[Eternal Student (OP)]

Hi.

    I have another "problem", "concern" or "puzzlement" of a scientific nature today and I'm asking for some other opinions and/or discussion   (you know... what a forum is meant for).   Don't spend too long here,  I know I'll be busy for a few days and may not make much reply for a while.

Background:
    This is Quantum mechanics.   It concerns "the double slit experiment" which I'll assume you are familiar with.   Basically, if you fire a single particle (say an electron) at a double slit then and have a detector screen at the far side (say a screen which is phosphorescent, something that will glow when an electron hits it),   then you do observe single glow spots on the screen.  The electron seems to behave like a particle at the time it hits the screen.     HOWEVER   when you repeat the procedure you will start building up the usual pattern where the number and location of hits on the screen does correspond to the usual wave diffraction pattern through a double slit.    The general conclusion being that the electron was behaving as a wave or QM object until it hit the screen -  it had a wave function and that was propagating through the space before it hit the screen.

    Now we're not here to discuss whether the electron did move as a wave or not.   Let's just assume that the usual QM stuff does apply and I'll choose the Copenhagen interpretation of QM for this problem.   So the electron always has a wave function, it evolves according to the time dependant Schrodinger Equation UNTIL a measurement is made.   On measurement the wave function is immiediately updated (collapses), so that it is now definitely in an eigenstate for that measurement.

    The question is:   Isn't the phosporescent screen always making a measurement?   If the screen does not have a glowing spot at time t,  then the electron is not at the screen at time t.   We should update the wave function,  it cannot be in any state where there was even a small probability to find the electron at the screen.    Conversely, if the screen does glow at time t, then the electron is there,  the wave function has collapsed in a much more dramatic way (to something like a dirac delta function of position δ(x-x₀) in position representation, furthermore we can now remove the electron (from the computer model I'm building - which I may talk about later).   It has been absorbed by the screen and will not propagate any further.

     The situation is very similar to "Quantum Zeno effect" which you can Google if you want some more background.   Specifically isn't it possible that by constantly making a measurment, the phosphorescent screen ensures that the electron's wave function cannot collapse to the state where it would be at the screen?   An easier to read background is obtained by Googling  "Zenos Arrow" but you MUST take a quantum mechanical discussion of that and not the original Greek philosophy by Zeno, there are YT videos on this if you don't even want to read.   Here's just one:
   

Why am I asking?
   Too long... I'll put this under a spoiler... it's not essential.

Spoiler: show

    I've been dabbling with a bit of computer coding lately.   Just to be clear - I'm not doing anything that will be new to the world but it's just new to me and has my interest.   I've made fair progress on a simulation of a wave function propagating through space in 1 dimension and encountering various potential barriers.   I'm ready to move it to 2 (or 3) dimensions.   What I'm using as a test case is the double slit experiment because we already have a good idea of the results that you should get.   I'll have the barrier represented as a region in 2-D space (let's say a thin rectangular region running parallel to the y-axis) of very high potential with "slits" that are 0 potential regions through that barrier.    I'll be modelling the electron as a Gaussian wave packet, the details don't really need to concern anyone but a Google search will furnish you with the details if you're interested.   It's enough to know that the wave function is known initially (at t=0) and we can give it a momentum to represent the electron being fired toward the barrier.   That wave function will evolve according to the time dependant Schrodinger equation, which we can do numerically on the computer.   
     Then we place a "screen" or detector at the far side of the barrier.   We are interested in what that screen will collect.   We would think (OK, I would but it's more natural to keep using the third person)) that the probability of the screen having a spot glow (i.e. having absorbed the electron) at  a given position and time,   (x,y,t),   will be proportional to the probaility density of wave packet at (x,y,t).   We can make this more precise,  the probability of a position on the screen between (x axis values)  x and x+dx  and  between (y axis values) y and y+dy  detecting the electron (starting to glow) in the time interval between  t and  t+dt is     
         ~    |ψ(x,y,t)|² .dt.dx.dy

     So with just a bit of integration we can find the probability of a given position on the screen glowing after, say 1 minute from when the electron was fired.   We can start to build up the expected pattern of hits on the screen directly from this.
     It seemed and still does seem natural to assume that once the screen has glowed, the electron has been located on the screen and absorbed.  It can be removed from the simulation (and we're ready to fire the next electron).    It was only after a bit more thought that I realised what we're really doing here is recognising the wave function collapse and thus updating our information immediately.   This is when it dawned on me that we have information ALL the time, if the screen hasn't glowed yet then the electron is NOT there, why don't we immediately update the wave function to show that instead of just continuing with evolution by the Schrodinger Eqn?

Best Wishes.

[Halc]

The question is:   Isn't the phosporescent screen always making a measurement?

