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Considering a wasted education in my youth and the limited ability to remember that seems to come with my age. I like SFN, and several YouTube host, I also have an app that lets my download k12 textbooks, and I am not ashamed to download the lowest grade text I can find to try and get a feel for the basics. I'm not afraid of getting it wrong because SFN members are gratefuly quick to set me straight when needs be. Though at times I feel puzzled especially when I ask a question about spacial density and it seems I'm sent on a snipe hunt. I can only guess that my question was so far off the mark that they were trying to help me along by making it sound like I had asked an intelligent question. I read those articles over and over to the point that I should know them verbatim, Sadly the only thing I can remember about them is that I never did figure out what they had to do with my question. Pretty much everything is new to me. Sometimes even the answers I thought I knew, are new to me, like the conversation about why electrons don't fall into the nucleus. An amazing question followed by an amazing conversation. I wanted to upvote the whole conversation, and I'm glad you Achilles thought to ask the question, cause I was apparently clueless.

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.

lol > G(p) = p + 1 = G^n(p) = 2^n You seem to be deeply confused about the equal sign.

Welcome back, I am just a newby here so you won't remember me.

Well, it can't do. (After all protons are pretty large and yet they only contain three zero-sized marks.) For all sorts of reasons. For example, the Heisenberg uncertainty principle means that the momentum would be infinite if the distance was zero. (See the thread about why an electron doesn't fall into the nucleus for more info.) The weak interaction is not really a force and it doesn't hold things together. And it wouldn't be able to overcome the massive kinetic energy you would need to give things to get them that close together. And any such system wouldn't be stable (after allow don't see any of this around us). And gravitational singularities do not really exist. But apart from every single aspect of it being impossible . . .

Count the dead civilians on each side ???? In WW2 almost 8 million casualties for Germany and less than half million for Great Britain. So you guys were the bad guys, not A Hitler. As for the UN condemnations, half of the UN human rights council is composed of states which should not be 'throwing stones' because they 'live in glass houses'. look up the membership and see how many you can defend.

I promised myself I wouldn't get involved since I know little of the OP subject... If I was a Palestinian I would have no problem walking around any city in Israel. Maybe instead of posting cute pics, John, you should comment on how long a Jew would last walking around in Gaza. I know a lot of people here have fancy names like 'whataboutism' for it, but if you condemn and boycott Israel for human rights abuses, while shopping at Walmart for Chinese products, with a car fueled by Saudi oil, you are a hypocrite. Actually, applying different standards of moral behavior to different people, races or religions has a different name. in the case involving Jews, it is called anti-Semitism. And you are absolutely right Mistermack, crime and crooks are created by police. Every nation on Earth is estabilished where former peoples were displaced. Lets all start shooting off rockets. and strapping on bomb vests

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.

Not really. All (well, nearly all) Christians believe in God. Only a small number of them deny the reality of evolution. There are also people who deny or dispute evolution even though they don't believe in god. So there is no obvious causal relationship between a belief in god and denying evolution. Your personal beliefs are not really relevant. OF COURSE. Because people do. Why not? Does it need another box labelled E = Itoero's irrational hatred of religion. I think it might be time to ask the mods to close this thread as you have the answer to your question and now you are just using it as a platform for your bigotry.

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...

What did you say that was hyperbolic? How about the claim that Israel slaughters children? Of course you throw such allegations around so often that they hardly register with you. Israel won all that land in battle in a war they did not start. Same as the land won from Germany. If you are so concerned about international law then why do you not even mention it in regard to the terrorist organizations bent on genocide? I am not sure which picture you are referring to regarding the child being slaughtered. Where is it? Is a child being targetted and deliberately murdered (as the Pals do when get a chance to catch some in Isreal) or are we talking about some kid who has been sent into an active battle area with the hope that he will be 'martyred'? Israel send bombs to bump off terrorist. They do not target civilians. That is a fact that you well know but avoid mentioning. When they bomb a fixed target they usually give the inhabitants a two minute warning. When has that even been done by anyone else in history? Until you are prepared to discuss the concept of targetting you are just evading the issue. If Palestinians wanted to house and feed their people then they would spend the money on that. Instead they spend tens of millions on rockets and tunnels for the purpose of targetting Israeli civilians. The tunnels are destroyed and the deaths of a few Israeli civilians benefits the Palestinian population on no way. The 'leaders' of Gaza do not care about that, of course. When was the last time they had an election?? I often wonder why pampered western leftists are so keen to support terrorism in Israel and other places. The more depraved the acts of terrorism the more effort these people make to excuse them. It seems to me that they prefer to side with the thing they fear rather than oppose it. It is certainly safe to be pro-Pal in a western university these days but imagine what would happen if you were pro-Israel! No. Much easier to just oppose the benign democratic state. Well at least you are honest enough to admit you support terrorism. By the way, the state of Israel does not target civilians for the purpose of wanton murder. People get killed in battles but if Israel really wanted to do what you claim then they have the power to eradicate all the Pals in about 24 hours. The Pals have stated that they would like to remove ALL the Jews. As a matter of interest do you also have a benign view of Alqaeda and ISIS? They can also claim legitimate grievances if you want to listen. SO I guess you have no problem with them murdering people on the streets of Western cities. Not sure how you label Churchill a liar simply using your own speculation as if it were evidence. Please explain that one. I suspect the answer is ZERO. Palestinian houses only get bulldozed when they are responsible of suicide attacks. So tell us how much land the Jews lost in Iraq, Yemen, Egypt, Syria, Iran etc when they were forced out once Israel was established. I notice you never mention that. Israel gave the whole of Gaza back to Palestinian control and what have they got in return? Rockets. What have the palestinians done with all the agricultural land they got? Nothing. If Israel disappeared the Pals would have nobody to blame for their state. In addition they would have no water and no electricity. They would also have nowhere to send their seriously ill patients. Did you know that Israel provides all of those to Gaza? I doubt you did! Again John Cuthber tries to weasel out of the point. It is quite safe for any person of any race or religion to walk around Israel. A Jew in Gaza is likely to be murdered because he is a Jew. Israel is a liberal democracy as opposed to a terrorist run enclave, despite what the leftist terrorist sympathisers will claim. I suggest we do an experiment. I will go to Israel and stand around eating bacon sandwiches and drinking beer whilst peacefully denouncing the Jewish religion and the local government. John Cuthber can then do the same experiment in Gaza.

