# Interpretation of Quantum Mechanics

• mimocs
In summary, the conversation discusses the interpretation of Quantum Mechanics, specifically in regards to the realistic, orthodox, and agnostic positions. The third question asks about the probability distribution for an ensemble of states prepared with the same initial condition, and the answers vary depending on one's interpretation. The minimal statistical interpretation provides a mathematical formula for determining the probability distribution.
mimocs
I want to ask you guys about the interpretation of Quantum Mechanics.

I am using Griffiths' Introduction To Quantum Mechanics as a textbook.

In this book, on chapter 1.3, there is an explanation about 3 different views of quantum mechanics, realistic, orthodox, agnostic.

My homework question is
Explain the followings briefly, based on the realist, orthodox, and agnostic positions respectively.
1. Where was the particle just before the measurement?
2. What happens if we made a second measurement immediately after the first?
3. What would be the probability distribution for an ensemble of states prepared with the same initial condition? Compare the three positions.

My problem is on the third question.
1 and 2 is just on the textbook so I have no problem with them.

However 3, I am not very sure.

In my opinion, answer is this.
realistic : Probability distribution looks like a delta function since the states are all the same.
orthodox : Probability distribution will be widely.

I actually have no logic for the answers.

This is, in fact, not a physics but a philosophy question. The answers depend on what your point of view concerning the interpretation is. It starts with the very subjective meaning of the word "realistic". I'm a follower of the minimal statistical interpretation which tries to only use the minimum of metaphysical ideas to apply the quantum-theory formalism to interpret observations in the lab. For me that's the most "realistic" interpretation, but some people have another understanding of "realistic" and call this point of view a non-realistic interpretation.

The only point that's independent of interpretation is 3) and that's why I can answer this question within the minimal statistical interpretation. The probability distribution to measure a certain value $a$ of the observable $A$ is given by
$$P(a|R)=\sum_j \langle a,j|\hat{R}|a,j \rangle.$$
Here $|a,j \rangle$ is a complete set of eigenvectors of the operator $\hat{A}$ that represents the observable $A$ for the eigenvalue $a$ and $\hat{R}$ is the statistical operator due to the preparation of the system in the corresponding state.

## What is the interpretation of quantum mechanics?

The interpretation of quantum mechanics is a philosophical and theoretical framework used to understand the behavior of particles at the subatomic level. It attempts to explain the fundamental principles and phenomena of quantum mechanics, such as wave-particle duality and superposition.

## What are the main interpretations of quantum mechanics?

There are several main interpretations of quantum mechanics, including the Copenhagen interpretation, the pilot-wave theory, the many-worlds interpretation, and the transactional interpretation. Each of these interpretations offers a different way of understanding the underlying principles of quantum mechanics.

## What is the Copenhagen interpretation?

The Copenhagen interpretation is the most widely accepted interpretation of quantum mechanics. It states that particles do not have definite properties until they are observed, and that the act of measurement affects the state of the particle. This interpretation was developed by Niels Bohr and Werner Heisenberg in the 1920s and is still used in many practical applications of quantum mechanics.

## What is the many-worlds interpretation?

The many-worlds interpretation suggests that every time a quantum measurement is made, the universe splits into multiple branches, with each branch representing a different possible outcome. This interpretation was proposed by physicist Hugh Everett in the 1950s and remains a controversial but popular theory among some physicists.

## How does the interpretation of quantum mechanics impact our understanding of reality?

The interpretation of quantum mechanics has significant implications for our understanding of reality. It challenges our traditional understanding of cause and effect, determinism, and the nature of reality itself. It also raises philosophical questions about the role of observation and consciousness in shaping our understanding of the physical world.

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