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antimony
antimony
12:52 AM
Is there a way to turn on latex rendering, or are you all way way better at reading latex syntax than me
 
danielunderwood
danielunderwood
1:13 AM
> For MathJax see meta.stackexchange.com/a/220976
The second link to the chrome extension works well if you have a chromium-based browser
 
 
2 hours later…
Manas Dogra
Manas Dogra
3:30 AM
I don't know who, but whoever removed an unkind comment from one of the users on my recently closed question prevented me from going into depression. Thank you moderators :)
 
More Anonymous
More Anonymous
4:24 AM
Hey all! Is phase space formulation the only approach to see how classical mechanics emerges from quantum mechanics?
 
abhas_RewCie
abhas_RewCie
4:47 AM
Just one question!
Why tf we are not taught Kaluza-Klein Theory and useless String Theory?
PS - Ik none are useless but they are because of Physics, whatever, I need the answer, not a question about the question about any professional String Theorist or anyone who knows them well
 
John Rennie
John Rennie
4:59 AM
@abhas_RewCie what are you asking? Why KK and string theory are not taught in undergrad courses? If so, that's because they are too complicated for undergrads.
 
abhas_RewCie
abhas_RewCie
@JohnRennie What is the meaning of undergraduate ? Bachleors or Masters?
 
John Rennie
John Rennie
Bachelors
 
abhas_RewCie
abhas_RewCie
@MoreAnonymous yes, (If I understand what you mean by phase formulation), see Rich Feynman's Line integral approach to string theory.... You'll see the other intuition of doing that (which also requires phase)
@JohnRennie Okay, I've a question to ask, perhaps some other room, I'll invite you
 
More Anonymous
More Anonymous
5:21 AM
@abhas_RewCie I was refering to the user of wigner functions etc
More specifically
1
A: Book recommendation for how classical mechanics emerges from quantum mechanics?

Cosmas ZachosBefore hitting the books, you might do your due diligence and review the basic Wikipedia articles, to understand the trail-map. You need to learn the language first, as an awful lot of nonsense has been lavished on the subject. The correspondence principle. The map Jess starts from, mapping Hil...

 
More Anonymous
More Anonymous
5:35 AM
@abhas_RewCie Honestly I'd be against teaching string theory even in a masters course
 
abhas_RewCie
abhas_RewCie
5:54 AM
@MoreAnonymous Then which course for string theory?
I thought String Theory was bachleors....
 
More Anonymous
More Anonymous
6:29 AM
@abhas_RewCie PhD
 
bolbteppa
bolbteppa
Any book discusses how classical mechanics emerges from qm, the wave function takes the form $\psi \approx e^{iS/\hbar}$ in the quasiclassical limit and as $\hbar \to 0$ one has to have $S$ goes to zero i.e. to a constant (the minimum, the condition for classical mechanics, and the action is only defined up to shifts in a constant so it can always be made zero)
 
More Anonymous
More Anonymous
6:56 AM
@bolbteppa I think the real picture is a lot more involved than that ...
No simple limiting procedure can yield Classical Mechanics
 
bolbteppa
bolbteppa
That post is wrong and basically makes no sense, arguing the 'state spaces' should be the same is a big misunderstanding
 
More Anonymous
More Anonymous
@bolbteppa Sorry can you elaborate a bit?
 
bolbteppa
bolbteppa
I think you should elaborate why this random blog post invalidates pretty much every QM book
 
More Anonymous
More Anonymous
"The most glaring problem is that the state spaces of classical and quantum mechanics are completely different, so you can’t have a simple limiting procedure unless you describe how you’re going to map one onto the other"
I think this is the main point
 
bolbteppa
bolbteppa
Nobody said you have to have a map between the spaces
 
More Anonymous
More Anonymous
7:10 AM
Your confusing me more
Ultimately the (complicated) limiting procedure should yield $R^3 \times R $
Why shouldn't that happen?
 
bolbteppa
bolbteppa
Why, the state space of qm is a bunch of wave functions, the state space of classical mechanics is a bunch of points in space, why should a set of functions turn into a set of points
 
More Anonymous
More Anonymous
Because you want to see classical mechanics emerge from quantum. That was the goal right?
 
