Correct; I was attempting to explain what, not why. To the best of my knowledge, the question of why an observation collapses the wave function has only been partly answered. Essentially, you have to ask (for every case) exactly how the observation was done. Most commonly, you bounce one or more photons off of the thing you want to observe (or you arrange for it to emit on or more photons). This appears to be the cause of the collapse. Hopefully someone who knows more than me will chime in with more detail?
You will find that the interference pattern is destroyed! You will instead get two blotches of electrons, one in front of each slit.
Mathematically? It's because the function that produces the probability values is time-dependent; the result is that the probabilities of the various values (momentum [not velocity] and position, to take your examples) change over time. Thus, if you wait too long after you made your first measurement, subsequent measurements of the same physical quantities will have "decohered" again.
Physically? Since there are lots of possible quantum states, and since the probabilities associated with those states are determined by the force/energies that surround your electron, then as time passes, the forces and energies interact with the electron, and so the electron's physical state is re-randomized. (Semi-randomized, actually, but never mind.)
Sorry, I wasn't clear: I'm not suggesting the other interpretations of QM are nonsense; I am suggesting that the statement that "the electron could be in two places at once" is nonsense. As the poster below me said, there are NO interpretation of QM (of which I am aware) that will make that claim.
(That said, the Copenhagen interpretation, whatever its ontological problems, has the virtue of having stood the test of time and--more importantly--LOTS of experiments.
(Sorry for the delay in answering; Sunday night movie with the wife.
The term "superposition" means, in this context, two things--or rather, one thing, but expressed two ways:
(1) Given a particular physical setup--the collections of forces (or, equivalently, sources of potential energy), both internal and external, that act on a quantum particle, along with the initial conditions of the system--quantum theory cannot produce a single answer to any question you might pose, but only a list of possible answers, along with the probabilities that a measurement of the relevant physical quantity will produce each possible result.
For example, if I ask "In my particular experiment, what is the magnitude of the orbital angular momentum of the electron in a hydrogen atom", quantum theory will produce a list of (say) 5 possible values, along with the probabilities of obtaining the 5 values: 2%, 10%, 76% 10%, 2%--when you make the measurement. Thus, after the measurement, the angular momentum has a definite value; but before the measurement, the most we can say is that the electron will be found in one of those states, according to the weighted probabilities.
But, that is a lot of words; so, the phrase "quantum superposition" was invented to mean all of that. The common phraseology is to say that "prior to measurement, the electron is in a superposition of these 5 quantum states".
(2) The math way to say exactly the same thing is the state function (i.e., the solution to Schrodinger's equation for the given potential energy function) is a function that is a superposition (a sum) of so-called "basis functions" (or "basis states"); each basis state is one of the 5 states mentioned above.
This is what people mean when they write things like "the electron can be in two places at the same time", but it is a horribly imprecise and misleading way to phrase it. --But I understand why writers do it; look how many words it took me; what newspaper editors would allow 400 accurate words when 40 semi-accurate words will sort of do, and who the hell besides a few physicists will care, or even know?
No, the electron is NOT "in two places at once". That is nonsense. Prior to measurement the electron (and indeed, any quantum particle) simply does not have a well-defined position; rather, there is a set of points in space where it could be found (weighted by the probabilities returned by the* wave function of the electron in the given physical setup ("the potential well")). It is only when a measurement is made that the probabilities resolve to a certainty--and the electron is then found in literally one position in space.
*Technically, the square modulus of the wave function.
Sorry for the physics rant; I feel better now.
If a specific venue wants to reduce the problem of ticket bots, they could simply have ticket purchases to be at the box office only. After all, if you are physically going to the show, you are physically capable of going there to buy tickets.
Edge cases: the venue is not in your current city; you have a physical limitation that greatly increases the inconvenience of going there to get the tickets (e.g., in a wheelchair); I'm sure people can think of others. Possible solution? For these cases, purchase over the phone.
(Note that the added fees that Ticketmaster and their ilk charges would disappear. ("Convenience fee" my ass))
What obvious problem with this idea did I miss, thus proving that I am an idiot?
