Wikipedia:Reference desk/Archives/Science/2017 June 6

= June 6 =

Do fresh mozzerella, paneer, and cottage cheese all really use the same process?
Two years ago, I read a recipe online about paneer. It simply called for whole milk, citric acid, and salt. I figured the salt was optional, so I just blended the milk with the lemon juice together and heated the mixture on the stove. The milk's protein bubbled and overflowed, so I quickly removed the pot from the stove and turned off the stove. Then, I tried to drain the milk through a cloth, cooled it so I wouldn't burn myself, and squeezed the cloth into a round ball. I tried not to squeeze too hard, because the cheese might go through the cloth. I sampled the cheese; it really tasted like saltless cheese, but I decided that I would not do the process again because it seemed like a waste of resources! I didn't know what I would do with the whey. If I had made soymilk from soybeans, then the soy pulp would be used to make okara scallion pancakes. Then, I found out the process of making mozzarella cheese. It seems to me that the only difference between paneer and mozzarella is that paneer doesn't use rennet while mozzarella uses rennet? Traditionally, cheese-making was done in the stomach of a ruminant. But does that mean raw stomach or cooked stomach? How does one make sure that the stomach's contents do not cross-contaminate the cheese? I also read a recipe for cottage cheese. The manufacture of cottage cheese is like paneer, but heavy cream is added. So, the only difference between paneer and cottage cheese is that paneer is the actual cheese, while cottage cheese is paneer, plus heavy cream? How do I make heavy cream from a ruminant's milk? 50.4.236.254 (talk) 03:06, 6 June 2017 (UTC)
 * They are all examples of fresh cheese, though they have their distinct differences. The difference between paneer and cottage cheese is the level of milk fat in the manufacturing process, paneer has less milk fat.  The sine qua non of mozzarella is the melting and stretching process.  The stringy texture of mozzerella comes from the way the cheese curd is heated and stretched (similar to salt water taffy.)  In simple terms, cheesemaking is cheesemaking: It involves curdling milk and then separating the solids from the liquids.  The differences in the end product comes from distinctions in the process: different milk products (different animals to produce the milk, or differing levels of milk fat)  curdling agents (lactic acid, citrus, rennet) and how the curd is treated (heating, stretching, culturing, aging).  You can even get a second cheese after the first is separated from the whey (see Riccotta) The basic overview is the same however.  -- Jayron 32 03:17, 6 June 2017 (UTC)
 * What is "low-fat cheese" or even "non-fat cheese"? How can cheese be non-fat? 50.4.236.254 (talk) 04:00, 6 June 2017 (UTC)
 * Cheese is coagulated milk protein. If you coagulate the proteins in skimmed milk you get cheese that has so little fat it can be labeled non-fat (your local food labeling laws may vary). Not all cheeses can be made non-fat; cottage cheese is usually low- or non-fat.  91.155.195.247 (talk) 09:58, 6 June 2017 (UTC)


 * How do I make heavy cream from a ruminant's milk? By skimming. See Heavy cream cream skimming. As for Paneer, it's far less expensive to make it at home than to buy it. They make it at restaurants in the same way. You won't squeese the cheese through your cheesecloth, I often press it with weights for a few hours to get a firmer texture. You can use the left over acidic whey in many ways, see here for examples and discussion. You can also dehydrate it  for storage and later use. As an aside, your questions are very interesting, and while many of us can help you find references, a good way to start is to look at your question, identify key words, then look at those Wikipedia articles, that would have gotten you to cream skimming in just a few clicks ;) SemanticMantis (talk) 16:15, 6 June 2017 (UTC)
 * We have articles on cheesemaking and whey. The article on whey points out its uses as a liquid in breadmaking, as a solid in nutritional supplements. Rmhermen (talk) 17:04, 6 June 2017 (UTC)

How fast do the inner electrons go in gold atoms, relativity
How much heavier do they get than electrons rest mass?64.134.238.111 (talk) 06:00, 6 June 2017 (UTC)


