Leaderboard

Your imagination is irrelevant. There are people who use heroin (under it's more respectable name of diamorphine) regularly for years. In terms of toxic damage done to the body, alcohol is worse- simply because the doses (ounces rather than milligrams)are so much bigger. Of course there is. Several countries have relaxed the legislation on drugs- notably Holland and Portugal. There is typically a small increase in the number of users of pot (and a slight drop in alcohol use). There's a huge saving on police time etc. The problem isn't people using drugs. There is a problem with people how use them too much, or too often. But there's a huge problem with people who are injured- not by the drug use, but by the illegality of that use. The people killed in gang wars over drug territories are killed by the fact that the drugs are illegal. The people who die of overdoses from drugs that were sold with uncontrolled strength and make-up were killed by the fact that the drugs are illegal. The people who die from infections from sharing needles are killed by the fact that the drugs are illegal. We could save most of those people. Why are we not donig so?

This is true, but it is not what the OP has asked. The original question was why the electron does not fall into the nucleus, i.e. how is an atom different from a purely classical system of a charge in free fall towards another (opposite) charge, which of course is not a stable situation in the classical domain. So the OP wanted to know how this is possible, so I have attempted to answer the question. The spontaneous tunnelling through the nucleus - or any other classically forbidden region - is not the same as the electron “falling in”.

Trump is the only politician I have ever witnessed that casts permanent condemnations on people. That is the childish way, the Nazi way. It started with Rosie O'Donnell over a decade ago in 2006. She criticized Trump for his treatment of beauty pageant participants, and he responded by calling Rosie a "LOSER" as well at fat, stupid, ugly, etc. That is when I realized that Trump was an idiot that became a billionaire. I was perplexed at how could such an idiotic character become so wealthy? Later I learned that was because his wealth was handed to him by his Dad on a silver platter. He was pampered his entire life with enablers, yes-men, yes-women, and yes-lawyers, who all signed non-disclosure agreements, and agreed with. No matter what he said, their reply was "Yes Donald, whatever you say Donald, great idea Donald." That is why he has such a cartoonish personality disorder. Loser is a permanent condemnation. Whomever is a loser is a lost cause, irredeemable, and should be cast out. He also makes permanent proclamations on the character of people with grammar-school-playground nick names, Crooked Hillary, Comey the "slime ball", Lyin' Ted Cruz, Liddle Marco Rubio, Low-Energy Jeb Bush, etc. Illegal alien gangsters are "animals" which he makes it sound to his supporters like illegal aliens are all animals, especially if they are from "sh*t-hole countries", by ambiguous pronouncements. But when it comes to blacks he attacks their intelligence: Low-IQ Maxine Waters, Don Lemon the dumbest person on TV, those "sons of b*tches" NFL players kneeling, and now Omarosa is a "low life." A low-life is a permanent condition. How can a "low-life" ever be redeemed? All of this is so anti-Christian that I'm baffled at his support from the Evangelicals. Remember, you are supposed to hate the sin, but love the sinner? This tells me Trump is an irredeemable, evil man.

I know what you mean Jajrussel. Very hard to read thread. I get the impression there is a misunderstanding on Argo's part. A dimension is not a 'place' that can contain points. Simply put, it is an axis of a co-ordinate system. And his 'points' don't seem to correlate to space-time events. I'm not sure what they are.

Thanks WTF, you make a good point. I have not chosen a probabilistic argument but, following your advice, I have given my proof some extra scrutiny. I have identified a weakness in my proof and so am in the process of buttressing it. Everything hangs on the properties of prime numbers and how they relate to even numbers. It seemed obvious that even numbers can be composed of the sum of two primes but then i realised that i need to prove that for my overall proof to be rigorous. Watch this space.

