Wave-particle Duality and the Uncertainty Principle
Most recent answer: 01/17/2014
- 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)
Follow-Up #1: Hidden Variables in the Double-Slit Experiment
- 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)