The h Bar

Semiclassical

19:01

The idea that the Schrodinger equation enforces an assumption of no particle trajectories is explicitly contradicted by the fact that I can construct trajectories which preserve the probability density under time evolution

bolbteppa

Well yeah, Schrodinger is just a PDE for a function, of course you can use it to end up with characteristics (curves) on a surface, i.e. trajectories

Of course if you just start with Schrodinger you'll end up with paths existing

Semiclassical

okay. that's what dBB takes to be the particle trajectories: a particle is piloted along one of the characteristics generated by its wavefunction

bolbteppa

I'm trying to be fair and nice, but if I was honest I would say this is very dishonest

Semiclassical

you don't know which one, but that's a matter of initial conditions

bolbteppa

If they assume paths exist, they simply have to start with classical mechanics

Semiclassical

19:07

if classical mechanics = paths exist, then yes. if classical mechanics is supposed to mean anything predictive, then no

if we take classical mechanics to contain anything as simple as the principle of inertia, then dBB is not classical mechanics

bolbteppa

I don't think it's science to assume paths exist, so that classical mechanics should hold, but then say, for no theoretical reason, we just can't use classical mechanics, because reasons... (saying 'experiment' as if that's a theoretical reason is just not science), that's really just ideology, we need serious theoretical reasons not to use classical mechanics, maybe Bohmists still just need to find it, which is always moving the goalposts, QM makes explicit why we can't use CM from the get-go

Now maybe dB does all this

I would really like dB if it did

Semiclassical

My bloody laptop

bolbteppa

I like what Bohm is trying to do, I am just a bit stunned I could find these gaps in the logic, and am thinking of ways to fix them, when I think I find a fix it leads to a bigger problem, I'd say it will take a while to really know if this makes sense, maybe I'm wrong also

Semiclassical

You’re having it both ways, though. Why do we accept the Heisenberg uncertainty relation as true?

bolbteppa

I don't accept them as true, I derive them from Heisenberg's claim that paths don't exist the way Landau does

Semiclassical

19:13

Ok. Then why do you accept that assumption?

bolbteppa

I accept that classical mechanics is wrong because the variables we use to set classical mechanics up don't exist on a fundamental level, they arise out of a limit arising from lack of measuring specificity, i.e. the quasi-classical limit

Once you go to that limit, it's fine and holds perfectly

Of course it's crazy nonsense to say paths don't exist, but that's QM

Semiclassical

Ok. But that’s basically assuming Copenhagen right from the get-go, and then assuming that anything you derive from that can only be justified on those grounds

bolbteppa

But once you accept that, the rest all makes sense more or less through math

Yeah that's right

Semiclassical

I mean, the simple fact that Bohmian trajectories are compatible with the uncertainty relation makes that implication specious in my book

bolbteppa

If Bohm could derive the Schrodinger equation based on paths existing but then being obscured for some reason, I think it would be a lot more acceptable

Semiclassical

19:18

Again, you keep focusing on Bohm 1952 as though that’s the entire story

Captain Bohemian

@bolbteppa why did you mention Ryder here? Does Ryder's QFT textbook use the term "nonlocal" somewhere? Excuse me for replying your message so late. Earlier I just had no time to reply because there were too many messages incoming here to read.

bolbteppa

Now, if I assume all the logic of Copenhagen holds because the path is obscured for some unknown reason, I'm thinking Bohm could make some sense, we don't know why it's hidden, but lets go with it, ignoring the fundamental issue with not just being able to use CM, the next problem is his re-interpreting the wave function, derived explicitly as (related to) a probability distribution and nothing more, his calling it a real force, and trying to use that to account for the path being obscured

That's really really in the 'up is down, black is white' realm

So I'm kind of getting stuck trying to make sense of what he's doing no matter what direction I go in

Semiclassical

Again, that’s Bohm putting stuff in a pseudo-Newtonian form

There’s a reason why people talk about dB and not just B

bolbteppa

I guess so, I think it's a good idea to try that, it's probably what everybody wants to be true :p

Like why can't we just say angels are causing these unknown forces to obscure things

QM is almost like a compromise, saying look, we have no F'ing idea what's going on, why the paths don't exist, all we know is that they don't, and a ton of stuff makes sense once we go on this

Semiclassical

I don’t really agree. The fact that something as simple as Newton’s first law isn’t valid for a particle piloted by a wavefunction is for me a darn good reason not to go for a pseudo-Newtonian formalism

There are uses for that, to be sure: It makes the emergence of the classic limit easier to see

bolbteppa

19:23

@CaptainBohemian you said that Ryder made a lot of mistakes and your advisor agreed with your pointing out the mistakes and you think you fixed them

Semiclassical

But there's a reason I start, as Bell did, with the idea that any particle trajectories which exist should preserve the probability density

which is, after all, the probability density of finding a particle at a given location

Captain Bohemian

@bolbteppa I remember I said that, but why did you mention it there? Is it related to "nonlocal"?

