exchemist

It means the particle behaves like a tiny bar magnet, with a North and South pole. Like a magnetised compass needle, it will tend to line up with any external magnetic field. Conversely, if you can get a lot of these particles, in practice electrons, to line up in a block of material, that will make the bulk material magnetic - which is what happens in a permanent magnet. You have a lot of atoms each with an electron that can be made to line up in the same direction, adding their effects together to make a stronger field. So permanent magnets are magnetic because - or mostly because - of the “spin” of electrons.

Hmm, whether this intrinsic angular momentum also represents energy or not is a bit of a moot point, since you can't stop the spin, i.e. you could never get any such energy out of the particle. These particles certainly do have energy associated with their mass, according to E=mc², but I don't think it's a good idea to think they have a kind of kinetic energy due to their "spin". Anyway, for GCSE, all you need to know is you can put a maximum of 2 electrons into each atomic orbital, which is allowed so long as one has spin "up" and the other has spin "down".

OK. Like a lot of things in quantum theory this is not like the behaviour we are used to at the scale of everyday life, so it may take a few iterations to understand it.

Yup, h is Planck's constant. The symbol h with a line across, known as "h bar", is h/2π. This quantity appears in a lot of places in QM maths, so it was thought worth giving it its own symbol to simplify algebraic expressions. When it comes to elementary particles they have angular momentum, just as a spinning top or wheel has. This is often referred to as "spin", but it's not really like a little ball spinning on its axis. For one thing this "spin" is intrinsic to the particle. An electron has a spin of 1/2 spin units*, always. You can't stop it spinning or make it spin faster. The spin value it has is fundamental to its identity as an electron, just as much as its -ve electric charge is, or its mass. This so-called spin is a way of saying they have a set amount of angular momentum. That is important because angular momentum is a conserved property, like linear momentum or energy. So in particle interactions, one rule is the total angular momentum of the system, before and after, has to be the same. That has certain consequences in physics. However, because these elementary particles don't behave like little balls, one can't talk of a speed of rotation or anything like that. They have have a set amount of intrinsic angular momentum and that's that. * I had better add a bit here so I don't get my balls shot off by the real physicists on the forum - always a risk here😁. You don't need really to know this. "Spin units" is just my lazy shorthand for saying the spin quantum number, s, of electrons is 1/2. The actual magnitude of the angular momentum is given by the angular momentum formula √(s(s+1)). h/2π, which for s=1/2 gives you √3/2. h bar. However the projection of the angular momentum vector along any specified axis is a bit less, 1/2. h bar, basically because of the way Heisenberg's Uncertainty Principle works for angular momentum (There's always a bit of angular momentum left over, that points in an indeterminate direction and which can't be pinned down). So particles like electrons are known as "spin 1/2" particles. The formula you are asking about is the magnitude of this projection - which is what matters in practice, in the lab and so forth.

There is also, I suppose, a nice point as to whether in black body processes one is right to say the atoms do the emitting or absorbing. The black body “oscillators” are systems comprising collections of atoms and it is those systems that do it rather the individual component atoms. In your steel bar, absorbing an IR photon, no single atom absorbs it, surely? I imagine it will initially excite the conduction band electrons and this will get converted into a lattice vibration, won’t it?

Continuing the guitar theme, time for a bit more Bach: Prelude from 1st Cello Suite played on the guitar by the lovely and talented Julia Lange: What I like about this performance is that, unlike some guitar performers of this piece on YouTube (there are quite a few) she doesn't try to make it all about herself by messing about with the tempo and inserting dynamic contrasts all the time, as if it were a Romantic piece. It's Baroque. She allows Bach's pulse (always very strong) to carry it forward and lets his cascades of notes do the expressive work, with just a little inflexion here and there to stress key moments. Very classy interpretation, I thought. And she looks as if she in a sort of calm and peaceful ecstasy throughout, which is rather delightful.

Ah, so you refer to atoms in bulk rather than individually, then, radiating or absorbing as a black body. Fair enough.

