joigus

Just to correct myself. There are cases in which you can say an electron changes its spin, of course. But not for spin-entangled states. For example, you put an ion in an ion trap and subject it to a magnetic field. The ion will flip its spin. The devilish property of a maximally-entangled state is that you cannot say its spin has any particular value whatsoever. Yes, it's very much like that; they're initial correlations. The tricky part is that correlations are quantum. All hell breaks loose when correlations are quantum and you want to think about the gloves as actually possessing all these properties at a given time. Quantum mechanics embeds a different (non-classical) kind of logic when you express it in terms of properties you can measure. 'Quantum gloves' need to be able to occupy states that are neither right-handed, nor left-handed (superpositions); neither black nor white, etc. And we need to be able to measure several properties of the gloves. If we want to have properly quantum gloves and display all the 'trickery' of quantum entanglement, we would need: 1) Several measurable properties. Take three observables, say: handedness (H), colour (C), and material (M). 2) Measurements of any one of these properties (observables) completely mess up measurements of the other; and you can't measure (H,C), or (C,M), (H,M), at the same time. (Incompatible observables.) 3) (For simplicity) the observables have a discrete dichotomic spectrum (possible values when measured): H {left-handed, right-handed} C {black, white} M {natural, synthetic} 4) When the gloves are in a definite state of handedness, the H-incompatible properties C and M are maximally scrambled, or 'blurry': Equally likely to be black or white; equally likely to be natural or synthetic. The gloves simply don't have those C, M properties when H is well defined! If they had, it's not difficult to prove that, for many series of repeated experiments on a given glove: Probability(left-handed & white)+P(black & synthetic) greater or equal than Probability(left-handed & synthetic) This is called Bell's inequality, and it's just a consequence of the properties H, C, and M actually having a value. Quantum probabilities violate this inequality for certain choices of observables. But wait a minute. Didn't we say that properties H (handedness) and C (colour) are incompatible? How can I even make sense of Probability(left-handed & white)? I'm not supposed to be able to measure handedness and colour at the same time! (for the same glove). Yes, but the whole basis of this combined-probability setup is based on the assumption that when I measure, eg, H for one glove and the result is 'left-handed', I know with certainty that, were an experiment to be performed at the other glove's location, it would produce the result 'right-handed' with total certainty. And sure enough, it does, when I do so. So I'm counting 'left-handed' outputs for the other glove as 'right-handed' outputs for this glove. This is very important to keep in mind. So the gloves would have to be kinda schizoid. But the whole thing is local. In order to see that, let's go back to a pair of electrons. We take electrons from separate parts of the world, completely uncorrelated. We bring them together and have them interact. They reach a maximally entangled state called the singlet. This only happens because they've been proximal and interacting (local!!!). Now (and not before) they display perfect anti-correlation. If I perform my experiment on them when they're still next to each other, they display all the craziness that I've just described. Now the state decays (splits apart). I perform the same sequence of measurements. The perfect anti-correlation is still there. It hasn't changed. So it didn't come from me doing anything on one of the electrons and the other 'sensing' what I did. It came from the initial interaction that produced the anti-correlations. Murray Gell-Mann was very frustrated that people, decades after Bell, Clauser, Shimony, and all that saga, still called this 'non-locality'. Just as an indirect evidence of how much confusion this term 'non-local' has caused in physics, here's a quotation: (taken from a scientific forum.) Ooooooo-kay.

Yes. Methane really is the killer. There are vast amounts of it and release seems potentially very fast in geological terms.

Oh, it's... nothing.

Agreed. And I'm pretty peevish myself.

Exactly what I was thinking, besides the volume thing.

If you know your neighbour's address, there's knowledge. Whether you decide to send them a love letter or a card bomb is up to you. Atomic energy destroyed life in 1945. It created tension between superpowers. But it's been saving lives on a daily basis ever since, and allowed many other nice things.

I totally concur with @swansont that entropy can never decrease in closed systems, and the next best thing is a system that keeps it constant, which is what this system seems to be. I assume --and correct me if I'm wrong, Swansont-- that the moment you wanted to amplify the signal or involve any circuitry in any way, the constant-entropy condition would be lost. I suppose it would be like a phenomenally efficient chronometer, rather than your regular timepiece.

Certainly Australia's landscape is unique. Uluru is of such beauty... I know you like docos, as you say. I remember Australia's first Four Billion Years. One of the geographical features that most impressed me was the McDonnell Ranges. Because this mountain system formed so early, erosion has eaten away even the highest mountains. At some point it looks like the skeleton of a gigantic beast. It's one of the most strangely wonderful geological features I've ever seen.

