in this paper, section 2.1 is just walking through the logic of how to correct the erroneously found non-zero change in entropy when considering a system of identical particles mixing vs. being separated by a membrane, right? ifi.unicamp.br/~cabrera/teaching/referencia.pdf
i wish i knew lagrangian mechanics and stat mech already :P
this paper would be much easier to read with the latter knoweldge XD
As I've said before, I have a soft spot for the Transactional Interpretation. It's just a shame that Cramer wasn't able to develop it, and he adopted some sleazy evangelistic practices of his own. But I still like to tease MWI people with it, just to demonstrate that I'm not a MWI "true believer" merely because it makes bizarre claims. :)
@LeakyNun No! Causality is a key issue in TIQM. It says "You guys are only looking at the retarded wave, but you also need to look at the advanced wave for causality to make sense". It says a particular outcome is observed because only in that outcome do the advanced & retarded waves reinforce each other. In contrast, MWI says you observe a particular outcome merely because you happen to be conscious of that branch. (And presumably other versions of you are conscious of other branches).
@SillyGoose Sort of. The config space represents the positions of all N particles as a single point. But the position can use generalised coordinates, so it's not necessarily N×R^3. Eg, the particles may be constrained to the surface of a sphere, so the underlying position space is two dimensional. See en.wikipedia.org/wiki/Configuration_space_(physics)
i think i understand that qualitatively, we want to mod the naively guessed configuration space $X^N$ by all permutations of points $x \in X^N$
if that understanding is correct, i do not understand mathematically what this "division" by a group action means
is it just a notation of this paper that $X^N/S_N$ means $X^N$ with all permutations of points removed
maybe i am just horribly biased but several hours to compute how many ways you can distribute several things into several things doesn't sound at all like one would learn any physics from it xD
@Slereah thank you for this suggestion hehe the sections on the classical theory are quite interesting in themselves and make me excited to learn mechanics >:D
When calculating the field / potential inside a charge distribution, will there be gross errors in the values? Reason is, when we write the integral $\frac{1}{4\pi\epsilon} \iiint \frac{\rho(r')d\tau' (\vec r- \vec r')}{|\vec r-\vec r'|^3} $, all is fine and good for particles well away from my field point. But suppose I have to analyse the particles very close to my field point. There ought to be errors right?
Keep in mind this $\rho$ is the charge density that is found by averaging over a macroscopically small, yet microscopically significant volume. This E field is macroscopic, and hence, $d\tau$ my volume element must be of the same volume as the volume i used to average our my $\rho$
@Mr.Feynman i understand that. My problem is that even when calculating the macroscopic field using the integrals above, I suspect we may still have a discrepancy, but my understanding is limited by the lack of precise definitions of the length scales in question. Some authors say that the volume used to average the field out, is the same volume used to average the density out. Others say the volume used for the density is much smaller than the field.
I'd really like if some authors put a number on these things
Because you see, when the length scales are comparable (those of the volumes used to average our these quantities) , our size of $d\tau$ gets affected, and consequently our ability to analyse the effects of particles close to the field point diminishes, as the size of $d\tau$ increases
@SillyGoose It's not "removed", it's a genuine quotient in the sense of equivalence relations, in this case $x\sim y$ iff they belong to the same orbit under the group action, cf. en.wikipedia.org/wiki/Group_action#Orbits_and_stabilizers
i.e. the idea is that you identify all the points with each other that are just permutations of each other, so that while points in $X^N$ are ordered $N$-tuples of elements of $X$, the elements of $X^N/S_N$ are unordered $N$-tuples.
@nickbros123 This formula is an electrostatic approximation which is already an idealization. It's not possible to confine a charged particle to an arbitrarily small region of space, it will shake and create a magnetic field, in shaking it will also be affected by magnetic fields... so how accurate this formula depends on the situation but yes in general the less confined the charges are and the closer you get to them, the field lines will diverge more than what this formula predicts
@nickbros123 That integral is fine if you just want to get the microscopic field. The problem is that this microscopic field is varying crazily in any material. The averaged, smooth fields that appear in macroscopic Maxwell's, is the ill-defined stuff, but is kinda needed for us to think about fields being somewhat constant inside materials.
