Archive for April, 2017


Skulls in the Stars

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…

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For the QM freaks, here’s something awesome…

Skulls in the Stars

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…

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An excellent explanation of the apparent mathematical magic called the matrix…

No Layman Left Behind

Most high school students in the United States learn about matrices and matrix multiplication, but they often are not taught why matrix multiplication works the way it does. Adding matrices is easy: you just add the corresponding entries. However, matrix multiplication does not work this way, and for someone who doesn’t understand the theory behind matrices, this way of multiplying matrices may seem extremely contrived and strange. To truly understand matrices, we view them as representations of part of a bigger picture. Matrices represent functions between spaces, called vector spaces, and not just any functions either, but linear functions. This is in fact why linear algebra focuses on matrices. The two fundamental facts about matrices is that every matrix represents some linear function, and every linear function is represented by a matrix. Therefore, there is in fact a one-to-one correspondence between matrices and linear functions. We’ll show that…

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