@MartianCactus You don't "use" a 2d wave. The wave is actually three-dimensional, but we only look at a 2d cross-section of it. Also, since the wave is not a wave in a medium, it doesn't "look" like anything. You can't see the crests and troughs of a light or matter wave with our human eyes.
Once on a (now dead) science forum, we were discussing the origins of various vegetables. Someone asked where does cos lettuce come from. I replied that it's the derivative of sin lettuce.
In other words, $\frac{d}{dx} \sin x (\text{lettuce})= \frac{d}{dx} x (\text{lettuce}) = 1 \cdot (\text{lettuce}) = \text{lettuce}$ i.e. it is the one true lettuce (since $\cos(x) = 1$)
This is a question about the validity of a paper recently published which claims that the "Copenhagen Interpretation of QM is incorrect" (same title, by "Guang-Liang Li and Victor O.K. Li, dated 22/10/18).
This is a question about physics, and it can be answered. A reminder, whether the Born rul...
it'll teach me to give a toss when it's not my turn
I want back the half-hour of my life spent scrutinizing Li & Li's awful paper
I mean, what is this?
> Theorem 1: For a probability space $(Ω, \mathcal F, P)$, there are values almost everywhere in $(0, 1)$ that the probability measure $P$ cannot take.
but that's saying that a "probability" can only be a countable set of numbers in (0,1)? Also I don't really remember how "almost everywhere" is defined lol.
and when confronted with the usual Lebesgue-Borel measure, they say it is "an assumption in the disguise of a definition" and that its construction "causes contradictions"
@enumaris no, a set can be uncountable and have measure zero
the Cantor set being the canonical example, as I recall
@EmilioPisanty Yes. Or Julia sets, with the seed point outside the Mandelbrot set. In fact, that's what led Benoît to discover his set. He was looking for a way to characterise which Julia sets are connected, and which ones are dusts.
@EmilioPisanty The charitable interpretation of that is that they reject Choice, without which the Lebesgue measure indeed can cause contradictions, or rather, doesn't exist :P
You can have a model where all reals are measurable, you can also have a model where the reals are countable, as well a host of other weird consistency results
@EmilioPisanty Well...it is consistent with ZF w/o choice that the Lebesgue measure doesn't exist, I think. I think you can also have funny models without choice where it does exist and every set of real numbers is measurable
As usual, giving up Choice leads to even more philosophically troubling results than accepting it :P
@ACuriousMind I think the correct relationship between that paper and Choice is that the paper's authors have made the choice not to care about getting the mathematics right
I wish next time, when a physicists is dealing with ZF, they wrote down which model they are using, because you can have models that give you a host of different results that are incompatible with each other
"If $n$ is not a prime, then its factors are to be found among the set of integers $\{1, 2, . . . , n-1 \}$, and so $(n-1)!$ is divisible by $n$, that is, $(n-1)!= 0 (\text{mod} \ n)$"
but for $n = 4 = 2 \cdot 2$ we have $(4 - 1)! = 3! = 6$ which is not divisible by $n = 4$ unless I'm misunderstanding basic number theory (again) :p
If $n$ is prime then in the set $\{0,1,...,n-1 \}$ forms a group (needs to be proved) which means all the elements have inverses in this set, so that $(n-1)!$ should be equal to the identity in the group, UNLESS some elements are their own inverse, and by squaring one can see $1$ and $n-1$ are their own inverses (proof the others aren't their own inverses), so that $(n-1)! = (n-1) \cdot 1 = n - 1 (\text{mod} \ n)$ so that $(n-1)! = - 1 (\text{mod} \ n)$ or $(n-1)! + 1$ is divisible by $n$ :(
@EmilioPisanty I was actually preparing a comment/answer to this question but chose not to post. Such bold claims rarely hold or are at least rarely accurately stated.
@EmilioPisanty It went HNQ. In the interest of not giving an exceptionally bad paper exceptional airtime, I have removed it, and will now ask for forgiveness in retrospect since we don't have any real policy governing HNQ-removal yet.
Any hint on this relativity problem? A body travers alond the x-axis of an IF S with velocity V. The S observer emits a monochromatic pulse of light towards the body. The pulse is reflected by the body and subsequently received y the observer S. Obtain a relation between the emission and reception frequencias as measured in S
In connection with the moderator elections, we are holding a Q&A thread for the candidates. Questions collected from an earlier thread have been compiled into this one, which shall now serve as the space for the candidates to provide their answers.
Not every question was compiled - as noted, we...
This is one of those moments it would be good to nominate oneself and then overturn the Ocelot ban and the continual closing of interesting questions, alas it is overall just an unimportant waste of time :p
This approach most definitely does work, it just doesn't give the fundamental theory of the strong interactions, it gives string theory. String theory was originally defined by Venziano's bootstrap formula for the leading term in an S-matrix expansion, and the rest was worked out order by order t...
Why do we still care so much about crossing the Van Allen Belt when Apollo 11 had already crossed it back in 1969? Are the radiation belts getting more intensified or are they making some other problem?
@DanielSank I both agree and disagree. I do think that the point you've made repeatedly in the past - that the text of the policy does not reflect what happens in practice - is accurate. But I also think any policy we make experiences this sort of "drift". And every time we want to "remake" the policy to realign it to the drifted policy, we'll basically have to rehash the discussion about the policy as such, with all the fatiguing battles between different viewpoints that entails.
@DanielSank Is the stonewalling you refer to that physics.meta.stackexchange.com/q/7162/50583 never seems to have had any practical effect, despite it being the top-voted answer by a large margin?
Let's talk specifics.
And by that, I mean, "let me be the first to shoot my own self-interest in the foot", and argue that this question, which I answered, was rightly kicked off the HNQ list.
