# What is Born rule: Definition and 47 Discussions

The Born rule (also called Born's rule) is a key postulate of quantum mechanics which gives the probability that a measurement of a quantum system will yield a given result. In its simplest form, it states that the probability density of finding a particle at a given point, when measured, is proportional to the square of the magnitude of the particle's wavefunction at that point. It was formulated by German physicist Max Born in 1926.

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1. ### I Carroll's Derivation of the Born Rule in MWI with Unequal Amplitudes

In Caroll and Seben's paper, Many Worlds, the Born Rule, and Self-Locating Uncertainty, they present a derivation of the Born rule. For the equal probability case their derivation is based on the following principles. Self Locating Uncertainty - "the condition of an observer who knows that the...
2. ### I Why do we experience the Born Rule in Many Worlds?

I hate to bring up an old saw again, but I've been listening to Carroll and some others wax poetically about Many Worlds. And Jurek's work on decoherence and pointer states seem to address some of the problems with the MWI. However, I haven't seen any compelling explanation as to why an...
3. ### I Entanglement and Born rule

Let be an entangled pair of photons 1 and 2, with the same polarization. The wave function is ##|12>=\cos\psi|HH>+\sin\psi|VV>## with ##\psi## the angle of polarization. The first ##H## (##V##) in ##|HH>## (##|VV>##) is photon 1, and the second one is photon 2. Alice observes photon 1 with a...
4. ### A Born Rule in Many Worlds Derived?

https://mateusaraujo.info/2021/12/08/a-satisfactory-derivation-of-borns-rule/
5. ### I Origin of Probabilities in Quantum Mechanics?

The non-normalized wavefunction of a general qubit is given by: $$|\psi\rangle=A|0\rangle+B|1\rangle.$$ The complex amplitudes ##A## and ##B## can be represented by two arrows in the complex plane: Now the wavefunction can be multiplied by any complex number ##R## without changing the...
6. ### I Born rule: time running forwards and backwards?

Can the Born rule be understood as time running both forwards and backwards simultaneously? The probability ##P_{i \rightarrow f}## that an initial quantum state ##\psi_i## is measured to be in final quantum state ##\psi_f##, after evolving according to the unitary time-evolution operator...
7. ### I How the Born rule is understood in various interpretations?

While intuitively we use 1) 3rd Kolmogorov axiom: probability of alternative of disjoint events is sum of their probabilities somehow QM allows to use instead: 2) Born rule: probability of alternative of disjoint events is proportional to square of sum of their amplitudes. This nonintuitive...
8. ### I Born rule in classical Ising model: Feynman -> Boltzmann ensemble?

Quantum mechanics is often said to be equivalent with Feynman path ensemble, which "after Wick rotation" becomes Boltzmann path ensemble, also called euclidean path integrals (popular for numerical calculations), or random walk/diffusion MERW (maximal entropy random walk). But Boltzmann path...
9. ### Quantum Which book best talks about the Born rule and its usage?

Hello, everyone. I cannot visit wiki. Can anyone tell me which books best talk about Born rule and its usage?
10. ### I How is the Born rule deduced from decoherence?

Weinberg says in his book "Lectures on Quantum Mechanics" that the born rule can be deduced from decoherence, and this solves the measurement problem. I'm looking for reference, book or article, to understand this better. Thank you
11. ### I Experimental confirmation of the Born rule

If we assume that a particle can be detected at a particular location, how can we do the detecting?
12. ### I A simple explanation of the Born rule?

Summary: Perhaps the Born rule can be understood by considering quantum transitions going both forward and backward in time simultaneously. The probability that an initial quantum state ##|\psi_i\rangle## becomes the final quantum state ##|\psi_f\rangle## is given by \begin{eqnarray*} P(i...
13. ### I Quantum Gravimeter: Exploiting the Born rule

Among the last of the classical tests of general relativity was the Pound–Rebka experiment performed in 1959. This experiment employed a variation of Mössbauer spectroscopy in which a moving emitter was used to counteract a gravitational redshift. The idea here is to exploit QED to measure the...
14. ### I Confusion About the Born Rule

Hey there! I’ve been thinking about the Born rule recently and whether it can be derived from the other postulates from QM. I’ve done a bunch of google searching, across PF, stackexchange and the arxiv, but most of it has felt a little opaque, particularly on whether anything has been...
15. ### I Can the Many Worlds interpretation state the Born Rule as a postulate?

