sethoflagos

A good dinosaur fossil can be a very valuable commercial property. Plus palaeostratigraphy (the dating of rock samples by eg their fossil assemblage) is big business in mineral extraction etc. Maybe it's graptolites and conodonts rather than dinosaurs in that case, but the economy still needs a good reserve of trained paleontologists to identify them.

That's actually quite mindblowing. Thanks!

You really have to look at these interactions holistically don't you. The photon momentum is relatively tiny, but it still must result in a small but quantifiable shift in the kinetic energy of the absorbing molecule which may be +ve or -ve depending on frame of reference. This in turn also impacts the relative values of initial photon energy and electron orbital shift energy. If this effect can be accounted for in doppler broadening, then at least my degrees of freedom issue may go away. I don't think you can use the word 'generally' when your justification is based on the specific case of a boolean relationship. Applying this reasoning to a continuous variable like photon frequency seems too big a jump for me.

Good point, however that doesn't appear to challenge the 1st Law in and of itself. Simple absorption is a little different. Okay, an atom can absorb an incoming photon of say 1MHz above or below its standard excitation frequency, but it I can't see it 'remembering' that it has done so. When the excited electron drops down to ground state, I'm assuming that it too could be say +/- 1MHz away from standard with the same probability as the absorption case and for the same reason - Heisenberg. But this leaves us with small accounting errors in both the energy and momentum budgets which even if they average out to zero in the long run introduce the same sort of fuzziness as raised in my 'How Sacrosanct is Conservation of Momentum in QM' thread. I wondered if the discrepancies could be dissipated thermally, but that runs into a degrees of freedom issue. One discrepancy can only balance one conserved quantity I think.

Of course. Blasted autocorrect. Aha! So it's bounded by the uncertainty principle. That makes sense. Thank you!

QM calculations these days are so precise, at least for the simpler species, that electron orbital transition energy levels can be calculated with great precision. This in turn defines the (minimum?) frequency of the energising photon with similar precision. The probability of receiving an energising photon of exactly the required minimum energy seems to me to approximate to zero, and yet the excitation definitely happens. What happens to the mismatch between orbital energy change and photon energy?

And not just any old doctor - a paediatrician no less: a professional specialising in child development.

Those addressed subsequently by @MigL.

Am I right in reading 'off shelf' as 'off shell' ie not a solution of the mass/energy equivalence eqn?

Reasoning in the absence of supporting evidence is just wishful thinking.

Not explicitly.

Exactly. Can we now develop @exchemist's point and address whether the random quantum fluctuations of the vacuum state can perturb the momentum of a gas molecule?

I guess I can take a couple of negs here and there, but it would be nice to know the reason.

That's actually quite a big deal.

And thus the language of our noble ancestors lies dying in the no man's land of post-modernist chutzpah

Presumably this is consistent with a classical picture of momentum exchange in the interaction of a gas molecule and a photon. How about interaction with a random quantum fluctuation? Can the gas molecule 'leak' momentum into displacement of such 'virtual' particles? I'm really asking about phenomena distinct from the measurement problem. I can buy some fundamental uncertainty in the actual path taken. More, I'm trying to narrow it down from some kind of random walk to a spectrum of possible paths all of which are straight lines.

I've seen statements such as this kicking around for decades and always been troubled by a niggling doubt. I imagine that the phenomenon can be explained by normal electron scattering and tunnelling without invoking any deviation to conservation of momentum. But is that all there is to it? Is the momentum vector of a particle subject to variability due to, say, random quantum fluctuation in local field strength? This idea seems somewhat belied by the near point image my eyes can make of a distant star, but even so... My primary contextual interest is in the absolute deterministic nature of gas molecule trajectories between collisions - ie how 'straight' are their paths through free space.

Not here. Within the circles I move in, beer is the social brew of choice. Only to geordies who ask daft questions. More the chutzpah of those who believe their taste in tea is somehow superior to anybody else's. There is no universal 'perfect cuppa'. Just an individual's preference. The similarity of sugar cellars to salt cellars in many establishments has caused most of us to have conducted unplanned experiments with salty tea.

It does. Been recycling tepid tea that way for years.

It'd need a minute in the microwave otherwise you may as well be drinking bathwater.

Bless their little cotton socks! What do they miss out? The preheating the teapot bit, or the tea cosy to keep the heat in?

There's likely as much arsenic in the water you stew it in. See https://pubmed.ncbi.nlm.nih.gov/25526572/

Personally I take my tea strong, black and well stewed. The more astringent the better within reason. But it seems there are some folks who just can't get enough blandness into their lives. Salting tea sounds to me as doolally as decaf, but whatever floats your ⛵.

Do you imagine that 'billions' is an appropriate counting unit for, say, all the different possible permutations of the up to 40+ billion base pair sequences of DNA? (Try running 4^4^10 through your calculator to get an idea)

Ditto @Bufofrog. Could be something as simple as an unsuitable mattress. At least, that's my experience.