Easy answer: Yes. More complicated: Yes, relative to the screen, just like the cat measures the poison bottle, so the bottle is not in superposition of closed/broke, but the bottle is still in superposition of those states relative to the lab observer. Copenhagen places a 'Heisenberg cut' at the boundary of where those states differ.

You seem to be asking if the electron misses the screen, is a measurement taken? Well, not by the screen (yet), but either the electron with interact with something else (and thus get measured by something else), or it never interacts, and is effectively nonexistent (according to any local interpretation at least).

Specifically isn't it possible that by constantly making a measurment, the phosphorescent screen ensures that the electron's wave function cannot collapse to the state where it would be at the screen?

Yes. The comment only applies only to interpretations where collapse is meaningful. You'd have to word it differently for others, but still, effectively yes.

[Eternal Student (OP)]

Thanks @Halc.

You seem to be asking if the electron misses the screen, is a measurement taken? Well, not by the screen (yet)

   We seem to agree that an electron (represented by a Gaussian wave packet initially) can "miss" the screen.    It wouldn't matter if the screen is made infintely long parallel to the y-axis (and we fire the electron toward it along the x-axis).    This is evidently quite different from a Newtonian view of particles and their movement, where the electron could not possibly be found beyond the screen without having impacted on the screen on the way.   Hmmm...  actually I might give the screen some potential above 0 in my computer model, for the sole purpose of reducing the number of electrons that will propagate through it.    One issue with the simulation is - how long do you wait for the electron to have been detected by the screen?   If the screen glows, great, you're done, you can fire the next electron.   If it doesn't, then the wave packet is still spreading out to fill all of space as time progresses,  so the probability of the electron being found at the screen never falls to 0.   Clearly, for the purposes of a simulation you cannot wait forever.   Once the group velocity of the wave packet has made it so that the wave packet is centred far beyond the screen, we must assume the electron has just "missed", the probability of it being found at the screen then starts to fall off exponentially with time as the distance from the screen increases.   So the integral we'd be interested in, representing the total probability of finding the electron at the screen from  'then'/ that time  to  infinity  is finite << 1.   Specifically we can assume the electron would never be found at the screen, write it off and just fire the next electron.
    Anyway, we were talking about a lack of detection at the screen as being a lack of measurement:   Well, that is still some measurement by the screen as far as I can see.   It is NOT at the screen at any time, although there are lots of other places it can be, so it is a little bit of information about its location.   I'm sure you were aware of that and the spirit of what you've said remains OK.

   

or it never interacts, and is effectively nonexistent (according to any local interpretation at least).

    This might be philosophy.   Is it possible for a thing to exist despite the fact that it hasn't and will not in the future interact with anything else?   Anyway.... there's always gravity which we don't tend to include in any Quantum Mechanics,   the electron is still providing some energy density and thus curving space, i.e. it is interacting with something else in some way (you would think).

- - - - - - - - -
   Overall,   I'm very grateful for your time and consideration.   It is re-assuring.   I haven't really pasued to consider how often we would need to update the wave function in any experiment (or simulation).   I'm thinking that the double slit experiment actually works and has results that are as clear as it does mainly because there are things going on that continuously make everything de-coherent (and also coherent) in the right ways.   For example, the electrons can encounter other particles and potentials en route to the barrier and/or screen.  We could imagine that these interactions change the wave function as much one way as the next interaction will change it the other way.  As such, modelling the electron as a simple localised wave packet, which stays reasonably localised throughout, while travelling (to the barrier and screen) becomes a reasonable approximation.      (  i.d.k. )

Best Wishes.

[Halc]

So the integral we'd be interested in, representing the total probability of finding the electron at the screen from  'then'/ that time  to  infinity  is finite << 1.   Specifically we can assume the electron would never be found at the screen, write it off and just fire the next electron.

Sounds reasonable

Anyway, we were talking about a lack of detection at the screen as being a lack of measurement:

Depends on your definition of measurement. In real life, measurement is epistemological. If the electron hits the lab wall, you're unaware of it and your epistemic wave function isn't altered by the event. In the sim, the sim would know that the wall was hit and the actual wave function would be altered, and the real wave function would collapse. The screen then also measures the collapse because the screen measures the wall; it becomes entangled with the wall state.

Well, that is still some measurement by the screen as far as I can see.

Yes, you know it missed, so the epistemic wave function is altered by the knowledge, even if it isn't 100% certain.

It is NOT at the screen at any time, although there are lots of other places it can be

Unless you're assuming a counterfactual interpretation, I think it a mistake to talk about where it is in the absence of measurement. But a lot of simulations do exactly that, so I suppose it depends how your sim is implemented. You know it missed, so the new wave function can yield odds of where it likely hit, and that's assuming that the lab is reasonably closed and it doesn't shoot off into space never to interact with anything, as so many photons never do.