I'm still taking my time to write something for your question.
@naturallyInconsistent But isn't it also the case that this specific formula is actually not taking into account the most general Maxwell's case? From what I understand, it doesn't take into account induced electric fields
@naturallyInconsistent I agree, the integral gives me the correct microscopic electric potential, wherever it may be. all the quantities in that equation would (have to) be microscopic. Is there an averaging technique I can apply here, on the microscopic potential (this particular equation, for the localised charge distribution) so that I can get the macro stuff?
and im having trouble understanding the physical meaning of $d\tau'$ in these integrals. From a mathematics perspective its ok, but we ideally want to write the above equation by being able to replace $\rho d\tau$ with $dQ$
@naturallyInconsistent okay thanks. I wrongly remembered that this integral in general is not right when $\rho$ is time dependent, I see now that I'm wrong (so what I wrote before is also wrong, it's not necessarily only correct in the electrostatic approximation)
@nickbros123 Actually, I think you are perfectly fine with $\mathrm d\tau^\prime$, and instead your issue is just over the specific procedure of which volume sizes to pick. And the answer that I will just tell you, inside Kittel, is the kind of trivial shit that you will be really sad about.
@nickbros123 What you're asking for reminds me of work related to things like "self energy of the electron" that some people were excited about before QM apparently solved that problem
@Amit Well, it is not wrong per se, but it is quite useless because it would fluctuate in time quite wildly. Nothing as wild as the fluctuations in space though.
And wild time fluctuations is also unphysical, because then by Maxwell's equations it should be radiating light. Just the radiation due to ions vibrating around their lattice points would be a problem. We all know that in the quantum realm, there would not be such radiation.
Changing magnetic field cannot be captured in that integral. That integral is for the electrostatic potential in the Coulomb gauge. Only vector potential can hope to capture that behaviour.
@nickbros123 Kittel did. And it would be somewhat obvious from the kind of usual standard shit we do in physics all the time.
Did I tell you that, one fine day back when I was at uni teaching as an assistant, I was shocked to find that my prof boss did not want to include this topic in his lectures?
And so I went to ask him to please teach it
and he said no, that belongs in basic EM, so he did not want to spend his solid state time to teach it
fair enough, so I dug up JD Jackson and showed that there was no mention of this averaging. (It only talks about the fact that you need to average, and that time averaging alone is not enough, you MUST have space averaging, and no helpful way to actually do this averaging)
If the grandmaster of EMT did not consider it suitable for EMT to teach it, then it is necessary to do it in solid state, so my boss relented and taught it
I'm thinking "consciousness causes collapse" is experimentally indistinguishable from Many Worlds. There are two classes of measurement problem solutions : 1. Objective Collapse theories 2. MWI/Consciousness-Causes-Collapse/Relational QM. The former can have many sub-theories. The latter three are indistinguishable and are "interpretatations" of the same theory
But doesn't that thing come up whenever we have a distribution? In CM, we have the integral over mass density for example when we calculate the moment of inertia. Same question applies there, how small a volume you need to get an accurate result
Measurement is not unitary, because it does not implement a unitary. It selects a unitary.
We can certainly say that a preparation $|\psi_i\rangle$ and (renormalized)
measurement outcome $|\psi_f\rangle$ are related by a unitary transformation $$|\psi_f\rangle = U_{fi} |\psi_i\rangle,$$ where...
This particular answer too, I really liked it. But the thread in general.
