[namaan (OP)]

So a random thought occurred to me. I have heard about this "pilot wave" idea that seems to provide an explanation for the strange results in the dual slit experiment. In fact I saw a science show (yes, a popular science show -__-) where an experiment was featured showing that under certain conditions the surface of water can be an analogue for these "pilot waves" thus guiding the (water-drop) particles in the wave troughs in such a manner that these particles are able to produce an interference pattern when traveling through two slits. Hold that thought.

Now looking at quantum tunneling, where particles are able to cross what should be impassable barriers, I had to wonder: certainly the particle crossed the barrier, but was the barrier able to stop its pilot wave from passing? I assume not since as far as I understand it, assuming these pilot waves exist, they should provide a direct measure of the probability of finding a particle at the quantum scale. And as the theory goes, the very reason a particle is able to cross this impassable barrier in the first place is because there was a chance of it existing there, and so it follows that this chance is represented by an actual pilot wave that passed through the barrier.

Still I think it would be a worthwhile experiment to have particles that pass through such a barrier via quantum tunneling to then be directed through a dual slit to see what sort of pattern appears on the other end. Any thoughts? Has such an experiment already been done?

[Edit: Oh, almost forgot, the whole point of the experiment would be that, on the off chance that these pilot waves are stopped by the barrier, then the particles should in theory produce two bands through the slits rather than an interference pattern since they have lost their guiding pilot wave.]

[Bill S]

Namaan, as random thoughts go, that is an interesting one.  Being a non scientist, I have no idea what to expect the outcome to be.  However, I too have a random thought.

In order to know that the particle had tunnelled through a barrier, you would have to observe it, to do that you would measure its position.  Would that not destroy its chances of producing an interference pattern, whether or not the pilot wave had passed through the barrier? 

[namaan (OP)]

Well, here goes two non-scientists discussing science. Hope all goes well...though I freely concede that I like to think of myself as a scientist at heart.

In order to know that the particle had tunneled through a barrier, you would have to observe it, to do that you would measure its position.  Would that not destroy its chances of producing an interference pattern, whether or not the pilot wave had passed through the barrier?

Sorry for my, potentially extreme, ignorance here, but why do we need to measure whether or not a particle tunneled through the barrier? I was thinking of a setup in which the only particles that will have the chance to move through the slit will be those that first were capable of tunneling through the barrier.

In such a setup, only those particles will "hit" the screen at the end which first tunneled, and then passed through the slit. Technically though, if I'm understanding tunneling right, there's always some possibility that any subatomic particle will randomly tunnel through all the experimental chambers and interfere with the result, but I'm assuming precise measurements and statistics can rule out this interference.

[JP]

You mean something like this:

[diagram=663_0]

If the particles come in from the left, some small proportion will tunnel through the barrier.  Then it will be like a usual two-slit experiment where you see them striking the detector in the regular interference pattern.  In the pilot wave interpretation, part of the pilot wave gets through the barrier and part reflects off it.

[Bill S]

Note to self for the future:  Ensure brain is properly engaged before posting.

[namaan (OP)]

You mean something like this:

[diagram=663_0]

If the particles come in from the left, some small proportion will tunnel through the barrier.  Then it will be like a usual two-slit experiment where you see them striking the detector in the regular interference pattern.  In the pilot wave interpretation, part of the pilot wave gets through the barrier and part reflects off it.

Exactly, though the straight forward delivery leaves me wanting. I'm left thinking the experiment probably isn't worth it then?

[JP]

Well, the experiment wouldn't show any difference between the Copenhagen and pilot wave interpretations.  Both cases say something (either the wave function or pilot wave) tunnels through the barrier.  That something then passes through the two slits as in the usual two slit experiment.  The only difference is that there's a chance the particle will not be detected on the detector as part of a two slit pattern because part of the wave function/pilot wave has reflected from the first screen and never reaches the slits.

[namaan (OP)]

Thanks, that makes sense, but if that's right, won't the reverse also hold true? I mean, let's say you positioned this experiment backwards where you have the usual dual slit experiment, but with a detector in the slit that "observes" the quantum-scale particle. This should, as per the usual, cause a dual band on the detector due to wave function/pilot wave collapse.

Now you adjust the experiment by putting a barrier in front of the detector. In this case, would it be accurate to say that due to wave collapse in either interpretation, there is no "chance" of the particle existing on the other side of the barrier and so no tunneling can take place? In other words, if the particle weren't observed, and wave function isn't collapsed, the particles would move through the dual slit and then tunnel through the barrier producing a much-weakened interference pattern on the detector (much-weakened obviously because only those particles should reach it that had to tunnel across).

