Quantum Mechanics: Superposition

[spanshcastlemagc]

I read a few interesting things about quantum mechanics, the two-slit experiment with electrons, sometimes going through one, sometimes the other, and sometimes, well both. It sounded nice when I read it, but now I can't remember anything else about it. Can anyone explain the concept in some detail but dumbed up enough for a Math undergrad to understand.

[bluesbassman]

[ QUOTE ]
I read a few interesting things about quantum mechanics, the two-slit experiment with electrons, sometimes going through one, sometimes the other, and sometimes, well both. It sounded nice when I read it, but now I can't remember anything else about it. Can anyone explain the concept in some detail but dumbed up enough for a Math undergrad to understand.

[/ QUOTE ]

Try this link:

Animation lecture of double slit experiment (http://video.google.com/videoplay?docid=-4237751840526284618&q=quantum)

[cambraceres]

The two-slit experiment is one of the best ways to express the wierdness of the Quantum world. The problem comes in when you try to understand what is actually going on. A famous physicist named Feynman said he had trouble teaching his students Quantum Mechanics because he didn't know what he was talking about and neither apparently did anyone else.
So if you don't understand, you're in good company.

The two slit experiment was first carried out by an outstanding English physicist named Young, he was trying to prove that light is manifested in either particles(corpuscles) or waves, and determine which one.

The experiment consists of a photon or light souce, aimed at a plate with two slits in it, behind which sits a light sensing backdrop. When the light source is on, and one slit is open, then there is nothing "special" going on, light diffracts through the single slit as if it were made of particles. Upon inspection, the backdrop will have a mass accumulation of photon markers near the middle of the screen, showing that the photons traveled predictably and in an altogether classical fashion.

If one were to open both slits at once, the situation changes and now the photons appear to be traveling as waves. They are said to be traveling now as waves because the absorbing screen that catches these photons now shows an interference pattern. Interference patterns are very familiar to those fluent in wave mechanics and were immediately recognized for what thet were in the original
experiment.

Like any great experiment, this lead to more questions and hardly any semblance of answers.

The experiment itself is that simple, but it's implications are a thick jungle of inconsistent concepts.
Your title mentioned superposition, that is a term used to describe the state of a certain quantum particle when it cannot be said to be traveling in one "classical" path or another. It is in a way suspended between multiple areas of discrete space, and is neither here nor there. Only upon measurement can one say with a level of certainty where it was at one point. But when you measure, you alter, and a new can of worms is opened.

This stuff is interesting, but I got to go bacck to work now

here's a link about the experiment itself

http://en.wikipedia.org/wiki/Double-slit_experiment

Cambraceres

[spanshcastlemagc]

the more accurately you measue a particles positions, the less accurately you measure its velocity, an observer changes the outcome simply by observing, that is some [censored] up [censored]

[cambraceres]

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the more accurately you measue a particles positions, the less accurately you measure its velocity, an observer changes the outcome simply by observing, that is some [censored] up [censored]

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Yeah it's crazy stuff, alot of fun to think about though.
I prefer the general oddities, like the two slit experiment, to think about rather than say Shroedinger's cat
or something like that.
I think the more common you can make a certain instance of Quantum phenomena, the more fun it is to think about, by virtue of being more accessible to a mind so simple as mine.

Do you have any more questions to further a thread on such an interesting topic?

[spanshcastlemagc]

well, when i was watching the cartoon in the first reply in this post, when it was talking about the sending just one electron towards the screen, it said that mathematically it went through one, sometimes the other, sometimes both and sometimes niether, anyone know the actual math to that? how do u get that out of strictly theoretical mathematics? its crazy

[Metric]

[ QUOTE ]
well, when i was watching the cartoon in the first reply in this post, when it was talking about the sending just one electron towards the screen, it said that mathematically it went through one, sometimes the other, sometimes both and sometimes niether, anyone know the actual math to that? how do u get that out of strictly theoretical mathematics? its crazy

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Statements like these usually come from the "path integral" formulation of quantum mechanics. To get the the quantum mechanical amplitude for a given process (say, for a particle to go from "a" to "b"), you have to add amplitudes for EVERY POSSIBLE path from "a" to "b." Each individual amplitude for a given path is easy to compute, but as you can imagine the sum (integral) of all paths is typically a very non-trivial thing.

[chrisnice]

You should check out some of the delayed choice double split experiments and quantum erasers. They realy drive home just how nuts this QM stuff is.