@Amit but my $d\tau$ in the case of classical mechanics can be the size of 1000 molecules if I want it to; mathematically I can still treat it as an infinitesimal because I'm integrating it over a huge (comparative) length scale. it rly doesn't matter in mechanics where things are all long distances. but in case of electrodynamics the size of $d\tau$ matters in my view, unless some mathematical stuff is going on that allows it to be truly infinitesimal
@RyderRude None of the workable interpretations can ever generate a different result than any other interpretations do. That is why people can ignore interpretations and get by
@naturallyInconsistent not really. There r two experimentally distinguishable proposals of solving the measurement problem: 1. Objective collapse 2. CCC/ Many worlds/RQM. Only the ones in the second camp can be called indistinguishable interpretations
But the two camps are distinguishable from each other
I think "interpretation" is a wrong word in general. Pilot wave theory also makes distinguishable predictions
@Amit no, it works much better there because there is no position dependence of the final results. You do not have to worry about how things here will affect field there. You can just blindly integrate over a big enough volume and get the answer
this is one of the reasons im looking for a scheme that can bring out the macro potential from the integral I wrote down above. in the case of a truly microscopic potential, my $d\tau$ is also like 10 molecules in size, that's truly infinitesimal in my books. whereas in the case of macro potential, the $d\tau$ (again, in my view point) has to be of the same order as the volume we are taking to find the charge distribution density, so that we can safely write $dQ=\rho d\tau $
@naturallyInconsistent With that I agree. But what @nickbros123 said is just a statement that in EM you often need to have smaller volumes, but in both cases for some volume size the approximation starts to fail, it just maybe a smaller size in EM because charges can be so small and distributed more crazily
@Amit yeah. This is what I meant when I said that there is no hope of deriving a single eigenvalue using Schrodinger evolution (without using Many Worlds)
@RyderRude the difference lies in that MWI has many branches, each seeing what collapse would see, whereas collapse picks only one. The only way to distinguish is to be able to experiment across universes, and that is currently outside the scope of science.
I think you ought to learn that it is NEVER too late to start theorising AFTER the data comes in, whereas it is often TOO EARLY to start theorising BEFORE the data comes in.
@nickbros123 no, no, infinitesimal integration volume elements have to be infinitesimal for them to make sense written as infinitesimals. Instead, you are asking about the choice of the sizes of the stuff you integrate over.
@RyderRude Not quite. It says that you can find a unitary transformation a posteriori the measurement, but it is not as far as I understood, the kind of unitary transformation you get from the usual Schrodinger evolution of the system
If you accept decoherence, then all time evolution is unitary. It is only that your viewpoint update due to measurement, i.e. you finding out which branch of the multiverse your universe is in, that gives the illusion of non-unitarity. This is outside the realms of current science.
@Amit every measurement operator comes with a complete set of eigenbases, by postulate. We can only dispute it when experimental evidence accrues that it is false.
Suppose u knew the exact state of the energy measurement device, and u applied Schrodinger evolution on two eigenstates. And then u applied Schrodinger on the sum of those eigenstates
This wud mean that ur measured state will have to be a superposition
@naturallyInconsistent we r assuming that it is an energy measurement device. So for energt eigenstates of the sub system, it gives u back those eigenstates
So for the sum of those eigenstates, the measurement shud give u the superposition
@RyderRude Sigh, how much must you dig holes instead of trying things out? Consider $$\mathcal H=h_0+H_0+H_I=\begin{pmatrix}a&0\\0&b\end {pmatrix}+\begin{pmatrix}A&0\\0&B\end {pmatrix}+\begin{pmatrix}0&c\\d&0\end {pmatrix}$$
If u have two entangled particles far apart and u measure them with different measurement devices, those devices would have randomised wavefunctions. So the two measurements would not be in agreement with the correlation that is observed
This is another reason that non determinism does not arise out of the ignorance of wavefunction of measuremenr device
My point is that non local correlations wud get destroyed, if measurement results depended on exact device wavefunction
I think the non determinism is not only related to the measurement device, but also to the fact that the measurement is a spacetime event in the classical sense e.g. we can approximate it as a point. Of course it isn't, something happens in that short time interval. Now IDK why this very "sudden" event appears to violate unitarity, but I am quite sure in reality it really doesn't. I think it's a complex matter analyzing this, involving more than just assuming a complex measurement device
@RyderRude Actually if you're referring to EPR experiments, I'm quite sure measurement devices in the real world can't be perfect. There will be an expected tolerance for failing to detect a correlation that has to do with the imperfection of the measurement accuracy
@Amit Not possible. If you really think about measurement in the context of thermodynamics, you will see that every humanly made measurement has to take a lot of time and a lot of space in order to be tolerably sensible for saying that we measured something. i.e. it should not be microscopic, but should be mesoscopic or larger.
