it did.) I had an old post go briefly and mildly viral last week. Big traffic spike with a very rapid tail-off. Most bemusing.

I’ll tell you about that, and about a spike on another post, this one weirdly seasonal — huge spike ever September for three years now. I have no idea what’s going on there. Most puzzling.

There is also a book about the friendship and conflict between Albert Einstein and Erwin Schrödinger that I thoroughly enjoyed despite it not being my typical sort of reading (I’ve never gone in much for either history or biography).

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Wave-Function Story

Last time I started with wave-functions of quantum systems and the Schrödinger equation that describes them. The wave-like nature of quantum systems allows them to be merged (superposed) into combined quantum system so long as the coherence (the phase information) remains intact.

The big mystery of quantum wave-functions involves their apparent “collapse” when an interaction with (a “measurement” by) another system seemingly destroys their coherence and, thus, any superposed states. When this happens, the quantum behavior of the system is lost.

This time I’d like to explore what I think might be going on here.

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Wave-Function Collapse

Quantum physics is weird. How weird? “Too weird for words,” as we used to say, and there is a literal truth to words being inadequate in this case. There is no way to look at the quantum world that doesn’t break one’s mind a little. No one truly understands it (other than through the math). It’s like trying to see inside your own head.

Since we’re clueless we make up stories to fit the facts. Some stories advise that we just keep our heads down and do the math. (Which works very well but leaves us thirsty.) Other stories seek to quench that thirst, but every story seems to stumble somewhere.

One of quantum’s biggest and oldest stumbling blocks is wave-function collapse.

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Many Worlds Insanity

I was surprised to discover I’ve never posted about the Many Worlds Interpretation (MWI) of quantum physics — I would have sworn I had. I’ve mentioned it a few times, and I know I’ve discussed it in comment sections, but it seems I never tackled the subject explicitly for the record.

It’s been on my mind lately because others have talked about it. Sean Carroll’s book promoting it generated a wave of discussion. The final push for me was Jim Baggott’s Farewell to Reality, which consigns MWI to the “fairy tale physics” heap.

Since I quite agree, this seems a good followup to yesterday’s post.

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