Category Archives: Science

August 30, 2021

Flat Space of the Torus

Flat Earth!

To describe how space could be flat, finite, and yet unbounded, science writers sometimes use an analogy involving the surface of a torus (the mathematical abstraction of the doughnut shape). Such a surface has no boundary — no edge. And despite being embedded in three-dimensional space, the torus surface, if seen in terms of compensating surface metric, is indeed flat.

Yet a natural issue people have is that the three-dimensional embedding is clearly curved, not flat. It’s easy to see how wrapping a flat 2D sheet into a cylinder doesn’t distort it, but hard to see why wrapping a cylinder around a torus doesn’t stretch the outside and compress the inside.

In fact it does, but there are ways to eat our cake (doughnut).

44 Comments | tags: 2D space, 3D space, cosmology, flat space, Flatland, space, torus | posted in Math

August 27, 2021

BB #75: Gloves and Shoes

By Wyrd Smythe

Speaking of Bell tests, I’ve noticed that science writers often struggle to find a good metaphor that illustrates just what’s so weird about the correlation between entangled particles. Bell tests are complex, and because they squat in the middle of quantum weirdness, they’re hard to explain in any classical terms.

I thought I had the beginnings of a good metaphor, at least the classical part. But the quantum part is definitely a challenge. (All the more so because I’m still not entirely clear on the deep details of Bell’s theorem myself.)

Worse, I think my metaphor fails the ping-pong ball test.

35 Comments | tags: Bell's Theorem, particles, quantum mechanics | posted in Brain Bubble, Physics

August 26, 2021

QM 101: Fun with Photons

By Wyrd Smythe

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.

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

August 25, 2021

QM 101: Photon Spin

By Wyrd Smythe

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.

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

August 19, 2021

BB #74: Which MWI?

By Wyrd Smythe

I finished The Quantum Labyrinth: How Richard Feynman and John Wheeler Revolutionized Time and Reality (2017), by Paul Halpern. As the title implies, the book revolves around the careers and lives of John A. Wheeler (1911–2008) and Richard Feynman (1918–1988). After Feynman graduated from MIT he became Wheeler’s teaching assistant at Princeton. The two men, despite very different personalities, became life-long friends and collaborators.

One of Wheeler’s many claims to fame is his promotion of Hugh Everett’s PhD thesis, The Theory of the Universal Wave Function. That paper, of course, is the seed from which grew the Many Worlds Interpretation of Quantum Mechanics.

The thing is, there are two major versions of the MWI.

3 Comments | tags: Many Worlds Interpretation, MWI, Paul Halpern, quantum mechanics, Sabine Hossenfelder | posted in Brain Bubble, Physics

August 13, 2021

BB #73: Wavefunction Collapse

By Wyrd Smythe

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.

10 Comments | tags: Paul Halpern, quantum mechanics, Schrödinger Equation, wave-function | posted in Brain Bubble, Physics

August 6, 2021

Sideband #73: Complex 4D

By Wyrd Smythe

I’ve written a number of posts about four-dimensional Euclidean space, usually in the context of one of my favorite geometrical objects, the tesseract. I’ve also mentioned 4D Euclidean spaces as just one of many possible multi-dimensional parameter spaces. In both cases, the familiar 2D and 3D spaces generalize to additional dimensions.

This post explores a specialized 4D space that uses complex numbers along each axis of a 2D nominally Euclidean space. Each X & Y coordinate has two degrees of freedom, a magnitude and a phase. This doesn’t make 4D spaces easier to visualize, but it can offer a useful way to think about them.

It also connects back to something I wrote about in my QM-101 series.

11 Comments | tags: 4D, complex numbers, complex plane | posted in Math, Sideband

July 9, 2021

MWI: Questions, part 3

By Wyrd Smythe

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.

14 Comments | tags: Many Worlds Interpretation, MWI, Schrödinger Equation, wave-function | posted in Physics

July 8, 2021

MWI: Questions, part 2

By Wyrd Smythe

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!

13 Comments | tags: Many Worlds Interpretation, MWI, Schrödinger Equation, wave-function | posted in Physics

July 7, 2021

MWI: Questions, part 1

By Wyrd Smythe

Back in January, in a post about unanswered questions in physics, I included the Many Worlds Interpretation of Quantum Mechanics (the MWI of QM). I wish I hadn’t. Including it, and a few other more metaphysical topics, took space away from the physical topics.

I did it because I’ve had notes for an MWI: Questions post for a long time, but shoehorning it in like that was a mistake. Ever since, I’ve wanted to return and give it the attention of a full post. I’m reminded about it constantly; the concept of “many worlds” has become such a part of our culture that I encounter it frequently in fiction and in fact (and in other blog posts).

Its appeal is based on a simplicity, but to me it doesn’t seem at all that simple.

8 Comments | tags: Many Worlds Interpretation, MWI, Schrödinger's Cat, wave-function | posted in Physics