@ACuriousMind i mean u can construct binary yes/no diagonal operators corresponding to the measurement of each eigenvalue. So a "non-measurement" also counts as a measurement of this operator
I don't see the term "non-measurement" anywhere there
and really whether the result is semantically "negative" in our human interpretation or not doesn't really matter to the QM formalism
you're measuring a projector, and you're getting 1 or 0 as the result. That the 0 isn't the eigenvalue of a "physical quantity" in this case but says "it wasn't here" doesn't really matter at all
sure, and if I find an explanation for what exactly happens during measurement, you'll then ask again why the world is like that
honestly I feel a lot of this talk about interpretations has never left that childish stage where you annoy your parents by asking "Why?" after every deeper explanation
But my problem is that we dont know when to apply those axioms. When to apply Schrodinger and when to apply Born. This leaves ambiguity. I wont ask for deeper reasons for axioms if the theory isnt ambiguous
It is unclear about how we should desscribe the combined system of a measuremenr device and the measured particle. How do u choose to describe this on paper?
Do u reduce the state vector or do u describe this as a Schrodinger evolution?
I think the obsession with interpretations of QM arises from a subtle hope that this or that one will give us a new idea for how to distinguish them experimentally... The fact that there are so many experimentally equivalent interpretations means it's really hard to cook up something that is experimentally correct without being also mathematically identical. Feynman once said something like: "It's very difficult to apply imperfections to a perfect thing and yet leave most aspects of it perfect"
@ACuriousMind yes QM is definitely a useful model in predicting the number on the measurement device. The quest for theories like objective collapse is the quest for a more accurate model
@Slereah That's a fair point. There's something about QM that attracts that much more. Probably all the hocus pocus that is associated with EPR, Two slits experiments, and all the other run of the mill examples of QM weirdness... and it's hard to convince people by just saying "your intuition is weird, nature is not"... lol, though that is probably very true
But trends don't really pass as much as they just transform. Now we think we understand all this stuff in terms of QM which is more fundamental we suppose, and the focus is there
Just remember that Michelson-Morley expected to find the aether, mostly because "EM waves might just propagate through vacuum" really didn't fit into their physical interpretation
The thing is... CM was always clear about its evolution laws and universe's ontology. QM isn't. QM seems like a temporary theory designed to predict the number shown on measurement devices until we find a better understanding of the evolution laws and the ontology
@Mr.Feynman i mean what things exist as a wavefunction and evolve according to Schrodinger and what things r messurement devices for which Schrodinger doesnt apply
classical mechanics doesn't make it clear when you can treat something as a single object and when you need to model it as being composed of smaller components either!
it depends on the situation and what you want to do
@RyderRude depends what you mean by "measurement behavior"... in the two slits experiment you know quite well how the thing will behave. it's the fact that you don't know exactly where each individual particle is gonna be detected that you can say is an "indefinite behavior" but that is also predicted by the model... Born rule is about probabilities, and probabilities even in math pertain to a large number of events
@ACuriousMind your philosophy does make QM very clear. But this is only becuz u r sticking to the "measurement happens when you see it" interpretation. This is not the agreed upon way to apply the QM axioms, which is what I mean by "lack of clarity" in defining the measurement.
@RyderRude and my point about classical mechanics and single objects or components wasn't really about this weird focus on reductionism you seem to have
I just meant that classical mechanics, too, has different ways of describing the same system depending on what you're doing
that in CM you think you can derive one of these descriptions from all the others (can you really? go poke the hornet's nest and ask people how statistical mechanics works) while in QM there seem to be two "fundamental but different" descriptions doesn't really bother me
@RyderRude the "agreed upon way to apply the QM axioms" is to not worry about this stuff at all
again, in no concrete case has an experimenter ever been confused about the problems you have
if interpretations mattered so much, you'd see a lot more QM papers that talk about interpretations
but unless the topic is specifically interpretations, they never come up!