 * Electrons don't "go" anywhere. You may be thinking of the old "solar system" model, or Bohr model, of electrons, where atoms run around the nucleus in little circles.  This model was found to be incorrect and was replaced by the quantum mechanical model, where electrons exist in and around the nucleus in clouds of probability. 91.155.195.247 (talk) 09:54, 6 June 2017 (UTC)
 * To work this out you can use Moseley's law to get the energy of the inner electron. Then from electron mass and E=mev2 you can work out the velocity. See if this is near the speed of light, and if it is, use formulas in Mass in special relativity. Graeme Bartlett (talk) 11:02, 6 June 2017 (UTC)
 * It's not hard to find this worked out on line. Various sources arrive at the answer that the expected value for the electron speed in the Bohr model of hydrogen is about 2000 kilometers per second.  Pretty fast, but a very small fraction of the speed of light. Looie496 (talk) 13:37, 6 June 2017 (UTC)
 * If something's not hard, it's best to do it. I found a good online discussion at stackexchange.  They point out that "The state of an electron (or electrons) in the atoms isn't an eigenstate of the velocity (or speed) operator, so the speed isn't sharply determined."  I would take that to mean that since electrons are "rolling around in a well", getting closer or further from the positive charge of the nucleus, their speed would vary with the interconversion of kinetic energy and potential energy, though I may be missing something.  Because of the quantum nature of the electron, "average velocity" might be taken to mean something philosophically different than the average velocity of an orbiting planet, but that difference is subtle.  The stackexchange and Quora discussions I found both refer to the virial theorem, which is that on average the energy of orbiting bodies is evenly split between kinetic and potential energy.  Now our article doesn't explain well, but I'm going to assume that the virial theorem applies under relativistic circumstances also -- in which case we can still figure out the kinetic energy is half the total "ionization energy" of an inner gold electron, and might merely need to use the relativistic formula for kinetic energy (or, alternatively and equivalently, take relativistic mass into account in the non-relativistic formula).  Problem is, we still need that - while someone can calculate a priori, it seems like a difficult calculation.  The stackexchange forum has a calculation, but notice all the ~ signs and "order of magnitude" disclaimers: I want a number  The standard ionization energy can't be used because that's the very outermost electron that is the least energy to pull out.  We need an absorption spectrum, I think, with the very highest absorptions in the UV for gold, representing a series similar to the Lyman series as inner electrons are blasted to the fringes of the atom.  But I didn't find that yet... Wnt (talk) 14:46, 6 June 2017 (UTC)
 * The electron speeds in very light elements like H are of course relatively small; Au is much further down the periodic table and relativity becomes important there. We have an article on this, actually: Relativistic quantum chemistry. For the 1s electrons, you can approximate their velocity rather well for each element as Zc/137; this gives nearly Looie496's answer for hydrogen, and for gold it gives about 0.58c, enough that I would start taking relativity into account. (Mind you, in the superheavy region, this is not very accurate because the nucleus is not actually a point mass, but gold is not so heavy that this becomes a problem: we're only at period 6, not period 7 or 8, where it is not obvious that periodicity can withstand the assault, and indeed experiments are being planned to see if it can.) Double sharp (talk) 15:17, 6 June 2017 (UTC)
 * So do the electrons actually travel round their probability distribution?   D b f i r s   15:41, 6 June 2017 (UTC)
 * The correct answer is "mu" (in the Buddhist sense). The answer "actually traveling around" becomes somewhat problematic for electrons; the short answer is no, they don't move, but they do have momentum. and thus a velocity.  Which is confusing AF if you're trying to think about electrons as "classical" particles like little planets.  The slightly less sort answer is that treating an electron like a moving planet would violate the Larmor formula, which maintains that any accelerating electron charge sheds energy in the form of EM radiation.  Since an orbit is an acceleration, that means electrons in atoms should be broadcasting EM radiation all day long (and also losing energy and crashing into the nucleus).  So we know they don't do that.  The more correct view of an electron is to treat it as quantum mechanics does, and use the principles of wave particle duality.  Which is to say, it has some properties like a particle (such as angular momentum and spin) and has some properties like a wave (such as wave interference) but it is not a particle NOR a wave, it is an electron.  As David Mermin once said "shut up and calculate", which is to say stop worrying about what an electron is or what an electron does.  We have very accurate mathematical models that can describe the behavior of an electron, so use those and get answers.  Which brings us back to my first point: the answer "do electrons actually travel around in their probability distribution?" is more no than yes, but it is not really either no or yes, and it is best to unask that question so we can get down to answering the more interesting questions... -- Jayron 32 17:23, 6 June 2017 (UTC)
