Many-world interpretation of double slit experiment

Question

Different interpretations of young's double slit experiment is available, I read Copenhagen and Feynman's path integral interpretation of double slit experiment; former uses the idea of wave function and later uses the idea of infinite paths and sum over the weight factors of each path obeys causality.

I Googled lot of time to see how double slit experiment is explained using Many-world interpretation of quantum mechanics, but unfortunately I don't find anything. It would be great helpful if someone give a nice explanation that, how famous double slit experiment is explained using Many world interpretation of quantum mechanics?

Answer 1

In the MW interpretation of quantum mechanics, the double slit experiment can be explained this way:

1. a single particle's wave function approaches the pair of slit apertures.
2. The wave function is spread out laterally so that it impinges on both slits.
3. The wave function goes through both slits and is diffracted, forming an interference pattern on the detector.
4. The detector can only detect the particle at one point, and the probability that it is detected at any given point is proportional to the squared amplitude of the particle's wave function at that point.

A reasonable person might ask, "What happens to the rest of the wave function - the portion that is not at the detected point?"

The MW interpretation answers that question by saying that #4 doesn't tell the whole story: that in fact the detection event at the detector must, itself, be described by a wave function. That is, the detection event exists as a superposition of possible outcomes, just as the particle's trajectory exists as a superposition of possible paths. Extend the reasoning farther, considering an observer to be put into a superposition of states, each "observer state" observing the detector indicate that the particle has been detected at a different point.

At first glance, it might seem that the observer would see all those states at once, but he/she doesn't because of the fact that the wave function is linear -- which means in effect that the different possible paths do not "see" or interact with each other. Each state represented in the superposition that describes the observer is invisible to all the other states, as if they don't exist.

The "branching" in the MW interpretation is just the recognition that at each event in the evolution of a wave function that describes a system, a set of new - mutually invisible and non-interacting - states may be added to the wave function describing the whole system. (E.g., the "event" might be diffraction at the slits, detection of where the particle hits a screen, or the observer's perception of where the detector says the particle hit the screen).

When the whole system (source, slits, detector, and observer) is included in the original wave function describing the double-slit experiment, there is much less reason to be confused by the MW interpretation of the experiment.

Answer 2

I think that the many worlds interpretation, as long as it is just an interpretation and not a new theory with testable predictions, is based on the Feynman path integrals formulation, so the mathematics of the FPI should be the same for the many worlds too. See this answer of mine .

As a new theory I suppose it has not reached the level to make testable predictions for the double slit, that is why your searched in vain.

Answer 3

Mathematically, the path integral is simply a way to derive the wave function.

The three interpretations you mention can broadly be summarised:

• Copenhagen The wave function is probabilistic and the selection of any given outcome is otherwise inherently random. Any underlying reality is inaccessible to science. Shut up and calculate.
• Path integral The probability function is the sum of every possible path throughout spacetime. Quite why one particular path wins out in any given measurement is not directly addressed; "hidden variables" are sometimes proposed but lack any scientific basis.
• Many worlds The paths are real. For each possible path (or unique outcome), the real world divides and each reality follows one of those outcomes. The extent to which different paths with the same observed outcome might first split into parallel worlds, and subsequently re-merge back into one reality, has varied in response to criticisms.

Answer 4

It would be great helpful if someone give a nice explanation that, how famous double slit experiment is explained using Many world interpretation of quantum mechanics?

In the "one photon double slit experiment" an infinite number of photons leave the light source, go through an infinite number of screens, and hit an infinite number of photographic plates.

A physicist, which is really an infinite number of physicists, adjusts the light source so that on the average it takes, let's say one minute, for some plate to become hit by some photon.

Some areas of the plate cluster absorb more photons than other areas, therefore there exists an "interference pattern". The infinite number of plates interact with each other somehow, that must be the reason for the pattern.

Some areas of the plate cluster are hit by incoherent stream of photons, those areas are the darker ones. Here "incoherent" means "two equal streams of photons whose phases are not the same, but rather opposite ones to each other".

(I used the word "incoherent" because I wanted to put forward the idea that the brighter area receives more coherent light than the darker area)