bolbteppa
bolbteppa
Yeah, and that happens because the action describes the path of the system when quantum effects go to zero as codified in the $\hbar \to 0$ limit, but quantum mechanics just goes away in this limit we don't have anything to say about it when we take this limit, $0/0$ doesn't exist so $\phi^{0/0}$ makes no sense, $f(x) = \frac{x^2-4}{x-2}$ doesn't exist at $x = 2$ even though it has a limit $\lim_{x\to 2} f(x) = \lim_{x\to 2}(x+2) = 4$, we're talking about $f(x)$ when $x=2$ which doesn't exist
The post might as well say, because the domain of definition (state space) of $f(x) = \frac{x^2-4}{x-2}$ (the real line without $x=2$) is different from the domain of $g(x) = x + 2$ (the real line with $x=2$), this means the limit $\lim_{x\to 2} \frac{x^2-4}{x-2} = \lim_{x\to 2}(x+2) = 4$ is not well-defined.
 
More Anonymous
More Anonymous
Okay first of all you can't just substitute a quantity with dimension $\to 0$. That doesnt make sense. $\hbar \to 0$ actually means $\hbar/x$ which is a dimensonless quantity. That you can take to $0$
(where $x$ has the same dimensions as $\hbar$)
 
bolbteppa
bolbteppa
zero centimeters is zero centimeters
It should be obvious these 'every book is wrong' posts are almost certainly going to have issues
 
More Anonymous
More Anonymous
7:27 AM
Feel free to post your own answer to the question:
2
Q: Book recommendation for how classical mechanics emerges from quantum mechanics?

More AnonymousQuestion So I read this interesting link: The most glaring problem is that the state spaces of classical and quantum mechanics are completely different, so you can’t have a simple limiting procedure unless you describe how you’re going to map one onto the other and was wondering if there was an...

quantum-mechanics classical-mechanics resource-recommendations quantum-measurement
Also in your example, the spaces of both functions are the same
 
Slereah
Slereah
8:07 AM
A simple enough way to see the classical mechanics from QM is to consider the time derivative of operators
\begin{eqnarray}
\frac{d}{dt}\hat{x} &=& [\hat{H}, \hat{x}] &=& \frac{\hat{p}}{m}\\
\frac{d}{dt}\hat{p} &=& [\hat{H}, \hat{p}] &=& - \nabla V(x)\\
\end{eqnarray}
Those are just the classical equations of motion
Taking the limit $\hbar \to 0$ will indeed give you the appropriate limit
 
Superfast Jellyfish
Superfast Jellyfish
@MoreAnonymous if you have an issue with taking $\hbar \to 0$, you can just rescale by dimensionless quantity $\epsilon$ and have $\epsilon\hbar \to 0$
 
Slereah
Slereah
The actual classical limit isn't quite $\hbar \to 0$, it's more $S \gg \hbar$
But in effect it's the same consequence
 
bolbteppa
bolbteppa
Operators becoming coordinates, commutators becoming poisson brackets, constants becoming non-constant, welcome to QM
 
Slereah
Slereah
There's even a midway point between QM and classical mechanics~
where you get a stochastic process instead of a position function
IIRC it's basically taking the first two orders of QM in $\hbar$ instead of just the first for classical mechanics
 
bolbteppa
bolbteppa
8:25 AM
The semi-classical approximation chapter of a qm book will go up to multiple orders usually
 
 
1 hour later…
abhas_RewCie
abhas_RewCie
9:40 AM
@MoreAnonymous If you are interested in Heisenberg picture (a bit different formulation of QM), where $\hbar \rightarrow 0$ changes quantum eqn to classical ones.
 
More Anonymous
More Anonymous
@SuperfastJellyfish agreed
@Slereah Any links? Would like to read up on this
 
Slereah
Slereah
 
More Anonymous
More Anonymous
why is everything good behind a paywall?
 
Slereah
Slereah
Paywalls do not exist if u know the ways of the physicist
 
More Anonymous
More Anonymous
@Slereah I know them hacks :P
 
Slereah
Slereah
9:48 AM
Stochastic processes will not be enough for QM unfortunately, because the fundamental problem of QM is that it doesn't use classical probability theory
 
More Anonymous
More Anonymous
@Slereah Good point
 
Slereah
Slereah
A lot of people mistake the lack of determinism as the big issue in QM, which, while unintuitive, isn't that hard to get behind
 
bolbteppa
bolbteppa
What's the big issue if not that
 
ACuriousMind
ACuriousMind
You need to discuss states. It's "easy" to say "$\hbar \to 0$ is the classical limit" to get classical dynamics, but you need to explain where you get the phase space from
 
Superfast Jellyfish
Superfast Jellyfish
Anybody have an idea why it’s most probable for an atom to de-excite at the time of excitation? As in, in the probability distribution of detection times from a single photon source, the peak is always at the retarded time of excitation. Why is that so?
 
