exchemist

Indeed, QM interactions are inherently probablistic rather than exact no/no go processes. So the probability of interaction goes up progressively as the match gets more exact. I think uncertainty broadening is also still present for a single atom, if the excited state has a significant spontaneous emission probability, which for electronic transitions it will do, if I recall correctly that it depends on the cube of frequency. But I’m rusty on this and away from my books.

Probably, but you can still tackle it in manageable chunks by learning selectively those bits that interest you. For me spectroscopy was one of them, after a hairy first term at university reading and having stiff tutorials based on Gerhard Herzberg's little green book, which did me a lot of good.😀 Keeping asking questions: they are not daft.

No, spectral lines have finite width for a variety of perfectly good reasons. (Finite line width means there is a range of absorbing or emitting frequencies of course.) These include the Doppler effect, from motion of the emitters relative to absorbers, and uncertainty broadening, due to finite lifetime of the excited state leading to uncertainty in its energy, by Heisenberg's Uncertainty Relations. In gases, this can be a function of pressure, cf. "pressure broadening", since collisions may shorten lifetimes of excited states and also alter their energy, due to transient proximity of second atoms, thereby disturbing the potential experienced by the electrons. And for matter in condensed states, atomic lines tend to get broadened into bands anyway, due to the overlay of vibrational and/or rotational fine structure. If you read up a bit about spectroscopy, there is quite a bit to it besides simple line emission and absorption.

If the soil is poor I should think a solution providing missing important elements might be appropriate. Fertilisers normally focus on N, P and K, in various ratios. There are commercial liquid fertilisers available. Anything that alters the pH is very risky, which rules out most of the things you have listed. Bear in mind plants make their own carbohydrate by photosynthesis, so it’s pointless adding starch or sugars to the soil.

I didn’t know this. Rather good. The reference to “Judenstrasse”, though fairly innocent in his time, has an eerie prescience. (I’ve just watched “Downfall”.) But he was wrong to say that dead nations don’t rise again, as it turned out. I’m reading, or rather re-reading, Martin Brasier’s “Darwin’s Lost World”, about Ediacaran and other Precambrian life. I’m enjoying it more second time round. Now that I have a son at St. Andrew’s, in the university mountaineering club, I feel I want to go to Loch Torridan with a geologist’s hammer and climb Quinaig.

Arf arf. To be fair I think all these techniques were already in existence by Bach's time, but he was the apotheosis of them all in combination. So much so that everyone wanted to go back to a simpler texture after he died and almost nobody played him for a century. There were even people of my grandparents' generation who referred to JSB as "Bach's father". I believe we have principally Mendelssohn to thank for bringing him back to the concert hall. When we were rehearsing the B Minor Mass, our director spent some time in one number on getting the tenors and altos to be aware of the interplay between their parts, so he got the accompanist to play just those two lines on the piano, for us to listen. We were mesmerised. I remember thinking people would pay good money to hear that played in a piano recital. And it was just 2 parts - and the inner parts at that! So the full 4 part harmony was pretty rich, dense stuff. One can see why people wanted a change. But Bach is an inexhaustible pleasure to sing. There's always something you hadn't spotted. He seems to write from the bass up, so the bass parts are always terrific and somehow very virile - provided you can do octave jumps easily and have three lungs. (Unlike Handel, he takes no prisoners where voices are concerned and you have to follow a line that could have been written for a string instrument or the keyboard.)

It's simply that velocity always has to be stated relative to something in order to have any meaning. 2 cars in adjoining lanes on a motorway may be travelling at 5mph relative to each other but at 75 and 80mph relative to a policeman by the side of a road with a speed camera, and at 20 and 25mph relative to a truck which it itself travelling at 55mph relative to said policeman. The problem is we unthinkingly assume "the ground" is our reference frame in daily speech, treating it a bit as if it were an absolute frame of reference, when in reality there is no such thing. (This should however be a bit more obvious in space.) So you can't say you have a spacecraft "travelling at 0.999% of c" without saying with respect to what. Hence I proposed a space station to provide a reference, so that these speeds have a meaning.

Yes Bach seems to be a great inflexion point in the evolution of Western music. All the pros play Bach, even rock musicians. I remember once talking to a Thai pianist, playing jazzy hotel stuff in a hotel bar in Bangkok. My colleague asked him what music he played for pleasure at home and he replied "Bach". I tried to persuade him to play some for me, as he was taking requests, but he said the hotel management wouldn't like it (!) and I could not convince him. I also recall once listening to an organ performance of the Art of Fugue in my room in Oxford, when a fellow chemist came in who was a jazz clarinettist (He had been a member of the Kent Youth Orchestra before coming up). One of the weirder fugues was playing and he couldn't make it what it was. He thought it sounded so edgy it must be some c.20th composer - Messiaen or something. He was amazed when I told him. But if you liked what I posted, this (opening chorus, 1st 7 mins) is another of my all time favourites as a choral singer, from Part V of the Christmas Oratorio (apologies if I've posted this one before at some point): You have to click the "watch on YouTube" link to see it. This is also in 3/4. My impression is Bach does not often use that time signature and when he does, he often thinks it's time for some gaiety. In the video you can actually see the musicians enjoying it. They are making eye contact with each other and smiling.

