Am I understanding superposition correctly? Is it equivalent to all-potential ?

1. Feb 17, 2010

MattAndMatthe

Am I understanding superposition correctly? Is it equivalent to "all-potential"?

In the double-slit experiment, when a single particle is "fired", it will pass through the slits as a wave but hit the receiving end (screen) as a particle. Each particle will clump on the screen, but after many single particles are "fired" it will still form an interference pattern.

(I think I got that right.)

And the seemingly bizarre thing is that the particle acts as wave by going through both slits but is still a particle, unless we observe it and it remains a particle and goes through only one slit.

So, does superposition mean that as the particle approaches the slits, it could potentially go through one slit, the other slit, or both slits, and so it does all three but remains a particle? Going back to the subject of my topic, is superposition a way of describing every potential position and/or state of a particle?

Any assistance to or correction of my reasoning will be appreciated. I'm desperate for facts and professional interpretation!

2. Feb 18, 2010

Demystifier

Re: Am I understanding superposition correctly? Is it equivalent to "all-potential"?

One should distinguish the concept of the particle from the concept of WAVE FUNCTION of the particle. Quantum mechanics (in its standard formulation) is a theory of the wave function of the particle, not of the particle itself. The wave function (which allways travels through both slits) determines the PROBABILITY of finding the particle on this or that position. What happens with the particle itself is not known. There are different interpretations concerning this question, but nobody knows with certainty which interpretation is correct.

3. Feb 18, 2010

Frame Dragger

Re: Am I understanding superposition correctly? Is it equivalent to "all-potential"?

...And to think you had a chance to make a convert!

MattAndMatthew: I'm not possessed of shame or morals as Demystifier is, so here's a thought: For Demyst, take a look at the two major Interpretations of QM that get discussed here. The first is The Copenhagen Interpretation (which I recommend only so you can appreciate that the math is ALL in QM right now), and the de Broglie Bohm Pilot Wave Interpreation, which is the only Hidden Variable theory to survive the great 'Bell' Purge

When you start wondering how both can be true, or something else (or like me you become an Instrumentalist)... you'll have reached the point where you want a valid description of quantum gravity as much as the rest of us. ;)

4. Feb 18, 2010

SpectraCat

Re: Am I understanding superposition correctly? Is it equivalent to "all-potential"?

The way I think about it is as follows. Quantum mechanics puts restrictions on the kinds of questions that can have "meaningful" answers in a given experiment. The only questions that have "meaningful" answers are those that address properties that are directly measured by an experiment. So in the context of the double-slit experiment:

1) you can measure which slit the particle goes through, in which case it is meaningful to ask the question, "Which slit did the particle go through"? However, you do not get any information about the wave-like nature of the particle.

2) you can measure the interference pattern, in which case it is NOT meaningful to ask "which slit did the particle go through?", because that information was not addressed by your experiment. You can however ask questions about the interference pattern (assuming that you do multiple measurements to reveal it), which derive from the wave-like properties of the particle.

3) you cannot "trick" quantum mechanics into giving you information about both cases by cleverly changing the configuration of your apparatus in the "middle" of the experiment. That is the fundamental result of the delayed-choice quantum eraser experiments.

4) There is a restricted class of experiments that allows *some* information about which-path and interference to be gained simultaneously, however the results have to be expressed probabilistically. For example, you can set up your experiment so that it is more likely that the particle will take one of the two paths. However, as you increase the bias between the two paths, you will find that your interference pattern begins to fade, until you reach the limit of the which-path experiment described in point 1. This is called the Englert-Greenberger duality relation.

Last edited: Feb 18, 2010
5. Feb 18, 2010

muppet

Re: Am I understanding superposition correctly? Is it equivalent to "all-potential"?

If you don't like the somewhat positivist language of questions without reference to an experiment being meaningless, I think quantum field theory provides a nice perspective on the wave/particle duality business. In that (advanced!) framework unifying QM with special relativity, you can no longer talk about fixed numbers of particles; you talk about "fields" that create and destroy particles. An intuitive illustatration of the need for this is afforded by the fact that when you switch on a lightbulb, you're creating trillions of photons that didn't previously exist; the kicker is that you describe electrons in more or less the same way!

The question of "motion" of a particle from a place x at a time t to a point x', at time t' (where obviously t'>t) is then replaced by the question of the field creating a particle at (x',t') having destroyed one at (x,t). (This turns out to be the same question as creating an antiparticle at (x,t) having destroyed one at (x',t') !)