Understanding Quantum Wave-Particle Duality: Explained and Clarified

[Curious6]

Please! Clarification Needed!

As I understand the wave particle duality of quantum mechanics, quanta exhibit both wave and particle properties. They:

(i) exhibit wave properties before being measured, i.e. the position of a single quantum object is spread out over space, and the wave amplitude of this object gives the probability of being found in a specific position. This lack of definite position before being measured (can just be calculated in terms of probability) means the quantum object exhibits wave properties.

(ii) exhibit particle properties once the measurement act has taken place, i.e. the position of a single quantum object is then localised, and the precision in its position reduces the ability to predict other quantities (the Uncertainty Principle).

The initial problem I had with the wave particle duality is that when I thought of quantum objects as being waves (in the traditional meaning of the word which I had learned at school, that is, a wave is a disturbance that transfers energy without transferring matter) I thought of it as not being a physical entity, i.e. it is not a tangible thing. Of course, this is not a problem with the particle part of the duality, because particles are actually tangible things.

However, as I now see it is that quantum objects are neither waves nor particles in the traditional sense of each word, but that they exhibit behaviours of both types but that they are still something physical, that is, something tangible (and not something such as a wave, which cannot really be described as a "thing", excuse the unscientific term).

Could anybody clarify if this is the correct interpretation? Am I right? Thanks anybody who takes some time in helping explain this concept.

 

[Curious6]

Anybody willing to answer?

 

[Fredrik]

I think you seem to understand it pretty well.

I wouldn't use the term "wave amplitude" though. The "wavefunction" is a function $$\psi$$ that takes a position $$\vec x$$ and a time $$t$$ to a complex number $$\psi(\vec x,t)$$. The wavefunction is the mathematical representation of a particle. How it changes with time is specified by the Schrödinger equation. The interpretation of the wavefunction is that $$|\psi(\vec x,t)|^2$$ is a probability density, i.e. a number that you have to multiply with a volume to get a probability. That probability is the probability that a measurement at the specified time would find the particle in a volume of the specified size around the specified position. (Actually that's only an approximation. The correct way to get the probability is to integrate the probability density over that region of space).

 

[Curious6]

OK, and does the sum over histories approach then refer to the moment before an actual measurement is taken? I suppose that once the actual particle has been localised the particle is not taking all the possible paths anymore.

 

[Fredrik]

Think of it as a sum over all different ways something can "happen" between two measurements. Suppose that a measurement reveals that a particle is localized near x at time 0 and another position measurement is done at time t>0. The probability that the result will be that the particle is localized near y is given by a sum (actually a really crazy kind of integral) over the probability amplitudes (complex numbers) associated with each path through spacetime that connects the two events (x,0) and (y,t).

What's important to realize is that even after the particle has been detected at y it would be wrong to assume that it took only one of those paths to (y,t). It would be more correct to say it took all of them.

This is the kind of stuff that's explained very well in Feynman's book "QED: The strange theory of light and matter". The book is thin, cheap and easy to read. I think you should get it if you don't have it already.