Skip to main content

# Questions tagged [born-rule]

The Born rule is a rule in Quantum Mechanics that states that the probability density $\rho$ is $|\psi|^2$ where $\psi$ is the probability amplitude.

206 questions
Filter by
Sorted by
Tagged with
1 vote
1 answer
114 views

### Did "mangled worlds" go anywhere?

"Mangled worlds" is an idea from Robin Hanson that attempts to explain the origin of the Born rule. AIUI, it asserts that interpreted as in MWI, decoherence of a superposition as a result of ...
• 761
0 votes
1 answer
50 views

### Where is my mistake in using a measurement operator instead of Born’s rule to calculate the probability of detecting photons at an arbitrary angle?

As I asked in this question: https://quantumcomputing.stackexchange.com/questions/36998/how-can-i-calculate-the-measuring-probabilities-of-a-two-qubit-state-along-a-cer/37000#37000 From here I know ...
1 vote
1 answer
73 views

### Understanding operator product of three mixed states with three projector operators

I am recently studying the triangle scenario in the context of Bell nonlocality (for reference, see for instance this article). In it, we have three parties, commonly referred to as Alice, Bob and ...
• 25
7 votes
1 answer
664 views

• 267
0 votes
0 answers
70 views

### Why does quantization lead to observed quantites becoming probabilities?

I am reading the nice discussion on this MO thread on the idea behind Quantization mathematically. This answer is quite nice, and for my question, I take some quotes from it: "quantum ...
5 votes
1 answer
174 views

### Non-normalizable eigenfunctions

I was reading Shankar's Principles of Quantum Mechanics when on page 65, he starts talking about infinite spaces and operators in them. He introduces an operator $K$, which in the $x$ basis takes the ...
• 129
4 votes
3 answers
734 views

### Probability density and wavefunction

I am trying to understand the link between the wavefunction and probability density. I can understand the probability density $\rho$ would be some function of the wavefunction, but I am unable to ...
21 votes
4 answers
6k views

### Do we actually need negative probabilities in quantum mechanics?

I was reading this thread and I'm a bit confused. The answer says negative probabilities can account for destructive wave interference and the events cancelling out. But if events just cancel out, ...
2 votes
3 answers
694 views

### Must a wavefunction be normalisable for a pdf to exist?

My course notes say, for normalised wave functions $\psi(x,t)$, the function $$\rho(x,t)=|\psi(x,t)|^2=\overline{\psi(x,t)}\psi(x,t)$$ gives the $\color{red}{\text{probability density}}$ for the ...
• 137
0 votes
2 answers
188 views

### The probability density function $|Ψ|²$ [duplicate]

Max Born stated that $|Ψ|²$ is the probability density of a particle, given its wave function to be $Ψ$. But why is this? Where does this come from?
3 votes
1 answer
148 views

### How are Gleason's and Kochen-Specker's theorems related?

If, on the one hand, I were to paraphrase Gleason's theorem, it would loosely state that if one can assign a truth value $p_k$ to each basis vector $\vec{u}_k$ such that $\sum_k p_k = 1$, then that ...
• 1,345
2 votes
2 answers
141 views

### Why do we only look at transitions between energy-eigenstates, when perturbing a system with an oscillating interaction?

I have some doubts about the usual explanation of sharply peaked emission / absorption spectra, that one can observe when one looks at quantum mechanical systems, for example the hydrogen atom. In ...
• 6,793
0 votes
1 answer
123 views

### If states cannot be written as superposition of eigenkets of observable, then how do we measure an observable for that state?

Usually, if we have a state $|\psi\rangle$, and have to measure an observable $A$, then all we do is expand $|\psi\rangle$ in terms of the eigenvectors of observable A, and then the probability of ...
1 vote
1 answer
134 views

### Why it is a longstanding challenge to reproduce Born rule in Everettian QM?

I'm reading this Sebens and Carroll's paper on Self-Locating Uncertainty and the Origin of Probability in Everettian Quantum Mechanics. Where they presented their derivations of the Born rule and ...
• 1,783
1 vote
3 answers
213 views

### Nature of expectation values and Born's rule and the measurement problem

Suppose we take a normalised quantum mechanical wave function of $\Psi (\mathbf{r} ,t)$. If we expand it in a certain form of spatial functions $\psi_{n} (r)$ which is complete orthonormal. Then we ...
• 131
0 votes
1 answer
114 views

### Is the Born rule a red herring in explaining the measurement problem? [closed]

Many explanations of the measurement problem try to derive the Born rule from Schrodinger evolution, for example Many worlds. I have two reasons to think the Born rule isn't fundamentally related to ...
2 votes
1 answer
191 views

-3 votes
1 answer
103 views

• 17
7 votes
3 answers
262 views

### Which experiments confirm that the Born rule is $|\psi|^2$ rather than $|\psi|$?

It seems like some experiments on quantum systems, like the electron $g-2$ measurement, do not rely directly on the Born rule, since they are more so measuring inherent characteristics of the ...
• 2,475
2 votes
1 answer
92 views

### I'm trying to understand this paper on Born rule in Many-Worlds Interpretation

https://arxiv.org/abs/1405.7907 In particular I would like to understand this paragraph, right before chapter 6: This route to the Born Rule has a simple physical interpretation. Take the wave ...
• 21
1 vote
1 answer
49 views

### Does Born's rule guarantee component-wise probabilities? [closed]

Suppose I have the wave function $\vec{\psi} = \begin{bmatrix} \psi_x \\ \psi_y \\ \psi_z \end{bmatrix}$. If I understand Born's rule correctly, the equality $\vec{\psi}^* \cdot \vec{\psi} = f(x,y,z)$ ...
• 326
3 votes
1 answer
94 views

### Born's Rule for states over supernumbers?

For Quantum-mechanics on a Hilbert-space over the complex numbers, the usual scalar product of two states $\langle \phi | \psi \rangle$ and gives the transition amplitude between the two states. The ...
• 6,793
1 vote
2 answers
78 views

### A question of the semantic meaning of the (non-relativistic) propagator

In the Wikipedia article it says "the propagator is a function that specifies the probability amplitude for a particle to travel from one place to another in a given period of time". Let us ...
0 votes
1 answer
159 views

### Interpretation of Born Rule In QFT

Can we born rule be used to find probability of a particle to exist in a region in QFT using the formula $\int_a^b \psi(x)\psi^*(x)dx$,where $\psi(x)$ is a fermionic field? If yes, please provide ...
• 73
6 votes
1 answer
695 views

### Wavefunction Amplitude Intuition

Reading the responses to this question: Contradiction in my understanding of wavefunction in finite potential well it seems people are pretty confident that, e.g., the wavefunction of a particle in a ...
• 545
-1 votes
2 answers
203 views

• 1,487
1 vote
1 answer
118 views

### What is the distribution for a function of different quantum observables?

Suppose we have a quantum mechanical particle prepared in a pure state $\psi$, and an apparatus that can measure the orbital angular momentum of the particle along a specified orthogonal axis ($x$, $y$...
• 164
1 vote
0 answers
31 views

### Can I interpret the squaring of the wave function like this? [duplicate]

Born rule states that the probability density of the wave function is equal to the square of the function over the given interval. I thought, "Why squared?". I came up with this: "We ...
• 692
1 vote
1 answer
257 views

• 1,801
11 votes
1 answer
403 views

### What does Hartle's derivation of the Born rule actually amount to?

There have been many questions asked here on the topic of whether the Born rule can be derived from the rest of the axioms of quantum mechanics. See, for example, this and links therein. However, I ...