What's the deal? Well, the question starts off with the title
Is the Born rule indeed wrong?
and...
@ACuriousMind I reckon it'd be good to hear your views as to what was in your mind when you were kicking that question off HNQ
@DanielSank The point of the election is to get moderators that will handle the day-to-day tasks of moderating. While no one can forbid you from resigning (or just not moderating), I would see that as abuse of the system and not look too kindly on it. I also think that you overestimate the power that moderators have on such policy discussions and would achieve little more than upsetting lots of users with such a move.
@ACuriousMind I think that's an unintentional straw-man argument. If there are identifiable aspects that have been subject to the same improvement for a long time, it seems wise to execute that improvement, other possible drifts notwithstanding.
@ACuriousMind Nope. I was referring to prolonged discussion held in this chat room wherein I felt that perfectly reasonable suggestions were rejected via straw-man arguments. I recall there was a specific refusal to make a small and generally agreed-to-be-good change, i.e. only large changes should be allowed.
@DanielSank My problem is that you think that your proposed change to the policy is that identifiable improvement, while others think "stop closing homework questions that are interesting" would be an improvement, too. Every time I think "we all agree what homework-like close-worthy means, right?", I think back to physics.meta.stackexchange.com/q/9086/50583, where no clear picture emerged when people were polled on what should be closed rather than voting on specific meta answers.
@DanielSank I'm afraid your memory of that is probably sharper than mine. Was there a meta post specifically about that change? If not, my advice now (and without the rest of the context) would be to simply make that meta post, asking for that change. Chat discussions are fleeting and don't reach most of the user base.
@ACuriousMind This is, again, besides the point. Asking the community "How should we fix the policy" is obviously never going to produce a consensus. Rejecting individual and orthogonal improvements by citing lack of consensus on an overall picture is not helpful.
My one suggestion was to get the term "homework" out of the picture. That seemed to be a pretty well received suggestion, and frankly the only counterarguments I've heard are
1) We can't do that because when we ask the community the open-ended question "What should the homework policy be?" there's no clear consensus, and
2) We can't do that because it's too small a change.
That's like rejecting a code patch that fixes a known bug because it doesn't fix all the bugs, which is obviously madness.
Soul-searching for the deeper meaning of the homework policy is doomed to failure both because the motivations of the usership are pretty varied and because the very name "homework policy" carries with it a certain context that unnecessarily constrains the discussion.
@DanielSank Sorry, I linked that post asking if that was what you referred to and you said "Nope", so I thought all this was about some other suggestion of yours.
I think we should also note that calling the homework policy the "homework policy" is like calling an anti-murder law the "Honduras policy": naming a policy after its biggest offenders is perhaps not really want we want...
Better to focus on the content of the policy itself, eh?
@EmilioPisanty You're probably confusing it with the similar-but-different earlier renaming of "homework" to "homework-and-exercises".
This is gonna sound like another stonewalling, but the post is three-and-a-half years old. Going completely off my imperfect interpretation here (I wasn't a mod back then), I think it wasn't implemented right away because DZ had hopes for renovating the policy entirely (which is what you mean by the rejection because it's "too small a change") in a reasonable timeframe. That collapsed.
Now it's years later, and I'm honestly not sure if it would be a good idea to implement it now without a more recent meta discussion. I mean, the mods certainly could do it without another meta round, but would it be a good idea?
"Beautiful" thread on this from 2014: Bite-sizing homework A bunch of highly upvoted rephrasings of what homework is, with no indication whether a consensus would be the union, intersection, cartesian product or some other funciton of the definitions, additionally confounded by some of the answers being pleas for the question type being defined being on-topic
@ACuriousMind Surely you can see that from my point of view, this is madness. Step 1) Propose a bugfix. Step 2) reject bugfix because it doesn't fix every single bug. Step 3) Notice that steps 1 and 2 happened, admit that trying to fix all the bugs failed (duh), but still refuse to fix the bug because the patch is old.
@DanielSank I sympathize. But bug fixes are objective, social policy is not. If that patch fixes a bug, I can just run the corresponding test (you did write a test, didn't you? ;) ) and verify it still does, then commit the patch. But implementing a three-and-a-half years old policy change now seems to me to strech the limits of the analogy. How many people active then that voted on it are still active now? (no way to tell)
I will agree that it was a mistake not to implement it back then, but I don't think it would be a good idea to implement it right now without a new discussion about it.
@DanielSank Yeah, there doesn't seem to be a good way out of this :( Or do you think just saying "hey, we just implemented what y'all voted for four years ago" would go off without a hitch? (Earnest question - maybe I'm overthinking this!)
@DanielSank I'm just saying that I can't run a test suite here to verify that your proposal is still as good an improvement as it would have been when people voted on it, excuse the strained metaphor :P
Surely there is something in the intersection of sets of what various users want to curtail.
Or at least, surely that intersection is not "homework".
I have never once cared whether a post came from someone's homework and there is no way for any reader to know that unless the OP explicitly uses the homework tag or says the question comes from homework.
Oh and by the way, re-reading that meta post, we could at least resolve the inconsistency that exists between the help center and the canonical meta post.
In connection with the moderator elections, we are holding a Q&A thread for the candidates. Questions collected from an earlier thread have been compiled into this one, which shall now serve as the space for the candidates to provide their answers.
Not every question was compiled - as noted, we...
Let's talk specifics.
And by that, I mean, "let me be the first to shoot my own self-interest in the foot", and argue that this question, which I answered, was rightly kicked off the HNQ list.
What's the deal? Well, the question starts off with the title
Is the Born rule indeed wrong?
and...
