12:01 AM
The orthodox way to understand it in terms of the SWAP gate is also straightforward
I think once it is recognised that quantum states lives in Hilbert space, which has little in common with the spacetime we are in, we will stop giving positions and associations their privileged character, and the Chireshire cat experiment will seemed less a paradox
2

12:40 AM
@Secret Almost every layperson resists this. And not a few physicists.
If—as I did—you got started wanting to understand things by taking them apart and figuring out how their component bits fit together anything that doesn't let you play with the cogwheels is a hard pill to swallow.
@Semiclassical I got the pop-over add, too. But it was easy to close. Uptodate firefox on Max OS.

12:56 AM

1:14 AM
@Secret interesting (popsci) writeup thx for sharing. fyi there are some classical systems with hilbert spaces with deep, eerie resemblance to QM but it seems to be mostly buried-to-unheard-of and extremely few have much curiosity/ drive/ initiative/ perseverence to pursue it further.

Ah here it was
Pic from reddit, I don't speak German :P

2:13 AM
Xi is easy. But zeta is a pain.

2:26 AM
@dmckee Well, for me, I will say quantum mechanics do have cogwheels, but it is a different kind. Thus what I did is to learn the foundations of this new system, understanding those new cogwheels and then build a new form of intuition based on them
Most science subjects can still be understood by the cogwheel like approach, but there are many things such as society, cultures, religion, philosophy cannot be taken apart that way
The Koopman–von Neumann mechanics is a description of classical mechanics in terms of Hilbert space, introduced by Bernard Koopman and John von Neumann in 1931 and 1932.As Koopman and von Neumann demonstrated, a Hilbert space of complex, square integrable wavefunctions can be defined in which classical mechanics can be formulated as an operatorial theory similar to quantum mechanics. == History == Statistical mechanics describes macroscopic systems in terms of statistical ensembles, such as the macroscopic properties of an ideal gas. Ergodic theory is a branch of mathematics arising from the study...
This one? you can see the classical counterpart of the virial equation there
Quantum mechanics also have a phase space formulation using Wigner quasi distributions
Anyway, I think the key thing about quantum mechanics to understand its non locality is that states and properties can be close in Hilbert space, but far apart in real spacetime
With that, it will become easy to understand how entanglement came to be: Spatial and temporal separation does not separate the subsystems that forms part of the state in the Hilbert space

3:15 AM
@dmckee I could only reach the X button in Chrome by going into full-screen mode
@vzn one interesting example of Hilbert space is in probability theory. See for instance inst.eecs.berkeley.edu/~ee126/sp18/projection.pdf
Basically: the random variables serve as the vectors, and the covariance as the inner product
Bam, inner product space. And if your space of random variables is finite-dimensional, then it’s a complete inner product space ie Hilbert

@Secret yes great stuff close to what have in mind. conjecture there is an (emergent) classical system with formalism identical to/ indistinguishable from QM. (proposition bells thm is not a disproof/ refutation.)

3:32 AM
hmm now that makes me wonder, what happens when we tried to physically separate two position entanglement states
guess nothing much different, since we cannot determine their positions without measuring it and hence separate them as if they are classical objects
and if we separate them by using some unitary operation, then whether the resulting state is entangled heavily depends on the operation in question on whether it rotate the entangled state into a product state

it has long appeared to me entanglement is analogous to a wave medium but which can only be "sampled" via quanta/ quantized. there exist such systems in classical mechanics but they seem to have mostly escaped much attn. cant quite nail down the math, need a modern von neumann or grossmann, still searching :|

4:29 AM
0

A cone of radius $R$ and height $3R$ is immersed in fluid of density $\rho$ such that the tip of the cone is at a distance of $2R$ from the surface. Find the force on the surface of the cone due to the liquid. (The central axis of the cone is parallel to the surface of the liquid) I solved t...

Can someone help me?

5:02 AM
Hello, all.

3 hours later…
8:30 AM
Afternoon dream (because I took a nap): Dreamt about that oil drop experiment that is commonly used as an analogy to Bohm, there's a pair of oil drops hopping on the surface and in between them is a line of oil beads that move towards or away from the beads and exhibit compression and rarefaction like a wave.
I then started to wonder how can true entanglement be produced in such analogue as information that can be relayed by the wave will have travel vast distance before the effect of one droplet can be transmitted to another after the first droplet bumped into something. Since any effect will be constrained by the velocity of the wave, which is always sublight speed, it seems very intractable.
I then entered a room where there are two glass panels transmitting some kind of photon barrage of quantum information, and in between, there's a vertical barrier of photons with a polarisation such that if the initial photons are not in the correct polarisation, destructive interference occurs and the barrage get stopped by the barrier

If you are dreaming about such things, something is wrong :P
In the interferometer experiment, when we send a single photon, it goes through both ways at the same time and its wavefunction probability position is forming an interference pattern. So my question is: Does the photon have that wavefunction before it splits to go both ways at the same time and how is there interference pattwrn when there are not any slits? It interferes with itself? But when it merges again the interference pattern wavefunction should collapse, no?