My problem isnt with the experimental use of QM. My problem is only in the ambiguity in how to apply QM, in principle. U define measurement as happening when "you see the outcome". Other people define measurement differently
And yes, none of this matters in experiments
As we have established : "All models are wrong. Some are useful"
QM is a useful model in predicting what the measurement device would show. And interpretations done come in the way of this at all
@RyderRude The Born rule is what defines the probability of different measurements doesn't it? In CM we don't even have that because measurements are implicitly assumed to be embedded in the description of the system... "just read off the variables" I guess you could call the equivalent of Born's rule in CM lol. So is the problem that probabilities are inherently ambiguous or something else?
@ACuriousMind But I think this also suggests that there exists an underlying theory which isnt about "predicting what the measurement device would show". That theory would work in the regime where QM doesnt. So this goes well with the philosophy of " All models are wrong but some are useful"
I mean there must be an underlying model to QM, which is more accurate and is not ambiguous, even in principle
What I find funny is how often "hidden variable'ist" are seen as kind of looney :) But they may have something interesting to say also imo
The thing with being open to everything is that it leaves you on the fence, and then it's just a matter of how much speculation you like to do before getting bored :)
I have no reason to expect there to be an "underlying model", because the models only exist in our brains anyway! Sure, maybe we'll construct another model we like better in the future, maybe not, who knows. It's even likely we'll find something else. But "there must be another model" imbues our scientific theories with exactly the ontological weight that I reject when I say that all models are wrong:
@ACuriousMind yes. QM may not have an underlying model. But in that case, we would need to make clear what the measurement axiom means. Does measurement happen when you see the outcome? Or is the measurement axiom supposed to be applied when the measuremenr device performs the measurement? (i.e. the measurement device isnt a quantum system itself).
Both these choices r equally good when we only care about predicting the outcome that the measurement device shows. But we will eventually need to make more accurate predictions
Like, our predictions may get sensitive to whether the measurement device is supposed to be quantum-mechanical or classical. Then we would need to make the choice bwtween these two "interpretations" of measurement
Let's say i have a situation in which the Laplace equation is satisfied at every point in space except one point, where there's a point charge. (Basically one can say the poissions equation is satisfied). Let's say i also want to obtain a solution using variable separable. What should be my boundary conditions considerations? And is this question even possible using sepn of variables
Ignore the fact that the potential is trivial
My guess is that such a separation is not possible. Situation is only tenable when another boundary surface of radius >0 exists (which is equipotential)
Actually one more question I wish to add that general relativity and special relativity of theory have important use in gos technology where sr used for the time measurement and gr relate to gravity so my question does gos satellite suffer time delay due to it's orbital speed? And distance between earth and satellite do affect the đŸ•’?
Most of the time entanglement is described using some instantaneous classical measurement from an apparatus, but it is possible to describe it between two quantum systems, with two systems $O$ (for the observer) and $S$ undergoing the following process
$$\vert \psi^O \rangle \otimes\vert \psi^S...
@Slereah oh yes.. This stuff is the idea behind decoherence
The measurement device can b modelled as a wavefunction and then u get the superposition that u mention in the post using Schrodinger evolution @Slereah
But if u buy this philosophy, u wud need to interpret the collapse as happening when you see the outcome yourself. This would lead to either "consciousness causes collapse" or "relational QM" @Slereah
Or this can also lead to Many Worlds, if u think the "collapse" in this philosophy is only apparent
@Amit By definition of projection, this particular case is definitely changed. i.e. you are wrong.
@RyderRude No, it is clear. The issue is that different interpretations prescribe different solutions to this, often in an ad hoc fashion
@ACuriousMind Copenhagen, by postulate, insists that measurement cannot be understood better than the sudden collapse. Decoherence, on the other hand, gives a prescription of how to understand the process of measurement as a finite-time evolution, that you can understand what happens in the intermediary states, and how to reverse the measurement in principle, etc. I do not think anybody who had considered this point would argue that Copenhagen does a better job at this than decoherence.
@naturallyInconsistent do u mean the "quantum-classical divide" philosophy is ad-hoc? I agree that this philosophy is a different theory from usual QM. Usual QM should model everything as quantum, which gives you either many worlds, relational QM or consciousness causes collapse
@RyderRude I consider any interpretation that requires classical objects to define fundamental things necessary for the operation of their interpretation, simply too wrong to be accepted as a contender for a valid interpretation. i.e. I reject Copenhagen as a contender, amongst so many other possible interpretations that I might dislike, but accept.
