arxiv.org/abs/1509.00767

@Semiclassical I have finished reading this paper, and I think I now understood surreal trajectories better now:

Surreal trajectories occurs because the first order dynamics of quantiles trajectories in Bohmian mechanics cannot cross each other

Thus if the bohmian wave function is not perturbed strongly due to entanglement being established between the pointer device and the bohmian particle, the bohmian particle cannot "switch" trajectories (the switching is possible because the nonlocal wave function itself get perturbed by the entanglement as one tries to do a position measurement, thus leading to the expected outcome of quantum mechanics

one thing to note: the trajectories never cross in configuration space

for a single spinless particle, that's the same as not crossing in real space

ok maybe I should say, trajectories cannot "switch" in some lower dimensional subspace of the configuration space (that's how the author of that paper treats it, he said the trajectories seemed to cross apparently, but that is an artefact because the trajectories are perfectly non intersecting in the full configuration space)

i know i've seen some discussion on that point. lemme see if i can find it

oh, he talks about that explicitly

It's near the end of the paper just before the conclusion, unless you mean more extended discussion

yeah

i think i've seen it elsewhere as well

Meanwhile, the Bohmian result occurs for "slow" pointers. A pointer is "slow" if its states cannot separate quick enough after interacting with the Bohmian particle, thus the wave function is not perturbed until another measurement occurs, and hence the Bohmian particle continue to follow its usual trajectory

i thought i saw it discussed in the context of trajectories for spinful particles

so far I'm only seeing stuff in the vein of Gisin tho

I need to re-read that 2016 paper where surreal trajectories is first reported, as I am curious on how they managed to get a bohmian measurement going in that paper

advances.sciencemag.org/content/2/2/e1501466

that one

yeah, and it seems the way they implement the "slow pointer" scenario is by using weak measurements

and in that paper, they reference this paper by Hiley as far as why the trajectories appear surreal: pdfs.semanticscholar.org/cb11/…

which in turn explicitly discusses the configuration space subtlety

That paper illustrate the points even clearly: The presence of the cavity modifies the wave function and hence the quantum potential. Thus we have the two kinds of trajectories going from bouncing off each other to simply passing over each other, both cases no trajectories are intersecting

That explanatory paper also clarified to me what a true surreal trajectory, if it exist, will look like: There will be a nonlocal transfer of information between two positions. It will be cool if some experiments in the future will show something like that, because that will be a nonlocal interaction that is signalling in principle but we cannot exploit because it will be probablistic

(ok sorry, entered scifi mode again)

....

Now the only mystery is this paper:

Quantum theory cannot consistently describe the use of itself

to me the simple lesson is the one Gisin gives: BM insists that positions are always meaningful, but this is not the same as saying that position measurements "merely" reveal this otherwise hidden variable

That is true, but I am terrible with reasoning about negative abstractions, which is why I tend to find a positive interpretation of the same thing

there are cases in which you can take position measurements as playing this role, but it very much depends on your measurement apparatus

I am not sure if that makes me bad at physics, but it is always more fulfilling to be able to explain why things happen, instead of why things is not necessary to happen

You can regard BM philosophically as solving the measurement problem, but its application to any specific system requires you to be precise

whereas part of the fun of quantum mechanics is how often you can get away with being imprecise about the setup :P

true

meanwhile, I think I agree with the authors on how there should be more interesting things in Bohmian mechanics than just surreal trajectories, but I guess I will check them out later

yeah

I think Bohmian mechanics is more ontologically satisfying (which is good for more philosophical and scifi minded people like me), but I am also ok with quantum mechanics, because you can pack everything into the wave function and not worry about whether you need a particle to be somewhere in between

that's one thing I do like about Gisin's paper: its admission that BM, whatever one can say about it philosophically, has not been fruitful in practice

I'm not sure I like the examples he gives for possible experimental ideas---putting upper limits on the speed of nonlocal communication? mehhh---but I like that attitude

(cont.) Or put it in another way, I am equally fine with treating quantum states as probabilistic blobs in Hilbert space or as real nonlocal wavefunctions guiding a probabilistic blob of bohmian particles

Point is, it is because they are probabilistic blobs that makes them interesting

Here's a question I'd love to see someone answer: Is there anything in the Bohmian story which is useful/instructive for building a quantum computer?

so far I haven't seen any examples of such

my own suspicion is that, when it comes to quantum software/algorithms, BM is not going to help much

BM can deal with n-level systems, but it does so by insisting that that system is embedded in a configuration space of appropriate size

I think that the trajectories are so sensitive to the hardware that a trajectory plot will be useful to figure which parts go to where. This is easier to be used as a blueprint than to consider all possible ways a quantum state can be manipulated and wrote into a wave function which the information on where to place what is indirectly contained in the wavefunction

the story works, but it seems unlikely to be a convenient framework for quantum algorithms

So I don't see that route being very productive

I mean, a quantum engineer will probably get more used to seeing a plot of level sets of the cumulative probability density than statistics on the outcomes (the former is more obvious on just what happens when you place some hardware at location X). But yeah, the challenge is that trajectories are more computationally expensive to compute than just computing the wave function evolution. Definitely useless for software design since they give similar algorithm and logic

But a quantum computer is also -hardware-, i.e. an actual experimental apparatus that can make measurements on that state

and that seems more plausible as an inroads for an interested Bohmian

It is also more intuitive to reason about level sets. Most people probably have experience on reading contours already

thus the training of future quantum hardware engineers should be easier with the Bohmian framework since it retains some classically intuitive notions in some form

to put it a little differently: designing algorithms was part of making a computer, but so was designing transistors

this is just speculation, though

2. The Bohmian view is important in giving a picture on the assembly of the hardware

I think that 2) is at least plausible

whether it happens, of course, remains to be seen

I should wrote a program to compute trajectory some day, after my chemistry PhD... there is a lot of things in the Bohmian view that is not explored, and its interplay with the orthodox view

it depends on what part of the Bohmian interest group you're talkign about, of course

The bohmian view also gain a boost recently due to that nature paper that pretty much nuke most of the interpretations

if you're talking about philosophers, then yeah---not a lot of computation going on there

i know there are some people who have worked on it as far as molecular dynamics go

i don't know how popular that really is, but it is out there in the literature

yeah there are some examples of bohmian formulation of path integrals in molecular dynamics, they are still pretty rare though

to me the question of whether BM is useful is as important a question as whether it's real

it sure give a more intuitive way to think about quartile trajectories, which can help to visualise the probability and statistics better, but for more technical level, I guess we need more people to apply it to analyse quantum experiments to be sure

"The second point listed above is interesting: one should distinguish quantum-position and Bohmian-position measurements. The latter are measurements that provide information about the position of Bohmian particles. It would be interesting to find out how to characterize such Bohmian-position measurements without the need to fully compute all the Bohmian trajectories."

that's another interesting bit of the Gisin paper

> It would be interesting to find out how to characterize such Bohmian-position measurements without the need to fully compute all the Bohmian trajectories."

yeah

I think that will be very important

since it will provide a framework to design better weak measurement devices

it goes to your point about the approach seeming to impose a substantial computational hurdle

that also