Every derivation from the MWI of the born rule is circular. http://fmoldove.blogspot.com/search?q=MWI So my question is, can the MWI state the born rule as a postulate (without deriving) and still be a coherent interpretation of probability? The most famous argument against this notion is by...
16. ### I Is this derivation of the Born rule circular in any way?

https://arxiv.org/abs/1411.6992 They derive the born rule from the MWI. Is this circular?
17. ### A In what sense does MWI fail to predict the Born Rule?

Please restrict your answers to criticisms of derivations of the Born Rule that are generally accepted by proponents of MWI. Please provide a verbal description of the issue where possible so that people like myself who are certainly graduate-plus* but rusty as hell have a chance of seeing what...
18. ### B Born rule and thermodynamics

Some say there is analogy in the Born rule in thermodynamics where the particles locations depend on the probabilities. In QM, the amplitude square is where you have the probability of the particles being there. How about in thermodynamics.. what is the counterpart of the Born rules, and what...
19. ### A Evaluate this paper on the derivation of the Born rule

I have encountered this paper "Curie Wiess model of the quantum measurement process". https://arxiv.org/abs/cond-mat/0203460 Another work by the same authors is "Understanding quantum measurement from the solution of dynamical models" https://arxiv.org/abs/1107.2138 I am still evaluating the...
20. ### I Understanding the Born rule

i have been trying to obtain a schema for the Born rule and have got to this result. The incidence of detection at a point (x,t) = the incidence of the particle being at point (x,t) multiplied by the incidence of the detector being at point (x,t) on detection. The incidence of the second term...
21. ### I Born rule for macroscopic objects

There is one thing that I don't understand when considering quantum mechanics for macroscopic bodies. It is said that classical mechanics is a valid approximation and that macroscopic bodies that we encounter on everyday basis have a small uncertainty in position and momentum. So far, so good...
22. ### I Many measurements are not covered by Born's rule

1. Within the framework of a Hilbert space for an atom one cannot find an observable in the sense of ''self-adjoint Hermitian operator'' that would describe the measurement of the frequency of a spectral line of the atom. For the latter is given by the differences of two eigenvalues of the...
23. ### Functional Born Rule in QFT

In QFT, we can work with functionals of fields ##\Psi[\phi(x)]=\langle \phi | \Psi \rangle## that give us the probability amplitude for the field to be ## \phi(x) ##. It seems to me that the Born rule we get here i.e. ##P(\phi(x))=|\Psi[\phi(x)]|^2=|\langle \phi | \Psi \rangle|^2## is not of...
24. ### Is Probability conserved in RQM?

Is probability (or probability current) conserved in RQM/QFT? I have never seen a simple answer to this question. As always, thanks in advance.
25. ### How can you actually measure the electron position?

Standard quantum mechanics text-books discusses Born rule, which states that the probability of finding a particle in a certain region in space is given by $$|\Psi ({\bf r},t)|^2d^3r$$ Thing is, I never have seen a discussion about how you can actually measure the particle position in a...
26. ### The Born Rule in Many-Worlds

I'm not 100% sure that this is the right forum to post this, but I think that the people who read the Quantum Physics forum might be interested: Sean Carroll has written a paper explaining how it is possible to derive the Born Rule in the Many Worlds Interpretation of Quantum Mechanics. I'm...
27. ### Understanding the Born Rule

We are taught that the probability of detecting a particle is <ψ*|ψ>. I understand it is a postulate of QM and required by the maths, but have often wondered as to why it seems to represent a joint probability. For a while it seemed to make some sense to me in the time symmetric QM...
28. ### Born rule and Feynman propagators

Let us assume that we want to describe the full process of photon emission by electron A and absorption by electron B. Therefore electron B must be on the forward lightcone of electron A. In the normal forwards in time description a virtual photon propagates from A to B depositing a certain...
29. ### Many-Worlds, Deriving the Born Rule?