Semiclassical

As an example, suppose I have a 1D system and I consider a Bohmian trajectory $X(t)$ of a particle subject to a wavefunction with probability density $\rho(x,t)$

bolbteppa

@Semiclassical so I'm thinking Bohm is saying 'look the paths obviously exist, but we don't know why we can't measure them, so QM should still hold so we end up not being able to measure them, but the path has to exist, so lets examine the formalism of QM and re-interpret it so that it explains why the paths are hidden', to me that's using Q to derive why 'not P' is true and then taking Q as your axiom, the clear flaw is Q is just a PDE which obviously allows paths

Semiclassical

misread you

bolbteppa

19:30

No worries

Semiclassical

What dBB is saying is that, if you make a position measurement, then you have indeed measured a point on a path

bolbteppa

@CaptainBohemian it wasn't related to non-local sorry, I just seen your response from hours before when I had sent it then

But you can't measure a path is the problem, you can measure it in random places at each successive moment in a way that we experimentally find no path exists in either dBB or Cop

Semiclassical

But the only paths it permits are the characteristics of the wavefunction

and once you measure the particle's location, the wavefunction will no longer be the same as what it would have been had you not measured

being unable to predict the further motion of a particle doesn't force the path not to exist.

bolbteppa

No matter how instantaneously successive measurements are made, the position of e.g. an electron measured at two successive instants is found in places which are so disjointed and random that one could never say a smooth path existed between successive places an electron is found

Semiclassical

a smooth newtonian path, no

a smooth Bohmian trajectory? that is most definitely allowed

bolbteppa

19:34

No, a smooth path in general, it can be any differentiable curve, doesn't have to be generated by the Newtonian F = ma second order ode

Semiclassical

I, quite simply, do not believe that's true

Given any sequence of position measurements, I most definitely can construct a bohmian trajectory for them

bolbteppa

That's why QM exists in the first place, explicitly because of this property

Captain Bohemian

@bolbteppa when you sent that message, I was away from the computer. When I came back, I saw so many unread messages which seem interesting, so couldn't reply you immediately.

bolbteppa

Dude what is a Bohmian trajectory

We're just talking about what measurements find

Bohm agrees with this

Semiclassical

It's one of the characteristics of the wavefunction

And the characteristics of a wavefunction evolve smoothly

bolbteppa

19:36

Bohm agrees with what I just said, that experiments lead to no path existing, he has to, the difference is he says a path exists it's just hidden, while QM says it just doesn't exist

Semiclassical

(characteristics in the sense of 'method of characteristics', to be clear)

What I'd say is hidden is what the particle was doing before you measured it.

within dBB, you can attribute a prior trajectory to the particle before you measured the location. but of course you cannot measure that prior trajectory anymore

there's nothing mysterious about having lost the opportunity to make a measurement

bolbteppa

His paper is saying the true path points are the 'hidden variables' no different to position and momentum of all the particles in a thermodynamic system being hidden when you look at thermal quantities

Semiclassical

If so, then he's speaking in a silly way.

bolbteppa

haha

Semiclassical

Again, just because Bohm said it that way doesn't mean I have to

bolbteppa

19:39

That's what a hidden variable was first defined as I think

Semiclassical

There is, as well, one big difference I can already point to

In thermodynamics, you talk about phase space density

bolbteppa

I actually think it's a great idea tbh

He just needs to make it work

Semiclassical

when you're doing thermodynamics, you do statistics by assuming some distribution in phase space, and appeal to Liouville's theorem in order to say that this phase space density is conserved under Hamiltonian flow

bolbteppa

(Deleted comment is a wrong thought I had while trying to understand it)

Semiclassical

in quantum mechanics, though, the uncertainty principle says that simultaneous measurements of position and momentum cannot exist

as such, it no longer makes sense to talk about a density in phase space. (at least not unless you do some Wigner stuff)

what still can make sense is a density in configuration space

bolbteppa

19:43

Yeah but he's saying that only no longer makes sense "out of practical necessity" and "not as a manifestation of an inherent lack of complete determination", on a fundamental level (non experimental) Liouville should hold etc

Semiclassical

He's saying that, yes.