But when you collapse the function by observing the particle as it passes the slit, it is unable to tunnel across the barrier and reach the detector at all. Sound reasonable?

[JP]

Collapsing the wave function doesn't mean that the particle can no longer tunnel.  If you somehow measured which slit it passed through, it could still tunnel through a barrier and hit the detector.  Only instead of a two slit pattern, you'd see a one slit pattern, reduced in intensity by the tunneling.

[namaan (OP)]

Collapsing the wave function doesn't mean that the particle can no longer tunnel.

Is that really a foregone conclusion under both interpretations? Well, I'm not really sure what it means for a pilot wave to collapse frankly.

[JP]

In the pilot wave interpretation, the pilot waves themselves can tunnel, so the particle, which is guided by the pilot waves, can still make it through the barrier.  If you force the pilot wave to choose one slit or the other, its the same as collapsing the wave function to choose one slit or the other, so you still destroy the two slit pattern.

[namaan (OP)]

Sorry, I'm speaking purely on logic at this point and don't mean to waste your time asking this but I thought that the very reason that particles go through one slit or the other when observed is that their (pilot)wave( function) collapses. And my best understanding dictates to me that we might consider this collapse as a destruction/absorption/using up of the wave in at least the pilot wave interpretation. And it would be this removal of the guiding wave that causes the particles to behave like, well particles. I arrive at this partly because a wave choosing one slit or the other doesn't make sense to me.

So if it's a removal of a wave that causes particle like behavior, then the observed particles should lose the capacity to tunnel...perhaps?

[JP]

And my best understanding dictates to me that we might consider this collapse as a destruction/absorption/using up of the wave in at least the pilot wave interpretation.

There's a mistake in that statement.

Tunneling is a consequence of the particle having features of waves, whether you interpret that wave as a wavefunction or a pilot wave (or some other interpretation of quantum mechanics).  If a particle passes through only one slit, this just means the wave passes through only one slit.  It's still a wave and can still tunnel.

[sciconoclast]

Great Idea for an experiment.

It would not determine if there is a pilot wave or not.  However, it would determine if when the probabilities occur for one path through a barrier if they could also occur simultaneously for an adjacent path through another barrier.  Whatever the answer it would be interesting.

[sciconoclast]

Oops; I miss-read your experiment. I thought that you where placing a barrier at each slit. Instead your are placing the barrier before the double slit. This is even better.

I suspect from my own observations that if there is a pilot wave that it is easily disrupted. In the original Bohm theory the pilot wave is continuously generated by bound, rotating, Dirac neutrinos. But, if the pilot wave is knocked off regeneration requires time and distance.

Therefore, if the appearance of a double slit interference pattern is shown to be dependent on the distance between the barrier and the double slit, you would have proven pilot wave theory.
           

[sciconoclast]

back again.

After reading all the post in this thread I fell obligated to describe the difference between pilot wave theory and quantum field theory.

There is no wave collapse required to produce a photon in the David Bohm pilot wave theory.  In this theory the photon is present from the beginning and generates a wave in space as it travels through it. In your experiment the photon would travel a path through the barrier and through one of the double slits. The actual wave would pass through both slits and interfere with itself and the photon to redirect the photon path.

In the Neils Bohr quantum field theory nothing actually travels the path nor passes through the barrier and double slit. The wave functions in this theory only describe abstract mathematical probabilities for a photon to occur on different vectors at different time intervals.  If there is a test for a photon, such as the presence of an electron in the detector, and that position represents one of the high probabilities, then the probability for a photon is realized at that point and all of the other probabilities for that photon are gone ( quantum field collapse ).

If there is a probable path through the barrier and then equally probable paths through each of the double slits, then the highest probability for photon occurrence is where two possible paths through the slits converge. These points are responsible for the interference pattern.  In some versions the photon itself is just a new set of mathematical abstractions for the photon characteristics.

As you can see these two theories constitute very different views of the ultimate state of things but are identical in producing results.  One of the few areas where they differ is where the interference occurs.  I have been performing experiments to determine this [ see my post that JP just moved to New Theories ].

Namaam; do not be discouraged by a lack of advanced schooling in physics.  The history of science is full of important advances stumbled upon by those who were unencumbered by the orthodoxy of their time