ACuriousMind
ACuriousMind
9:55 AM
It's unclear what $\hbar \to 0$ "does" to a state, and certainly position/momentum eigenstates are as far from a classical state as can be
so you need to discuss coherent states in some sense, whether a good notion of these exists for arbitrary quantum systems, whether their limit really gives back something that has the structure of a phase space, etc.
 
bolbteppa
bolbteppa
The $\hbar \to 0$ limit turns a quantum state into nonsense, $e^{i0/0}$ is meaningless, does not exist, just as a function $f(x) = \frac{x^2-4}{x-2}$ is not defined at $x = 2$. You can't say coordinates start existing when some parameter in the theory takes on some special value when the most fundamental statement of the theory is that they are defined to not exist.
 
Slereah
Slereah
10:11 AM
@bolbteppa contextuality!
 
bolbteppa
bolbteppa
How can the (infinite-dimensional) matrix $\hat{x}$ literally turn into a coordinate $x$ when $\hbar = 0$
 
Slereah
Slereah
@bolbteppa a functor, probably
 
bolbteppa
bolbteppa
haha
Maybe there's a way to make sense of this, but you're going to have to find a flaw in QM and invalidate all the arguments made in 20's and 30's etc which nobody even knows anymore that scared people into running away from this stuff
 
Slereah
Slereah
I think we tried discussing it a few weeks ago
 
Thomas Klimpel
Thomas Klimpel
@ACuriousMind Where do you learn about coherent states? My QM textbooks didn't talk about them, and neither did my solid state physics textbooks. The first time I read about them was in "Quantum Computation and Quantum Information" by Michael A. Nielsen and Isaac L. Chuang. I also encountered them in "Coherent Quantum Physics" by Arnold Neumaier.
 
Slereah
Slereah
10:15 AM
Because there's a lot of very fancy techniques to get quantization, but the classical limit tends to be fairly handwavy
@ThomasKlimpel usually it's talked about in more experimental-oriented books
 
bolbteppa
bolbteppa
Coherent states seem to come come up when discussing systems with a large number of degrees of freedom in cases where $a_n |n> = \sqrt{n(n-1)} |n-1> \approx n |n>$ makes sense, so you wont really get much discussion in qm books
Coherent state
In physics, specifically in quantum mechanics, a coherent state is the specific quantum state of the quantum harmonic oscillator, often described as a state which has dynamics most closely resembling the oscillatory behavior of a classical harmonic oscillator. It was the first example of quantum dynamics when Erwin Schrödinger derived it in 1926, while searching for solutions of the Schrödinger equation that satisfy the correspondence principle. The quantum harmonic oscillator and hence, the coherent states arise in the quantum theory of a wide range of physical systems. For instance, a coherent...
 
ACuriousMind
ACuriousMind
@ThomasKlimpel they usually show up in many-body or optics contexts where the hep approach of just thinking about scattering momentum eigenstates is a poor fit
 
Thomas Klimpel
Thomas Klimpel
@bolbteppa Thanks. I have trouble making sense of this sentence from the introduction: "The coherent state describes a state in a system for which the ground-state wavepacket is displaced from the origin of the system."
 
ACuriousMind
ACuriousMind
the P and Q representations on phase space are based on them, but it's again usually non-hep contexts where you'll find the phase space picture being considered
@bolbteppa this isn't really an argument - "how can the coordinate $x$ turn into a matrix $\hat{x}$ when we quantize?!?!"
both quantization and the classical limit are more than just taking a literal limit in the sense of analysis, that's obvious
but we "know" what quantization is supposed to be: A map between classical and quantum observables, and things like geometric quantization even construct the Hilbert space from classical data + some choices
 
Slereah
Slereah
10:30 AM
Quantization is taking the limit $\hbar \to \hbar$
 
ACuriousMind
ACuriousMind
but as far as I can see we don't really know how to formalize the classical limit - should it map quantum observables to classical ones? should it generate a phase space out of the Hilbert space?
 
bolbteppa
bolbteppa
Right, but the point the blog post above above was that because the 'state spaces' are different when you take this limit means that this limiting process is "One of the great crimes against humanity" lol
 
Slereah
Slereah
Wouldn't quantization take the image of the field operators as the phase space?
Since it's the space of measured quantities roughly
 
ACuriousMind
ACuriousMind
do you mean de-quantization?
 