I'm not

bolbteppa

Fair enough :p

Semiclassical

I think there is some shifting on the part of Bohm over time as well, though

I'll also point out that Bohm wrote the paper under the influence of Einstein, and I think that shows in how he poses certain points

there's obviously aspects of the theory which didn't set well with Einstein

bolbteppa

Yeah he talks about Einstein on the first page

Semiclassical

but in terms of his language I think there's a pretty strong influence

I think the basic difference between dBB with regards to completeness and Newtonian physics is this

with Newtonian physics, you'd say that if you know the Hamiltonian H and are given an initial point in phase space, then the entire trajectory in phase space is determined

bolbteppa

19:51

Yeah

Semiclassical

with dBB: if you know the classical Hamiltonian and are given the initial wavefunction + the initial point in configuration space, then the entire trajectory in configuration space is determined

knowing the initial wavefunction is then enough to determine the time evolution of the wavefunction. that wavefunction will have time-dependent characteristics in configuration space, and the particle follows the one which passes through the initial point

Moreover, the flow in configuration space generated by these time-dependent characteristics will preserve the configuration space density

which means that if there's a certain probability of finding the particle in a given region of configuration space, and you allow that region to evolve with the flow, then the probability remains the same

The reason I like this story is that it parallels Hamiltonian mechanics in at least one respect: The trajectories in configuration(phase space) preserve the configuration (phase space) density.

bolbteppa

Well my point is, with B not dB for now, there is zero reason to even mention the word wave function or bring in random PDE's like Schrodinger, he just does it axiomatically

Semiclassical

Well, yes. But the point of the exercise is not to show why such a story is necessary; it is only to show that it is possible.

I'll also note one selling point people give (though I don't know enough on this point to actually defend it)

namely, that QM is not just the Schrodinger equation. it's also the measurement postulates

e.g. measurement of an operator projects the wavefunction onto an eigenfunction

What dBB people assert is that you can actually show how the measurement postulates arise in this analysis

bolbteppa

Motl tends to focus on B and just imply dB is a cheap version of it or something, while a few of the guest posts he has by dBB people basically say one should accept dB not B

Semiclassical

yeah

I mean, B definitely has a big role

I think people attribute my remark about 'showing how quantum measurement works' to B, and in particular state that dB didn't have that when he was at Solvay

bolbteppa

20:07

All that projection stuff, you have to be careful with it, QM fundamentally has to be applicable to path integrals, density matrices, wave functions and not tied to one formalism

Semiclassical

the path integral formalism actually isn't too big a deal I think

the basic object in the path integral formalism is the propagator

and that's something which makes sense in the dBB picture to the same extent as it does in the usual one

the only real issue is that it's not a normalizable state, and that's true in any case

the real problem, I think, is when it comes to finite-dimensional Hilbert spaces

dBB is, above all else, a story about position measurements

so, for instance, if you've got the Stern-Gerlach experiment, with outcomes being spin-up and spin-down

well, that's not enough info by itself to have a dBB story

you'd need to actually have a schematic for the setup, e.g. two magnets creating a magnetic field gradient

once you do that, then you can run the dBB story and get trajectories, as in this paper: arxiv.org/abs/1305.1280

specifically, figure 2: i.sstatic.net/o6Gmd.png

vzn

@bolbteppa was just thinking the concept of hidden variables might be helpful in understanding dBB although its not always phrased that way. its an intrinsic historical aspect. you keep talking about paths and trajectories and suggest you stick to Bohms own words/ sentences. try quoting him exactly in here & lets look. certainly really appreciate the idea of going back to his original ideas/ papers although they evolved a lot after the inception. cqi.inf.usi.ch/qic/bohm1.pdf

Semiclassical

So, given sufficient context, you can make a dBB story

The problem is really that any experiment described in terms of finite-dimensional Hilbert space will be contextual

bolbteppa

Yeah I don't know how dBB could have an issue with path integrals in principle if dBB makes sense

@vzn I did quote him exactly

Semiclassical

The real issue is not so much dBB as a formulation of QM---that's pretty airtight

@bolbteppa and I objected to that... :P

What dBB says, imo: If someone gives me the full experimental context of a given system---e.g. the locations/strengths/orientations of the magnets in an SG device and how the electrons are prepared i.e. the initial wavefunction---then I can construct the position-space wavefunctions and from this the dBB trajectories which preserve the probability density in configuration space.

By necessity, these trajectories will be consistent with position measurements and will preserve the probability density

In that way, I'll have obtain 'complete' accounts of how the particles moved in the course of a given experiment.

....the problem is, that's a lot of work, and what does it give you?

we can argue about whether it's conceptually helpful. But empirically, it really doesn't give you anything new. The wavefunction generates the same probability densities regardless of whether you think of this as an abstract computational device or as being generated by the set of possible trajectories.

moreover, those trajectories will inevitably be subject to Bell's inequality and can therefore exhibit nonlocality.

So to me the question is not "is the dBB story consistent within its domain of nonrelativistic QM." The question is what does it gain you and what does it cost?

and unfortunately that cost-benefit analysis hasn't been favorable. I think that's partly a sign of relatively few people working on it, but it also just doesn't seem a very productive perspective

bolbteppa

20:28

@Semiclassical maybe dBB says that, I am just questioning the legitimacy of even using words like wave function, probability, Schrodinger equation

vzn

@bolbteppa what pg (its 14pp)

bolbteppa

B is unacceptable if it really simply postulates the Schrodinger equation out of thin air basically

Semiclassical

@bolbteppa depends what you're wanting B 1952 to do

if you want him to be formulating a full mature theory, I agree

vzn

@bolbteppa surely you can think of other physics theories that were revised/ reinterpreted in a similar way! need help?