9:19 AM
These days I wake from different dreams every day. Today I dreamt we went to a place where I saw a facility like what is typically seen in an amusement park; we all wish to take a ride of it, but it costs a very expensive price to take a ride of it; nevertheless, Father took out money to let us each take the ride, because he thinks our wish is more important than money. This dream made me recapture the virtue of my father, who always spent his money as possible as he can to indulge our wish.

9:38 AM
yesterday I dreamt that we were going to be beaten, and I was very scary because I thought it would be very painful. But when the two beats really fell on, I found it not as painful as I imagined, thus feeling a relief.

9:56 AM
the day before the day before yesterday I dreamt a big meeting including a lot of senior folks in my school. And my aunt was also in the meeting. It's unusual this kind of meeting was held in school. Usually the meeting held in school is an academic conference. So dreams are often abnormal.
several days further back I waked from a dream I got a position in an office where one of my previous collaborators and one of my previous classmates also work in. So after long time not meeting them, we met again.

10:13 AM
What happens when we observe the electron? Its wavefunction of probability collapses and then what?

I think that depends on what way you observe an electron. Either the wave character or particle character of an electron will be demonstrated.

particle

10:35 AM
I think you mean you observe the position of an electron.
you can also you observe the linear momentum of an electron.
whatever observable of an electron you observe, you get a certain eigenstate of that observable.

10:56 AM
So the electron at first doesn't have a defined position nor momentum, but has a wavefunction of probability where it's most likely to be? And when you observe the electron, it takes a definite position but it's momentum is lost?

2 hours later…
1:22 PM
0

Eight months ago, I asked a question here that had almost immediately received a negative scoring with little to no constructive criticism on how I could improve the question. I, however, got a useful answer, so I was satisfied. That would've been good enough for me, but now that very same quest...

1 hour later…
2:40 PM
in RPG.SE HNQ Worthy Questions, 1 hour ago, by doppelgreener
This room is for RPG.SE citizens to link to questions that seem worthy of being in the HNQ, but aren't for some reason. Do so by just posting the question link alone in a message. Use your personal judgement. Some of this data may be used by SE staff for tuning the HNQ algorithm in better capturing our worthwhile questions.
That's an interesting idea.

@Secret The trouble I have with this attitude is that any experimental apparatus I know how to construct is, ultimately, going to exist in position space
I'm not saying one can't do without it, but it's hardly obvious to me that one can

@rob That is interesting. Mods aren't able to push a question to the HNQ, right? I assume it would still require community effort (or SE direct action) to get those to HNQ?

@JMac That's right. Though any user with 75 reputation can push a question to the "featured" list by offering a bounty.

@NovaliumCompany if you want to think about QM one of the postulates is that a quantity isn’t defined until you measure it. It exists in a vector space of probabilities.

2:55 PM
@Semiclassical That's really the orthodox way to look at it, because you have a range of options from using the wave function as a tool to summarise your knowledge on the system, that the wavefunction is a real wave thing of probability amplitudes exists in some Hilbert space or the universe literally got into a superposition, to observables never exists until a measurement occurs, but operationally speaking, all we ever see in an experiment context:
Is we have pointers translating to positions as dictated by the dynamical rules when the quantum system interacts with them, in particular, whenever we prepared a setup (i.e. a distribution of entities with some notion of position) we always observed the pointers to deflect in said correlated way regardless of what the outcome is
and no matter how far the pointers are separated, that deflection does not get altered. Thus this allow us to postulate that there is some abstract space where the dynamic take place, and is largely insensitive to separation of the subsystems
So it really boils down to:
1. Either we accept that whenever we position experiment devices in a certain way in spacetime, there's always these curious correlations in the statistics of positions obtained in the pointers which cannot be reasoned with classical rules
2. Or that there is something called a quantum state and it lives in a space called the Hilbert space and governs the occurrence of those correlations in the pointer outputs
3. Or that we have a physical wavefunction that is inherently nonlocal and hence space like separated positions are actually correlated and influences by t

@JakeRose That doesn't answer my question. What happens when we observe? If we observe so we get the position, the electron will take a definite position (according to the probabilities of the wavefunction) but such thing as momentum will not exist. If we measure so we get the momentum, we will know the momentum but nothing about the position?

It's really the same idea back in Danielsank's discussion on arguing whether a field exists or is just an accounting tool, because everything we will ever observe are electrons get pushed around
Thus in a sense, yes, strictly speaking, all we ever observed are position distributions and all experiment setup are events that can be localised in spacetime, but they display all these intricate correlations in such a consistent fashion that one can postulate a framework that governs them
Now that brought out an unrelated thought: If we have physics phenomenon where even these correlation are probabilistic or even indeterministic, will there exists a model consists of a consistent object that can describe it?
After all, the reason why we can build abstract constructs in our models from electromagnetic fields, to stress energy tensors, to Lagrangians, to fluids etc. is all because regardless of how varied the physical phenomena is, they always behave in some consistent manner
It is this consistency that allows the constructs in each of these models to be "static and unchanging, except evolves under one parameter that captures some notion of time"
Even GR can be said to be "static" in the sense that you don't need to suddenly change equations when you move to a different scenario

3:24 PM
@NovaliumCompany You can't determine the electron's exact position, with infinite precision, you can only determine that it's in some small region. But if your equipment & lab skills are very good you can make that region very small. But the smaller the uncertainty in the electron's position, the larger the uncertainty in its momentum, in accordance with the HUP. And if the uncertainty in a particle's momentum is high, then its momentum must be high, so it won't stay in that location for very long.