@naturallyInconsistent suppose there is an energy measurement device of exact wavefunction $\psi$ and a system of wavefunction $|E\rangle$ and $|E_2\rangle$ If we do $U(t) (\psi \otimes E_1)$, it gives u $E_1$ (by definition of an energy measuremenr device). Similarly $U(t) (\psi \otimes E_2) =E_2$ (upto phase factor). By linearity of $U(t)$ : $U(t) (|E_1\rangle +|E_2\rangle)=|E_1\rangle+|E_2\rangle$
@naturallyInconsistent But that's not how we model QM interactions, and that's what we think we're measuring
@naturallyInconsistent I mean it was really part of my point, but I didn't really phrase it correctly, we think of the QM events that we want to measure as very small spacetime chunks, but the measurements are as you point out significantly bigger spacetime chunks, aren't they? So I was pointing out this is another "blind-spot" that needs to be carefully analyzed
@Amit my point is that correlation would get completely destroyed if u make the final outcome dependent on the exact states of the TWO measurement devices which have independent wavefunctions
I already gave a very obvious example of how the measurement apparatus and the system may start in energy eigenstates and end up each in superposition.
AND IT MUST, BY DEFINITION of what a measurement apparatus must be able to do. It must start with some initial state, and end up in measurement result states. This can _only_ happen if there is some way to get to all those different states. The measurement process cannot be diagonal in Hamiltonian eigenbasis
@Amit people who analyse the concept properly would have taken this into account.
@RyderRude Why? That's implying that the measurement devices aren't sensitive... I am not denying that the measurement devices tell us something about the state of the measured system, but the measurement interaction must have some effect as well is what I'm saying -- how do we know it doesn't obey unitarity if we can't very accurately describe this process?
@naturallyInconsistent Then I am in agreement with this. There is a final superposition obtained. But it's just that the two eignavalues are in different universes (theyre correlated to the two possible final states of the measuremenr device)
@Amit this effect that u r proposing is called the "preferred basis of decoherence". This effect has no saying in the eigenvalue that is selected
@RyderRude thanks. And that was why I was telling you to just actually write down some maths rather than make handwavy arguments. It is very dangerous!
@Amit If the effect had a saying on the eigenvalue that is selected, then there would be no Born rule, as it would be impossible to get a rule describing the results of measurements without any dependency on the measurement device. Born rule shows that eigenvalue selection is completely dependent on the state.
