@enumaris Thanks :)

arxiv.org/pdf/1307.1714.pdf talks about it in more detail, in particular the suggestion that the foliation could be covariantly extracted from the wavefunction

I dunno, though.

also, you should look at the list of 'derivations' on that page

hey @HDE226868 fancy meeting you here :)

@Green I'm often a lurker listener here.

@HDE226868 rare lurker for me.

If anyone knows, please feel free to share.

@Semiclassical I'm not sure why you can't just copy Bohm's paper with, say, the Dirac equation

It seems Bell was really convinced by this paper

Don't get me wrong - I think it's a good question you have there.

@bolbteppa well, for one, what’s the relativistic equivalent of the Hamilton-Jacobi equation?

I don’t know what that is

For another, the attempts to formulate dBB have largely taken the first-order strategy I.e. take the appropriate wave equation and determine the corresponding velocity field

@Green yeah the ignition voltage should be higher than the extinction voltage. You're looking for a Pachen curve I believe

@Semiclassical The H-J equation is just another expression of the principle of least action. Start with a relativistic action and you get a relatvistic H-J equation.

@danielunderwood Hah! Good! My intuition wasn't crazy wrong. Thanks for the pointer to Pachen curve.

Fair enough. In truth I don’t know what the efforts to formulate relativistic pilot-wave theory along the lines of Bohm’s paper have looked like

And thank you very much.

No problem! That was actually one of my senior lab projects. Though we used air rather than pure hydrogen

Relativistic actions are usually inherently actions with gauge symmetries though since they have some sort of reparametrization invariance, so stuff gets subtle since the naive degrees of freedom are not the physical degrees of freedom

@Semiclassical It seems Bohm starts from non-relativistic Schrodinger, uses $S = R e^{iS/\hbar}$ and then makes the result look like HJ

@danielunderwood I'm aiming for an experiment with 95% H2 mix with argon and methane mixed in then igniting a plasma in the mixture with 2.4GHz microwaves.

For relativistic HJ you sub $p_{\mu} = - \partial_{\mu} S$ into $p_{\mu} p^{\mu} = m^2 c^2 $ to get $\frac{1}{c^2}(\frac{\partial S}{\partial t})^2 - (\frac{\partial S}{\partial x})^2 - (\frac{\partial S}{\partial y})^2 - (\frac{\partial S}{\partial z})^2 = m^2 c^2$

But the Dirac equation is a first-order Schrodinger equation, hmm...

I.e. from a conceptual viewpoint one should first develop a general Bohmian treatment of gauge theories and then apply that to relativistic actions.

(although that is never the historical way things develop - general treatments of gauge theories are much less common than people just trying to figure stuff out for specific gauge theories)

This again falls firmly into my category of “if no one has done that yet, I’d like to know why”

I need to know regular gauge theory properly :p

You can look at what Bohm does as basically setting up the semi-classical approximation in normal QM, I guess there is a nice write-up of the semi-classical Dirac equation

I better get off this Bohm stuff soon and back to the 'normal' theory of susy as the square root of a Dirac operator :p

ill note that, for all that I’ll defend the internal consistency of the first-order strategy in the case of non-relativistic QM

@Green I will say that my answer was that you don't need to keep putting as much energy after it's initially ionized. I'm not sure about your other numbers. I think you'd have a difficult time getting a plasma at 1 bar. We were working at 10^-2 T and had a 300W 13.56MHz radio source attached to parallel plates. I'm not sure of other ways of creating a plasma though

I don’t have a clue about what lessons if any it should have for QFT

Looking back at the data, the highest pressure we were able to ignite with that supply was 0.3T

One thing I'm not sure of yet, Bohm seems to say he interprets the wave function as a real physical force field on page 170, almost the same as the EM field, well, you can turn Maxwell's source-less equations into a Schrodinger equation for the modes pretty nicely, so in this case the wave function is literally a force field, and you can also show this literally cannot describe the position of a particle

In particular, the suggestion that a trajectory formulation for quantum fields should exist seems far more of a stretch

One point in that regard: through the guidance equation, a wavefunction determines the allowed trajectories in configuration space

In that sense, it acts on any particles in the system

Yeah, he seems to give a justification for this interpretation on page 170, but he also blindly starts from the Schrodinger equation, I would bet money there is a big contradiction there but not sure yet

By contrast, one really doesn’t speak of said particles acting on the wave function

So there’s a seeming asymmetry there

One response I’ve seen is to compare the role of the wavefunction with that of the Hamiltonian in Newtonian mechanics

If the wave function is a force field, the whole anti-particle thing arising via fields would probably be may more likely to make more sense than normal QM where one tries to treat it as a position probability distribution, idk

One doesn’t speak about particles acting on the Hamiltonian in that scenario; rather, the Hamiltonian determines what paths are allowed in phase space

I dunno where I stand on that

I’ll also point out, though, that I don’t think there’s any notion of being able to directly measure the wavefunction in any case

If you're saying that Bohmian mechanics does not afford the Hamiltionian the same role as in classical mechanics, then that alone is a reason to dislike it - "the Hamiltonian is the generator of time translation" is a much too powerful unifying slogan for me to easily give it up.

well, you still have it playing the same role when it comes to the time evolution of the wavefunction

But in that regard it really is a funny story: the wavefunction is so connected with the Hamiltonian, whereas the guidance equation really isn’t

@Semiclassical There is elegance in being able to say that applying the Hamiltonian to a state gives the infinitesimal time evolution of said state. In classical mechanics application is on a phase space distribution through the Poisson bracket, and quantum mechanics it is on a density matrix through the commutator (von Neumann equation).