Also here are some arxivs that explore the dynamics of quantum non equilibrium states:

@NovaliumCompany It might help if we discuss a "toy" 1 dimensional system, so it's easier to visualise. We have a finite line segment, containing a single pointlike particle that we can perform various position and momentum measurements on.
If we try to get a sharp position measurement the particle's position (at the time of measurement) will have a narrow range, but its momentum will be in a broad range. And conversely, if we try to get a sharp momentum measurement, its position will be somewhere in a broad range.
We can represent this in a 2D graph, with the horizontal axis for position, and the vertical axis for momentum. (This is a simple example of what's known as a phase space).
No matter how we measure our particle, we get a rectangle in the phase space, either a tall thin one if we localise the particle position, or a short fat one if we localise the momentum. Or a square one if we try to get a reasonable idea of both position & momentum at the same time.
The HUP says that even if our measuring equipment were perfect, there's a minimum area that our measurement rectangle will have. We can squish the phase space blob how ever we like, but we can never reduce its area to smaller than that minimum.
This applies to a real 3D electron too, but it's a little harder to visualise because we need 3 dimensions for the electron position and 3 dimensions for momentum, and human minds aren't built to visualise 6 dimensional spaces. ;)

We can even construct a phase space for multiple particles, but because we need to consider their positions & momenta independently, if we have N particles, we need a phase space of 6N dimensions. That might sound scary, but it's pretty handy, because a single point (or should I say blob) in that space represents the positions & momenta of all N particles. That makes it easier to do calculus on systems with multiple particles.
@Secret How come you and @CaptainBohemian use this chat as a dream diary?

Is there any post in PSE about the discussion of building CEPC (Circular Electron Positron Collider) in physical views?

@PM2Ring Not really, I only share dreams that may contain things to be discussed about, e.g. the above one related to the oil drop experiment, and some previous ones where I fell into black holes
Any dreams I posted here, are a small subset of the physics dreams I have, which is a small subset of all the dreams I have. I used to do that back in 2014, but I stopped doing that by 2018

Background: Whether China should build CEPC arouses a huge disscusion around the country, both in society and in physics, I wnder if there're some discussions in this site in physical view. Reference:ihep.cas.cn/dkxzz/cepc
I searched through the site, only found this question

Ok so quantum born non equilibrium states will have probability distributions to not be constrained by the dynamics of the wavefunction, and hence trajectories can exhibit unusual behaviour, which some of these can be captured by some drift velocity field

4:07 PM
about 80 minutes before I go talk in the math deparment

@PM2Ring Got it, thanks. It's an interesting visualization of the uncertainty principle :P

@NovaliumCompany No worries.

4:24 PM
Guys, I forgot, in the Schrodinger Cat experiment, how do we know that the cat wasn't in one of the boxes all of the time and was in a superposition of both possible outcomes? (you get the idea of my question) I used to remember the answer, but I forgot :P

4:35 PM
7

Superposition is often claimed, particularly in popular physics texts, to be "an object that is in two states at once", but this is in fact quite misleading. Superposition states, in fact, go beyond this property. Say I have a box, and I claim that I claim contains a cat that's both dead an...

Here's the best description I knew of for that
Basically, you cannot rotate a classically dead cat back alive, but you can do that for a quantum dead eigencat

4:48 PM

@Secret Nice work, @EmilioPisanty.

Thus that vixra made the mistake in the computation of the H field, which is not circular, instead it is dominated by the magnetic moment which is in parallel to the electric field, thus the potyning vector is miniscale

Is it just me, or has he got this backwards? a slower time causes a high velocity From physics.stackexchange.com/questions/478408/…

5:05 PM
well technically, one cannot really assign causal relationship between these two quantities, because it is observed that something travelling with a relative velocity experience time dilation

@Secret It's Poynting

though we tend to think of that as higher velocity slows down time

@Secret In the context of how it was used then... it seems pretty nonsense. They seem to be asserting that it is slowing time which increases velocity, and are explicitly stating that the opposite perspective is false. That seems strange to me

@Secret What JMac said. Sure, you can't have one without the other (in SR), but to say that the time dilation causes the velocity sounds like putting the cart before the horse to me.

I always kinda assumed that with relativity, stating one is true and not the other basically slaps the whole concept in the face; but I've never really studied it so i have no idea on actual conventions

5:13 PM
The only thing I can say is that he tends to be rude, but as for how correct he is, I don't know
Thus I can only say is that SR commonly understood as "high velocity slows down time" not the other way around
even though no experiments can tell between the two

@JMac In Galilean relativity, if you increase your speed relative to some observer, it affects your motion through space, but your motion through time is unaffected. In SR, you can't just affect your motion through space, it also affects your motion through time, relative to the observer, due to the geometry of spacetime. But even so, when you do that stuff, the point is to change your velocity & location, the time dilation stuff is more like a side effect.
I realise you know that stuff, I'm just trying to express my attitude. ;)

I don't get the point of insisting some cause and effect to it. It almost seems like it's taking it beyond physics. Even saying "high velocity slows time", I would say most people aren't insisting a cause and effect; but more just pointing to the relationship between velocity and the passage of time, and not trying to make a hierarchy of "one is the cause of the other"

The whole concept of causation is a mess.