 * Hydrogen eigenstate n3 l2 m2.png) where the direction of the angular momentum is superposed/unknown.]] What you say is an accurate consensus of what people think who know exponentially more about QM than I do.  And yet .... my intuition still rebels.  I feel like saying "shut up and calculate" is exactly the wrong advice, like there is a way to make intuitive sense out of quantum entities.  At some fundamental level angular momentum or linear momentum in a region seems to come in Planck constant units, and we ought to be able to understand that momentum in terms of motion...  in the figure I show, for example, I feel like you can look at the complex eigenstate and see the two Planck units of momentum laid out around the axis.  Each sequence of colors seems to be the momentum, visible, in front of us.  I'll admit that I don't really understand where all the momentum is in something like a benzene molecular pi orbital ... there are articles like geometric phase and papers like  that might contribute to understanding the idea further if I made sense out of them.  Note the last section of geometric phase includes "the geometric phase γ {\displaystyle \gamma } \gamma picked up by the electron while it executes its (real-space) motion along the closed loop of the cyclotron orbit." -- is that error, or a different understanding?  I feel like there has to be some simple way to look at QM and all of a sudden it all feels intuitive... Wnt (talk) 19:12, 6 June 2017 (UTC)
 * The issue is that you, and especially your human intuition, is based on a perspective of the world which is incomplete and inaccurate. That's why your intuition rebels, not because QM is wrong, but because you are a machine which approximates reality in a narrow set of conditions of size, time scale, and the like.  When one does that, one introduces all sorts of questions which aren't just wrong, they are not even wrong.  The classic example is the question "What does an electron look like?"  Seems like a simple question, until you realize that it's a nonsensical question.  Here's why: What does it mean to "look" at something?  It means to detect the light bouncing off of it.  When I look at a wall, I see the particular way light bounces off of the wall.  My eyes detect those photons, my brain constructs a working image of that wall, etc.  The issue is, that process makes no sense if you replace the word "wall" with the word "electron".  Electrons interact with light in a very different way than does a wall, so when someone asks "What does an electron look like", it isn't an answerable question.  In the exact same way, other concepts we deal with in the world on size scales and time scales our brains work at don't make any sense at the scale of an electron.  Instead, we have to deal with the electron on its own terms and not put our human terms on it.  And that's what "Shut up and calculate" means.  What does science do fundamentally?  What it does is create working models and theories so we can make predictive statements about the way the world works.  We have those working models for an electron.  It's called quantum mechanics.  Those models don't have nice pictures that make ANY sense in the big world, but that's fine.  Not every good model needs a picture I can draw with a crayon.  So, throw your intuition away.  It does you no good here, because the way you have intuition is through the way your senses interact with your brain, what's called qualia.  Qualia aren't useful to explain quantum mechanics.  Equations are.  Shut up and calculate.  -- Jayron 32 19:24, 6 June 2017 (UTC)
 * I knew I'd be sorry I'd asked, but thank you Jayron and Wnt.   D b f i r s   20:17, 6 June 2017 (UTC)
 * *Applauds Jayron* You should copy and keep that last passage for re-use – it's an excellent clarification of the confusions that often arise over atomic and quantum phenomena and are asked about on this desk. {The poster formerly known as 87.81.230.195} 2.217.208.38 (talk) 10:20, 7 June 2017 (UTC)
 * It's really quite easy to say what an electron looks like - we have solvated electrons that, like many things, look blue at low concentration and gold at high concentration. This is a function of interaction with water  - you can say of course that when we look at the wall we are also seeing electrons, in different states.  Indeed, people even talk about a distinction between wet and dry electrons  though I'm not sure that isn't just a snarky name.  Still... something in water, interacting with water, is wet, I suppose. Wnt (talk) 11:49, 7 June 2017 (UTC)
 * Honestly I think it is not so hopeless to talk about this as Jayron is implying. Jayron's claim that the electrons "don't move" is implicitly working in a basis where all the states have a well-defined energy (that is, they're eigenstates of the Hamiltonian).  The time evolution of such states is only a global phase change, so there isn't any "motion" in the usual sense, even though there's momentum.
 * That is a very convenient basis for a lot of purposes, but for this particular question it almost seems designed to avoid answering. There are lots and lots and lots of other possible bases.  In some of them, the energy is not completely well-defined, but the position of the electron within its orbital is better defined, though still not precisely.  You would still have clouds where the electron might be found, but the clouds would be more concentrated, not spread out over the entire orbital.  And the time evolution of these clouds would, I think, see them moving around the nucleus.
 * Going to the extreme in this direction, you get Feynman diagrams and the path-integral formulation. --Trovatore (talk) 20:48, 6 June 2017 (UTC)
 * The Chandrasekhar limit is where the electrons are going very close to the speed of light so their mass grows instead of their speed as a star contracts. Dmcq (talk) 17:03, 7 June 2017 (UTC)


