KJW

Why do you think that doing maths is some magical thing? Did it ever occur to you that the underlying basis of the laws of physics may be mathematical?

With these two statements, you are begging the question.

Is this anything like a Turing machine being a mathematical idealisation of an actual computer?

This is a myth that MythBusters busted. They found that flour beetles and fruit flies can withstand higher amounts of cobalt-60 radiation than cockroaches, with the flour beetles able to survive the most lethal dose of radiation that was used.

Considering the chemotaxis, adherence, and internalization steps above, it is my understanding that foreign bodies not directly recognised by macrophages can be tagged by opsonins so that they become recognised by macrophages. Thus, it would appear that mirror bacteria can be killed by the immune system even if the process is less efficient.

What's the largest protein molecule that currently can be synthesised by purely chemical means? Does the technology exist to synthesise proteins in vitro from mRNA using purified ribosomes and the tRNAs? I'm aware that attaching an alternative amino acid to a tRNA molecule will place that alternative amino acid into the growing polypeptide, so that one could synthesise mirror proteins from the mirror amino acids alone (using natural mRNA, ribosomes, and tRNAs).

It's my understanding that the innate immune system is designed to detect foreign bodies. It seems unlikely to me that it would limit itself to the "correct enantiomer" It's my understanding that a particularly important way that the immune system kills pathogens is to use "bleach" on them, and "bleach" does not stereochemically discriminate. It seems to me that this is based on the incorrect assumption that an antibody consisting of natural enantiomer components will only bind to antigens consisting of natural enantiomer components. For example, while it is generally true that a receptor that binds to a particular enantiomer of a given compound will not bind to the opposite enantiomer of that compound, it doesn't mean that there isn't a different receptor, composed of the same chirality building blocks, that can bind to that opposite enantiomer. Thus, even when presented with a mirror antigen, the immune system ought to be able to find an antibody that binds to the antigen.

Although it doesn't fully answer your question, this may help: https://en.wikipedia.org/wiki/Perkin_rearrangement

Trump says the drones should be shot down, not point a laser at them. A bullet probably wouldn't reach a plane. 🤪

The way I see it, Wikipedia (or other encyclopedia) articles, textbooks, and research papers are distinct sources of information in terms of their scope and purpose. They are not interchangeable. For example, if you want to learn about a broad subject, then you should study a textbook, not a Wikipedia (or other encyclopedia) article, and not a research paper. It is not about the quality of the information, as each of the above sources can be considered high quality sources of scientific information. Nor can it really be said that it is about the assumed level of knowledge of the reader. It is more subtle than that. A textbook comprehensively covers a subject in way that is specifically designed to teach a student about the subject and may include worked problems or problems to be solved. By contrast, research papers are about specific research topics, covering why the research is being done and the various experimental procedures and results of the research. The target audience may be interested in the particular research topic, or they may simply be interested in some particular aspect of the experimental procedure. For example, a chemist might only be interested in the procedure for synthesising a specific compound used in the research without any interest in the research topic itself. I think a scientist would consider themselves lucky if the entirety of their research papers makes it to a paragraph of a textbook. A Wikipedia (or other encyclopedia) article is in some sense intermediate between a textbook and a research paper, but not really a substitute for either. For specific topics, a Wikipedia article will provide more detail than a textbook but isn't organised in a way that facilitates learning for students. On the other hand, a Wikipedia article does not provide sufficient detail required by a researcher. For example, although Wikipedia does provide synthesis pathways for specific compounds, it doesn't provide specific procedures for each of the steps. Nor does it cover as many compounds as the chemical literature, focusing more on compounds of general interest rather than any compound that has ever been made (and published).

The cosine of any fraction of π is the real part of a root of unity and is called a trigonometric number.

Entanglement is not without communication and the item communicated is called ‘information.’ The no-communication theorem says that entanglement can't be used to communicate information. Presumably, if entangled particles did communicate their states, then this could be exploited to provide communication between people, in violation of the no-communication theorem. But suppose entangled particles do somehow communicate their states. How could this be demonstrated without violating the no-communication theorem? And if it can't be demonstrated, then what value does the idea that entangled particles communicate their states even have? If this is being considered from a metaphysical perspective, then you need to consider why it is necessary for the correlation due to entanglement to be the result of communication, rather than accept that correlation can occur without communication. My understanding is that the violation of Bell’s inequality and the EPR effect demonstrated a violation of normal realism. Entanglement was a newly observed phenomenon not a “new property” in Occam’s sense as something made up ad hoc to explain the results. Entanglement is observed but the non-local interaction is not observed, and it is the non-local interaction that runs afoul of Occam's razor.

This indicates a misunderstanding of not only how particles become entangled, but also why particles become entangled.

One thing not already mentioned is the metabolism of the drug. For example, drugs are often metabolised by oxidation, and sometimes an oxidation product is toxic, a process called "toxication". One way pharmaceutical companies combat this problem is to make the drugs resistant to oxidation, typically by adding fluorine atoms to the molecule.