Insisting a cause and effect relationship seems to just be an attempt to water down the details and instead opt for a lazy explanation

Even once you get to newtons 3rd law, it's like the whole cause-effect relationship becomes obsolete

5:23 PM
I'll never get tired of bringing up Norton's dome when it comes to causation :P

o yeah, that one is a classic indeterminism dynamics that is not probabilistic
the GR counterpart involves all sorts of non globally hyperbolic spacetimes and Cauchy demons

But in this case of velocity and time dilation, it's not even clear to me what is being asserted. In what way is "time dilation causes velocity" supposed to be different from "velocity causes time dilation"?

I am guessing it might have to do with human thinking of time as something passive whereas velocity as something more active...

how different is sunlight causing a plant to grow and a plant growing causing sunlight

@ACuriousMind I still don't find Norton's dome useful to me. It basically seems like pure math that just so happens to fit with how Newton defined things; but the derivation is so bogged down with terminology that I don't even understand how it is making it's point

5:27 PM
"time dilation causes velocity" is classically intuitively weird because it is basically saying that we can even walk because the surrounding environment slows down

@KenWang There is a temporal order there and makes it possible to talk about causation - first the sunlight is being emitted, then the plant absorbs it, then the plant grows

And some research on Norton's dome got me to some pages that showed Norton's dome implied that there was actually a snap or jounce or something acting at t = 0, which obeys newtons laws; but still implies there was energy in the system that was on it's way to being imparted into the ball; but there's nothing physical mentioned to explain it

But the relationship between velocity and time dilation is instantaneous.

"plant growing causing sunlight" is even weird because we are talking about somehow having a plant growing on earth can lead to a series of event that lead to the existence of the sun

xkcd 925

5:29 PM
I know that in a double slit experiment, when we shoot an electron, in order for it to interfere with itself (go through both slits at the same time) it must be in a superposition. I get that, but in the Schrodinger's Cat experiment, there is no real superposition since it's in the macro world right? I mean, Schrodinger's cat is just an analogy?

@Secret Thanks. I've often seen him post controversial stuff in comments, but I've mostly tried to avoid confrontation. I'm sure he knows a lot of stuff, but that some of his assertions are based on stuff that he's misunderstood, or personal deductions that are just plain wrong.

and one can easily show there is a temporal order as stopping the plant from growing or absorbing light will not extinguish the sun

@NovaliumCompany There is no fundamental difference between the microscopic and the macroscopic that would make quantum mechanics apply to the one but not the other

(that's how people usually elucidate causal relation btw, by knocking out something in the causal chain and see how other events are affected)

@ACuriousMind So you are telling me the cat is actually in a superposition? How do we know that? In the double-slit experiment, we know that the electron is in a superposition because of the interference pattern, but in the cat example?

5:33 PM
The reason macroscopic objects usually exhibit no "quantum behaviour" is that they are constantly interacting with the world around them and have no chance to evolve into such strange superpositions.

@NovaliumCompany Isn't the point of Schrodinger's cat that the macroscopic cat is in superposition because the state of the cat hinges on some microscopic quantum event that hasn't been observed, even though the cat itself is macroscopic?

@ACuriousMind The interferometer experiment? Quantum fluctuations that destroy the wavefunction?

Superposition pure states are very rare in the Hilbert space. You are more likely to end up in some partially entangled mixed state given an arbitrary unitary evolution
o wait, mixed states cannot be produced by unitary evolution...

@NovaliumCompany What state the cat "is" in is hard to answer. When you open the box, you'll find the cat in one of two states (dead/living), dependent on the state of the radioactive trigger. This is a fact, and it does not change whether you believe the cat "was" in a superposition or not.
Modeling the box as a quantum system and the cat's state as a quantum superposition entangled with the radioactive trigger correctly predicts this outcome.

@ACuriousMind Exactly, and how do we know that the cat wasn't dead or alive the whole time?
@ACuriousMind I haven't gotten to entanglement yet sorry :p

5:37 PM
@NovaliumCompany That is a matter of interpretation, as it makes no observable difference.

Wow
Yes, but in the slit experiment, we see that the electron is in fact in superposition, and we cannot interpret it as going through only one of the 2 slits the hole time?

Asking how you know the cat was dead or alive the whole time seems similar to asking how you know that the electron wasn't a particle the whole time

@NovaliumCompany Adherents of Bohmian mechanics would disagree

I actually believe an electron is neither a wave nor a particle, nor anything we ever can describe in words

The belief that there is a persistent state - not a true superposition - is what is called "realism" in this context. Bell's theorem prohibits a local and realist interpretation of QM, but if you choose to give up locality, you can save realism.

5:40 PM
Oh, that's interesting. I'll research this realism a bit. But in the slit experiment, there is no way you can think the particle wasn't in a superposition since the interference pattern is your proof. But in the cat experiment, you have no proof and you can interpret?

The different interpretations war over the exact ways in which we want to give up locality and/or realism.