 * The expectation value of the velocity is zero, but the expectation value of the gamma factor which depends on the square of the velocity is not zero. This expectation value can be easily calculated using just the expression for the energy eigenvalues. The exact solution for the energy eigenvalues of a one electron atom with nuclear charge $$Z$$ is:


 * $$E = \frac{m c^2}{\sqrt{1+\frac{Z^2\alpha^2}{\left(n - \left(j+\frac{1}{2}\right) + \sqrt{\left(j+\frac{1}{2}\right)^2 - Z^2\alpha^2}\right)^2}}}$$


 * where $$j$$ is the total angular momentum (spin +orbit angular momentum) quantum number, and $$\alpha$$ is the fine structure constant. A result from perturbation theory is that adding a term $$\epsilon V$$ to the Hamiltonian leads to a shift in the energy eigenvalues which to first order in $$\epsilon$$ is just the expectation value of $$\epsilon V$$ in the unperturbed energy eigenstate. Suppose then we modify the potential energy term by changing $$Z$$ to $$Z + \epsilon$$ and we treat the change in the potential $$-\frac{\epsilon e}{r}$$ as a perturbation. Then to first order in $$\epsilon$$ the change in the energy eigenvalues is given by the expectation value of $$-\frac{\epsilon e}{r}$$. But since we have the exact solution, we can compute this also by differentiating $$E$$ w.r.t. $$Z$$ and multiplying by $$\epsilon$$. This means that the expectation value of the potential energy is given by $$Z \frac{\partial E}{\partial Z}$$. The expectation value of the kinetic energy plus $$m c^2 $$ is therefore given by $$E - Z \frac{\partial E}{\partial Z}$$, and dividing this by $$m c^2$$ gives you the expectation value of the gamma factor. The result for the ground state where $$n = 1$$ and $$j = \frac{1}{2}$$ is:


 * $$\gamma = \frac{1}{\sqrt{1-Z^2\alpha^2}}$$

For gold this is 1.22, so the "relativistic mass" of ground state electrons is approximately 1.22 times the rest mass (but note that we're then ignoring the interactions due to the other electrons). Count Iblis (talk) 22:10, 7 June 2017 (UTC)