Just come across this Flashmob video from Lausanne, in the course of revising the bass line in my favourite chorus from Bach's St. John Passion: The cellist plays part of one of Bach's Cello Suites and ends on a (baroque pitch) G, from which the basses can get the C they need to start the fugue. The conductor pretends to be a waiter delivering beer to the next table, until the moment arrives. They sing it very well, especially given the acoustics of a busy restaurant. Pretty cool, I thought. This chorus is in 3/4, with real JSB swing, syncopation and drive. Fantastic music.

No, you've got it, that's the point. You obviously don't add the velocities, as you would in classical dynamics.

OK I give up.

You can only define a speed relative to some other object. So far the only objects you have mentioned are the two spacecraft. Is 99.999% of c measured relative to the other spacecraft or to something else? If the former, you have already stated the answer. If the latter you need to say what that something is. You could for example say each space craft approaches the same space station, from diametrically opposite directions, at 99.999% of c relative to the space station.

99.999% of c relative to what, though?

This looks like a ridiculous gimmick to me, designed to get silly people to waste their money while feeling somehow vaguely "green" as they do so. I'm tempted to suggest the "Y" in the brand name is a misprint. There's just no way having a thing like this bubbling away in a corner is going to give you measurably more oxygen, which in any case you don't need. As for the nebulous claim about capturing "pollutants", what pollutants are they talking about and what evidence is there that these algae will capture them?

OK I take your point. I had not looked into the sources they are relying on for the claim of low Mo in the pre-GOE oceans.

I've never heard this and it seems extraordinarily unlikely to be true. Can you cite any examples of this claim being made?

Well obviously life did not have to wait for nitrogenase before it could start. No one is making a claim of no fixed nitrogen, just that there was much much less and not enough to sustain a biosphere on anything like the scale of later epochs.

Hmm, I don't think I buy that explanation, for the simple reason that before the evolution of nitrogenase, life on Earth must have very sparse, constrained by........... the scarcity of fixed nitrogen. So the low Mo in the Archaean oceans can't be attributed to lifeforms scooping it all up. Life would have proliferated only after nitrogenase appeared. So for that hypothesis to work, one would expect to see a fall in Mo at a certain point. That would be dramatic evidence for the onset of nitrogenase-exploiting organisms, but it is not what they report. Mind you, it isn't clear to me exactly how they have deduced a low level of Mo in the Archaean oceans.

Sure. If you read the link, this is all gone into, but apparently there was very little Mo in the early oceans, hence the interesting question of how the first nitrogenase (or nitrogenase cofactor) was able to employ it. Reading more about all this, it seems that iron-sulphur complexes are widely prevalent in biochemistry, which is certainly suggestive of volcanic origins, though in the reducing environment pre-GOE, Fe(II) at least would apparently have been available in the oceans.

I admit I've slightly lost the plot on where we are these days on the various scenarios for abiogenesis. I had the idea thermal vents had gone out of fashion a bit for some reason, but I agree these heavy metal biochemistries suggest something like that. The use of sulphide sulphur is also a bit suggestive.

Yes, Loeb’s recent claims did indeed turn out to be a load of, well, spherules. 😆 Not surprising people start to wonder if he may have a personal agenda that is warping his judgement. Personally, I suspect Loeb has actually become a crackpot.

This has prompted me to revise the bonding scheme for transition metals with carbon monoxide: https://en.wikipedia.org/wiki/Metal_carbonyl This involves a dative σ-bond from the lone pair on C to the metal and a π back bond from occupied d orbitals on the metal to low-lying π* antibonding orbitals on CO. So donation of an electron pair in both directions, preserving neutrality overall. The effect of the involvement of the antibonding orbital is to weaken the C≡O bond (nominally triple in the free CO molecule) and strengthen the M-C bond. This I think gives a clue as to how such metal atoms can weaken the N≡N triple bond (preparatory to adding H atoms), N≡N being isoelectronic with C≡O. It starts to become clearer........ N.B. The need for an electron pair in a metal d-orbital to make the back-bond requires the metal to be in a low oxidation state.

I haven't seen any mention of Ni in the paper or the Wiki article on nitrogenases that I quickly read to try to understand more about them. But it is interesting I think to reflect on how many of these heavy metals play such critical roles in life. We often think in terms of H, C, N, O, S, and P, plus a handful of s-block cations, but actually a huge array of heavy elements gets pressed into service as well. Their multiple oxidation states and d orbitals turn out to be pretty important.

Yes I think there is a reference in the paper on the other thread about the means organisms use to keep oxygen away from the active centre. I can imagine that a metal site that can bind N2 might also bind O2 - even might prefer to do so - which would stop it working. (Reminiscent of how carbon monoxide blocks haemoglobin, though perhaps not an exact parallel.) In chemical terms it's really fascinating, since the N-N triple bond is so notoriously hard to break.

OK, I've now started a thread on the evolution of nitrogenase, in the Evolution section of Biology. I knew nothing about this at all until a few days ago. 😀