@Secret an electron is obviously just a hyper-negative quantum mass existing in a flat space over a curved time dimension which leads to the illusion of dark matter. BRB posting this word salad as an answer to every question tagged "Dark-matter"
6

@NovaliumCompany For example, in Bohm, the nonlocal wavefunction passes and diffracted by both slits, and the bohemian particles starts out with some inaccessible initial position distributions, then get guided to the screen deterministically and form the slits depending on where they are in the initial position distribution
@ACuriousMind Which interpretation gave up both?

@Secret Sorry, didn't quite understand how that answers my questions. (I don't know exactly what Bohm means :p)

@NovaliumCompany You don't observe an "interference pattern" for a single electron. You see a single dot on the detector. If you believe there is inherent randomness in even the most controlled initial conditions - as Bohmian mechanics does - then you can believe that every single electron follows a well-defined trajectory. Bohmian mechanics is engineered precisely so that the dynamics for these trajectories reproduces the same pattern on the detector screen as standard QM
I'm not saying you should "believe" in Bohmian mechanics, mind you

5:44 PM
Sorry, what again does Bohm mech imply in simple terms please?

I'm just saying that quantum interpretations are subtle, and you need to carefully distinguish between what we observe and what we're reading into these observations.

I guess I believe that each photon has that wavefunction of position probability so that many electrons together form the interference pattern. And also for that wavefunction to exist, there must be two slits and therefore the electron must go through both at ones. (superposition)

In particular, claims about what "really is" are usually interpretive. The formalism of QM gives us a mathematical machinery of how to predict the distribution of outcomes of experiments like the double-slit or Schrödinger's cat. But it doesn't tell us what the wavefunction "is", or where the particle "is" during a QM process.
2

That's just how I understand it, I don't believe in any Bohms, Mohms, Johms.. and so on :D

Bohm mechanics implies deterministic trajectories of particles. Skadoosh

5:47 PM
@enumaris Finally someone who speaks my language :D

:)

But those deterministic particles still behave exactly like the probabilistic particles of other interpretations

this is because their initial conditions are probabilistic

And what describes their trajectory so that they form the interference pattern? A wavefunction?

@NovaliumCompany Have you gotten to the point yet where putting detectors at the slits destroys the interference pattern?

5:49 PM
@ACuriousMind Yep, quantum eraser right?

Because that is difficult to reconcile with the naive idea of it "going through both slits at once", to!

@ACuriousMind Isn't that what superposition does :P?

@NovaliumCompany the quantum eraser is even one step further - the interference pattern returns if you "throw away" the which-way information from the detectors.
@NovaliumCompany So what does "the electron goes through both slits at once" mean if detecting it at one slit can make it so it definitely never went through the other?

It's like it travels back in time and fixes itself when it senses observation :P

Congratulations, you have discovered the Copenhagen interpretation :P

5:52 PM
Clearly, someone needs to do the double slit experiment with kittens.
3

Man I love how weird QM is. The implications of the double slit experiment and how it naturally evades attempts to "cheat" is just such a mindbender. I don't even really try to understand, I just try to accept all these weird consequences

@PM2Ring preferably with their grin separated and then swapped

@PM2Ring Well, at least calling their states fuzzy is accurate in any case :P

@NovaliumCompany You may enjoy Cramer's Transactional interpretation of QM.

5:53 PM
I am still trying to find an interpretation that discards both realism and locality
most interpretation I read either discard locality or realism, but almost never both

Quick question: What's the difference between realism and locality? (plz simple words xD)

@NovaliumCompany Realism is the belief that all observables have definite values at all times ("no superpositions"), locality is the belief that what happens at one place cannot superluminally affect what happens at another place. This answer of mine might be relevant in this context.

> Furthermore, Bell's theorem states that any theory that agrees with quantum mechanical predictions is either non-local, or has no unique predetermined measurement results (isn't realist). This means that you cannot ever get a theory that answers our questions of "Why?" as we wishes it did, because every theory that predicts unique results violates the idea that stuff can only influence each other at the speed of light, and every theory that plays nice (...)
I wonder, if bell theorem allows an interpretation which is as insanely nonlocal as Bohm, and insanely nonrealist as copanhagen

So simple said, anyone can interpret is however he/she likes. We don't have a true answer to whether the electron is going through both slits at once, or goes back in time and "fixes" itself...

@Secret You can find various claims that even Copenhagen is non-local, mostly by people pushing their own, "better" interpretation :P

6:04 PM
Acuriousmind: ah interesting
The more I study into interpretations, the more I felt that the least amount of classical baggage we assumed in the interpretation, the closer we can understood quantum mechanics
(that's pretty much operationalist...?)

The Pilot-Wave theory (Bohm...) suggests that the interference pattern is always there, and when we send an electron it follows the wave with eventual probability position determined by the wave (pilot)?

I've never actually studied QM... do the interpretations actually have a direct impact on anything, like experiments, or is it all just how people are choosing to consider things in their head, even though they all do the same analysis?