What makes a cell "alive" as opposed to being a clump of organic molecules?
Cells may use organic molecules as fuel. But the cells themselves are also made of organic molecules. So, is it really a clump of organic molecules behaving in a pattern and manipulating free organic molecules in the environment? 140.254.70.33 (talk) 17:50, 6 June 2017 (UTC)
 * Unfortunately, the precise boundary between a simple living organism and an (apparently) well-ordered but non-living thing, is fuzzy. See Life for a discussion of this. LongHairedFop (talk) 17:59, 6 June 2017 (UTC)
 * Defining life or if something is living or alive is problematic, because the term is too vague. This and this one too.  That second was is important; as a basic definition it includes a nice description as one would expect to get on the first day of a biology class.  But the most important sentence in it for our purposes is "The question of what it means to be alive remains unresolved."  There are all sorts of edge cases.  For example, are viruses alive?  They are clearly made of the system we call "life" (viruses would not exist outside of a system that supports life), yet are they, themselves, "life"?  What about prions?  The issue is that life is a system and not a substance; being alive has certain conditions, and certain products of "life" are themselves not "alive".  It's nuanced and messy.  -- Jayron 32 19:14, 6 June 2017 (UTC)
 * (ec) Defining life is a notoriously philosophical task. I personally would tend to place a very high value on homeostasis for making this determination, in terms both of the complexity of interacting processes and the degree to which the strength and direction of these regulatory phenomena has been optimized, e.g. by evolution, for maintenance of steady state conditions.  Thus, for example, molecules outside the cell that are maintained at a constant level by design (humic acid/melanin, antibiotics, mucus) would seem more alive than molecules outside the cell that are not (grains of India ink), in proportion to the number of different ways that they are sensed by the cell and produced by the cell, and also perhaps in proportion to the selective disadvantage to the cell of their removal from its environment.  But this is not a standard answer, just a rumination I'm afraid. Wnt (talk) 19:22, 6 June 2017 (UTC)


 * The sorites paradox is the name given to a class of paradoxical arguments, also known as little-by-little arguments, which arise as a result of the indeterminacy surrounding limits of application of the predicates involved. . The limit (in chemical complexity) between non-life and life is as indeterminate as the limit (in the number of sand grains) between non-pile and pile. Dr Dima (talk) 21:40, 6 June 2017 (UTC)


 * Humans are notorious for inventing a word and then trying to make something natural fit into it. Hence the debate over whether Pluto is a "real" planet or a "dwarf" planet. Pluto is what it is, and how we choose to label it is our own problem, not Pluto's. Likewise, single-cell organisms and viruses are what they are and they do what they do, regardless of how we label them. I've often heard it said that the planet earth is "alive". Maybe not in the narrow sense of how we try to define life, but nonetheless it does things. ←Baseball Bugs What's up, Doc? carrots→ 22:09, 6 June 2017 (UTC)
 * Adding a link to Gaia hypothesis for anyone wanting to follow up Bugs' last observation. {The poster formerly known as 87.81.230.195} 2.217.208.38 (talk) 10:38, 7 June 2017 (UTC)
 * In the case of planets and dwarf planets, people understand that a distinction was drawn without much philosophy, making it mostly just a word. Sometimes, post hoc, a philosophy *can* be proposed though .  In the case of a "pile", there may be a real basis, but there may be more than one, making it hard to decide.  But in the case of life, we have a sense that there is "really" something different between living and non-living things, and that this is so fundamental that all living things ought to share it.  That makes it more than just an exercise in semantics - we want to propose and understand that thing. Wnt (talk) 18:47, 7 June 2017 (UTC)

Quantum coin toss
I just watched a science programme in which a scientist said "Every time I flip a coin, heads or tails, that is just some little quantum accident". Is that correct? Does any "quantum uncertainty" impinge upon the outcome of a coin toss? (I am not entirely sure whether he was literally talking about the coin toss, or whether the coin toss was just meant to be a visual metaphor for a "quantum decision".) — Preceding unsigned comment added by 86.190.213.181 (talk) 19:40, 6 June 2017 (UTC)
 * I'm almost entirely certain that he's speaking metaphorically, using the coin to represent quantum uncertainty and random behavior. There is certainly nothing in quantum mechanics which is useful in explaining the particulars of the coin toss.  -- Jayron 32 19:58, 6 June 2017 (UTC)


 * Coin tosses are certainly not random. It is trivial to find a plethora of studies showing that the position the coin originally faces influences the toss as well as the design of the coin. So, it isn't a quantum mechanics issue. It is mostly a classical physics issue having to do with net forces and air resistance. 209.149.113.5 (talk) 20:04, 6 June 2017 (UTC)