Semiclassical

but, again, I think the 1952 paper is mostly of interest because it shows that the Schrodinger equation is not incompatible with paths

bolbteppa

20:31

I already said the Schrodinger equation is trivially not incompatible with paths

That's fair, maybe Bohm's paper has been improved on

vzn

big elephant-in-room example: blackbody radiation/ "ultraviolet catastrophe"

bolbteppa

I would be shocked given how fundamental these issues are, but I'd love to see a paper not simply assuming the Schrodinger equation

Semiclassical

Does the wave satisfying the Schrodinger equation have characteristics?

bolbteppa

Or one of those 6 derivations we seen

Semiclassical

If so, then it's got paths

bolbteppa

20:32

A quantum mechanical wave function has characteristics, that doesn't mean particles live along those characteristics or are even related to them necessarily

Semiclassical

It's not forced, no. But it's not incompatible with it

bolbteppa

Yeah I agree

vzn

...QM itself is a hidden variable theory (revising classical mechanics) o_O

Semiclassical

Obviously, there is nothing forcing you to interpret the characteristics of the wavefunction as possible trajectories.

bolbteppa

@vzn he's trying to say CM doesn't hold experimentally because the variables are hidden from us for some reason, that's not a bad idea necessarily

That could be the 'truth' for all we know

vzn

20:35

@bolbteppa in that way it is similar to ideas/ rethinking circulating at the inception of QM

Semiclassical

However, there is at least one benefit to it: If they can only move along those trajectories, then they'll automatically preserve the configuration space density corresponding to the wavefunction

bolbteppa

One thing, if I took a paper, say Schrodinger's first paper, no assumption is wrong, it's just incomplete, it may be the case Bohm is also simply incomplete, my point is, assuming I'm right which I'm not sure of yet and more than open to being wrong, it fundamentally can't be correct, but I need to look and think more

vzn

@bolbteppa searching, the word path does not appear a single time in the 1952 ref... "putting words in his mouth"? o_O

bolbteppa

Those guys were open to whatever would happen, wherever the theory would lead, Bohm is forcing determinism which is a big difference, he knows where he wants to end up, it's very natural, but this is why QM is nuts

Semiclassical

i.e. if you consider a little sphere $S[X(t])]$ centered at $X(t)$, where $X(t)$ is the position of a Bohmian particle at time $t$, then $\int_{S[X(t)]} \rho(x,t)\,d^n x$ is time-independent

I really hate my notation there but oh well

vzn

20:39

@bolbteppa sometimes the experiment drives theory, sometimes vice versa... yin-yang! actually it is obviously Bohr who "forced" a lot of highly questionable/ basically radical ideas on physics! Bell called him an obscurantist o_O

bolbteppa

@vzn I have explained that in classical mechanics the mechanical state of a system is determined by knowing it's initial position, velocity and either the path itself or the differential equations generating the path it follows. That is what is meant by 'determinism' at the most fundamental level, the level people like Kant, Newton, Einstein etc... were referring to, if you can't generate a path, you have lost determinism

Semiclassical

I'll again say, though, that while Bohm's paper served a certain purpose---to show that a pseudo-Newtonian formulation containing definite paths is not incompatible with the SE---I definitely find the whole $\psi =Re^{i S/\hbar}$ approach to be artificial

enumaris

hmmm...I basically completed all my work for the week this morning...now wut

Semiclassical

There's some computational use to it, maybe

But conceptually it feels unmotivated

bolbteppa

I have no problem with the Schrodinger equation allowing for paths to exist, it obviously does

vzn

20:42

@bolbteppa bohm uses the word trajectories 8 times in the paper and maybe consider each sentence carefully, his actual/ exact words!

Semiclassical

With the dB side of it, it has more the feel of: You look at what measurements you can make consistently, i.e. position measurements of an identically prepared system, and you determine what law of motion you'd need in order for the particles to be consistent with that

(though this feels a bit like a reconstruction on my part)

bolbteppa

My sense is, with dBB, if you skip the basic meaning of what you're doing, you can use the math to derive things, most of it is just normal QM, some of it, like analyzing characteristics, is math which is fine, but you could do this in normal QM too it's just meaningless

vzn

@bolbteppa it all leads somewhere, its a milestone... early baby steps that are now at a "crawl" or even "walk"

Semiclassical

It is not considered as meaningful with the Copenhagen interpretation, no

The formalism of QM, however, says nothing either way

bolbteppa

Yeah, but the formalism of CM lets you derive PDE's like Hamilton-Jacobi, we don't interpret the classical world as a bunch of surfaces :p