@JMac They do not make any experimental differences, that's why they are called interpretations
Bohmian mechanics however, do stood out as it can potentially lead to different experiment outcomes depending on how strongly the quantum equilibrium hypothesis holds

@Secret No, operationalism is the position that only claims that have observational impact matter. It is usually identified with a strident "shut up and calculate" approach that considers quantum interpretations mostly pointless.

ah, that's very different then

6:11 PM
I guess what I don't understand is... isn't the interpretations essentially pointless if they hold no actual predictive power?

Well, some of these provide an ontology and hence inform certain future experiments easier than others
but in terms of direct predictions, no
One reason philosophy can be useful is because it point us where to look next in the conceptualisation process

@JMac Yes, if you believe that raw predictive power is the only relevant quality of good physics, then they are pointless. As you might see from the large and long-lived discussion around interpretations, it turns out not many people hold a view quite that extreme.

QM tells us the probabilities of the various possible outcomes in an experiment. The interpretation tells us why the universe behaves that way.

So Bohm theory believes in some "hidden variables" that drive the whole system?

yup
and such is inherently nonlocal

6:14 PM
What exactly hidden variables?
I mean, who "knows" those hidden variables? The wave that drives the particle?

May 3 at 20:14, by PM 2Ring
I find it fascinating how polarising QM interpretations are. "My interpretation is mostly satisfactory, it just has 1 or 2 problem areas. But your interpretation is patently absurd!" ;)

@PM2Ring ...and after all, "Why?" is the question that fascinates people, not "what is the mathematical prescription to compute the pattern of dots on a screen?". Humans love good stories
3

Also, every answer to why translates to a how in the future

that the question may be fundamentally ill-posed doesn't stop them :P

@ACuriousMind Certainly! That's why Discworld runs on narrativium, not physics.

6:16 PM
e.g. one reason I hope the wavefunction is real is so I can think about directly controlling it, down to the detail on where I want its nodes are

@PM2Ring I guess that sums up the mentality that I don't really understand. I'm obviously not invested in the subject at all, so I'm probably naive about all this. I can understand the benefit of considering interpretations, I don't see the benefit in pushing for one interpretation as the true one when it doesn't really get you anywhere besides maybe setting your own thoughts in stone a bit

that's human nature. It is human nature to defend their own beliefs, and such does not necessary lead to productive outcomes
(cf politics)

When I was a kid we had an excellent science show on Australian TV, presented by the American physicist & educator, Julius Sumner Miller. It's title was "Why Is It So?". But he never really explained the "why" behind the phenomena he demonstrated.

Copenhagen interpretation encourages superposition and Bohm interpretation doesn't?
I'm confused which one is locallity and which one realism.

Copenhagen is nonrealist (wavefunction collapses from superposition into eigenstates upon measurement, it is agnostic on the ontology of the wavefunction) and may or may not be nonlocal depending on which variants you are talking about. Bohm is nonlocal but realist (in both Bohm particles and the wavefunction)

6:23 PM
Got it. What exactly was locality again :P? (Sorry for being stupid..)

@SirCumference What do you have against Squiggle? (that's it's official name as I'm told)

@ACuriousMind I call it "tornado" :P
The meme from earlier describes my feelings perfectly

@NovaliumCompany events in one place cannot affect events at another place faster than light

@NovaliumCompany It's hard to really explain before you know entanglement because e.g. the double slit alone does not exhibit the apparent non-locality of QM.

Got it. I'll come back when I get through entanglement part of the book :)

6:27 PM
@SirCumference One of my lecturers instructed us that it's drawn "like a happy little balloon".

@ACuriousMind [sic]?

no, typo :P

@ACuriousMind You teachin'?

But yeah, I've never liked the xi symbol either. It doesn't seem to flow the same as other greek symbols or something

@NovaliumCompany Only on this site :P By day, I'm a programmer.

6:29 PM
@ACuriousMind Oh yep, I remember.
Well if you have any programming questions, ask me :D
I'm a wiz in that area.

I took a semester course in C, and once used Matlab for a numerical methods course, so I'm basically a master programmer myself
I can probably still even write a hello world function

Pet peeve of mine: I have a tendency to ascribe ontological existence to the most unchanging mathematical entity of a physical theory
That's how I build intuitions from scratch using the math formalism
As far I am aware, QFT is the theory that violates even this intuition framework of mine, which is one reason why it can be interesting
In particular, QFT goes one step further by not allowing us to talk about where things are, but only "in the region, what is the probability that stuff happens"

6:50 PM
What if the pilot-wave theory is true in the sense that there are particles, there are waves, they exist and interact independently. Particle with the wave, and wave with the wave. We have electron-particle, electron-wave, photon-particle, photon-wave, and so on.
I ask John Duffield, what does he think.
:-)

@Secret and string theory etc ;)

7:07 PM
Less than an hour till the election finishes, anyone wanna take bets on who will win ;P

@DanielSank Quantum Relativity and General Mechanics

Pilot waves can't even deal with relativity, would be very careful extrapolating from what it says

7:41 PM
2 days ago, by DanielSank
General mechanics and quantum relativity?
:P

Hey
@bolbteppa I mean, there is a story one can tell. It being a credible story, is the problem
(And also to what extent it’s a productive story at all. In the context of wave mechanics I think it’s reasonably so, but life isn’t just wave mechanics)

Skimming Greiner's explanation of hidden variables, it seems they are trying to say that in the case of say measuring the spin of a particle $s_z$, the other components $s_x$ and $s_y$ of a 'real spin vector' should also fundamentally exist just be intrinsically 'hidden', I wonder if this contradicts basic Lie theory

@bolbteppa How could it contradict "basic Lie theory" if this is precisely true in classical mechanics? The angular momentum algebra is the same classically and quantumly!