@RyderRude After it decoheres to the preferred basis probably some other theory comes in :) IDK. This is not serious on my part to debate from this point without some very careful analysis which I haven't done. I'm just saying that if Einstein decided to follow through on the assumption the $c$ is constant for all observers, I think it makes sense to take as a guiding principle that the world obeys unitarity :)
if we need to create an infinitude of universes to preserve unitarity in some global, multi-universe wave function, then I think it's avoiding the issue, just a personal hunch :)
Anyway, the measurement device makes the couples with a system in such a way that, for the microscopically long yet macroscopically short time of the process of measurement, the Hamiltonian of the system is diagonal in the measurement's basis, and so if you start the system with an eigenstate, it always returns the eigenstate, (and any classical mixtures thereof in the density operator)
Q : The state of an electron is 1 billion : 1 for spin up : spin down. U r asked to bet on spin up. If it comes spin up, u get 1 dollar. If it comes spin down, u lose everything
Ok here's my follow up que: Now u believe in MWI. If u take this bet, there r 1 trillion copies of worlds where u get 1 dollar and 1 copy where u get the solitary confinement
I will reply that there is greater variability in the human appetite for risk than there is variability in the correctness of those views, and so this bet is moot
@RyderRude No, on the contrary, I'm saying maybe my fundamental resistance to playing Russian roulette under any circumstance is an indication that I'm a closet MWI person :D
The entanglement between young me and the university has left me in less weird in the astrology sense but much weirder in basically every other way. Maybe weirdness is a conserved quantity
For me, this is like it doesnt make a difference whether u give me 1 dollar in a single world, or u give me 1 dollar and make an octillian copies of that world. I dont weigh the latter scenario as advantageous over the former
So when MWI proposes that a bet is supposed to beneficial to me just because my success world will get copied a zillion times, it seems like a moot point to me
@naturallyInconsistent yes, this is my argument. Despite expectation value being same, MWI's shenanigans about world duplication does not make a bet look more attractive. In Copenhagen, the expectation value's interpretation is in terms of likelihood, instead of duplication.
This is y we think bets r beneficial. It's because of likelihood. In MWI's duplication philosophy, bets dont get more attractive just because the event of success gets duplicated
No, that is not the argument I'm making here. I'm not worried about the guarantedness of loss, as much as "why is a bet supposed to be more attractive just because the success world gets duplicated? "
Do u really care if u r successful in a zillion clones of the same world
I dont think these clones add anything to making a bet more attractive
That's equivalent to the statement that picking a black ball from N balls with N-1 being red, is the same as getting a ball in a box that you know has a chance of 1/N being black
@naturallyInconsistent but in MWI, you can no longer reason in terms of "I'm more likely to end up in the success world", because these statements become meaningless. Your current self ends up in all of the worlds. So the only reason you find the bet attractive is because you think a billion clones of the "successful you" will get created.
you can no longer reason in terms of "I'm more likely to end up in the success world" -- incorrect! that's a very correct reasoning, and it's basic probability that justifies this reasoning
that's what I tried to demonstrate with the N balls example
@RyderRude Just postualte the Born rule and then you can speak of "I'm more likely" FFS I have not the patience to keep arguing with you over such things.
@RyderRude I'm "more likely to end up with choosing a red ball" is the equivalent of saying you're likely to end up in a "red" universe lol. The probability is a mathematical fact and it becomes irrelevant how you calculated it
To give a simple derivation of Laue's condition for x-ray diffraction, some people give proof by simple vector addition of $\vec{k} + \vec{G}= \vec{k'} $ and squaring them. I don't understand what's the reasoning or how it's done. Can someone expalin this is simple terms..
@Amit No, this interpretation does not work in MWI. You cannot say that your current self is more likely to end up in the red ball world. You cannot define what you mean by this likelihood
It's because your current self is the history of all the worlds that are created. Your current self ends up in all of the worlds
There's no concept of "I'm more likely to end up in this world"
I understand MWI says you end up in them "all". But there are two "you" involved when we speak about this in English lol. There's the local you and the global wavefunction you, right? the local you is what you can make probabilistic statements about, as far as I understand
I still think we may mean different things by "current self"
That "current self" is not an entity uniquely bound to one universe in MWI. But you can talk about a current self in a unique universe, otherwise you are denying reality, lol
In this reality that I hope you're not denying, probabilities work as we know they should
@JohnRennie I don't answer them when it is blatantly obvious that they are not even putting in effort. I just pick and choose what is interesting to me.
Of course. But I think I read somewhere that MWI was presented to him as something he may like, because it explains the non determinism that he disliked about QM. But I think he was unimpressed -- I am trying to find the source of that quote, hopefully I'm not mixing him with another physicist.
Oh apparently I must be wrong. MWI was proposed in 1957. Einstein died in 1955.