 * The ballistics of the coin is not random, except over long enough trajectories where the effect of air density fluctuations perturbing the coin gets sufficiently amplified as the coin is tumbling through the atmosphere. I can't quickly find a good source on coin ballistics, but I'll do a more thorough search in the evening. However, this does not mean that the outcome of the manual coin-toss is not random. Indeed, even if a human would like to toss a coin in precisely the same way multiple times, this is not physically possible. There are fundamentally non-deterministic quantities of neurotransmitter released in every one of the many synapses involved, in the exact timing of the neuronal action potentials, and so on. Peter Latham had a paper a few years back showing that a single extra action potential in the cortex, under certain conditions, may cause something like 28 other action potentials (although the effect eventually dies out rather than causes an avalanche), see here . However, that paper allows for two opposing interpretations: (a) cortical coding is rate-code (deterministic) rather than individual action potentials (probabilistic), that is, individual action potentials are non-informative out of their population context; or (b) the motor output (behavior) is actually a lot more probabilistic than we realize. It is therefore an open question how random a human (manual) coin toss is. Dr Dima (talk) 21:27, 6 June 2017 (UTC)


 * There is actually no such thing as "classical randomness", all randomness in nature is always a quantum randomness, the relevant probabilities are always a squared norm of an amplitude pointed out in this article. So, there is no such thing as a classical randomness a la Laplace where the probabilities fundamentally arise from ignorance about an otherwise deterministic process. If you attempt to construct a deterministic counterexample, like whether the 10^100 th binary digit of pi is 0 or 1,, then the probabilistic nature of the result is ultimately due to the lack of correlation between the processes in the brain that come up with that number 10^100 and the value of the binary digit, the stochastic nature of former is a due to quantum mechanics. Count Iblis (talk) 21:48, 6 June 2017 (UTC)
 * Count Iblis, some of that is hard to understand, especially for anyone that is unfamiliar with those concepts but, simplifying the first part of your comments, you are saying that quantum randomness models are fundamental for which things like classical models of die rolls are mere inaccurate approximations. In other words, you, as have others, claim that all stochastic processes are ultimately due to quantum mechanics. That I'm clear on, but deterministic processes are a different animal, so I can't make sense of your comparison of a pi calculator with the brain where both will give 1 for the first digit (3 for all bases equal to or greater than 3) and the ith is easy to calculate (here is the formula for base 16). Any lack of a statistical correlation between either the brain or the calculator that merely guess would be mere ignorance of the underlying math. Of course, there are lots of reasons that either may malfunction. Therefore, even though pi is absolute and we might err in calculating it I don't see how that has much to do with any physical theory. Modocc (talk) 23:13, 6 June 2017 (UTC)
 * The thing with the digits of pi is that as soon as you consider a process that uses these digits that's truly random like someone picking random digits, then the source of that randomness does not come from pi, rather from the random choice. Count Iblis (talk) 19:43, 7 June 2017 (UTC)


 * The apparent randomness of a die toss is due to the sensitivity of the system's initial conditions and this is known as the Butterfly effect of Chaos theory and the butterfly effect article has a subsection that discusses its relationship to quantum mechanics here. Additionally, with respect to cascading events like Schrödinger's cat we have the uncertainty principle and the correspondence principle to consider. With regards to various cause and effects the poem For Want of a Nail seems relevant too. -Modocc (talk) 03:31, 7 June 2017 (UTC)


