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The GHZ experiment cartoon

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I'm still a bit obsessed with the GHZ experiment.  This is the one where you prepare a GHZ state $\lvert 000 \rangle + \lvert 111 \rangle$ and send one qubit to each of 3 protagonists: Alice, Bob, and Charlie.  (I will be ignoring shared normalizer constants throughout this post, as I find they don't add anything to the understanding.) If you do the maths it turns out that when all three choose to measure in the $\lvert + \rangle$, $\lvert - \rangle$ basis (shorthand for $\lvert 0 \rangle + \lvert 1\rangle$ and $\lvert 0 \rangle - \lvert 1\rangle$) then they are guarranteed to get a parity zero result.  On the other hand if only one measures in this basis and the other two measure in the $\lvert +i\rangle$, $\lvert -i\rangle$ basis (shorthand for $\lvert 0 \rangle + i\lvert 1\rangle$ and $\lvert 0 \rangle - i\lvert 1\rangle$) they are guarranteed to get a parity one result.  As I showed in an earlier post this appears to be incompatible with the outcomes being prede...
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How To Make ASCII Diagrams Beautifuller

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I've discovered an excellent tool in asciiflow.com .  The website makes it really easy to create ASCII box diagrams like this They put these things in fruit machines you know! This is ideal for source code banners, which I think should contain helpful documentation - but most programmers think it's a good place for the COPYRIGHT information and nothing else. But wait! we can make it beautifuller... and easier to read... by replacing some of the ASCII characters with ones available in UTF-8: There!  Isn't that better?  (Although some purists may object to non-ASCII characters in your code base.) SOURCE CODE: #!/usr/bin/python2 # coding: utf-8 # + gets converted in different ways depending on it's 4 neighbours # # . N . { nsew(N,S,E,W) has bit 3 set if N in "+|<>" # W + E { nsew(N,S,E,W) has bit 2 set if S in "+|<>" # . S . { nsew(N,S,E,W) has bit 1 set if W in "+-^v" # { nsew(N,S,E,W) has bit 0 set if E ...
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Tides

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Why is it tides are semi-diurnal ? That is, why do they occur every 12 hours when they are caused by the gravitational pull of a moon that we turn to face once a day?  The straightforward answer is that water bulges out on both the side nearest and the side furthest from the moon.  (We'll ignore the Sun for simplicity, but adding it in doesn't change anything.) The Earth rotates while the bulges remain in place, causing tides 12 hours apart.  However, this doesn't explain why there should be two bulges.  The reason becomes clear when you change the frame of reference.  Instead of thinking about a frame in which both the moon and the Earth rotate, set the origin to be the centre of mass of the two objects, and choose a rotating frame in which the moon is stationary.  In this frame there is a "fictional" centrifugal force of $\omega^2 r$ which combines with the gravitational force from the moon, $GM_{\text{moon}}/(r-r_{\text{moon}})^2$ The two forces match a...
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