Wikipedia:Reference desk/Archives/Mathematics/2017 November 30

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November 30

"rangle ?" ???

I have studied mathematics like trigonometry (incl. addition formulas, theorems etc), geometry, polynome, derivation, max-min studies, integral calculus, differential calculus, logarithms,
complex numbers (incl i), statistics, probabilities, standard deviation, Pascale's triangle and I have also used a lot of math within physics, static mechanics, dynamic mechanics, point of gravity for complex items and/or several material with different densities, cogwheels/gearboxes (including empiric formulas with some 25 variables, of which several require a look in various tables or yet other empiric or proven formulas) and other structural elements of which a certain knowledge of math is required like various bearings, mechanic strength/solidity etc - and DC, AC within high voltage/current as well as binary numbers, octal numbers, hexadecimal decimal numbers, both low-level programming and high-level programming like basic, C, C++/OOP etc etc.
But I do not get what's meant by this "rangle", like this ${|0\rangle +i|1\rangle }$ , its not about " i " (the imaginary solution for x^2=-1, and |2-8|= 6, absolute value), but the "|>"; called "rangle" in the syntax text, have I never ever encountered before (at age 53) - so could someone please explain just what's meant by for instance ${|0\rangle }$ ? It's very annoying to me, to not really grasp this at all, not beyond pure guesses
Like
$e=\lim _{x\to \infty }\left(1+{\frac {1}{x}}\right)^{x}$
I can (try to) explain, like this - e (the base of the natural logarithms; approx 2.71) equals the limes (what value will "be approached") for an x which grows larger and larger towards infinity, for that expression (1 + 1/x)^x. If using x=100 , the value will be close to e, but with x=10000 more closer etc. Could someone just try to help me to understand my question, about that way or better ? Boeing720 (talk) 20:31, 30 November 2017 (UTC)

Well, "rangle" means "right angle bracket", and you shouldn't be seeing it in the rendered mathematical text. It'll be part of the LaTeX (or maybe HTML?) markup.

What the notation means is a different question. It's called a "ket". See bra–ket notation. --Trovatore (talk) 20:33, 30 November 2017 (UTC)

As to the specific instance you've provided — my guess is that this is the state of a qubit. It means that the qubit has a probability of 1/2 of being found in state 0 or state 1. The i is a phase, which has no classical interpretation — see quantum superposition. --Trovatore (talk) 20:38, 30 November 2017 (UTC)

(edit conflict) It's called Bra–ket notation, and its used in quantum mechanics to represent certain linear algebra functions. I'm afraid I've killed the parts of my brain that used to know more about this, having not used it since the mid 1990s. --Jayron32 20:42, 30 November 2017 (UTC)

Protip: When you have a question, just ask the question, don't go into a whole speech about how much mathematics you know... It comes off as very arrogant.

Also, you don't need to be offended by the fact that there's a piece of notation you're not familiar with. Mathematics (and Physics) is huge, and different areas use their own specialized notation.

By the way, the | in Bra-Ket notation is not related to absolute values in any way. Often, the same symbols can be used to refer to entirely different things. -- Meni Rosenfeld (talk) 00:09, 1 December 2017 (UTC)

I didn't necessarily take the OP's description of his/her background as bragging. When responding, it's useful to know how much the questioner already understands. (For this question, it would have been useful to know even more about the questioner's background, namely how much he/she knows about quantum mechanics.) --Trovatore (talk) 01:18, 1 December 2017 (UTC)

[No comment on the math itself; I don't know the subject at all.] I agree. As a librarian, I really appreciate it when the reference transaction (whether at the desk or in an online chat setting) begins with the patron explaining a little bit about their background in the area: the introductory part of the reference interview is simpler, because I know a bit about the patron's awareness level before I start asking clarifying questions. Nyttend backup (talk) 01:42, 1 December 2017 (UTC)

Reply to Meni Rosenfeld. I didn't mean to be boastful. But simply I don't get this either - then what about other readers, with less knowledge of math ?. Our math-related articles, are in my opinion not aiming to reach readers with "normal" knowledges, but just those how have studied mathematics at a university level for many years. Not all articles, but too many. A general help is always one example of a certain equation or formula etc, I think. Boeing720 (talk) 13:44, 1 December 2017 (UTC)

Well, this is a constant point of contention. Quite a number of math articles are about topics that simply cannot be explained to people without quite an extensive mathematical background. The choices are, present material that can be used by people who do have the necessary background, or don't present it at all. I don't see any good argument for the second choice.

