The h Bar

Mithrandir24601

18:01

You could possibly argue that it's less that Bohmian mechanics and the Copenhagen interpretation are different ways of describing the same thing and more that they are the same thing, not different ways of describing some underlying theory, but the same thing

So believing one over the other just... Doesn't make sense

Novalium Company

Well, ok. I'm just beginning in QM so I'm no one to talk on this topic :)

Mithrandir24601

Ugh, honestly, I've yet to see a course that teaches QM well (for people who are just starting out learning QM)

Rudi_Birnbaum

"In which explanation of the collapse in QM do you guys believe?" you asked a question

we try to explain to you why this question doesn't really make sense,

Novalium Company

Yep, I got it now.

Rudi_Birnbaum

we do so since we accept that you do not know it which is perfectly fine.

Mithrandir24601

18:03

@Rudi_Birnbaum Resource/reference frame theory leading to decoherence leading to a classical probability distribution :P

Novalium Company

I barely understand the copenhagen and bohm interepretations so I have a lot to learn... Although I do understand the multiple-worlds interpretation, which is pretty interesting.

Mithrandir24601

@NovaliumCompany It sounds like you want to do metaphysics or philosophy, not physics

If you do, study what you like, but these questions are very rarely asked by physicists

Novalium Company

Well... it only sounds like it then :P

You are correct, I'm more interest in what physics mean, rather than calculate numbers...

Rudi_Birnbaum

@NovaliumCompany which might makecphysicsists hugely unhappy google "Feynman, Why"

Mithrandir24601

@NovaliumCompany I'd argue that physics is more about coming up with new/improved ways of calculating numbers [theory] as well as calculating the numbers [simulation] and coming up with experiments to find those numbers [experiment]

Novalium Company

18:07

@Rudi_Birnbaum I'm not here to make physicists happy.

Rudi_Birnbaum

duckduckgo.com/…

you have to take into account that you possibly won't find the answer to such a question in physics

Novalium Company

I don't want to get into the depths of the complex math behind QM. I just want to have at least a little idea of what exactly it is. But now I find out that most people don't know what QM actually is exactly lol :D

Rudi_Birnbaum

what is your idea about classical mechanics then? Do you have a little idea of what classical mechanics is?

Novalium Company

Well, you can always know and learn more. I don't have a particular base to which I can compare my knowledge because I'm self-taught.

I mean, what is "little idea"?

Rudi_Birnbaum

well you have used the term

" I just want to have at least a little idea of what exactly it is"

I think QM is a lot less mysterious than it might appear.

Especially if you are a beginner to Physics.

Novalium Company

18:15

My interpretation and understanding of the term "little idea" is probably different from yours. So everyone is free to interpret it however he/she wants. :)

Rudi_Birnbaum

When I say a classical object moves in trajectories, than that is about as much as you can get to the heart of things (lets say).

When you go the microscopic world (quantum world) then this "paradigm" does not hold anymore.

Quantum objects don't move in trajectories (=(more or less smooth time dependent) paths

no thats maybe the most important thing a beginner could learn

Novalium Company

Well, I'm not your definition of a beginner then :D

Rudi_Birnbaum

More or less everything else emerges from that basic reality

Novalium Company

Maybe I am super-beginner xD

bolbteppa

Episode 45: Leonard Susskind on Quantum Information, Quantum Gravity, and Holography

►

Novalium Company

18:19

I see the quantum world as everything being a cloud or probability when not observed and the only thing you can know is the wavefunction that predicts the probability of the object's position when observed. (Something like this :P)

Rudi_Birnbaum

Now you know. Have you got an imagination of what it means that a microscopic particle can't possibly be described by a trajectory?

Sir Cumference

Oh hey @Mithrandir24601 you're a mod now?

Rudi_Birnbaum

It means you cant give a position of the particle and at the same time a speed and direction.

Thats impossible

Novalium Company

Uncertainty principle :)

Rudi_Birnbaum

Either is has a position that is defined or a momentum but never both. Also none of them is possible.

yes.

