# Question on the Collapse of the wave function?

1. Jan 9, 2010

### fdesilva

Fact 1.From relativity we have come to view the universe as 4 Dimensional. That is 3 Dimensions of space and 1 of time. As such I have the following questions.
Questions
1. Given the universe is 4D, does it not follow that all objects within the universe is 4D?
2. If 1 is true, does it mean that all objects must have 2*4 boundaries that define it? That is 6 special boundaries (The familiar 3D boundaries) and 2 boundaries over time?
3. If 2 is true then would it mean that at a quantum level also we would expect to see 8 boundaries?
4. In quantum experiments when measurements are carried out, is it possible that one of the defining boundaries over time, is created by the measuring device? That is the object whose property is getting measured has just been given an end boundary condition to the past and a starting boundary condition to the future at the point of measurement?

Fact 2. In Quantum experiments prior to measurements there is an "uncertainty" as to the outcome. That is the outcome can be 1 of many possibilities, each possibility having a fixed probability of occurrence depending on the properties of the measuring device. (Operator applied)
Further Questions
5. Is this "uncertainity" precisely because the measuring device is forming that undefined 8th end boundary condition for the object undergoing measurement?
6. If 5 is true does it not follow that the collapse of the wave function is to the past? That is, if say the spin of a particle is getting measured from time T0 to T1. The measuring device is getting applied at T1. Then prior to measurement the spin has an equal probability of a clock wise or antilock wise spin relative to the measuring device at T1. However it is only when the particle encounters the measuring device that this spin becomes defined or created in say the clockwise direction. Thus the spin is in the clockwise direction for the period T0 to T1 once the measurement was applied at T1? The spin of the particle to the future (For time > T1 ) will depend on the boundary condition in the future?

2. Jan 10, 2010

### Fredrik

Staff Emeritus
1. The set of points that represents the object at a given time t is 3-dimensional (because a hypersurface of constant t is 3-dimensional, and we're talking about a subset of such a hypersurface). The curves that represent the object's motion fill up a 4-dimensional region of spacetime.

2. No, but the region where those curves are located has a 3-dimensional boundary. Note that in a 1+1-dimensional spacetime, the boundary would be a closed curve (not necessarily a rectangle, which seems to be what you have in mind). In a 2+1-dimensional spacetime, the boundary would be a closed surface. In 3+1 dimensions, the boundary is 3-dimensional, like a closed surface and its interior.

3. This one is a bit tricky. If we're using the path integral formulation, you'd be dealing with infinitely many boundaries, and even infinitely many copies of each boundary (because there are infinitely many different ways to distribute the world lines of the component parts in there). The standard formulation on the other hand, doesn't describe things in terms of world lines. You'd be talking about superpositions of localized states, which "collapse" into a single localized state due to interactions with the environment.

4. Yes, it's quite common to use QM to calculate the probability of detection at a specific event, given emission at another event.

5. No.