Slereah
Slereah
Yes
Re-classization
 
ACuriousMind
ACuriousMind
10:33 AM
well you wrote 'quantization' so that was confusing :P
I think the problem is "how do you do that"? If we want to express the classical limit we shouldn't start from the assumption that the system has been the result of quantization
 
bolbteppa
bolbteppa
we know $\hat{x}$ has to be replaced by $x$ when we break QM by dividing by zero by setting $\hbar = 0$, but we had to break qm to get there
 
ACuriousMind
ACuriousMind
because then it's trivial - if you assume the system is the result of quantizing the classical system $X$, then the classical limit is trivially $X$
 
Slereah
Slereah
@ACuriousMind i guess it would be hard for say QFT
 
bolbteppa
bolbteppa
It's not clear that this whole field isn't just a waste of time tbh
 
ACuriousMind
ACuriousMind
but without starting from a classical theory, how do you identify "$x$" and "$p$" among all the other operators?
 
Slereah
Slereah
10:35 AM
Since the quantum operators don't give you a field upon measurement
 
ACuriousMind
ACuriousMind
how do you know that spin should "disappear"?
 
Slereah
Slereah
@ACuriousMind do you need to, though
Does the classical theory you get have to be expressed with the same quantities
 
ACuriousMind
ACuriousMind
no, but if you started by quantizing a classical theory the classical limit should always produce a theory equivalent to it, no?
maybe you don't need to identify $x$ and $p$, but again, how do you get the phase space? How do you get the classical Hamiltonian?
 
Slereah
Slereah
Well yes, equivalent is fine
If you pick $e^x$ instead of $x$ that will be fine
 
DarkRunner
DarkRunner
Hi everyone
 
Slereah
Slereah
10:37 AM
If confusing
 
DarkRunner
DarkRunner
I don't mean to interrupt, but I have a question about Electromagnetics
 
Thomas Klimpel
Thomas Klimpel
@ACuriousMind Thanks for the information. I will now study the two wikipedia articles ("Coherent state" and "Coherent states in mathematical physics"). Looks like your original discussion it taking up steam again, and I don't want to interrupt.
 
DarkRunner
DarkRunner
How does the Electromagnetic Field change for a charge moving close to $c$ s.t. $\gamma >> 1$?
In particular, where does the $\frac{1}{{c}^{2}}$ term in ${B}_{\perp}$ arise from?
 
Slereah
Slereah
If you consider the function $x : H \to R^3$ defined by $\langle \psi, \hat{x} \psi \rangle$, the image of that function should be the whole configuration space, no?
I guess you need to find all the observables necessary and sufficient to do the whole theory to get a phase space
 
bolbteppa
bolbteppa
All you need is that when you take the classical limit, the system you're describing becomes completely described by the classical theory you quantized, that's the only constraint, there's zero implication that any more is needed
With $\hbar = 0$ you're doing a jump to a system being described by variables that don't exist when $\hbar$ is not $0$, it's a whole new theory. It's switching off one theory and switching on another. It seems more likely that at best one will get some fiction pretending this makes sense...
 
DarkRunner
DarkRunner
10:45 AM
We basically set the Lorentz Force Equation for both Observers' Reference Frames equal. Hence, one stationary observer sees only a Magnetic Field, whereas the other observer with a moving frame sees a Magnetic Field and Electric Field.
 
Slereah
Slereah
The two theories should be isomorphic though
I think?
 
ACuriousMind
ACuriousMind
@Slereah The possible expectation values will always be the interval between the lowest and highest possible eigenvalue, won't they?
 
Slereah
Slereah
I would guess classical limit is unique
 
bolbteppa
bolbteppa
Same with this wave function of the universe stuff, if there's no observer obeying classical laws enabling one to measure, it doesn't really makes sense
 
DarkRunner
DarkRunner
But I'm still struggling to understand why that $\frac{1}{{c}^{2}}$ term is there.
 
Slereah
Slereah
10:46 AM
@ACuriousMind I mean most such fancy observables have more structure
 
DarkRunner
DarkRunner
If anyone can help, that would be great
 
Slereah
Slereah
Symmetry groups and all
 
ACuriousMind
ACuriousMind
@DarkRunner the units don't match if it weren't
@Slereah Sure, but the image of your function is just the possible expectation value for some observable
how do you pick which one produces the configuration space?
 