Semiclassical

20:49

For wave phenomena we do!

bolbteppa

When we do HJ we clearly are working with the characteristics on those surfaces

Semiclassical

At the very least, we definitely take wavefronts to be a meaningful object of consideration in wave optics

bolbteppa

HJ is a wave equation for the action, we interpret the variables of that action as the waves, not the action

vzn

@bolbteppa youve got a bunch of analogies, try the Galton board. early discovery of emergence/ hidden variable theory/ particles vs wavefn/ probability etc

Semiclassical

Sure. That’s why de Broglie viewed what he did as a unification of waves and Newtonian mechanics

bolbteppa

20:51

@vzn haha

Semiclassical

Wave-particle duality is understood in a rather literal way for dB

So it doesn’t seem that crazy to adapt HJ in a way that unifies it with wave physics

vzn

@bolbteppa all your objections could be phrased in terms of the Galton board. Galton presumes the ("pre existing") gaussian distribution rather than derives it! he imagines hidden paths/ influences where there are none! etc!

bolbteppa

Well, it doesn't seem any crazier than accepting QM knowing only a classical world :p I would accept it if it made sense if I am able to look at it

@vzn ahaha whattt... how does he assume it?

Semiclassical

That’s again why we’re not talking about Newtonian physics. In that context, it indeed wouldn’t make sense to use HJ in that way. (One fact, in passing: Schroedinger and Bohm were both fond of the HJ equation, but dB eschews it as far as I know)

bolbteppa

He is trying to show how the normal distribution arises naturally from a binomial distribution in the limit, what's this theorem called, central limit theorem

@vzn that's such a basic misunderstanding tbh

vzn

20:55

@bolbteppa this is rather similar to what Bohm is doing in spirit...

bolbteppa

@vzn literally, you have it backwards, the last thing he wants to do is presume the Gaussian distribution!

Semiclassical

has nothing to say about Galton

vzn

@bolbteppa the Galton board was probably quite mysterious to the scientific community on its introduction! think there might have even been critics/ disbelievers

bolbteppa

@vzn are you serious? I think you are, that is simply unbelievable haha

Semiclassical

I will note, though, that Bohm was very much not inclined to think of his 1952 proposal as a final theory

And was apparently pretty appalled by people calling it Bohmian mechanics

bolbteppa

20:57

@vzn you have to be joking, I am very gullible :p

(I don't think that's a joke)

vis.supstat.com/2013/04/bean-machine

Semiclassical

When it comes to questions of history like that, primary sources help a lot

bolbteppa

19

A: What intuitive explanation is there for the central limit theorem?

Intuition is a tricky thing. It's even trickier with theory in our hands tied behind our back. The CLT is all about sums of tiny, independent disturbances. "Sums" in the sense of the sample mean, "tiny" in the sense of finite variance (of the population), and "disturbances" in the sense of plu...

vzn

@bolbteppa the central limit theorem was only proven in the mid 20th century afaik (acc to my univ statistics teacher)... anyway it would maybe take a kuhnian historical expert to analyze the galton board reception, but think it likely that someone educated at the time might have disputed his claims.

bolbteppa

@Semiclassical Weinberg asking about this stuff bohmian-mechanics.net/weingold.html

Semiclassical

What Wikipedia says: “The bean machine, also known as the Galton Board or quincunx, is a device invented by Sir Francis Galton to demonstrate the central limit theorem, in particular that the normal distribution is approximate to the binomial distribution.“

So that seems to point from knowledge of the Gaussian to the construction of the bean machine

vzn

21:02

1889! what shape was the field of statistics in then? o_O

Semiclassical

but that’s assuming WP is presenting it accurately, and uh

I dunno about that

bolbteppa

Mathematically one can start from the binomial distribution and derive the Gaussian distribution, the central limit theorem more generally says that any distribution satisfying certain conditions will arrive at the Gaussian, the Galton bean machine is just a binomial distribution generator and it naturally ends up looking like a Gaussian, the way the Wiki is written it looks like it assumes the Gaussian, but it's the other way

If you interpret the phrase 'approximate to' 'the other way' it makes sense, it's like elegant language I guess

Semiclassical

Again, I think you’d need to have a primary source in order to settle this

vzn

its all so obvious 1¼ century later o_O

Semiclassical

And stats was pretty well along I think

bolbteppa

21:04

I just linked to a stack post explaining this as well

vzn

(highly) educated skeptics are as old as humans...

bolbteppa

The wiki says the point is "to demonstrate the central limit theorem"

Semiclassical

When people refer to the CLT only being proven in the 20th century, I suspect that’s quite different from people being aware of it

bolbteppa

Central limit theorem

In probability theory, the central limit theorem (CLT) establishes that, in some situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution (informally a "bell curve") even if the original variables themselves are not normally distributed. The theorem is a key concept in probability theory because it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions. For example, suppose that a sample is obtained containing a large number of...