Novalium Company

18:21

But I have a question.

bolbteppa

If you have two identical particles (say electrons), and you measure them both at two separate instants, you can't tell which particle went into which position because they didn't follow paths between those two points

Rudi_Birnbaum

OK go on

Mithrandir24601

@SirCumference As of over a year ago, yep

Sir Cumference

Oh, well...belated congratulations lol

Don't remember that, huh...

Novalium Company

Let's imagine a quantum particle that is not yet observed. (e.g photon) We can imagine it as a cloud or probability density of where it'll eventually be, and the wavefunction describes where the probability is higher for it to land and where it is less. So how can we apply the uncertainty principle (before and after collapsing) to this photon?

Rudi_Birnbaum

18:23

So for the beginner its maybe clearer not to repeat the word "uncertainty principle" but better to see it as that a quantum object cannot have a trajectory.

Novalium Company

@Rudi_Birnbaum yep

bolbteppa

@NovaliumCompany curveball - the wave function for a photon position does not exist, can only use 'position' wave functions for non-relativistic objects, but you can use it for 'momenta'

Rudi_Birnbaum

@NovaliumCompany the uncertainty principle is there to tell you how badly the system at least deviates from being described by a path/trajectory

its not really that you "apply" the uncertainty principle like you apply a tool from a toolbox to achieve something.

Better to use electrons as examples to start with.

Novalium Company

What is a non-relativistic object? A microscopic object?

bolbteppa

An object which doesn't move at speeds near the speed of light, a photon is clearly at the speed of light

Rudi_Birnbaum

18:27

soemthing that moves much slower than the speed of light

better use electrons as examples

for beginning.

Novalium Company

Alright let's start with an electron. But again, it doesn't have a defined pos nor momentum. So we only have a wavefunction that describes where it's most likely to be when observed, no?

bolbteppa

It has a well-defined position, or a well-defined momentum, but it does not have both simultaneously, only one

Rudi_Birnbaum

when electrons have a very low energy (of motion) i.e. if they are very slow they behave very obviously like quentum objects

Novalium Company

@bolbteppa Got it. (That's basically uncertainty principle)

Rudi_Birnbaum

Lets go back to the trajectory. If it would move in a path we could give both momentum(vector) and position.

but it doesent, so we cant.

Novalium Company

18:30

yep

Rudi_Birnbaum

The obvious question is now what can we tell at all?

Novalium Company

Only one of the two, with certainty, but know nothing about the other?

Rudi_Birnbaum

And the answer is that we can to some degree confine the possible distributions of places and momenta

@NovaliumCompany at most!

Sometimes you know neither

bolbteppa

Basically experiments show that when you measure say an electron at one instant in time and then measure it at subsequent instants, there is no way you could ever interpret what you measure as showing the electron was following a path, it appears in random places (in the region where you found it) at each instant,

if you measure it less and less accurately it starts to look more and more like it was following a path like Newton's laws predict, but the more accurately you measure the more random it becomes.

Rudi_Birnbaum

The point of QM is that "we can to some degree confine the possible distributions of places and momenta".

Novalium Company

18:33

@bolbteppa That's the wavefunction predicting a position (with places more likely and less likely for it to appear)?

How do we measure the momentum/speed of an electron? We can't use a speedometer :D

bolbteppa

So if experiments show random behavior when measuring things like position or momenta probability is clearly the only way to try to describe where we'd measure something at a given moment, but this completely destroys all of classical physics, however whatever theory of probability we try to set up is constrained by the fact that it should reduce to classical physics in some to-be-defined 'limit' of less and less accuracy

Rudi_Birnbaum

I have to leave, cheers!

bolbteppa

So by playing with the idea of probability, you can show that 'wave functions' are a convenient way of describing probabilities

Novalium Company

In the double slit experiment, when we send an electron, it doesn't have a position nor a momentum, that's why it interferes with itself? There isn't "one electron"?

@Rudi_Birnbaum Bye and thank you for explanations :)

Rudi_Birnbaum

@NovaliumCompany welcome!