However, in this particular case, there's no reason that bras and kets shouldn't be explainable to someone of your background. Can you say where you saw it? Maybe that article can be improved. --Trovatore (talk) 19:32, 1 December 2017 (UTC)

Agree to a certain point. Naturally cannot every reader comprehend all of our math-related articles, that's absolutely true. But for instance, just a single example (in hard numbers, when possible) could well be of tremendous help to not so few, I would say. Without any examples (or explanations of other kinds), we really don't offer much extra, compared to external math-related web-pages, I think. Here I think some printed encyclopedias still are ahead of us (although the number of math-related articles might be fewer). Finally, just a simple example that $\Delta$ (usually) means "difference" are almost always forgotten. At the very least each element/variable in an equation or formula could be explained in a list, I think. Our illustrations are often very good and enlightening however. Anyways, thanks Trovatore for making things clearer, and yes I happened to see the "ket" in the qubit article. Boeing720 (talk) 03:30, 2 December 2017 (UTC)

... an article which includes a short description of the notation before it is first used, provides the name of the notation, and gives a link to another article with more detailed information. There is nothing writers of an article can do to prevent readers from not reading what is written. --JBL (talk) 03:43, 2 December 2017 (UTC)

Right, so on the one hand I think a lot of readers need to adjust their expectations as regards the amount of effort needed to read a technical article. You can't think that just because you read all the words you're going to understand what's going on. Not even if you know all the words.

If it takes you an hour of hard work to get through a half a page, well, sometimes that's just what it takes. It doesn't necessarily mean that the writing was poor or that you're not smart (though of course neither of those will help :-) ). And if you don't know some of the words or concepts, and have to go learn them, naturally it will take even longer.

On the other hand, part of that work may be coming to the reference desk to ask, and we ought to honor that and do what we can. I thought of an example that might help. @Boeing720: how much do you understand about polarized light? It makes a pretty good model here. You can think of (say) horizontally polarized light as your $|0\rangle$ ket, and vertically polarized as your $|1\rangle$ ket. Then let's say you add the electric fields together, with the same phase, so that you get 45-degree polarized light. Any photon from that beam will have a 1/2 probability of getting through a vertically polarizing filter.

But you can also add them together 90 degrees out of phase, and get circularly polarized light. A photon from that beam will also have a 1/2 probability of getting through the vertically polarizing filter — but the two beams are not the same.

The first case corresponds to $|0\rangle +|1\rangle$, whereas the second corresponds to $|0\rangle +i|1\rangle$. (Or could be $|0\rangle -i|1\rangle$; doesn't matter much.)

Does that help at all? --Trovatore (talk) 04:20, 2 December 2017 (UTC)

I didn't say the OP necessarily was trying to be boastful, only that it can appear this way and detract from the question.

I agree that understanding an asker's background can help when answering. But it depends on the type of question, and usually what needs to be explained is the background pertaining to the topic of the question. It's rarely useful to know the background of someone asking about an unfamiliar piece of notation - the appropriate answer is often literally just a link to an article explaining it. And I doubt it's ever useful to present a "grocery list" of all topics the asker is familiar with.

It's also a matter of quantity - 10 lines for a question that simply could have been "Hi guys, what does this notation mean?" is way too much.

I must say I'm quite surprised I'm the only one bothered by the OP's exposition. It's not really something you see in all the other questions here. Trovatore, by your own admission the long list of known topics was ultimately useless in figuring out what you needed to figure out about the OP's background. But I'm not even quite sure why you feel you needed to know that - the OP asked about the notation, not about how QM works. And mathematically speaking, the Bra-ket notation is just a fancy way to write down vectors and their dot product. The interpretation as a superposition of quantum states is more appropriate for WP:RD/S - or, more likely, whatever article it was in which the OP encountered the notation. -- Meni Rosenfeld (talk) 19:23, 2 December 2017 (UTC)

You are not the only one: the intro was long, pointless, and detracted from the question. If I had been the first person to come across it, I would have been mildly tempted to redact it. --JBL (talk) 20:04, 2 December 2017 (UTC)

I didn't say it was ideal. I do think it's useful to know something about the questioner's background, and I'm not convinced it's useful to take them to task for small suboptimalities in how they convey it. As for it just being a way to write down vectors and dot products, sure, abstractly that's true, but in my experience the notation is not really used outside of quantum mechanics. --Trovatore (talk) 21:44, 2 December 2017 (UTC)

Actually, I've once made a (kind of) thesis in optical mechanical tension (in polarized light the plastic material which I guess is called Araldite in English, reveals mechanic tension excellently), so yes I'm fairly acquainted with such "dividing" of light, at least from a technical point of view. Your explanation also makes sense, have read some physics too. Thanks for your efforts, Trovatore. Boeing720 (talk) 5:02 pm, Today (UTC−5)