The h Bar

2:13 AM

Xi is easy. But zeta is a pain.

Koopman–von Neumann classical mechanics

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

Semiclassical

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

vzn

@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

vzn

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 :|

Manvendra Somvanshi

4:29 AM

0

Q: Cone immersed in a Liquid

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?

DanielSank

5:02 AM

Hello, all.

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.

Q: How can I improve this question?

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?

Physics Meta

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...

support

rob

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.

Semiclassical

@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?

rob

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

Jake Rose

@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:

arxiv.org/abs/0911.2823

@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. ;)

3:50 PM

iopscience.iop.org/article/10.1088/1751-8121/aa9e97/meta

ncbi.nlm.nih.gov/pmc/articles/PMC4197476

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?

Andrews

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

Andrews

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

Semiclassical

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

A: What's an atomic superstate/superposition, and how is it possible?

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

John Rennie

4:48 PM

Huh?

@Secret Nice work, @EmilioPisanty.

How to correctly calculate the potyning vector of an electron

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

as Anna's answer showed

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

For reference, safesphere is not someone without controversaries

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. ;)