Thread: Wave-function collapse

Hey all,

Can you guys please explain this concept?

A particle-wave travels and interacts with itself as a wave but is positionally detected (Arriving and departing) as a localized particle

I don't understand this wave-function collapse...what causes it? is it possible for it to ever de-collapse? If so, how?

Thanks a lot,
First time poster

Hi curiousman! The full answer to your question isn't so easy (at least not to me). So, unless you want to get into fairly heavy-duty math, you had better accept the following two assertions:

The (Schroedinger) wave function, ψ, describes the time-independent energy of a point particle. It's solution is some sort of "sine wave" times some constant; i.e. takes on values between -1 and 1.

The probability density for the position of this point particle is the square of the ψ function.

(Noting that (-1)² = 1, 0² = 0, and that the square of any negative is positive, we easily see that this might be the case, because, by definition, probabilities are between 0 and 1.)

What's a "probability density?" you ask. Very roughly speaking, it is the probability of finding some object at some place at some time. (Urk...)

Anyway. If you know the energy of a particle, you know it's ψ function, which squared only gives you the probability of it being in a particular place at a particular time .

Suppose now you know where the particle is. Then the ψ² plot is a flat line with just a single peak, that is, at the peak the probability of the particle being at some place is 1, and is 0 at all other places.

How do you generate such a plot? The only way to generate such a plot from a wave function is to allow them to interact in such a way that "peaks and troughs" exactly cancel at all places except one - this interaction, if you care is called superposition, and the canceling superposition is confusingly called "wave-function collapse".

But having allowed this interaction of many ψ functions, you no longer know which particular ψ function, which energy, applied to the particle in question, therefore you cannot, as a matter of principle, simultaneously know the position and energy (momentum) of any particle subject to quantum laws.

So can it be reversed? Easily! Just ignore one of the measurements.

Umm, on re-reading this, I'm not sure I've answered the actual question you asked. Anyway, there it is

I'm confused.

Well, well! Do you have a question?

Yes.

I == seek to understand what make Einstein think space is curved.

Get on the floor!

Originally Posted by streamSystems

Yes.

I == seek to understand what make Einstein think space is curved.

Well, first, neither Einstein nor anyone else thinks "space is curved". Get a grip.

Second, the curvature of spacetime has nothing, absolutely nothing to do with this thread.

If you want a lesson in Riemannian geometry, river_rat is your man, in fact there is a live thread on it if you truly wish to understand it. Do you?

thanks a lot, guitarist. you have definitely cleared up a lot of confusion.

Originally Posted by Guitarist

Originally Posted by streamSystems

Yes.

I == seek to understand what make Einstein think space is curved.

Well, first, neither Einstein nor anyone else thinks "space is curved". Get a grip.

Second, the curvature of spacetime has nothing, absolutely nothing to do with this thread.

If you want a lesson in Riemannian geometry, river_rat is your man, in fact there is a live thread on it if you truly wish to understand it. Do you?

Yes, yes I do (sorry for not replying earlier).

The context of my question regarding the curvature of space-time is that I seek a definitive equation that resembles the curvature of space-time, not space-time being proposed as a curvature, a fudge, because contemporary equations don't add up.

I think I know where the term "space-time curvature" came from, and it represented a use of terms that could bring fudgy equations together, like why does light seem to bend in space-time, and so on. You see, I have developed a general equation of light being 0 mass and INFINITE mass, two conditions, that precisely explains the curvature of space-time, and also explains how light can be both a wave and particle, both freeform to space-time and intrinsic to space-time. I would like to compare those notes with any contemporary equations on the curvature of space-time.

I never said I thought Einstein thought space-time was curved, although someone said he would be impressed with the equations that suggested it was.

You see, equations relevant to wave-function collaspe should also point to equations relevant to the tapestry of space-time; that is why I was a little confused. The equation you provided seemed all too short.