People uniting for a good cause is devoutly to be wished... sometimes. For a good cause. Your example is a good cause, as the goal is to thwart violence. But it's got me thinking. The Khmer Rouge were strongly united, when you think about it. It seems to me unison per se is not necessarily good. I think we've missed that possibility in our discussion. So, when is unison a good thing?

An electron doesn't change spin because the other has changed spin. There's no such thing as the electron changing its spin. It's more like the electron potentially being able to produce either + or - as a result of the measurement. Pick one projection of spin; say z-projection for electron (1). Now measure its value. It can give either +1/2 or -1/2. If it gives +1/2, and you measure the same projection of spin on the other, you know with absolute certainty it will produce -1/2. And vice versa. But you can't chose electron (1) to have any projection you want. This is key. If you could, you would be able to code a word in binary; say X=00101011010111 and have a person placed where electron (2) is, read the message and write down 11010100101000 (the opposite word). If you could do that, you would be able to send the word X. But you can't. You can only send random words, but those are not messages. Also, the correlations are initial. When you prepare a singlet state \( \left|+\right\rangle \left|-\right\rangle -\left|-\right\rangle \left|+\right\rangle \), all the correlations are initial. All the correlations are already there from the beginning. So nothing is sent instantly.

When you think about it, that could be anything.

I know. I wasn't going for a complete list. Pity he had to go to Russia to show his talent, as there was no academic position for him in Basel. He did some sick things with infinite power series. Please, try to use the quote function; it's easier to guess when you're addressing me. By the way, nobody mentioned tourism, banking, cheese or chocolate. My whole point is that trying to shoehorn a country like the US into the pot of cliches that you just did is about as silly and misguided as trying to shoehorn Switzerland into a similar list of Swiss cliches. Do we understand each other now?

Ah, yes. I remember about this one. Nice.

Not exactly. That's proof that Harry Lime didn't know about the Bernoulli family of mathematicians --and many other things like: Velcro The Swiss army knife Muesli ... https://www.thelocal.ch/20180822/what-a-trip-eight-great-swiss-inventions/ Maybe Harry Lime didn't appreciate mathematics, or never had a use for Velcro.

There you are. Music is another thing that unites people. I wasn't familiar with the Wreck of the Edmund Fitzgerald song. I like music with a story. When a tune lives on for generations there's always an important reason behind. Music has the potential to unite people from different centuries. What about that? Ditto.

I would like to take the opportunity to welcome you and @Peterkin to the forums. Both of you are very welcome 'acquisitions'. This is one of those topics in which I don't have a very strong opinion, but yes. Focus on the show-business part without any emphasis on sport for everyone, is kind of the obvious 'dark side' of sports. In a manner of speaking, it's about praising Titmus for her feat, while saving Russell Crowe from heart disease. And I love Australia, by the way. I have Waltzing Matilda committed to memory.

Interesting related point in interesting article: https://www.theguardian.com/commentisfree/2021/jul/24/tokyo-olympic-sport-displacing-athletes David Goldblatt IOW: I'd rather see more people cycling to work than eating cheetos in front of the TV while they watch the Tour de France.

I do. You look young & rugged, @J.C.MacSwell looks young & smart, and @beecee looks ageless & 'iconic'. I can't say I didn't expect Weinberg's passing one of these days, but it makes me feel older suddenly anyway.

Pity even.

Read all the answers, because they're very helpful. Make a drawing with @TheVat's hints. The June-December clue gives you a baseline. Remember your trigonometry.

Awesome book. Totally compliant with Einstein's alleged* motto 'as simple as possible, but not any simpler'. The Making of... might be worth checking out. *https://www.nature.com/articles/d41586-018-05004-4

Pitty. You have never disappointed. 👍

Hyperbolic functions. It's done in relativity all the time. Whistle if you need more help. Clues: Rescale x and y; then assign hyperbolic cosine (cosh) and sine (sinh). z goes along for the ride.

He was. He didn't have the aura of genius that others have accrued perhaps, but nudged physics into common sense many times.

https://www.washingtonpost.com/local/obituaries/steven-weinberg-nobel-winning-physicist-who-united-principal-forces-of-nature-dies-at-88/2021/07/26/75d8d24a-ee31-11eb-bf80-e3877d9c5f06_story.html Nobel-Prize-winning Steven Weinberg dies at 88. One of the makers of the standard model. His influence in the world of physics in the second half of the 20th century has been only comparable to that of giants as Feynman, Gell-Mann, and 't Hooft. His books Dreams of a Final Theory and The First Three Minutes are a must-read for anybody willing to understand physics and how physicists think. He was notorious for his view of a universe without a purpose. May he rest in peace.