Novalium Company

18:37

I mean, to what extent will the electron interfere with itself. I mean, what if we added 100 of slits?

I mean, how big is that probability density cloud of the position (which is what's allowing that interference with itself)

bolbteppa

In the double slit experiment, if you observe the light as it moves, it moves like classical particles do, so you need to do the experiment observing only the end points where the photons land. If you do it with two slits open, it turns out the distribution of photons on the other side you measure is spread out along the crests of a wave interference pattern,

this pattern does not arise when one slit is open, which shows the probability distribution of potential final places acts like a wave for each possible event (i.e. way of going through the slits) and they can combine like waves do to affect the overall probability

So the function determining the probabilities of possible measurements acts like a wave does in that sense, but it's talking about probabilities of finding certain measurements, not a real wave

Novalium Company

This doesn't answer my questions :P

bolbteppa

Why is nature such that whatever goes on as the photon goes from emitter to detector is wave-like, nobody knows, indeed QM claims that it's in principle un-knowable and a meaningless question, Bohm says there are hidden variables controlling what's going on

Mithrandir24601

@SirCumference Thanks :) It's probably because I haven't been in here so much over the past number of months?

bolbteppa

How can an electron interfere with itself, the point is that the final most likely measured positions of the electron are the places where waves for the two slits interfere constructively

Mithrandir24601

18:46

@bolbteppa At least from a practical point of view, I'm going to disagree with that, from the sense that an actual photon is really a wavepacket

bolbteppa

What does that mean, all of physics assumes things like photons are point-like

Mithrandir24601

@bolbteppa That's news to me

Although I suppose it depends on complications like what exactly you mean by 'photon'

bolbteppa

You can model like non-relativistic quantum systems with wave packets (to allow for an initial uncertainty in knowing where it's position is) if that's what you mean (but in principle it's initial position is measurable to exact accuracy non-relativistically)

Novalium Company

A question: How big is that cloud of probability of position in the case of a shot electron through slit experiment? I mean, that size will determine how far of a slit the electron can interfere with itself through?

Mithrandir24601

@bolbteppa I sort of mean that, to someone in a lab, different photons from the same source will be observed to have a distribution over frequency, so they similarly are observed to have some distribution over space

e.g. if you create photons from a crystal, you don't know where the photon was created within that crystal

But then, technically, you could make the argument that you're not actually creating a photon at all

bolbteppa

18:58

Yeah you're basically forced to use wave packets for such situations but it's not like any choice is more fundamental than all the others

Semiclassical

presumably the wavefunction you use in that case is device/system-dependent

Mithrandir24601

Sure

@Semiclassical Yeah, also depends on what you want to do with it

Long story short, photons are weird

Semiclassical

One paper I know (a pilot wave paper, fwiw, though the math point being made is irrelevant) models wave packets as being of the form $\Psi(x,0)=e^{i k_0 x}\phi(x)$ where $\phi(x)$ is some smoothed box function

Mithrandir24601

@Semiclassical We'd normally say that it's Gaussian (or something similar at least)

Semiclassical

it's specifically not Gaussian in this case

Mithrandir24601

19:01

Interesting

Semiclassical

main claim being that, if the central wavelength $\lambda=2\pi/k_0$ is much less than the packet length $L$ (and also less than the smoothness scale $a$) then the wavepacket remains coherent

I mean, it's all a matter of time scale: it'll eventually disperse

back later

Novalium Company

How big is that cloud of probability of position in the case of a shot electron through slit experiment? I mean, that size will determine how far of a slit the electron can interfere with itself through?

bolbteppa

Basically in the rest frame from $\Delta x \Delta p \approx \hbar$ you have $\Delta x m c \approx \hbar$ giving the maximum uncertainty in the position as $\Delta x \approx \hbar/mc$ so any wave packet with this uncertainty will do as your best approximation for things like photons

Novalium Company

@bolbteppa Is this an answer to my question?

bolbteppa

No sorry

Novalium Company

19:09

I think it answers my question to some degree xDD

What's the maximum difference between the slits in order for an interference pattern to appear?