DarkRunner
DarkRunner
@ACuriousMind Why not just $\frac{1}{{v}^{2}}$?
 
Slereah
Slereah
@ACuriousMind not sure
 
bolbteppa
bolbteppa
10:49 AM
The $1/c^2$ comes from doing a Lorentz transform
Classical electromagnetism and special relativity
The theory of special relativity plays an important role in the modern theory of classical electromagnetism. First of all, it gives formulas for how electromagnetic objects, in particular the electric and magnetic fields, are altered under a Lorentz transformation from one inertial frame of reference to another. Secondly, it sheds light on the relationship between electricity and magnetism, showing that frame of reference determines if an observation follows electrostatic or magnetic laws. Third, it motivates a compact and convenient notation for the laws of electromagnetism, namely the "manifestly...
The wiki links to a book which shows how you get it
 
DarkRunner
DarkRunner
@bolbteppa OK. Let me take a look at "Introduction to Electromagnetic Theory: A Modern Perspective". Thanks for letting me know
 
Charlie
Charlie
helo
 
Slereah
Slereah
Is there an example of two identical quantum theories with different classical limits
Because of the wrong choice of basic variables
 
ACuriousMind
ACuriousMind
you have to define the classical limit first to be able to talk about that!
 
Slereah
Slereah
Well, take a theory with a Hilbert space isomorphic to $L^2(R^3)$, with the appropriate Hamiltonian operator
 
bolbteppa
bolbteppa
10:54 AM
@DarkRunner this hepweb.ucsd.edu/ph110b/110b_notes/node69.html is basically what you want to work out
 
Slereah
Slereah
Can you pick some operators such that their respective classical theories aren't isomorphic
 
ACuriousMind
ACuriousMind
@Slereah all separable Hilbert spaces are isomorphic to $L^2(\mathbb{R}^n)$ for any $n$, you need to stipulate some representation stuff there otherwise that's an empty statement :P
 
DarkRunner
DarkRunner
@bolbteppa I know only the basics of tensors; I'm trying to find a "tensor-free" derivation. Thanks nonetheless
 
ACuriousMind
ACuriousMind
that's the first step here - to talk about the "classical limit"we first need to pin down what data exactly defines "a quantum system"
 
bolbteppa
bolbteppa
 
Slereah
Slereah
10:58 AM
@ACuriousMind maybe the CCR are required here
 
DarkRunner
DarkRunner
@bolbteppa Yes! "You see that a velocity times the magnetic field has the same dimensions as an electric field. So the right-hand side of Eq. (26.9) must have a factor $\frac{1}{{c}^{2}}$"
Thanks! @bolbteppa
 
Slereah
Slereah
Can you have a version of the CCR that doesn't pick specific operators
Similarly to the symplectic structure
Something something Heisenberg group
 
ACuriousMind
ACuriousMind
@Slereah sure, you can say that there should be a representation of the CCR on the space, and then the Stone-von Neumann theorem applies to some systems. You don't know which of the two operators is position and which is momentum just from the CCR
but you also have systems like a particle on a ring where position has continuous bounded spectrum and momentum is discrete and unbounded
in theory one could imagine a quantum system where it's the other way around - position is discrete and momentum is not - but you don't get that by quantizing a classical system so we don't usually talk about it
 
bolbteppa
bolbteppa
It all comes back to:
"A more general theory can usually be formulated in a logically complete manner, independently of a less general theory which forms a limiting case of it, Thus, relativistic mechanics can be constructed on the basis of its own fundamental principles, without any reference to Newtonian mechanics. It is in principle impossible, however, to formulate the basic concepts of quantum mechanics without using classical mechanics. The fact that an electron has no definite path means that it has also, in itself, no other dynamical characteristics. Hence it is clear that, for a sy…
Secretly all this QM limit stuff is trying to avoid the problem in this passage by defining QM in such a way that it neatly becomes CM so we can just say QM is all that matters, but it's been a century and it seems like people are simply unaware of the basic issue that QM says (x,p) don't exist, CM says (x,p) do exist, so trying to get (x,p) from NOT(x,p) from some math trick is at best a game
 
Slereah
Slereah
11:30 AM
@ACuriousMind could be trickier yes
Although maybe there is a class of quantum theories one can classicalize
I'm guessing probably every theory that relates to a classical theory has a Hilbert space that is square integrable functions on the configuration space up to some measure
 
Slereah
Slereah
11:57 AM
But then again all hilbert space are etc so how to select the proper one
How much structure do you need to define
 
Physics Meta
Physics Meta
0
Q: Did the question really deserve to be closed?

