Born Rule Derivation: A Closer Look

In summary, the Born rule is a commonly discussed topic in physics, where P represents the probability of a particle appearing at a specific location and psi is the wave function. In the double slit experiment, the interference pattern itself represents the probability of an electron hitting the screen at a certain location. This pattern is a superposition of two wave functions, which raises questions about the Born rule and why we take the absolute value of psi and square it. Many posters on forums mention that the Born rule was a lucky guess, but there was a thread discussing it on Physics Forums.
  • #1
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Hello,

I hear a lot about the Born rule ##P = |\psi|^2## where ##P## is a probability of a particle appearing at some location and ##\psi## is a wave function.

When i look at double slit experiment interference pattern it seems to me that the pattern by itself already represents the probability that electron will hit a screen at some location. So if that interference pattern is a superposition of two wave functions i would intuitively say that:

[itex]
\begin{split}
P &= \psi \\
P &= \psi_1 + \psi_2
\end{split}
[/itex]

So to me it is verry bizare that in a Born rule we take absolute value of ##\psi## (why do we do that?) and square it (why do we do it?).

Is there any derivation at all on how they derived or made up the Born rule? Most of posters on other forums allways say it was a lucky guess... I can't bare the mind of that.
 
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  • #3
Thank you.
 

Related to Born Rule Derivation: A Closer Look

1. What is the "Born Rule" in quantum mechanics?

The Born Rule is a fundamental principle in quantum mechanics that describes the relationship between the physical state of a quantum system and the probability of its measurement outcomes. It states that the probability of observing a particular measurement outcome is equal to the square of the absolute value of the system's wave function at that measurement point.

2. Why is the Born Rule important in quantum mechanics?

The Born Rule is important because it provides a mathematical framework for understanding and predicting the behavior of quantum systems. It allows us to calculate the probabilities of different measurement outcomes and make predictions about the behavior of quantum particles.

3. How is the Born Rule derived?

The Born Rule can be derived from the fundamental postulates of quantum mechanics, specifically the postulate of wave function collapse and the postulate of measurement. It involves using mathematical tools such as complex numbers, vectors, and operators to describe the state of a quantum system and calculate the probabilities of measurement outcomes.

4. What does a closer look at the Born Rule derivation reveal?

A closer look at the Born Rule derivation reveals the underlying mathematical principles and assumptions that lead to its formulation. It also highlights the importance of understanding the fundamental postulates of quantum mechanics and their implications for the behavior of quantum systems.

5. Are there any limitations or controversies surrounding the Born Rule derivation?

While the Born Rule is widely accepted and has been confirmed by experimental evidence, there are ongoing debates and controversies surrounding its interpretation and application. Some physicists argue that it is a fundamental law of nature, while others suggest it may be derived from more fundamental principles. There are also ongoing discussions about the role of consciousness and the measurement process in the Born Rule.

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