Also would it work if the slits where vertically aligned? An intereference pattern should appear but vertically orientated?

bolbteppa

Double-slit experiment

In modern physics, the double-slit experiment is a demonstration that light and matter can display characteristics of both classically defined waves and particles; moreover, it displays the fundamentally probabilistic nature of quantum mechanical phenomena. The experiment was first performed with light by Thomas Young in 1801. In 1927, Davisson and Germer demonstrated that electrons show the same behavior, which was later extended to atoms and molecules.Thomas Young's experiment with light was part of classical physics well before quantum mechanics, and the concept of wave-particle duality. He...

Novalium Company

This doesn't answer my questions but thank anyways :)

Sir Cumference

19:53

Oh wait that's not what we're talking about

Novalium Company

:P

What I'm trying to understand is: The cloud of probability density of the position (wavefunction) of a shot electron through a double-slit is what creates that interference pattern that will build up as you shoot more electrons, right? So how far can the slits be? Does that get determined by the size of the cloud of probability of position, so somehow the electron can interfere with itself?

Semiclassical

20:17

@Mithrandir24601 here's the approach (in a form that doesn't talk about pilot wave stuff) arxiv.org/abs/0910.1513

Jake Rose

@NovaliumCompany it depends what you mean. You have to quantify it somehow.

basic diffraction equations will tell you about how big the slits have to be

roughly speaking it has to be about the same size as the wavelength

(for example using some basic Fraunhofer stuff you’d see the sink function and be able to quantify it that way)

peterh

20:52

The VtC/VtR votes are very hard decisions on the PSE

compared to the VtC/VtR on other sites.

Novalium Company

When we have an electon shot through one of the slits, we say it goes through both at once, because it doesnt have a defined position?

If the slits are far apart, why wouldnt the electron split? (Then combine and land at a place with probability dictated by the wavefunctuon)

Emilio Pisanty

0

Q: What limits the projectile speed and power of a ballista?

Suppose that I have arbitrary quantities of some material A, a string material B, and I make a gigantic crossbow/ballista out of it, making an arm out of A and the string out of B. What happens as I scale up the dimensions of this ballista? Can I scale things up proportionately indefinitely and ...

Ooooohhhh, boy is @KyleKanos going to love that question

I commend OP, frankly. Topical question, strictly on the physics, no spoilers unless you already know what's going on.

Rudi_Birnbaum

21:10

@EmilioPisanty What I meant was actually if from $\vec{f(\vec{r})}=h(\vec{r})\nabla \rho(\vec{r})$ it follows that there is a scalar function $H$ such that $\nabla H(\rho(\vec{r})) = h(\vec{r})\nabla \rho(\vec{r})$?

or better : What I meant was actually if from $\vec{f(\vec{r})}=h(\vec{r})\nabla \rho(\vec{r})$ it follows that there is a scalar function $H$ such that $\nabla H(\rho(\vec{r})) = \vec{f(\vec{r})}$?

Novalium Company

What has decoherence have to do with macro objects. I understand the interferometer experiment but it doesnt explain why we dont see things such as superposition in the macro world?

Kyle Kanos

21:25

@EmilioPisanty it is an interesting question. I might have to think more about it before commenting (distracted by finance things ATM)

Jake Rose

21:47

@NovaliumCompany well it could but the larger you make the slit the more it behaves as if there is no slit there (because it’s to small to really ‘see’ it)

@NovaliumCompany the reason you don’t see quantum superposition in the macro world is because the wavelengths are too small

and even that I sort of disagree with because you can see diffraction effects in lots of places

Sir Cumference

23:07

Can $\xi$ be banned from the greek alphabet already

2

I think I recall a petition from a physicist to do so

enumaris

no

it's used a lot in GR lol

Sir Cumference

23:46

@enumaris It's used a lot everywhere but it's a pain to write lol

no clue why it's so popular a choice, aren't there like 20 other greek letters available?

Secret

23:58

scientificamerican.com/article/…

That seems straightforward to understand also in the Bohm perspective, since particles and wavefunctions do not occupy the same "space"

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