But no, I think I was referring to something else.
@Slereah precisely. There are half a dozen different, and incompatible with each other, Copenhagen variants all claiming to be the one true Copenhagen. Any sensible discussion of interpretations has to first start with forbidding the use of Copenhagen, before people can get anywhere.
I can defend the defensible stuff that I dislike. After a lot of training into studying the interpretations (and general physics theorist education), one learns to treat things objectively.
Oh, I am one of those rare unicorns that like transactional. I think of it similar to Feynman Wheeler style, that part of why we needed to specify the future, is that the time symmetry of the basic components of the universe says something important about how our universe actually works, despite the apparent need to obey causality
@Slereah but, as I judged, it is not even a valid contender for an interpretation. There is no such thing as a classical object in our universe that is suitable to state the half of the measurement postulate. Not to mention that you yourself understood that there are so many vagueness in Copenhagen
That is so optimistic. I was just sent by my company to be lunch conversation entertainment for this ex-dean of a very famous local university, who had a physics degree and was opining about how Einstein-Cartan torsion field is the key to "connecting to the website of Jesus".
I eat very slowly. Usually takes hours. My boss was like "Wow, I have never seen you eat so fast!"
@RyderRude But it does not need to do so. As long as you care about consistency, you have to treat your measurement apparatus as part of your quantum world, and thereby include its wavefunction in your description. The insistence upon some kind of separation is the thing that is artificial
There is a superstition here in Italy about opening umbrellas inside (I don't know if this is a thing anywhere else). I remember that during a lab class someone's umbrella opened and a guy or a girl, I don't remember, panicked. I stood up from my seat and asked them to leave the department :P
@naturallyInconsistent yes. This is a nice way to make QM clear. But this also means that collapse or "apparent collapse" only happens when you see the outcome. This leads to Relational QM or Many Worlds
@RyderRude No, you manifestly can. Why should measurement devices, which are made of quantum materials, be not subjected to QM laws?
how many times must I remind you that no, it is not that simple. Even within the decoherence family you have an abundance of choices, and there are also others that reject decoherence.
And you again use the word collapse to just mean the effective projection of the state vector. This is just so many layers of wrong. Decoherence can easily get you the effective projection of the state vector (just do conditional probability properly). The only one thing decoherence is yet to be able to make inroads into, is Born rule.
@naturallyInconsistent I mean, I said it was in Italy because I don't know if it's a thing in other countries but I'm not saying everyone believes that :P
Yes. But not everyone agrees with this philosophy. Copenhagen is still the most agreed upon interpretation. It says that measurement devices cannot be in superposition.
@RyderRude You are getting caught up because you keep using the wrong terminology. What you mean as the "experimental use of QM" is QM itself. What you call "ambiguity in how to apply QM, in principle", is just the lack of consensus on which interpretation is the correct one. That is not an ambiguity in QM itself.
@RyderRude As mentioned very many times (thanks to my love of talking about it, sorry), there is no such thing as a standard Copenhagen. There are plenty of Copenhagen people who do not agree that measurement detectors "cannot be in superposition".
@nickbros123 It is very funny that you are concluding something wrong about the one case that all textbooks cover. You should study some ODE PDE theory. The boundary conditions have to be added manually, usually from thinking about the physics.
I think if we take all postulates of usual QM on face value, it just gives u "consciousness causes collapse". i.e. treat the entire universe as quantum, and apply the Born rule when u observe the outcome. Everett also mentions this Quantum solipsism stuff in his thesis
But this stuff completely ignores decoherence. This is y i personally anticipate a modification of QM which leads to irreversible dynamics upon measurements
@RyderRude for goodness sake, can you please actually study the various interpretations, logically work out what are actually derivable deductions and inferences, and not just randomly sprout your gut feeling about how things are related? The "consciousness-collapse" viewpoint has always been a minority viewpoint in physics.
