exchemist

Most people don't seem to think I'm dense: but I suppose it's all relative. With you I struggle because I don't understand why you seem so anxious about this issue. The links you provided seem to me to show only a very tentative, and possibly non-existent, association with cancer in humans under the conditions of use for this drug in practice, viz. short regimes of treatment lasting only a few days. Plenty of drugs have been associated with cancer. Here's a report of a meta-analysis of some of them: https://pubmed.ncbi.nlm.nih.gov/24310915/ I would agree it might be nice, if the time and resources were available, to conduct some long term follow-up, but it would need to be over decades, and require a very large sample (thousands) of people who like me were once prescribed this drug for a few days. But this would not be easy and it would have to be prioritised relative to other research projects. What I miss from you, perhaps because I'm so dense, is what makes you think the risk with metronidazole sticks out as a matter of urgent concern, compared to all the other drugs that have also been associated with cancer.

Is this a problem of terminology, perhaps? Mathematics is abstract, but I’m not sure it helps to question whether abstract concepts are “real” or not. Many, possibly most, of the concepts we use in thinking and communicating are abstract in some sense.

Most household chemical products are not a single substance but a preparation involving a mixture of different substances. On prolonged storage some of these may slowly interact with one another, with the air, or with the packaging (corrosion of metal, "panelling" of plastic, softening of cardboard etc). Even if this is not expected to happen, it may be hard for the manufacturer to be 100% sure without conducting very long term storage testing, which would be impractical to do before every product launch . This is why, for instance, when I worked in the lubricants industry, we generally had a nominal 5 yr shelf life for lubricating oils. Having said this, I've checked my shampoo and soap and there is no shelf life limit or expiry date stated. There is of course a batch number, but that is something different: a quality control measure so that, in the event of a problem being discovered, the batch concerned can be identified and possibly recalled.

My father had a bone scan using this, to check whether his (very slow-moving) prostate cancer was progressing. All rather absurd, as he was 90 at the time and showing no symptoms. I had to take him to the hospital and wait while they dosed him, left it to migrate into the bones and then tested him. But while I was waiting I was very intrigued to find Tc99m was used. I had not even realised excited states of radioisotopes were a thing - though of course it makes sense.

OK. I'm afraid the pop-sci version is all we got as chemists at university (e.g. in my copy of Cotton and Wliklnson's Inorganic Chemistry), since while we were familiar with the Schrödinger equation, the Klein-Gordon one would have been out of scope. I know just about enough to realise it's rather handwavy and unsatisfactory, but that's it.

Is that on the basis of still using Schrödinger's equation, in which case I suppose you must mean some correction to the Hamiltonian (?) , or would it be on the basis of the Klein-Gordon equation, as @Mordred suggests.

There are real physicists on the forum who are better qualified than I on this but I think so, yes. As I say, the Schrödinger equation almost always works for electrons in the atom and that does not consider relativistic effects, which would not be so if the electron were treated as moving at a significant fraction of c. To treat a case like gold in terms of the Schrödinger equation, my understanding is one has to resort to "relativistic mass" to account for the observed absorption in the blue part of the spectrum that makes gold appear yellow, i.e. the electrons behave as if they are heavier due to effectively travelling at relativistic - though undefined - "speeds". But this explanation is not very rigorous (modern physics does not use the concept of relativistic mass any more). I'm sure the real physicists would do the whole thing over using other mathematics. As for motion of quarks within the nucleus, that is out of my league.

You can in principle choose anything, of any size, and consider it either from the point of view of its own frame of reference or that of one of its components (if it is a composite entity) , depending on what you are trying to do. In the case of an atom, one would normally take the frame of reference of the nucleus as the reference frame of the atom, as that is quite pointlike for most purposes and happens to be where the centre of mass is - and the centre of any electric field, in the case of an ion. The electron is problematic, as it has neither defined position nor a defined path of motion.