Semiclassical

People were aware of Fermats last theorem, and could even prove many special cases of it, long before the full theorem was proven

bolbteppa

21:06

"The actual discoverer of this limit theorem is to be named Laplace; it is likely that its rigorous proof was first given by Tschebyscheff and its sharpest formulation can be found, as far as I am aware of, in an article by Liapounoff"

Semiclassical

So I suspect one would need to clarify what is meant by “prove the CLT”

vzn

suppose Galton goes to his scientific friend, and makes the claim without proof. would his friend believe him instantly? the fact was discovered in 1889...

bolbteppa

Laplace basically invented the main theory of probability theory iirc , later people fixed the problems, e.g. Kolmogorov giving the most general form or something

Semiclassical

This looks authoritative: books.google.com/…

bolbteppa

I guess Laplace 'proved' it in the loose way that was acceptable at his time, then Cauchy came along and forced more rigor and others cleaned up his ideas

Semiclassical

21:10

In there, it’s very clear that Galton was quite familiar with the normal distribution throughout his work

bolbteppa

The cool thing about the CLT is you don't even need to know what the bell curve is, it's what you get from any distribution satisfying it's assumptions naturally, i.e. it's unavoidable, Galton's board shows how the binomial distribution leads to it, the most common example of getting Normal since it's so directly derivable

vzn

@Semiclassical but all the (sophisticated) modern understanding of Gaussian curves was not available at the time... further thinking, there might be some history of scientists rejecting gaussian statistics...

Semiclassical

Eh, the Gaussian itself is not a sophisticated object

The sophisticated part of CLT is the generality

bolbteppa

Yeah

(Basic probability is confusing enough)

Semiclassical

By comparison, the binomial distribution is a specific case

vzn

21:15

anyway there are many unintuitive aspects of probability, this is proven in psychology, and humans are not accurate probability-calculating machines in many cases, there are many clever experiments designed to prove this... think monte hall problem gotten wrong by top scientists/ statisticians! o_O

bolbteppa

@vzn any links on people denying the Galton board?

Maybe it's linked to evolution and people weren't happy about that side of it?

vzn

@bolbteppa will keep looking but again dont find it implausible/ inconceivable :P

Semiclassical

In the specific case of the binomial, the passage to the Gaussian is far more straightforward and so would have been known of long before the full CLT

So I find it pretty plausible that Galton would’ve known of it

bolbteppa

My only point is, sure Galton knew about the normal distribution, the point of the board is just to show how it arises naturally based on the assumptions of (what we now call) a binomial distribution, which seems to have no link to something like a Gaussian

vzn

@bolbteppa there is maybe some dissent on the idea of gaussian curve wrt IQ which maybe galton was connected with. that was/ is very controversial subject. but maybe getting away from our original subject.

bolbteppa

21:18

Yeah

Semiclassical

Stats as a mathematical topic is not nearly so thorny as it is as a sociological one

vzn

> In one of Galton's 1st major works, Heredity Genius (1869), Galton made much use of the normal curve in the context of mental heredity... following Quetelet...

Semiclassical

What I mostly wonder is what the inspiration for the bean machine would have been

Some more detail here: books.google.com/…

bolbteppa

One history question, why did Bell say something like 'why didn't Bohr, Bohm bring up Bohm's ideas, even just to say they were wrong' even though Pauli, Heisenberg etc wrote rebuttals to it

Semiclassical

Also here, from the same book as earlier: books.google.com/…

vzn

21:26

@Semiclassical interesting, he started experimenting in 1877 but maybe didnt publish until 1889. it seems, Galton himself took years, maybe close to a decade to figure it out...

Semiclassical

@bolbteppa I think the rebuttals were more private than public? I remember some history people though saying that Bell’s recollection was flawed

bolbteppa

I guess the internet didn't exist then :p

Semiclassical

Not the same, but this is what I had in mind: arxiv.org/abs/1006.0499

bolbteppa

Peierls was his advisor, one of the guys who nearly tore apart QFT with Landau, and he translated Landau's books

vzn

@Semiclassical apparently an earlier version in 1873. so close to ~1½ decade between experiment, discovery, and published analysis... seems like it attests to some subtlety there... it looks like it took awhile for Galton himself to believe it...! o_O

Semiclassical

21:30

(I think my feeling was that there’s a difference between what von Neumann said about his proof, and how the community at large interpreted it, with Bell’s reaction reflecting the latter)

@vzn i’d have to know a bit more about the life of a prof in that era to say much

It sounds like he was already using it as a lecture prop

vzn

@Semiclassical the point is, 2020 hindsight, its all obvious to us now, but science advances at the speed of human discovery... "they" may have understood the idea of a "typical" curve on the Galton board ("emerging") but didnt realize immediately it was gaussian in the limit...