Not sure I follow that last bit. Surely atoms do only gain or lose energy in discrete amounts, don’t they? But knowing you, you have some subtlety in mind: can you elucidate?

You (and Tetrode) are describing the emission of a photon by an atom and its subsequent absorption by another - obviously at a different location. That is not what entanglement is. To produce entanglement one needs a process that results in a pair (or more) of QM entities together, such that they are correlated: their quantum state can only be described for the combined system and not for the individual entities. You do not have that when an atom emits or absorbs a photon. You have misinterpreted what Tetrode was talking about. I think you have also misunderstood what the Cramer & Mead paper is about. It proposes a mechanism for wave function collapse in the course of an interaction. That has nothing specifically to do with entanglement either. It is completely general to all QM interactions, whether the participating entities are entangled or not. (By the way, it looks to me as if it assumes an interpretation of QM in which the wave function is a physical thing, rather than a description of information about the system. As such it would appear to be at odds with some other interpretations of QM, such as the Copenhagen or the Relational interpretations. But I don't profess to be expert on that subject.)

There is nothing about entanglement here. It sounds like an idea for how light might transfer energy as discrete quanta - something they were wrestling with at the time, after Einstein's work on the photo-electric effect.

But that makes no sense as an explanation. Tetrode didn't use the word "electron" in the passage you quoted. He said "atom". Why would the translator explain the possible meaning of a word Tetrode didn't use? (An atom is not an electrically charged particle, of course - not that electric charge has any bearing on entanglement.)

Your quote from Tetrode has nothing to do with entanglement. This was an early (1922) speculation about excited states of atoms, not electrons. (Don't try to tell us Tetrode did not understand the difference, as you did earlier.) The idea of entanglement only came into existence in 1935, a decade after the initial development of quantum mechanics, which really started in 1925 with Schrödinger's equation and Heisenberg's matrix mechanics. Your attempt to apply this quotation to entanglement looks both anachronistic and inappropriate.

I remember having to learn "une longue serviette éponge" at school in the 1960s, for a vocabulary test, which my parents thought hilariously pointless. It was only decades later, staying at a pretty rough little wayside hotel in Normandy with my French wife, that I realised the significance of this phrase for Englishmen travelling in France. The bathroom in this place provided towels that were like dishcloths: thin, small things that got wet quickly and didn't really allow you to dry yourself. My wife told me this was what towels were like in France back in the 60s.

If you have taken in what @Markus Hanke was saying, shouldn’t you be asking yourself what an angle of infinity could possibly mean?

Are you sure? I thought arctanh (1) was ∞.

I've tracked down the alleged quotation from Tesla now, on Wikiquote: "Disputed If you want to find the secrets of the universe, think in terms of energy, frequency and vibration. My brain is only a receiver, in the Universe there is a core from which we obtain knowledge, strength and inspiration. I have not penetrated into the secrets of this core, but I know that it exists. First attribution is to Ralph Bergstresser who claims to have heard this from Tesla in a conversation "following an experience with the Maharaja's son"[1]." So it seems the supposed quote is just hearsay. And the supposed Einstein one is indeed most definitely bullshit, just as I thought: https://quoteinvestigator.com/2012/05/16/everything-energy/. Furthermore, again as I suspected, it comes from some New Agey ballocks that some charlatan* has tried to retrofit to Einstein. * Appropriately called Darryl Anka. (One feels there is a leading W missing.😆)

Could be. But it was my personal experience of vignette ads, on this and other sites, (plus the terrible, jumping ads on the Independent newspaper site) that finally convinced me to install an ad blocker. So vignette ads have ended up greatly decreasing the number of ads I see. I will be just one of millions, forced by the increasing intrusiveness of ads into taking countermeasures. So it is indeed a vicious circle.