"...but I was dashed if I could see why he couldn't do it with a bright and cheerful smile."
(Nice to encounter another Bertie Wooster fan!)
I agree that fingerprint sensors are nowhere near reliable enough to use on a device that you are depending on to save your life. Since a significant percentage of slashdotters are hardware and/or software folks, does anyone here have an idea as to how the reliability of these sensors could be improved?
Imagine, going to sit down at a computer, and small, very short range, wireless signal authenticates you to the computer, unlocks your email, etc.
Welcome! The future is here! That is exactly what happens when I sit down at my locked Macbook (running Sierra) while wearing my Apple Watch; the laptop and watch exchange a key, and my laptop unlocks.
Actually, that is now past tense; thanks to this story (and others I've read recently), I have turned this feature off. It's clever and convenient, but not worth the risk of getting inadvertently swept up in some overzealous search warrant issued by a lazy and/or technologically-ignorant judge.
(The next generations of Macbooks will have the fingerprint sensor, and I will be unwilling to use that, too. Sigh.)
I hope Apple cares as much about privacy as they claim to, and figures out a solution to this problem. I am afraid to use these cool features of my devices, which makes these features no longer a selling point.
Oh, I have no interest in excusing it. Comey apparently did, however. So either he had a personal/political/job security reason to not pursue (very possible), or he honestly believed HRC's actions didn't rise to the level of criminal behavior that you describe. I have no idea which, and we may never know.
But the Constitution (that thing they all claim they're defending and protecting) says "innocent until proven guilty"; so, like it or not, she is guilty of nothing, at this time.
Am I not bothered by this? I should be, but I'm not. Cynically, I assume that similar levels of rule-stretching, rule-breaking, and illegal actions have been going on since about 12 minutes after the founding of the Republic, and is just part of the grease that keeps the machinery of government running. Then too, I also suspect that much of what is marked "Classified" gets that way merely to hide things people want buried.
My understanding is that FBI director Comey decided that a prosecutor would not be able to persuade a jury that she intentionally did anything illegal. (That's not the same as saying she didn't do it; just that they'd never get a conviction, and probably not even an indictment.)
Your next four points seem to be concerns over what may come to light upon further investigation. That's reasonable. I appreciate your saying that no "smoking gun" has yet been found.
Diplomacy...Our enemy today is our friend tomorrow...England, Spain, Germany, Japan, Viet Nam, Iraq...
I agree, stupid decisions. I wonder why nobody managed to talk her out of all this.
Thanks for those links. (I have to say that the NYT article seems much more reliable that anything I saw on Infowars.) I read the NYT article; man, was that byzantine! Hard for me to tell whether anything illegal happened; if so, by whom; and if HRC was directly involved. But, definitely bad optics. I can see your point on this one.
What I've never quite understood is: what, specifically, bothers people about this email issue? The worst case scenario is, of course, that one or more of the deleted emails shows some sort of criminal activity (separate from the act of having an unauthorized email server, that is-- granting, arguendo that having such an email server is in fact illegal). Nothing I've read has suggested that such an email has been found, or exists. Absent that, then the most it shows, as far as I can see, is that she felt she was above the rules, that the rules applied to everyone else but not to her. That's bad, but I'm not sure it's worse than what most of us put up with from our managers every day.
I've read several stories about people emailing requests for access to Hillary, or to her staff; a prominent example was the Crown Prince of Bahrain ( http://www.politico.com/story/... ). Admitting up front that I don't really know that much about what the State Department does, or is supposed to do; but the crown prince of Bahrain sounds exactly like the sort of person who could access the State Department, who should get a response from the State Department. And, the linked story doesn't indicate any favors or quid pro quo, as far as I could tell.
Let's further grant (for the sake of argument) that she lied about what emails she had, what emails she released, what emails she deleted. Perhaps I'm cynical, but I have the impression that lying is half of a politician's job; just to get through the day; A necessary evil just to get anything accomplished.
So again, my question is: what, specifically, about this email issue bothers you?
We can defeat gravity. The problem is the paperwork involved.