Ten Oz, I suggest you read the descriptions of Trump in the media and from the 'celebrities' if you want to know what smears I mean. Or are you saying that this is the first you have heard of Trump being smeared, insulted etc? You neglected to mention in your employment stats that there was a major adjustment by Obama in the way that the stats were measure when part time employment was lumped in with full time employment and given equal weight. ie a fudge. In any case the fact remains that employment really is up despite the claims that Trump would trash the economy. I have to admit to an error earlier. The Democrats did actually manage 100% black employment a while ago before their scheme was destroyed by a republican president (Abe Lincoln) You are desperate to play down Trumps success in DPRK. I guess it is all you can do. The fact is that Kim is already in ful control of DPRK and any progress we make there is a lot more than was achived by any previous administration. You seem to think that none of the problems you list even existed prior to 2016. Airbrush, As you well know Trump gets plenty of abuse. Why would you try to deny it? ODonnel calls him a traitor a racist and a pig so he responds in kind. What is the problem? You don't like it when someone pays back?? Misrepresented? One example from above - he was a self made bilionaire before he inherited anything. So why the need to misrepresent that fact? YOu have just done it again with your point 4. Trump was worth a billion when his dad died and left him 200M. You just cannot deal with the fact that someone you hate (despite not being able to tell us why) is also someone who is successful. So you seem to be saying that Trump is building on the 'success' of Obama? So what exactly did Obama do to create this 'success'? Was it by making energy more expensive? Was it all the extra government workers? Was it be making healthcare more expensive? Banning gas fracking? Giving money to Iran? What was it?? Fake news? What area? General? OK, the 'news' that Trump dumped all the carp food in the pond in Japan. That was memorable because apart from being false it showed that even the most trivial and unimportant detail is still going to be misrepresented by the media simply because they see that as their job. SO they have no credibility when it comes to more important stuff like the whole 'Russian Collusion' fiction. Two years and still not a shred of evidence! Once again John is desperate to convince himself of the inheritance story. Trump was loaned a million dollars and he turned it into a billion before his dad died. Putting it in a bank would NOT have delivered that return. Trump has not been bankrupt so that is another popular misrepresentation. Five of his businesses have failed. That is what happens sometimes. Given that he has started about 400 that is not a bad rate. In any case the smear is all that matters to you. The fact that you can tell me that a self made billionaire is not a financial success is just ridiculous and goes back to what I said earlier - some people are so deranged that they cannot accept simple facts. Trump is a billionaire and he did it himself, no matter how much you wish it were not so! The family of servicemen asked him to intervene. The fact that you have to misrepresent that is just beyond lame. And finally you try and tell us that the economy is doing nothing. Well, if it makes you happy to convince yourself then keep clinging to it.

Funny reading this thread that people are dismayed that when they attack someone that person might push back. What sort of mindset do you grow up with when you cannot even see the obvious? Everyone sees it as a right to abuse, smear and misrepresent facts about Trump but are shocked when he responds. I guess that has never happened before. You see your political foes as punchbags with absolutely no right to retaliate. Well it seems that things have changed since the days of GWB so you had better get used to it. What is also odd is that you seem to think that if someone is your political enemy then he has to be a cartoon baddy in all possible respects. Absolutely no positive qualities allowed. Well here is some bad news - Trump was a self made billionaire long before he inherited 200M from his dad. That is just a fact. Can you deal with it or do you feel you have to misrepresent reality? But it gets worse. Much worse. Under Trump the economy is booming and unemployment is way down. But it gets worse still. Unemployment for Blacks, Hispanics and Youth are all at all time low. So many of the people who have never worked before have now got jobs for the first time in their lives and most of them are NOT from privileged pampered middle class graduate communities who have the leisure to gripe about Trump on a website. Oh, and also, his dealings with Kim Jong Un have already yielded up the remains of some US servicemen who fell seventy years ago. But of course the real problem is how he described Rosie oDonnel and that congresswoman who was trying to incite violence against republicans.