In an atom, the nucleus does not move much relative to the reference frame of the molecule it is part of, and the electrons' wave-particle behaviour is modelled successfully in most cases by Schrödinger's equation which is non-relativistic. (There are exceptions with the electrons in some heavy elements with very high nuclear charge, for which relativistic treatment is needed. Famously, the colour of gold is accounted for by this.) So actually relativity does not come into biochemistry that much (unless you are a purist who demands that particle "spin" be treated ab initio rather than as a given feature.) Where do you get 0.7c from, for the electron? In an atom one can't really speak of the electron's velocity (Heisenberg etc), so that sounds a bit dodgy to me.

Good, so there's no burning issue, then and doctors can go on prescribing it for serious infections where there is no good alternative. I'm glad that's settled.

It increases it by 2/10ths of F-all, to judge by the studies you cite.

That’s not what I claimed. If it had been, it would have made no sense for me to go on and discuss the balance of risk.

What claim would that be?

OK so you start with a "being" (I assume this is a language issue and you mean just an entity of some kind) that has energy as one of its properties. But that means you don't start "from nothing", then.

Well you would be wrong, then. Energy is just a property of a system denoting, as @Mordred says, the ability to do work. You won't find anyone with competent physical science training who claims energy can exist on its own. That sort of thinking is Star Trek, not science. There are many quantities in science like this: momentum, temperature, entropy, electric charge..... Energy is just one of those. In fact, your (1) illustrates the problem immediately. You can't talk about "change" without saying what is changing. And then you give a formula including mass. Mass of what? None of this makes sense until you specify some physical system to which it can be applied.

It's not mass but momentum, p. For a photon, E=pc. The change of momentum when a photon is reflected at normal incidence will be 2p. A boat sail uses Bernoulli's principle, i.e. that of an aerofoil, so that is very different.

A review on metronidazole: an old warhorse in antimicrobial chemotherapy (2019) No, it's not insane and yes, you are missing something. Nobody takes metronidazole for more than about 2 weeks in a course of treatment. It tends to be used to treat serious protozoan or bacterial infections that would otherwise be very debilitating or ultimately lethal, and then stopped. Nobody takes this stuff prophylactically. I've used it twice, in both cases to treat giardiasis I picked up on travels in the Far East. One was a 3 day course and the other 7 days. There is no drug on Earth that has no risks attached to it. The evidence for metronidazole being carcinogenic in practice is very weak, whereas its benefits are great. Taking it out of the medical arsenal would certainly result in more deaths, and would thus be counterproductive.

Your explanation, of the way skin grows from the bottom, accounts for objects embedded in the skin being expelled. But what about objects that are further inside the body? Can they also work their way out and if so how does occur?

The first problem with this is that energy is just a property of a system, not a free-standing entity in its own right. So starting with energy immediately begs the question “energy of what?”. In other words, it solves nothing, since you must first postulate some system, before you can speak of energy.

In fact this discussion reminds me that Schrodinger’s “wave” equation in its time-dependent form is actually a diffusion equation. The time-independent form however is a standing wave equation, I understand, hence the way it is often named. But I expect this is straying a long way from the OP question.

That’s very interesting. I was not aware of these. I actually think the Briggs-Rauscher reaction may be an even better example as that one does seem to exhibit regular, rather than chaotic, periodicity: https://en.wikipedia.org/wiki/Briggs–Rauscher_reaction However these processes are not in fact examples of diffusion, but of chemical reactions, in which diffusion inevitably plays a part. I struggle to believe there are any examples of purely diffusive processes that exhibit periodicity.

What real life scenario would such periodic behaviour correspond to? Or is this just an abstract artifact of the maths that has no real life application?

Diffusion will continue so long as a concentration gradient remains. So it doesn’t generally stop after a definite time interval. It will gradually slow down, asymptotically, as equilibrium concentration throughout is approached. The concept of the diffusion coefficient is that there is indeed a constant, for given substances and a given concentration gradient, at a given temperature.

You can’t express a distance , which has dimensions of L , in units of 1/T. A light second still has dimensions of distance. The speed of light has dimensions L/T. So a light second, c x t, has dimensions L/T x T = L, i.e. distance. There is no cycle of time in a diffusion process. It is not a periodic phenomenon.

Thanks.