Semiclassical

well, that’s why I wonder what the inspiration was for the board

Ie did he see something similar to it in everyday life and realize that it should represent a binomial distribution

bolbteppa

@Semiclassical why do you prefer dBB to Copenhagen

Semiclassical

I don’t know if I prefer it, exactly. But I am sympathetic to it

Part of that is simple familiarity: I saw it, learned a bit about it, and got curious

vzn

the Galton board analogy is more than shallow believe it or not because there is some idea in the newer dBB variant theories that the "hidden variables" are related/ due to some kind of ulterior random walk-like phenomenon. ie just like the balls in the Galton board...

Semiclassical

21:37

Another big part, though, is that I get frustrated by people assuming that QM says more than it does

And people acting as though dBB can’t possiby be consistent, when it quite simply is (at least within certain domains)

The tragedy is that consistency isn’t enough

bolbteppa

Fair enough, I would like to be sympathetic to it, need to think about it

Semiclassical

I’d say I’m also quite allergic to any explanation of QM that invokes consciousness

bolbteppa

My honest sense is it really isn't consistent and doesn't make sense and that there aren't a bunch of different interpretations, there's just Copenhagen, I'd say this consistent histories stuff is unjusifiable as well, I'm happy for more interpretations to exist, but I need to figure out how to make sense of it like properly

Semiclassical

Or many worlds for that matter

vzn

...which reminds me, again, the atomic hypothesis was supported by Einsteins work on brownian motion of pollen grains, cited in his nobel prize... one might say random walks rule the universe... even more than is currently admitted...

bolbteppa

21:42

I think Gell-Mann thinks many worlds is fine if you interpret it very carefully

Murray Gell-Mann - Working on quantum mechanics, the work of Everett (160/200)

►

Semiclassical

@bolbteppa for me, “particles have paths which can only be observed in the weakest sense possible” is more preferable than invoking consciousness or many worlds

bolbteppa

I spent over a year trying to make sense of the very basics of QM, kept trying to stretch things etc, so I'd say I'd need to devote that much time to other interpretations and it'd be a waste since (if they are flawed) I'd guess it comes down to ideology if people believe other interpretations that have subtle flaws, so I guess the main positive is kind of just to test my QM knowledge

Semiclassical

On the other hand, in the relativistic context it seems like dBB would necessitate the existence of an absolute reference frame

...which, yuck

vzn

@bolbteppa dBB is far more than an interpretation at this point for anyone paying attn, its a platform/ launching point

Semiclassical

(Here I will note the difference between inflation and deflation.)

Anyways, that’s why I emphasize the non-rel context so much.

bolbteppa

21:47

@vzn well that's what I think as of now anyway, I think it's a radical claim way more general than QM and Bohm even says this in his paper but that's not all of dBB I guess, perhaps the updates restrict it's applicability

Semiclassical

Within that very specific domain, it seems like an interesting and internally consistent story

Outside there. I am not at all sure

vzn

@bolbteppa take a look at Adler sometime, need to delve into it myself, would appreciate another set of eyes :) so far its been very quiet around here on all that :|

Semiclassical

I would also distinguish dBB as such with the pilot-wave hydrodynamics of Bush-Couder

You can construct theories for which Bohmian trajectories emerge in an average sense from subquantum fluctuations

But dBB as such doesn’t do so

vzn

@Semiclassical it looks like from much of his writing Bohm was searching/ leading in that direction (he nearly says so directly...)

Semiclassical

It’s not a direction I find personally appealing, but I agree on that reading of him

vzn

21:54

@Semiclassical lol dont know why it would be "unappealing" given how similar it is to QM origins itself etc... (history repeats itself?)

Semiclassical

Because I’m more interested in knowing what one can already do with QM rather than obsessing over whether a subquantum scale will appear

vzn

@Semiclassical lol fair enough but one answer would be "more" :P ... btw one might argue that Einstein, Bohm, Bell et all "obsessed over a subquantum scale"...

Semiclassical

Yeah, well

Obsessing over the interpretation of QM as such has led to quantum information theory and the possibility of quantum computing

Obsessing over the subquantum has done...what?

vzn

yes! seems likely there will be practical applications if a subquantum scale exists. even if not, its physics. we spent tens of billions on LHC and its running out of gas so to speak... the subquantum scale is a new frontier... obsessing over strings for decades has done... what? :P

bolbteppa

From the first page of the Bohm paper: "Moreover, the modifications can quite easily be formulated in such a way that their effects are insignificant in the atomic domain, where the present quantum theory is in such good agreement with experiment, but of crucial importance in the domain of dimensions of the order of $10^{-13} cm$, where, as we have seen, the present theory is totally inadequate."