Off the top of my head there were two with Vandrey as first author, which had a very small cohort. A larger group was queried in a follow up. I will have to search a bit to find the precise references, though. Let's put it the other way round. Assume that we just punish any drug use severely. Does this drive down addiction rates? Empirical evidence shows that it is not the case. Rather, addicts just end up in jail, become poorer and once leaving institutions have massive relapse rates. In other words, punishing drug use does not reduce drug users, but in fact adds harm to a harmful situation. So what would change if we treat it as a medical rather than a legal problem? The focus here is to reduce drug related damages. Key is that possession for personal does not carry a criminal penalty in itself. For example, drug addicts would be targeted with rehabilitation rather than with criminal penalties. Trafficking and production could still be illegal (which probably would be considered decriminalization rather than legalization? not sure about the legal implications). Providing needle exchange and dispensaries have shown to limit deaths and spread of diseases. In Germany, for example it has been ruled that drug addiction or possession for personal use is not considered a crime and drug injection rooms were established. Likewise, treatment of addicts are covered by health insurance. Portugal has taken broader steps for decriminalization and at least for certain risk groups saw health benefits in terms of reduced HIV infections and drug-related deaths.

I would 100% agree with charge being neutralised pretty quickly, it was the static solution [zero angular momentum] that had me somewhat disturbed. But as you say, probably never been observed. OK, I believe I can live with that...thanks for the answers and clearing up a couple of misconceptions.

If your buffers are clean DNA should be stable for at least a year at -20.

Please stop posting until you are off the meds. You are going to be rather embarrassed otherwise...

What do you mean? DNA storage? Depends on application. You can freeze dry or speedvac them for long-term storage or just use appropriate buffers and keep them at -80 pretty much for years.

No, not really. The Pauli principle states that no two fermions can share the same quantum state, but I assumed in my answer that there is only one electron anyway. I guess my answer comes down to the fact that the ground state (i.e. lowest possible excitation) of a single electron around a nucleus is non-trivial, meaning it is not just a point centered at the origin where the nucleus is; instead, it’s a spatially distributed probability cloud with corresponding non-vanishing energy. Note that we are talking bound states here - it is of course still possible to fire an electron at the nucleus, and hit it in the process, but that is not a stable bound state, and won’t happen spontaneously.

I agree the most probable radius of finding the electron is the Bohr radius. From http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydr.html#c1 So there is a factor of r^2 corresponding to the surface area at any radial distance. The surface area corresponding to the nuclear radius is tiny compared to e.g. the Bohr radius so the ratio of these surfaces is tiny. If the electron density was uniform throughout space, the probability of finding the electron at a given radius would be proportional to r^2. The probability per unit volume (for s orbitals) increases as the nucleus is approached and is higher inside the nucleus than anywhere else. Probability per unit volume is not used much since it doesn't provide much of use like e.g. the Bohr radius and the calculation of probability very near the antinode would be difficult and probably pointless. Probability per unit volume might be useful here.... The problem with radial probability, especially for s orbitals, is that it is often conflated with probability per unit volume.

Because the electron is not a classical particle (“little ball of mass and charge”), but a quantum object. As a first approximation, you can picture an electron as a 3D standing wave around the nucleus - you can only get standing waves of a given wavelength in specific places, which is why orbitals come in discrete levels. Crucially, there is a lowest energy level, which corresponds to the minimum distance an electron can be with respect to the nucleus (let’s assume here there is only one electron) - and that lowest energy level is not zero. Therefore the electron cannot fall all the way to the nucleus, it can only fall into its lowest energy level, which corresponds to an orbital that is still some distance outside the nucleus. This is a direct consequence of the laws of quantum mechanics, and coincidentally one of the questions that motivated the development of quantum mechanics in the first place.

Let's be clear here. There are people who are very good at making money, the way others are very good at carpentry, or cleaning, or computers. I'm not sure Trump is one of those, though. When you already have a lot of money, it's easier to make more just because you have the capital to take advantage of good deals and great ideas. Trump is probably a person like this, based on how many times he's filed for bankruptcy, and how badly he did running his casino business (where the odds are heavily in an owner's favor). Trump is a hater, and a narcissist. People like that hear someone criticizing them, and they have to trash them to their core, in order to remove as much of the sting of truth as possible. But I disagree that his condemnations are permanent. All one has to do is apologize and kiss the butt, and he's more than happy to parade that person around as an example of a convert. It's just that many people have integrity, and refuse to pucker for tyranny.

A rose by any other name would smell as sweet; if the bible wasn't written by man, then who did? Literally the first sentence...