Like, spin arises from the representation theory of groups allowing for the double/multiple cover stuff, and you're talking about eigenvalues of the representation of one of the Lie group generators $s_z$, the idea the $s_x$ and $s_y$ exist seems to basically say we can simultaneously diagonalize the (representations of the) generators of a Lie group but because of MAGIC we just can't determine those values

...I guess classical mechanics is "MAGIC" then :P

7:54 PM
In classical mechanics you're not looking for simultaneous eigenvalues of three operators which do not commpute

@bolbteppa And neither are you in any hidden variable theory. You're right that a hidden variable theory can't be a theory in which the values of observables are fundamentally such eigenvalues. but that's just saying that standard QM is not a hidden variable theory.

@bolbteppa Why? EM waves can deal with it. I am thinking on classical, or nearly classical waves, like the EM waves, interacting with particles. All of them have a wave equation, a wave equation of a single-component wave, and also the particles have motion equations. And Lagrange says, who moves and where.

In the middle of that page Greiner explicitly explains what he means by hidden variables, about the $s_x$ and $s_y$ fundamentally existing
So if the $s_x$ and $s_y$ fundamentally exist, but are hidden, what are they if they are not eigenvalues of $R(L_x) = S_x$ and $R(L_y) = S_y$ ($R$ the spin rep), if they're not eigenvalues of those operators it seems like we're veering off into nonsense just defining things which break logic to be what we want, if they are eigenvalues it seems like we're denying basic mathematics

It was done, just 4 minutes ago, but no results yet. The page looks interesting.

@bolbteppa An imaginary classical physicist's response to QM: "If the values of observables are not the definite values of phase space functions we're denying basic mathematics!".

8:04 PM
@ACuriousMind that literally would be true - which is why QM explicitly says paths don't exist so we don't run into that issue! ;)

Once in my life I've seen an empty SE site. The engineering.stackexchange.com . Unfortunately, I had no time to create a screenshot of it - I was to busy to write its first question.

There is no reason at all the description of observables of an underlying theory must match that of its effective theories. If QM with its operators can have CM with its phase space functions as a limit, it is equally possible for an underlying hidden variable theory with whatever else as observables to have QM with its operators as its limit

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The claim is very explicitly that the $s_x$ and $s_y$ of a spin vector for which $s_z$ is an eigenvalue of $L_z$ actually do exist but are just not measurable, if they are not associated to $L_x$ and $L_y$ as eigenvalues then why not add a billion extra hidden variables to a spin vector, maybe there are, this is pretty much childish, on the level of angels pushing the planets around the sun etc
We're not even talking about a quantity which has a classical analogue as well

8:11 PM
@bolbteppa Hidden variables seem wasteful, inelegant and superfluous to me as well, but I find it nevertheless important to not conflate such aesthetic judgement with them being factually wrong (like "denying basic mathematics" would imply).

8:30 PM
@ACuriousMind I agree, that's what I'm bringing up, whether the idea of hidden variables in this example is 'factually wrong' i.e. contradicts basic Lie theory, what are the $s_x$ and $s_y$, if they're not eigenvalues (seems like they should be because, as he says: "We assume they exist, but it is not possible to determine them at the same time as the previously chosen component (which can be any of the three components"),
If they're not eigenvalues then why not add just 'angel' and 'Beelzebub' variables, and what does it even mean if they're not eigenvalues since we can initially measure one component and it could be any of them in some given example... I'm not even saying hidden variables are a bad idea necessarily, but this way of using them seems very iffy...

@Secret @PM2Ring thanks for the kind words

In QM the idea of a spin vector is fine, but for hidden variable stuff to go out of it's way to claim the components of it are intrinsically real things is really a gigantic claim, (even the whole idea of spin in this BM stuff is super questionable as to whether it even makes sense)

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@bolbteppa Note that he talks about the "real spin". The "real spin" is not a collection of eigenvalues, it's a collection of hidden variables, only one of which at a time can become "unhidden" by measurement.
What these hidden variables "really are" - and how they relate to the eigenvalues of the QM operators, if at all - depends on the specific hidden variable theory, but I believe the page you quoted is just looking at how hidden variable theories have to work generically, so it can't tell you anything more specific about them.

