"Measurement disturbs the system."

xts

The assumption about mere existence of "path" leads to paradoxes. Take double slit experiment performed with single electrons (photons, whatever else) at a time. If you insist that electrons have defined paths, you could divide (just in set theory sense, you don't need to tag individual events to which class they belong) events into two classes: those going through left slit and those going through right one. The pattern created by all events should be a sum of patterns made by L and R classes. We know what pattern is created if only one slit is open. Experimental pattern is different than sum of patterns with one slit open. So - if you want to say that "electron passed left slit" you must accept that behaviour of the "electron travelling through left slit" is magically affected at a distance by opening or closing the right slit.
As above - it makes no sense to use the term "path" regarding the particle. The particle may be observed at some point (rather some area), but between observations "path" makes little sense.
You may also create lots of experiments in which the straight line between source and detector is blocked, but particles are still observed.
If any I would rather prefer the second view. Personally, I like most Zeilinger's approach: we use the word "particle" only regarding the very moment of detection or emission. In between we should speak about evolution of the wavefunction, but not about particle.

Ken G

Yet this is just what Bohmian mechanics asserts. Remember, we can generalize Arthur C. Clarke's "any sufficiently advanced technology is indistinguishable from magic" to "any physical effect we don't understand is indistinguishable from magic." I believe Bohm showed that quantum mechanics does admit the interpretation that a particle does always have a definite position and momentum, but it requires adding another layer to the theory, it requires a "pilot wave" to shepherd the various possible trajectories into acting as though they were indeterminate about those quantities if one can't see what the pilot wave is doing. Of course, a more standard interpretation of the situation is that if you can get rid of the pilot wave by invoking indeterminacy, and the pilot wave has no measurable consequences, then this is what you should do, and that's what you are doing. But there is no observation that tells us "the particle does not have a definite but unknown position and momentum at any given time."
For the same reason, perhaps we should just say "there is no empirical evidence that it makes any sense to use the term 'path', and little but a kind of classical prejudice motivates its use in quantum mechanics. Of course, some view classical prejudices as a good idea, it really depends on personal preference."Yes, the notion of purely classical trajectories is definitely out the window. But pilot-wave guided trajectories are still possible, we just don't know and might not get to know.

xts

Of course, we may insist for "existence" of something which is fundamentally impossible to observe. It is a matter of taste, and metaphysical and religious formation.
I (like Carl Sagan) keep an invisible dragon in my garrage.

Bohmian mechanics preserves classic-like image of the particle of well defined parameters at the terrible expense of introduction of non-measurable 'real' entities, acting non-locally and backward in time, while still having problems to interprete some phenomena. It is a matter of taste if the 'reality' of particle between interactions is worth of such price. My Occamian nature definitely dislikes Bohm...

Fully agreed!
My positivistic nature tells me that in science we should not speak about existence of anything which is not backed by empirical evidence...

Ken G

Mine too, I merely recognize he achieved something important in showing why we can't really say we know there is indeterminacy in the "actual reality." To me, all these differing interpretations are just a kind of caution to us that we're still pretty far from knowing the reality, if indeed it even makes sense to make that our goal.
It does seem to be the only way to remove opinion from the issue. But maybe that is itself only an opinion-- rationalists are quite rightly quick to point out that we have no empirical evidence that the only things that exist are what we have empirical evidence of! In other words, to be completely consistent, must the empiricist replace the last seven words of your statement with "except the observations themselves"?

xts

I am far from advocating Mach's extreme positivism ;) We just should keep common sense and be practical. It is convenient to speak, e.g. about electric field as about something real and it rarely may lead to paradoxes. We should just remember that 'electric field' is not something 'fundamentally real', but rather our mathemetical construct, resulting from Coulomb's experiments.
As we go into troubles with it, we don't cry being forced to throw it out, and switch to other view (exchange of virtual photons) to describe electric interactions.
Here we are in the same situation - our well established intuitions about reality of paths may be quite useful not only in common life, but also regarding particles. The 10 MeV electron in a tracking chamber has well defined path. But we shouldn't use that word when it leads into paradoxes, by bringing in all the baggage associated with 'existence'.

StevieTNZ

What happens if we measure a particle's momentum? Would that indicate a path the particle is travelling on? (I guess we'd need to add forces/interactions into the equation)

xts

If you measure the momentum, you may find the direction the particle comes from, but to measure it accurately, the aperture of your tool must be large - thus you don't know its path, as it could be shifted to left or right by significant displacement

That's a classical version of Wheelers experiment: in double slit, you may find accurate positions where particles hit the screen - or - you may use a telescope installed at the screen plane to see if the particle comes from left or rather right slit. But in order to measure the direction precisely enough, the aperture of your telescope must be bigger than distance between fringes.