Wave-particle Duality and the Uncertainty Principle

Is the uncertainty principle due to a particle being spatially distributed by the Gaussian wave packet? Would it be accurate to say that a particle does not occupy a single position in space but that it occupies a region of space? Is this what leads to the inability to simultaneously determine its position and momentum? Does the Gaussian wave packet harmonize the particle and wave properties at the expense of uncertainty?
- Noel Delgado (age 41)
Oro valley, AZ, US

Hi Noel,

I think that's fair to say.

To be a bit more specific, the uncertainty principle comes directly from the Fourier relation between two variables (in this case space and momenta, or x and k). There is an uncertainty principle for any wave or wave packet, even in classical mechanics. For example, if you have a short pulse of radio waves (narrow Δt) , it will always contain a large range of energies (ΔE), since ΔE*Δt ≥ ħ/2.

The "wave properties" of a particle come mostly from the fact that the wavefunction is an extended distribution that evolves according to a linear, wave-like equation. The "particle properties" of a particle come from the weird "measurement postulate", which says that when you measure something, you collapse the state to an eigenstate of whatever operator (e.g. position, momentum, etc) you measured.

p.s. Not all wavefunctions have a Gaussian shape. But that's an interesting and useful case to think about, and the logic above holds for other functions as well.

David Schmid

(published on 01/17/2014)

Hello my question is regarding double slit experiment... In double slit experiment with one electron passing slit at a time we still get interference pattern after performing this experiment with many electrons (when both slits are open and unobserved). But when only one slit is open or we detect from which slit electron pass through interference pattern disappears. The common agreed upon answer for this is that single electron acts as a wave when unobserved and produce interference pattern but when detected its wave function collapse and it acts as particle. But don’t we think about alternate mechanism like say some underlying mechanism (field) in which this quantum particles ‘flow’ in space. And electrons do not obey both wave-particle duality but they are always in particle like mode in double slit experiment. Is it not possible that when both slits are open or electron is detected at slit with detector electron does not change its ‘mode’ from wave to particle or particle to wave but underlying medium in which particle flows change (get disturbed) and we get apparent pattern of wave – particle duality , wave function collapse and other stuffs. Thanks.... -Umang.
- Umang (age 25)
Ahmedabad,Gujrat,India

Hi Umang,

That's a great question. The basic idea that you are asking about is: what if quantum mechanics isn't complete?

What if there is an underlying cause which quantum theory doesn't take into account, and which would explain  weird experimental results without invoking counter-intuitive notions (like wave-particles or entanglement). In your example, you discuss an "underlying medium," but in principle there could be all sorts of underyling causes that we just don't know about yet, like extra forces or instructions of some sort, telling the particles to do certain things in certain cases. In quantum theory, we call such causes "hidden variables".

Hidden variables are a great idea; rather than believe current (weird) interpretations, you might try to hold out for some more simple, as-yet unknown hidden variables. This is what Einstein and many founders of quantum theory tried to do. However, in the 1960's, John Bell came up with a theorem which allows us to experimentally test if there are local hidden variables. Local hidden variables are the most intuitive kind of hidden variables; these variables don't depend on distant (not causally connected) positions or events.

Bell's theorem has since been tested experimentally, and many different experiments have confirmed that local hidden variables cannot exist. So, if quantum mechanics has some deeper explanation, it must be a weird nonlocal one, in which particles at one location are instantaneously affected by things that are far away. Physicists have tried to construct such nonlocal theories, but none have been convincing enough to gain widespread acceptance.

The best nonlocal hidden variable theory to date is known as , which preserves determinism and realism. This theory postulates that there is a "pilot wave," or "guiding wave," which follows a wave equation and drags particles around with it. In the double slit experiment, the guiding wave travels through both slits and interferes with itself, but the particle along with the wave travels through a definite trajectory and only through one slit.

This is very similar to what you suggested, and has a cool analogy in classical physics: . These scientists found a macroscopic fluid dynamic system in which waves carry around particles in a similar manner to the pilot wave. This system can reproduce the double-slit experiment, tunneling, and more. However, true Bohmian mechanics is a more subtle, and isn't at all pleasing to the common sense for several reasons.  First of all, particle motion depends on the value of a guiding wave at all locations in the universe. Worse still, this guiding wave doesn't even exist in physical space. Bohmian mechanics reproduces the results of quantum mechanics, but it isn't any more intuitive.

So the short answer is, your idea is a good one, but it has to be inherently nonlocal. So no one has found a satisfying way to create a proper theory out of the idea.

Cheers,

David Schmid

(published on 03/18/2014)