Is it possible for a thing to exist despite the fact that it hasn't and will not in the future interact with anything else?

A matter of definitions. What does it mean to exist? There's conservation laws, so of course it exists. It merely lacks a location/momentum.

  Anyway.... there's always gravity which we don't tend to include in any Quantum Mechanics,   the electron is still providing some energy density and thus curving space, i.e. it is interacting with something else in some way (you would think).

For example, the electrons can encounter other particles and potentials en route to the barrier and/or screen.

Always wondered about that. Do they regularly do the electron-gun thingy in a vacuum to avoid that sort of thing?

[Eternal Student (OP)]

Hi.

Do they regularly do the electron-gun thingy in a vacuum to avoid that sort of thing?

     As you seem to be aware - most texts just tell you the gist of what was done rather than the fine details of how or where it was done.   
     I've always assumed a vaccum of some standard will greatly increase the number of electrons that will actually make it to the screen.    There are a few comments on the internet suggesting it would always be done in a vaccum but there are also a few that suggest it doesn't have to be.
     Let's try to put some objective and more factual information here:

1.     It seems the experiment done by  Akira Tonomura et al in 1987 ( http://aapt.scitation.org/doi/10.1119/1.16104 )   was done in a vaccum (of some standard but clearly not a perfect vaccum - nothing on earth will give a perfect vaccum).

2.     The more widely cited but later paper by  Bach et.al.   Published in New Journal of Physics (2012)  and available here:  https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1110&context=physicsfacpub
   actually doesn't have the word "vaccum" in it anywhere.

- - - - - -
   More generally, the diffraction works well enough for light in just air, although it is expected to display a 0.03% error in the fringe locations compared to a vaccum    (you can get this estimate just using the refractive index of air  vs.  vaccum)  - but bear in mind that we can get a laser pulse to a low enough intensity that we are effectively only sending one photon at a time - so this diffraction in air is a form of particle scattering when you consider it as a particle.
     The experiment should also work well for electrons in air where all the distances between gun, barrier, and screen are kept short.    The main requirement is just that the medium is transparent enough to get most of the electrons / photons to the screen.     (My opinion:  Well, you'd use a vaccum of some standard because it would help, the sort of standard they reach inside an old fashioned  Cathode Ray Tube  (TV set) would be sufficient).

    Whether or not the electrons actually do interact with other ordinary particles en route to the screen, I'm still going to use it as a turn of phrase or metaphor for what is happening:     The conditions are far from being perfect (information) insulators of the electrons from the environment.   Quantum computing often relies on developing some container for some Qubits where no information can pass to/from the system and the environment, the system must not become decoherent.   These sorts of ideas were not well understood when the double slit diffraction experiments were first being done.   I'm quite confident that the experiment was not done in some perfectly sealed and (information) insulated container, where everything from microscopic magnetic fields from the electrons through to light passing from the apparatus to the experimenters eye had been prevented from entering / exiting the system.  Loosely speaking, the electrons were interacting with "stuff" in the environment even if that stuff wasn't some ordinary type of air particle.

Best Wishes.

[alancalverd]

 Let's just assume that the usual QM stuff does apply and I'll choose the Copenhagen interpretation of QM for this problem. 

And there is the source of your conundrum. All the stuff about measurements and wave function collapse are reasonably predictive models of reality but can't claim to be reality.

If you want to pursue the wave function model, it isn't actually zero anywhere, just infinitesimal in most places.

And yes, it is almost impossible to do any useful experiments with free electrons of less than about 1 MeV in anything less than a fairly hard vacuum. The range of a 1 keV electron in ambient air is about 0.05 mm.

[Petrochemicals]

The experiment is repeatable with atoms and even molecules.

https://en.m.wikipedia.org/wiki/Double-slit_experiment#Variations_of_the_experiment

This would suggest that it isn't necessarily reliant on reading the results, but it does however not rule out any interference from the locale in the form of gravitational waves, electro magnetic influence or what effect the screen may have on the results.

[alancalverd]

so this diffraction in air is a form of particle scattering when you consider it as a particle.

I can't apologise for being pedantic - it's the very essence of physics. Scattering and diffraction are rather different phenomena.
The angle θ between the incoming and outgoing vectors in scattering  is essentially random with a probability distribution that is usually somewhat polarised along the incoming axis: could be a forward or backward teardrop or even, in principle, a sphere (the unique case between teardrops). Diffraction, on the other hand, is characterised by an interference pattern of the form  nλ = dsinθ where d is a characteristic of the scattering medium/slit pattern/whatever.

The energy of a scattered particle or photon is less than the incident particle energy. The diffraction pattern, however, is formed by particles with exactly the same energy as the incident beam. So there's an interesting conundrum: clearly there has been some interaction with the slit material, but no energy has been exchanged!