BuraianThe question Op didn't format the question in a very nice/ didn't put a lot of background.. however I do think that what the actual substance of the question is actually high value. I recall being very confused about how the vectors behave under different transformations when I first started lea...

discussion
 
Faded Giant
Faded Giant
12:17 PM
@PhysicsMeta The actual question was just:
> I just need an answer in a paragraph . I will be very grateful if i get a quick answer
 
B. Brekke
B. Brekke
12:41 PM
I am holding my first internal seminar about my Master's thesis in a couple of weeks. One of the professors dislikes bullet points appearing one by one, while I really like it, when used sensibly. Is it unprofessional to use it, or does anyone have an opinion?
The alternative is to have all of the slide appearing at once
 
Philip
Philip
@B.Brekke I think the people at Academia might have something to say about that. I personally like them appearing one after the other when, as you point out, it's used sensibly. But I also like to spend some time with all the points on the slide so that people get a global sense of the argument too.
 
DarkRunner
DarkRunner
1:45 PM
Is $\frac{dA}{dt} \times B = A \times \frac{dB}{dt}$?
If anyone can help, that would be great
 
Slereah
Slereah
1:56 PM
$$\frac{d}{dt}(A \times B) = \frac{dA}{dt} \times B + A \times \frac{dB}{dt}$$
is the appropriate formula
 
More Anonymous
More Anonymous
2:13 PM
@bolbteppa Have you read about the wigner function?
 
bolbteppa
bolbteppa
Vaguely
 
More Anonymous
More Anonymous
It does given a nice method to talk about the phase space
 
DarkRunner
DarkRunner
@Slereah OK OK Thanks!
 
bolbteppa
bolbteppa
Phase-space formulation
The phase-space formulation of quantum mechanics places the position and momentum variables on equal footing, in phase space. In contrast, the Schrödinger picture uses the position or momentum representations (see also position and momentum space). The two key features of the phase-space formulation are that the quantum state is described by a quasiprobability distribution (instead of a wave function, state vector, or density matrix) and operator multiplication is replaced by a star product. The theory was fully developed by Hilbrand Groenewold in 1946 in his PhD thesis, and independently by Joe...
 
bolbteppa
bolbteppa
2:49 PM
@MoreAnonymous maybe this (p.4) and this are what you are hoping for with the classical limit
"this density can take provocative negative values and, indeed, these can be reconstructed from lab measurements"
So this perspective on QM goes into negative probabilities, says they are measurable, and promises a better way to take the classical limit...
 
John Rennie
John Rennie
 
Faded Giant
Faded Giant
> But every time it rains
You're here in my head
Like the sun coming out
Ooh, I just know that something good is going to happen
 
Slereah
Slereah
3:35 PM
@JohnRennie I recall some cloud seeding incident where it worked a bit too well and flooded the city
 
 
2 hours later…
JingleBells
JingleBells
5:47 PM
I need free narration over promotional vid
 
Charlie
Charlie
Why not use your own voice?
 
JingleBells
JingleBells
cuz I'm from Bulgaria and my dialect is bad
I can use computer generated voice
I have a new idea and I'll validate it first (without building it) to see if there are people who need it.
 
Charlie
Charlie
6:01 PM
What decides whether an algebra is defined by an anti-commutator (eg. the poisson bracket, the clifford algebra) or a commutator (eg. most common Lie group algebras)?
Is it just a definition?
 
JMac
JMac
@JingleBells Videos with computer generated voices generally creep me out. I doubt that is a good route for a promotional video honestly.
 
Philip
Philip
6:49 PM
I doubt the answer is yes, but is there a way to "observe" which slit a photon is going through and collapse the interference pattern in a standard double slit experiment with, say, a laser?
 
Vishesh Mangla
Vishesh Mangla
7:31 PM
chemical engineering people fluid mech/transport pheonomenon here?
need help in understanding what is in momentum and out momentum in shell momentum balance
youtube.com/watch?v=sMsw8BPT578 stuck at 25:26 from 5 hrs. I 'm unable to understand this.
 
 
3 hours later…
Buraian
Buraian
10:59 PM
hi
 

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