Semiclassical

22:01

Kept grad students employed :P

bolbteppa

Another goal of his was to get a theory that went beyond QM as it stood

I'm not sure what that means tbh

Semiclassical

More seriously, I’m not a string guy so i can’t say much about that. But I share a certain amount of skepticism there as well

Similarly with the various speculations people had for the LHC

vzn

@bolbteppa its an ideological dissatisfaction/ lack of acceptance of the copenhagen interpretation not because of something personal against Bohr, but on the basis of science/ physics

Semiclassical

Until something shows up, worrying about what the LHC or some other random experiment will discover doesn’t appeal to me

That doesn’t mean other people can’t be interested in it

vzn

@Semiclassical sigh Vinante et al 2017 has shown up

Semiclassical

22:05

It’s just not something I find appealing

@bolbteppa that’s the Compton wavelength, isn’t it

When did QED come about?

bolbteppa

I mean Dirac's book was 1930's and already had RQM, other books were coming out in the 30's and 40's getting there

Semiclassical

True

I think that line might reflect knowledge at the time, is what I’m wondering

bolbteppa

"Originally published in 1936 as part of Oxford University Press's famed International Series of Monographs on Physics, this book is a classic reference text."

store.doverpublications.com/0486645584.html

Semiclassical

My main reference point is this: suppose you localize an electron to a narrow width dx, say as a Gaussian wave packet (centered in both position and momentum space)

The Bohmian trajectories in that case will all start from rest, at some initial position which is distributed as a Gaussian

Within a short time, though, a particle on one of these trajectories will have accelerated to a final velocity, with said final velocity being proportional to the distance of the electron from the center of the packet

Which means that the final velocities are distributed like the initial positions ie Gaussian

enumaris

time to read some clinical studies

booyah

Semiclassical

22:15

The nice thing, when you work out this velocity distribution, is that it’s width is (memory time)

bolbteppa

@enumaris boo

enumaris

yah

danielunderwood

reading anything relating to SUSY kind of makes me giggle

> ...used to refer to charginos. These four states are mixtures of the bino and the neutral wino (which are the neutral electroweak gauginos), and the neutral higgsinos.

Semiclassical

Ugh, can’t do it from memory on my phone

Laptop time

Semiclassical

22:36

had to step away. but what you end up with is that the final Bohmian velocities would depend on the initial position of the particle $x_0$ as $v_f = \frac{\hbar x_0}{2m\sigma^2}$ where $\sigma$ is the width of the initial Gaussian packet

since $x_0$ is distributed according to this same Gaussian, you'd end up with the rms value of $v_f$ being $\overline{v_f} = \frac{\hbar \sigma}{2m\sigma^2}=\frac{\hbar}{2m \sigma}$

and if you take an upper bound on such a velocity to be meaningful as $\overline{v_f}=c$, you get $\sigma >\frac{\hbar}{2mc}$ as a bound on how much you can localize a particle

which, interestingly, is the cutoff scale at which QFT is expected to become important (c.f. en.wikipedia.org/wiki/…)

not sure that's anything more significant than dimensional analysis and the uncertainty relation but hey, still neat

so the length scale for which typical bohmian velocities are luminal is the same as the QFT length scale

which for an electron is about 200 fm = 2e-11 cm (so probably not what Bohm had in mind)

@bolbteppa similar thoughts as to some I've expressed above: books.google.com/…

Semiclassical

23:17

also, you might like this later paper of Bohm & Hiley 1982, summarizing the theory: scalettar.physics.ucdavis.edu/p298/pilotwavetheory.pdf

if only to compare/contrast with the original paper

bolbteppa

I really can't believe people claim the wave function is a real thing

vzn

23:38

@bolbteppa lol, it was Bohr who told a very convincing/ influential/ persistent ghost story

Semiclassical

I will point out that, in at least one respect, the pilot-wave story does hew closely to Bohr

e.g. Bell invoking Bohr in order to defend the contextuality of spin measurements via Bohr stressing "“the impossibility of any sharp distinction between the behavior of atomic objects and the interaction with the measuring instruments which serve to define the conditions under which the phenomena appear.”

So there is at least some influence of Bohr there, while the pauli/heisenberg side has much less truck

@bolbteppa another point of note: I mentioned at one point a 'nomological' view of the wavefunction. that's a relatively recent development, starting I think from this 1995 preprint of Goldstein: arxiv.org/abs/quant-ph/9512031

prior to that, I think you mostly have (as you might have noticed in Bohm) a view of the wavefunction as indeed some 'real' thing

bolbteppa

23:58

"Many physicists pay lip service to the Copenhagen interpretation, and in particular to the notion that quantum mechanics is about results of measurement. But hardly anybody truly believes this anymore—and it is hard to believe anyone really ever did" sentences like this, in any context, anybody can see what's going on

We all fool ourselves, it's natural, sentences like this, are when you are in deep

Semiclassical

yeah, lots of polemics

bolbteppa

The worst one of these was when they started questioning symmetry principles

Transcript for