@naturallyInconsistent Homework is homework whether the user has put in effort or not. The point is we don't want the SE saturated with JEE questions. We close the questions to discourage people from ásking them, and when you answer the questions it undermines this effort.
@RyderRude That is total nonsense. Copenhagan is not even attempting, and so it necessarily has to be less scientific. MWI might have to be augmented with Born rule, but at least it attempts to take unitary evolution fully.
@naturallyInconsistent That's not so clear to me. It can be more scientific at times to say "We don't know and claim no hypothesis" than making an irrefutable hypothesis :)
One of the latest questions I answered was closed as homework. I'm pretty sure it wasn't homework because the OP initially phrased the problem wrongly (he asked basically what would happen in a certain situation if applying $x$ Newtons of force, and we know that isn't a well defined thing), then he changed the details of the question -- all in all, I do think he had a conceptual question that he just tried to put into a format that looked similar to a textbook question, but I don't think it was
@RyderRude I think you will fully understand and accept as normal that I am totally sceptical of your continued claims that MWI has this or that properties, and thus that I would not take your claims about this seriously either, from this point onwards. I am not going to continue entertaining them at the intensity that I have thus far been, but of course, feel free to continue.
@Amit That is simply not true. Some variants of Copenhagen are literally saying that "we insist that measurement cannot be understood, even in principle". Assuming unobservable universes is not much more complicated than assuming unobserved fields.
No, I was not attempting to silence you. I am just saying that I am pulling out of the conversation.
@naturallyInconsistent That's fair, though you did say Some -- I also don't want to stretch this discussion much more. If his was a dead horse, he's been beaten excessively in this universe quite enough even without having to assume parallel ones, lol
@Amit We have a small group (not including me!) that seem to interpret everything that involves any form of calculation as homework. I find myself voting to reopen questions closed as homework several times a day. But we do also get questions that really are homework.
@JohnRennie Yes I completely understood also in this particular case why it appears to look like HW. But yeah there is probably room for improvement, ofc it is time costly to dig into every question to see if the OP has a conceptual difficulty or is just looking for someone to do his HW :)
I tend to err on the side of keeping a question open if it's even a it conceptual, but as I say we don't want the SE to become a venue for solving JEE questions.
I also think the content of the answer is a big factor in this, the answer can be a really good conceptual one that doesn't solve the particular problem that the OP wants to solve, but can be worthwhile for other users. It happens sometimes that good answers turn bad questions into good ones in that sense :)
@naturallyInconsistent Like a guy that some days ago asked me what is "physical definition of a Hilbert space" (not the physical reason why we model quantum states with a Hilbert space but, again, the physical definition)
Otherwise "we'd just be doing Math" lol
I was getting quite worked up on that, but then their bus arrived
Just because experiment has the final word in Physics doesn't make theory redundant. In the same way that just the mere existence of the place you want to travel to doesn't make your car redundant, lol
It is much worse than that. If you look at relativity, Einstein is completely correct that it is theory that tells us what it is that experiments are measuring. Experiments can just be completely confused by time dilation and length contraction without needing an explanation of why they differ from their expected values.
Which is why Einstein replied to Heisenberg that quantum theory should also be the same.
To play devil's advocate a bit then: but what if there was no Einstein and someone found a completely different way to explain these effects, and let's say it would have been done with a purely mathematical model more similar how QM looks like. Would we be better or worse off? It can be argued that something like the Einsteinian ontology, as elegant as it is, can also hold us back because it creates more prejudices than a purely mathematical model
But I'm really digging into the devil's advocate position here, personally I think that we need such ontologies, we just need to feel free to question them once in a while too
Well, we do not need to consider it as a theoretical scenario, because we have it as a real world history. Poincaré and Lorentz had two different mathematical work on relativity and they never did fully understand what Einstein was talking about. They never did fully grasp the paradigm shift needed to understand why relativity is talking about the nature of the universe, as opposed to the confusion that they were thinking are sufficient explanations of the phenomena.