I'm with you on this. I do feel the only way to put a stop to this march of enshittification is if websites start resisting the more intrusive type of advertising gimmick, when it really impacts the use of the site. I found this from Google, https://support.google.com/adsense/answer/13992041?hl=en , which suggests the frequency - and indeed whether or not these sodding vignette things are enabled at all - may be at the website owner's discretion. This link : https://www.webnots.com/how-to-increase-adsense-revenue-with-vignette-ads/ also suggests it is up to the website what ad formats it enables. If that is true, then I think we should definitely suggest to the owner of this site that they militate against use of the website and will diminish site traffic in the long run. I note that earlier this year we did ask for vignette ads to be stopped - and they were stopped, for a while. But then, mysteriously, they came back. It starts to look as if the site owners have decided to inflict them on users after all, in spite of our request to get rid of them. I also found this rather amusing, pope-discovered-to-be-Catholic-shock-horror piece from an ad agency on the topic: https://www.adsbyana.com/blog/ad-fatigue-vs-ad-blockers-are-consumers-fighting-back. Basically, for all their mealy-mouthed platitudes about user "engagement" and tailoring to supposed "preferences" (which I suppose means avoiding triggering the most violent of users' Pavlovian avoidance reflexes), users hate ads and will do everything in their power to shut them out. What is interesting is they seem to think the upsurge in use of adblockers is partly what has led to the increase in frequency and deployment of more intrusive and disruptive ways to present ads, as the advertisers desperately try to keep up the ad-eyeball interaction count, in spite of users' best efforts to stop them. The article tries - to my mind somewhat unconvincingly - to suggest ways to break out of this vicious circle.

The first quote is total nonsense, so it can't possibly have been said by Einstein. It sounds much more like the words of some charlatan like Deepak Chopra. Tesla was a bit off his rocker towards the end so (which is why he a favourite of cranks) so there's no telling what he might have said. From your previous posts, you seem to have a thing about "energy" and "vibration", I notice. This is usually a sign of a crank, peddling pseudoscience. I'd stop that, if I were you. Energy is a property of a physical system. It is not "stuff" that exists on its own, any more than momentum, mass or electric charge is. Vibration, or its quantum-mechanical counterpart, is certainly present in a lot of systems in nature, but by no means in all.

It has already been pointed out that no action is involved, and no energy exchange.

Surely what this sub-thread is about is a (dubious) assertion about communication, or action, taking place between entangled entities that are spatially separated. But a pair of electrons sharing a molecular orbital are not spatially separated, so there is no observational implication from them being entangled.

Nope, it still seems rather nonsensical, to be honest. You are dealing with neither the point I made, about life being impossible at the high temperatures of the early universe, nor the other point about life merely releasing low temperature waste heat, converted from the stored chemical energy in nutrients and from high temperature energy absorbed from the radiation from the sun - and similar stars in other solar systems. There is no reason to think that life contributes greatly to the rundown of energy , i.e. the increase in entropy, of the universe, when there are so many other large-scale inorganic processes that already do that. So I can’t at the moment see how your idea can get off the ground.

But none of this is relevant to a pair of electrons in the same orbital, which is what we were talking about. For a start they have the same energy. And swapping states would in such a case imply swapping spin orientations, since that is the only difference between their states. As this, if it were to occur, would have no observable consequences, it seems to me to be an example of what Pauli described, in another context, as an "uncashable cheque", i.e. a notion that can be disregarded on the principle of Ockham's Razor. P.S. Tetrode is someone I've only previously come across from a thing I dimly recall from Stat. TD, called the Sackur-Tetrode equation. The only reason I remember the name at all is because I thought at the time what a curse it must have been to be named after a thermionic valve. 😁

I can’t make sense of this, I’m afraid.

They can't share the same quantum state because they are fermions (Pauli Exclusion Principle). They have 3 quantum numbers that are the same, which are the 3 that define what we call in chemistry an orbital. But the 4th is the spin orientation quantum number and that is opposite sign for the two. So they don't have the same wave function in full, if you include spin. I've never heard of them swapping states. Where do you get that from?