To me this goes to what lessons one should be learning from the various formulations/interpretations

Sacrificing this very clear analogy just because we don't like non-realism strikes me as...overkill.

And the fact is that the lessons which one learns from the Schroedinger equation directly have been very effective

By contrast, it’s hard for me to see what lessons dBB is supposed to have outside that context

That’s why, when people talk about “quantum orthodoxy”, I find it hard not to be annoyed

haha

for me it’s not “that which is correct” but “that which has a proven track record”

I think there are some reasons to appreciate the dBB story, but the sheer fruitfulness of the quantum orthodoxy is hard to understate

i don’t think it’s a settled question, but the onus is on those who find the story interesting to justify why other people should as well

And any “conceptual clarity” one gains is simply not sufficient for that

I'm just doing my absolute best to stifle my bias that dBB is probably the QM version of 'intelligent design' dressing up of creationism (realism) :p and yes it's an argument from authority that virtually all the big names said it was wrong if not mocked it or at least ignored it, but in terms of evaluating it without knowing the theory, you have to include afa's

I think if Bohm's paper legit makes sense though, then it's not ID, but if it makes sense, I think people should be paying a lot more attention to this stuff

The two big exceptions I’ll emphasize in that tradition are Bell and Feynman

Yeah tcm.phy.cam.ac.uk/~mdt26/PWT/lectures/bohm7.pdf says Feynman was friends with Bohm for years and was sympathetic to his ideas but didn't work on it, and Bell was really convinced

Yeah

The Feynman example cuts two ways tho

He found Bohm worth taking seriously, but that didn’t extend to finding it worth working on the subject

@ACuriousMind Hey, you're a computer scientist right?

@SirCumference No, I'm a programmer.

Welp, would you know about search algorithms?

Enough to know that that's an ill-defined question unless you say what sort of data structure we're searching in ;)

@ACuriousMind Don't really know much about comp sci to answer that...

But here goes:

I have two sorted arrays of numbers, A and B. I'm wondering what is the best search method to determine if at least one number from A is present in B?

E.g. an algorithm that works on a sorted binary tree certainly won't work on an unordered array :P

For clarification, B is much larger than A in length

So while I find the mockery/ignorance of the dBB story quite irritating, I can definitely understand an attitude of courteous disinterest

I'm hoping there's a better solution than multiple binary searches

I don't think that you can do better than performing a binary search on B for each element in A without any further knowledge on A and B.

Hmm, I see

Thanks

If B is very large, it might be marginally useful to first search for the largest element in A, then only search the sub-array of B smaller than that element for the rest

Hmm, the problem is pretty tricky. I'm actually trying to write a userscript that greys out the vote button if you can't vote on it, e.g. it hasn't been edited since you voted. I can get a list of every date someone has voted since the edit, but I can't tell if the user specifically voted since then.

The idea would be to search all those dates in the user's upvotes/downvote list on their profile

The list can be massive, so I'm thinking of ways to optimize it

I've got 81 pages of upvotes on astronomy. The search usually finishes after ~3 seconds, but I imagine it could be a lot worse

I'm gonna go out on a limb and say that the site doesn't already do that precisely because the "you already voted on this and can't undo it now" determination is comparatively slow and so should only be executed if someone actually clicks on the vote buttons.

@Loong "The old unit amu isn't used anymore since 1960/1961. " Oh! How I wish that had actually been true of the pedagogical materials I was subjected to (starting in the late 1980s).

@ACuriousMind Presumably, yeah. But it could be a fun/slightly useful userscript if it only takes 1-2 seconds. I'm trying to see the best I can possibly do and consider if it's worth anything.

I'm pretty lucky that the list is sorted, at least.

@SirCumference Well, I don't know if this works in a userscript, but you could just load all the voting dates once and compute a structure with O(1) access (i.e. some sort of hash access) from them, so that "searches" just turn into hash computations.

Gonna be slow on the first access, but no search times on any subsequent page loads

@ACuriousMind Sadly, the voting dates are on separate pages. I don't seem to have any way to access them all on a single page.

My binary search would involve checking the middle page, comparing the dates on the page, and seeing which page to go to next

I was thinking to load all the voting info e.g. on the first load of an SE page (just loop over all voting pages), and then using the hashed array/dictionary/whatever-you-want-to-call-it the rest of the time, but as I said I don't know if that's feasible in a userscript

@ACuriousMind Wait, I think you gave me an idea

The only thing I'd have to worry about is the voting info changing whenever the user upvotes, but reloading every time still seems better

Sigh I really wish I'd signed up for a data structures class