8:54 PM
It depends on the theory, yeah. Simplest pilot-wave story I know has the “spin” of an electron—ie how it reacts to a stern-gerlach device with a particular orientation—being entirely determined by 1) the form of the incoming (spinor) wavepacket, and 2) where the electron is within that wavepacket. So while you do have two wavefunction components, the electron doesn’t carry a label which says what spin it’ll have relative to a certain axis.
the extent to which a spin measurement reveals a hidden variable, in that story, is just as it usually is in pilot wave theory: it reveals something about the particle’s position, in this case it’s position prior to passing through the device

It's not clear what this 'unhiding' thing is, why the other variables are not eigenvalues and how you can call them real if they aren't, super confusing

Electron goes into device with a particular orientation and comes out deflected in a certain direction. If you put two identical such devices in sequence, so that all up-deflected electrons go into the second device, then they’ll all be deflected up by the second device as well

@NovaliumCompany I don’t understand what your question is

In the first case, the electron spinor wavefunction is split into two spatial components, one traveling on an upward angle and the other on a downward angle. If the electron starts off in the top of the packet, it’ll be guided by first packet and move off along with if.
The form of that wavepacket (being a spinor-valued wavepacket) is now such that the entire packet now is deflected upward by the second S-G device. Hence the electron must now be deflected up by the second S-G device. No need for a spin vector there; to the extent that there’s spin degrees of freedom, it’s in the use of a spinor-values wavefunction— just as you’d use anyways in QM in that scenario
The “unhiding” is literally just “does it go up or down”
And the only hidden variable being revealed is the only one you ever talk about being revealed in pilot wave: the position of the particle

9:16 PM
If I stare at my cat all day, wouldnt it age slower? :D Zeno effect, no?
In an electron tunneling microscope, how and of what exactly is an image constructed of? I mean I know some electrons will tunnel through the air gap and generate a small current so what?

I think the spin vector exists at all times and measurement is supposed to simply spit out one of the components as the spin along some axis with the others supposed to not be measurable, the issue is trying to claim the other components mean anything, I think this question could probably abstract to everything but just focusing on what's written on the page sent above

You’re fine to want such a story. My point is that it’s not necessary: pilot wave theory does not require the particle to carry a spin vector. It does require spinor-valued wavefunctions, but so does the bare QM formalism

I'm not sure about that - the Greiner page seems to be saying that any hidden variable theory inherently claims the spin vector exists and all of it's components are meaningful?
"The assumption that each individual particle has a well-defined but not measurable spin vector $\mathbf{s}$ is the basic postulate of the theory of hidden variables"
In QM you can always set up a spin vector, it's fine, it's related to spinor wave functions, the only real difference here is in the meaning of the components in one vs. the other theory

9:33 PM
Just because Greiner says that, does not mean it’s true
I mean, it may be a common assumption by some people doing HV stuff. But it’s not a necessary assumption

He's just trying to demonstrate what it means for a theory to claim that there's a hidden variable behind any observable, and chooses spin as an example. There's no need for theories to be "all or nothing", they can well claim hidden variable behind some quantities but not others.

And doing it without an extra spin vector seems to be the more common approach in pilot wave theory

Spin is just a popular example for any QM foundational explanations because its theory is simple (compared to the subtleties that come with continuous position) and it's experimentally accessible through Stern-Gerlach type experiments.

Plus it’s a pretty easy jump from there to Bell-type experiments
For better or worse, position has a privileged status in pilot-wave theory
By contrast, spin measurements are not required to have such status. (You can choose to grant that to then, but it’s not obligatory)

I think he's using spin because he was explaining Bell or someone's example which shows a (local) hidden variable theory predicts different results from normal QM before setting up and proving Bell's theorem which is on the surrounding pages

9:43 PM
Yes, that also makes sense. In order to establish that Bell's theorem forbids certain kinds of hidden variables, you first need to establish what a hidden variable theory would predict!

Yeah, Bell’s setup is two electrons entangled in a singlet state and sent through spatially separated detectors

It's particularly galling to claim you can attach meaning to all the components of say a spin or angular momentum vector where one of the components is the eigenvalue of an operator but the other components are just not yet still mean something, it might be okay to do this, I'm not convinced just need to think about it maybe

Well, hence why I favor leaving spin as a property to the wave and not the particle. Going to spinor-valued wavefunctions is natural enough
Insisting that the electron had a particular position in an incoming wavepacket seems a lot less baggage than insisting that it somehow carries a label for whatever detector it might enter

@bolbteppa It's not an eigenvalue! The hidden variable theory is not QM, none of the spin components needs to be the eigenvalue of anything, any more than the classical angular momenta are the eigenvalues of anything. You're still trying to shoehorn the hidden variable theory into the formalism of standard QM, that's not possible - as standard QM is not a hidden variable theory.
The hidden variable theory only needs to be compatible with the actual predictions of QM, not with its underlying formalism of states and operators

^
A HV theory is certainly -constrained- by the formalism

9:51 PM
@NovaliumCompany what was your question. I didn’t quite understand it.

In fact, if this is for Bell's theorem, the entire point of constructing the hidden variable theory is to show that it cannot be compatible with QM predictions if it is local. If you could show incompatibility of hidden variables with QM as easily as you seem to think, Bell's theorem would be entirely trivial and we wouldn't need to restrict to local hidden variables

insisting that a HV be expressed in exactly the same terms as the QM formalism, and then being surprised when it doesn’t work, seems rather unproductive to me
@ACuriousMind fun fact: I gave a talk at a math-physics seminar today which included a deduction of Bell’s inequality
So that was fun, if stressful

@JakeRose Which question buddy?

10:14 PM
hmm... this stuff is a good way to see if one understands aspects of normal qm at least...

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I'm just curious on how that community has grown over the years.

@NovaliumCompany you said I did t answer your question, I didn’t understand it :)