Yes, this is all rather standard about quantum entanglement. It's not really that mysterious once one grasps the mathematics of quantum mechanics. This seems to be about the Transactional Interpretation of quantum mechanics rather than about quantum entanglement. Also, I was asking about "quantum swapping", which you did not address. This view is somewhat simplistic and somewhat classical. It doesn't take into account the complexity of quantum reality compared to classical reality. For example, an arbitrary two-particle quantum state is almost certainly entangled. That is, it is actually the non-entangled two-particle quantum states that are rather special. These non-entangled two-particle states are either classical two-particle states (correlation but no superposition), or they are completely independent quantum two-particle states (superposition but no correlation). To consider entanglement to be an interaction is to be unable to see past the non-entangled two-particle states, particularly the latter, where a remotely distant pair of probabilistic states are expected to behave independently in terms of their statistical outcomes, where correlation is regarded as impossible in the absence of some form of communication between the single-particle states. The notion that entanglement is a non-local interaction in violation of causality runs afoul of Occam's razor in that it requires the invocation of a new property for particles, the property of interacting non-locally contrary to causality with other particular particles. Entanglement between two particles does not require the two particles to be of the same type or of any particular type. It does not require the same level of correlation between single-particle states. It can be transferred to other particles that have never interacted. Subsequent interaction with other particles can alter the original entanglement. So how does a particle decide which possibly remotely distant particle it is entangled with and the level of that entanglement? It seems to me like an enormous burden to impose upon a particle. And what is the precise nature of the interaction? Bear in mind that entanglement is fully described mathematically under standard quantum mechanics without invoking a non-local causality violating interaction, or indeed any interaction at all.

I'm not sure what you're asking. Dirac delta function position and momentum states are the basis states of the position and momentum domains, respectively. However, I am restricting the discussion to Minkowskian spacetime. Yes. The reason I invoked the HUP is because it demands the existence of superposition. I wasn't suggesting that all superposition is a consequence of the HUP.

In principle, does "uncertainty" even exist? I mean, mathematically, any wavefunction can be expressed as a superposition of Dirac delta "functions" (distributions). Just because it's not possible in practice to exactly measure a particle's position or momentum doesn't mean that exact positions or momenta don't exist theoretically.

How is a|1> + b|2> a consequence of the HUP? The Heisenberg uncertainty principle implies that if a particle is a definite position state, then it is a superposition of definite momentum states. Similarly, if a particle is a definite momentum state, then it is a superposition of definite position states. And in between these two extremes, a particle must be both a superposition of definite position states and a superposition of definite momentum states. A particle cannot be simultaneously a definite position state and a definite momentum state. Thus, as a consequence of the Heisenberg uncertainty principle, superpositions are unavoidable.

Superposition is a fundamental aspect of quantum mechanics. Superposition is a necessary consequence of the Heisenberg uncertainty principle, which is a fundamental property of conjugate variables. I think you need to elaborate on the notion of "quantum swapping". In particular, you need to establish whether such phenomena are purely the result of quantum entanglement rather than a physical interaction that satisfies causality. I don't think the no-communication theorem is saying that only classical communication is disallowed. The proof, which is based on standard quantum mechanics, is saying that there is no action that Alice can take that would be detectable by Bob. This seems to go beyond mere communication. No one mentioned a "classical point of view". Entanglement can't be explained classically because it requires quantum superposition, a non-classical phenomenon. The correlation itself is classical in the same way that two billiard balls become correlated after collision. But if the two billiard balls are replaced with two particles whose trajectories are in quantum superposition, then any collision between the particles will be a quantum superposition of each of the collisions of each of the trajectories in quantum superposition, and the two particles will be entangled after the collision, unlike the two billiard balls. I used the word "logical" to distinguish the connection between entangled particles from a physical connection. "Non-local" doesn't say what I wanted to say and tends to suggest a physical interaction that violates causality, contrary to the nature of entanglement.

What @rathorebc is referring to is the notion that alloy compositions have discrete value percentages of the individual components, similar to the high-resolution mass example I posted earlier, where the molecular formula can be obtained because the number of atoms of each type in the molecule is discrete (an integer). But to be successful, the density measurements of the alloy and of the individual components of the alloy needs to be very accurate.

Entanglement is the quantum superposition of correlated multi-particle states. The correlation already exists within the superposition so that when a particle is measured and the superposition "collapses", the state of the other particles are determined as well, without requiring those other particles to know anything about the measurement of the first particle. Note that entanglement can't be used to communicate information (no-communication theorem). I think entanglement is best understood as a logical connection between particles rather than a physical connection. Thus, multi-particle states can exist in quantum superposition without restriction by notions of causality.

How is this a fundamental improvement compared to requiring that representatives and the people voting for them be (for example) landowners, men, white, etc?

A dimensional analysis of your formula says "no".

I acknowledge that there is little time left before Trump takes office, and that I have seen no indication of a follow-up to the letter from Stephen Spoonamore to Kamala Harris. And it seems unlikely to me that a follow-up could be done on the quiet.

What's "idrolization"? I've not come across that term before. You didn't say what the source of the vitamins you are extracting is. Perhaps the water improves the interaction of the solvent with the source material.