 * "Quantum mechanics!"
 * We love throwing that word around, and at the same time, we spend so little time defining it!
 * Let's start with what we mean when we say quantization - it is the mathematical modeling process of projecting our observations on to the set of integers. We might say that this is to construct a mapping-function from "observation space" onto the set of integers, ℤ.  That's a purely mathematical statement, and the astute physicist will observe that I did not define "observation space"!  (It might be ℝ, ℤ, ... some hyperspace, ... doesn't matter!)
 * We have deduced a whole set of physical consequences that follow from these mathematical abstractions. The most commonplace application of quantum mechanics, which is to say, the study of the behaviors of subatomic particles, takes things a step further with some strong claims: the projection on to the quantized model is a complete and correct description of observation-space.  That is to say, physicists who believe the strongest claims of quantum physics do not believe that their math left out any detail.
 * So, if you start looking at the precise meaning of the words, a coin toss can be modeled using a quantized description: the coin is either heads or tails, and nothing in between. This is a model of real physics, and for many cases, it's a working and useful model.
 * But unlike quantized models of fundamental physical properties - such as the quantum of electric charge or angular momentum - we have the knowledge and technology to break the quantized model of a standard coin toss. We know of numerous variables - in addition to the "heads-or-tails-state" - that affect the outcome.
 * Consider the definition of the word "atom" - that which we cannot subdivide - and consider how it applies to the coin. (The astute physicist will consider the impact of the force of both history and of accelerated particles on our fundamental use of these words).
 * If you fired a high-powered rifle at the coin, the coin would probably deflect, deform, and quite likely would pulverize on impact. The simple quantum model of "heads" or "tails" would no longer apply to your coin toss.  This is wholly dissimilar from, say, a lepton: we do not know any possible way to fire an electron at another electron and cause either electron to "shatter."  We can use a more powerful electron gun to shoot at the electron, and yet she persists.   For this reason, we call the electron a fundamental particle, and we believe its quantized properties (such as its electron spin number) to be essential to the description of the electron.  We can write complicated mathematical equations, based on our observations about conserved quantity, to describe how electrons behave when you interact with them, proceeding forth from the assumption that the fundamental properties are quantized.
 * This is not like a coin toss. In a coin toss, it is true that the coin may land either on heads ("up", 1, ...) or tails ("down", 0, ...).  But it is physically possible for us to do other things during the coin toss.  We could put the coin toss in a very hot furnace and melt the coin.  "Heads" and "tails" are not fundamental, indestructible properties of a coin.  Any physical model we derive about coin-tosses, proceeding forth from the assumption that "heads/tails" state is quantized, can not possibly be a general theory.  Nonetheless, we may still use such a model, as long as we understand and respect the physical limits of its mathematical implication.
 * We can construct an approximation to the coin toss by pretending that we can never under any circumstance have any value other than heads or tails. We can model the heads/tails state as a consequent of other properties, like air turbulence, the trajectory of the throw, and so on.  But here's the important bit: our experimental data will not - and can never - reveal any very profound principles of physics.  We  know that "coin state" should not be a conserved quantity - there is no law-of-conservation-of-heads-or-tails.  We know this because we know that the model is incomplete.
 * We can observe statistical data about the coin toss. We can even derive good empirical laws with strong predictive power about the coin state.  If we expend a lot of thought, we can make really useful models.
 * If you compose a model from an ensemble of smaller quantized models, with each parameter also quantized (ergo, neatly residing in the space of integers), then you have a very complicated but fundamentally quantized description of the coin toss. And if you are lucky and diligent, you might be able to deduce a causality chain from one single quantized parameter all the way through to the final "heads/tails" state.  This is what is suggested by the original question: some single quantum parameter accidentally had a causal effect on the macroscopic outcome.
 * But if we want a profound insight into the workings of the universe, this model has shortcomings.
 * Nimur (talk) 14:13, 8 June 2017 (UTC)

Predation vs cannibalism
How close do two species have to be in order to be considered "cannibalism"? If another hominid species still exists to this day and hunts down humans like they would to other animals, then would that be considered "cannibalism" or merely predation? 50.4.236.254 (talk) 23:33, 6 June 2017 (UTC)


 * Cannibalism is defined in the dictionary as "1. the usually ritualistic eating of human flesh by a human being, 2. the eating of the flesh of an animal by another animal of the same kind", etc. . It leaves undefined the notion of "kind": whether "kind" means population, species, genus, or something else. Our article defines cannibalism (zoology) to pertain specifically to the same species, but does not give a reference. Does this help? Dr Dima (talk) 01:40, 7 June 2017 (UTC)


 * Would monkey brains qualify? ←Baseball Bugs What's up, Doc? carrots→ 11:51, 7 June 2017 (UTC)