Yes, it's just interesting to imagine what would happen if they would have taken their work further without Einstein interfering with his brilliant ideas that made sense out of everything, which to a large extent foreshadowed their work. Actually, I think Poincare could well have gotten to the same point Einstein did, because I think he was the one who reformulated the symmetrical form of the Lorentz transformations. Maybe he would have reached the same conclusions... but who knows
I was saying that both Poincaré and Lorentz essentially finished their discussion of the subject until Einstein came along and gave a totally different viewpoint.
The same thing applies much more sharply however to GR of course :) Where would we be without Einstein becomes a much greater unknown. It's much less clear we would have a theory even resembling GR.
Oh, we did not need Einstein for GR. Einstein rushed to publish GR before he heard Hilbert was putting effort into it, and Hilbert got equivalent results a few months after Einstein published, using a totally different method.
Yeah, I think we're on the same page. I am just saying that there's an argument to be made that a non mathematical viewpoint (I hope calling that an ontology is correct) is a double edged sword: it can carry you a long way forward clinging to such principles like Einstein did, but it also inevitably creates "prejudices" that may or may not hinder further progress
Ohhh right -- I forgot about the Hilbert story, he did it via a least action method if I recall, right
But the history becomes more complex there -- Einstein already published many papers on relativity and seeded various ideas
@Slereah They say he worked on GR for 10 years... and the geometric ideas were already embedded in the mathematics he was using, even if he didn't pay much attention to it and needed Grossman for private lessons in differential geometry every so often :)
@Slereah Einstein did not argue persistently to drop the æther. All he did was not include any discussion of æther and quietly not mention it in any teaching of the relevant subjects. Then let the thing just quietly die away.
ah okay. Just asking 'cause I commented on this buoyancy question, linking to a similar question with relevant information. I think the OP thought I'm trying to suggest it's a duplicate (I didn't flag it as such) and deleted it, and now he reopened a near identical one, lol
Some users that do this stuff, aren't aware that the mods see all that
@Amit It's not just the mods. The system software tracks that stuff and automatically imposes question bans on low rep OPs who post too many low quality questions. And mods cannot reverse such bans.
It's can be a bit unintuitive because deleting a question with a non-positive score is penalized by the Q-ban algorithm, especially if the question has an answer (although the OP can't delete if an answer has a positive score or is accepted). So lots of new OPs delete poorly-received questions, thinking they're improving things when in reality they're increasing their likelihood of getting Q-banned.
@naturallyInconsistent If a question has potential, but is likely to get closed as homework-like, you can try to help the OP convert it to a conceptual question so that it's on-topic.
OTOH, that can be pretty hard to do with the majority of homework-like questions, but occasionally you can tell that the OP really has a conceptual question, but it's buried under a bunch of algebra & calculations.
@Amit While we do indeed see more than people might assume, please feel free to flag instances where someone deletes and then reposts a question
@PM2Ring Yeah, the UX for new users that have downvoted or closed questions is pretty terrible from a contemporary standpoint. Much of SE's interface was built in the context of an internet that no longer exists where the assumption was that people would lurk around a site before they joined it
@ACuriousMind Fair point, but I still think it's reasonable to expect people to explore a site a little and get a feel for the place before they post. OTOH, many OPs are truly surprised to learn that deleting bad posts doesn't make the badness go away, and the Help pages should spell that out more clearly. There are tons of posts about this issue on MSO & MSE.
if i send some spin particles through a stern gerlach device and then recombine two of the resulting beams such that you cannot tell from which beam the particles came from, what is the resulting object representing this state? is it a superposition of the states of the two resulting beams?
Measurement is not unitary, because it does not implement a unitary. It selects a unitary.
We can certainly say that a preparation $|\psi_i\rangle$ and (renormalized)
measurement outcome $|\psi_f\rangle$ are related by a unitary transformation $$|\psi_f\rangle = U_{fi} |\psi_i\rangle,$$ where...
