# Quantum Paradox: Interfering Imaginary Slits?

• dx
In summary, the conversation discusses the concept of probability amplitudes in the double-slit experiment where the slits are imaginary. The amplitudes for indistinguishable final states interfere with each other, leading to a single overall amplitude. The discussion also mentions the use of an imaginary point between the screen and source to consider all possible paths. However, there may be an issue with considering all paths as indistinguishable.
dx
Homework Helper
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Hi, I'm just beginning to learn about the quantum world, so excuse me if this is naive.

Consider the double-slit experiment except that the slits are imaginary. call the slits A and B.

you have a probability amplitude that a particles goes to the point x on the screen via A (an imaginary slit) and also an amplitude that it goes to the screen via B :

$$< xA | s >$$
$$< xB | s >$$

these two amplitudes are clearly the amplitudes for indistinguishable final states and therefore should interfere. but since the slits are imaginary, you could also write it as a single amplitude <x|s> and the probability is then just |<x|a>|^2.

you could object that I am not considering all possible paths to the screen, so let me modify it a little.

instead of two imaginary slits, say we have an imaginary point between the screen and the source. then there are two possible classes of paths to the screen : the amplitude for the paths that go above the point and the ones that go below the point. the final states by the two types of paths are indistinguishable and so the amplitudes interfere with each other.

What's the problem? Everything is fine if one uses the amplitude
$$<x|A|s>+<x|B|s>+...$$ for n paths
which becomes
$$n<x|A|s>$$
when n paths are 'indistinguishable'.

## What is the quantum paradox of interfering imaginary slits?

The quantum paradox of interfering imaginary slits is a thought experiment that explores the strange behavior of particles at the quantum level. It involves a hypothetical scenario where two imaginary slits are placed in front of a particle, and the particle is able to interfere with itself and create an interference pattern, even though it only passes through one slit at a time.

## How does the quantum paradox of interfering imaginary slits relate to the double-slit experiment?

The double-slit experiment is a real-life experiment that demonstrates the same phenomenon as the quantum paradox of interfering imaginary slits. In the double-slit experiment, a beam of particles is directed towards two slits, and an interference pattern is observed on the other side, despite the particles passing through only one slit at a time. This experiment provided evidence for the wave-particle duality of particles at the quantum level.

## What is the significance of the quantum paradox of interfering imaginary slits?

The quantum paradox of interfering imaginary slits challenges our understanding of the behavior of particles at the quantum level. It shows that particles can behave as waves and exhibit interference, even though they are considered to be discrete particles. This paradox highlights the complexities of the quantum world and the need for further research and understanding.

## How do scientists explain the quantum paradox of interfering imaginary slits?

Scientists explain the quantum paradox of interfering imaginary slits using the principles of quantum mechanics. They propose that particles exist in a state of superposition, meaning they can exist in multiple states at once. When a measurement is made, the wave function collapses, and the particle is observed in a single state. The imaginary slits in this thought experiment represent the multiple states a particle can exist in, and the interference pattern is a result of the superposition of these states.

## What implications does the quantum paradox of interfering imaginary slits have for our understanding of reality?

The quantum paradox of interfering imaginary slits challenges our traditional understanding of reality. It shows that at the quantum level, the behavior of particles is unpredictable and can contradict our classical understanding of the world. This paradox has implications for fields such as physics, philosophy, and technology, as it forces us to reconsider our understanding of the fundamental nature of reality.

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