@naturallyInconsistent i will try. Thanks. Right now, i really dont think usually QM implies anything other than consciousness causes collapse, either "apparent collapse" like in Many worlds or "actual collapse"
@naturallyInconsistent I got a question.. If u agree that the measurement device goes in a superposition, then what other choice do u have than saying that "the state vector reduces to a single eigenvalue only when you see the outcome"?
I think our only two choices r this consciousness stuff or quantum-classical divide. I favor the latter becuz decoherence supports it
Otherwise, I wud be buying Relational QM or Many Worlds
Well, decoherence explains that the combined system+detector(+environment) wavefunction, the system and detector parts become entangled, and then that also gets entangled with the environment. After a while, the lack of control on the noise cause the phase relationship between the different measurement outcomes to be so out of sync that each system+detector eigenstate shifts out into its own branch (where branch is merely borrowing MWI terminology, but could easily be Pilot Wave, say).
Once the phase relationships are sufficiently mixed up that there is no hope for reversal of the entangle…
Some people ascribe the duality to the duality between the classical appratus and the quantum microscropic system, but I think this is a little old-fasioned. The quantum description also works for a bad apparatus and a big apparatus--- like my eye looking at a mesoscopic metal ball with light shi...
@ACuriousMind Ok but decoherence is a consequence of Schrodinger. Claiming that it derives collapse is claiming that Schrodinger derives collapse, which is wrong
decoherence is more of a consistency check: It shows that it doesn't really matter if you model the apparatus as a quantum object and then "measure" the apparatus+system when you observe it or if you immediately model the apparatus as performing a measurement
And in the meantime, people are perfectly happy with the fact mixing the phases up by a few turns is already sufficiently decohering wavefunctions enough to get single eigenvalues.
yes, but the idea you're arguing against there is not really the point of decoherence! you've completely missed the point here but I'm exhausted by this conversation and don't really want to go another round
Decoherence manifestly explains why each branch of the wavefunction sees a single eigenvalue. That you fail to see it is not something we can really help you with.
@SillyGoose Yes, every acceptable interpretation of QM has to agree that the density operator essentially agrees with the partial trace of the environment, leaving us with Born probabilities of each entangled system+detector states
And hence why each branch in there, sees just their own eigenvalue and no others.
@naturallyInconsistent But again, if they have any interference, I would say one eigenvalue hasnt been obtained. The state is "all the eigenvalue at once". This is also the standard interpretation of Schrodinger's cat
Decoherence allows u to pretend one eigenvalue has been obtained. But this pretense is not technically true, if u r treating everything as perfectly quantum
What the actual post-measurement postulate of QM really should say, is that the subsequent evolution of a system after measurement _is mathematically equivalent_ to that which is "collapsed" as only one eigenvalue. This is the version you can derive from decoherence, because despite the fact that you can still have Many World branches, each single branch operates independently and keeps up the pretense that there is only one branch left.
The post-measurement postulate in the density operator form is much clearer as to what actually should be happening.
But my point is that it is not mathematically equivalent, if you are treating everything as perfectly quantum! @naturallyInconsistent . U never get a perfect density matrix. If u instead stop treating everything as quantum, u may get what u want. For this you would need a quantum-classical divide
Otherwise, u r just pretending that u have obtained a single eigenvalue. Decoherence allows u to pretend this and it would give more or less accurate results
If this works out, then the measurement problem is no problem
And Copenhagen is the certified correct interpretation
With "collapse" replaced with "decoherence"
@naturallyInconsistent i will try to find something supporting my argument
@naturallyInconsistent First, let me confirm ur view. U r saying that Decoherence does yield u non-interference of the branches and there is no approximation involved. And the only thing lacking is the Born rule probabilities.
I will never accept the use of the word "collapse" for the interpretation that I am using. And I have repeatedly urged you to use the terminology with more care.
If you take the MWI, then there is no state reduction, only the illusion that the state reduced. Although I do not believe in MWI, this aspect of decoherence is something I agree with.
Most of the time entanglement is described using some instantaneous classical measurement from an apparatus, but it is possible to describe it between two quantum systems, with two systems $O$ (for the observer) and $S$ undergoing the following process
$$\vert \psi^O \rangle \otimes\vert \psi^S...