Lately I have been interested in the many-worlds interpretation, and in particular the way it is described by Wallace in his latest book The Emergent Multiverse. In the book he tries (or succeeds) to derive the Born rule from unitary dynamics by using game-theoretic arguments. But for this he...
30. ### Commutativity of the Born Rule

The born rule, written in the following way: P(ψ/\varphi)=|<ψ|\varphi>|^2 As a consequence, P(ψ/\varphi)=P(\varphi/ψ) I don't see it as an obvious fact from real life, do you? Why does it happen? Is there any intuitive reasoning / experience behind this commutativity of states? Thanks!
31. ### Born Rule Derivation: A Closer Look

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...
32. ### Born rule for degenerate eigenvalue

The probability of measuring a value a for an observable A if the system is in the normalized state |\psi\rangle is |\langle a|\psi\rangle|^2 where \langle a| is the normalized eigenbra with eigenvalue a. This is more-or-less the formulation of the Born rule as it appears in my text. But...
33. ### I am aware that physicists are trying to derive born rule from unitary evolution

I am aware that physicists are trying to derive born rule from unitary evolution. Has there been any success? What is the current status of that program?
34. ### Two Derivations of the Born Rule

Hi there. I found a paper ( http://users.ox.ac.uk/~lina0174/born.pdf ) which states that has derived the Born Rule. More or less, what I understood is that: 1) Consistency condition: if we are going to represent an experiment through different, but coherent representations (ie, different...
35. ### Publication advice for Born Rule paper

Dear everyone, I know this is not exactly on topic here, but I thought it was even more off topic in the other sub-forums, so please forgive me for posting it here. I'm looking for some advice and maybe some help. Recently I have finished my work on a paper about the emergence of the Born...
36. ### Deriving the Born Rule from the operator-centric formulation

Since the issue of deriving the Born rule comes up from time to time in the forum and I'm always a little mystified by some of the opinions people have. I recently fleshed out the details about the derivation I'm about to present and realized it pretty much makes the Born rule a triviality, so I...
37. ### Zurek's Born rule derivation

Zurek has proposed a http://lanl.arxiv.org/abs/1105.4810v1" (Phys.Rev.Lett.106:250402,2011) based on these assumptions: (i) States “live” in Hilbert spaces (ii) Evolutions (including measurements) are unitary. (o) Hilbert spaces of composite systems have tensor structure. (iii) Immediate...
38. ### Born rule derived from pure QM by Max Tegmark

Sorry if this had been already discussed: http://arxiv.org/abs/1008.1066 So, what I see (assuming that Universe is infinite, this is an important assumption, not proven of course, but if this is true): 1. The 'Interpretation war' is over, amen, the most important weakness of MWI has...
39. ### Does the Born Rule conflict with determinism in quantum mechanics?

I'm a layman. I understand the basic of the Hilbert Space and can imagine what are basis vectors and eigenvalues (allowable values) and observables (properties like spin, position, momentum, etc) and know operators are operations that involve observables. I also know the basic of the...
40. ### Exploring the Debate on MWI & Probability: Will It Ever Make Sense?

I've been thinking a lot about MWI and probability lately and I can't say desicion theory is very convincing. Obviously if MWI can't derive at the Born Rule, it is falsified. So what do the proponents and opponents of MWI think about this? Do you feel that MWI will ever make sense with...
41. ### Why MWI cannot explain the Born rule

Here I propose a VERY SIMPLE and intuitive argument that MWI, with its MINIMAL set of assumptions, cannot explain the Born rule. The argument goes: The minimal set of assumptions defining MWI is: 1. Psi is a solution of a linear deterministic equation. 2. Psi represents an objectively real...
42. ### Revisiting the Born Rule: Implications for Cosmology

http://arxiv.org/abs/0903.4888" [Broken]
43. ### Exploring the Origin of the Born Rule in Quantum Experimental Phenomena

With regard to quantum experimental phenomena, might not one think of the movement (light and sound indicators and subsequent recorded data streams) of some piece of macroscopic instrumentation as the results of measurements of the energy of wavelike disturbances within some volume of space...
44. ### Derivation of the Born rule

Hello all, Attached is the draft of a paper entitled, Derivation of the Born rule from outcome counting and a solution to the quantitative problem of the MWI, (MWI = multiple worlds interpretation), which I am considering for submission to Les Annales de la Fondation Louis de Broglie. I would...
45. ### Probability and Wave Amplitude: The Born Rule

In 1926, Born suggested that the square of the wave at any point is proportional to the probability of finding the particle at that point. Born was led to this interpretation by relationship between the intensity of light and the square of its amplitude. Since we can renormalise the function...
46. ### Attempts to make the Born rule emerge explicitly from outcome counting

Attempts to make the Born rule "emerge" explicitly from outcome counting I would like to compare and contrast the various attempts to date to reconstruct the MWI so that it: 1) assumes outcome counting instead of the Born rule, but also 2) makes correct experimental predictions. This is an...
47. ### My paper on the Born rule

Hi, A while ago I discussed here about a paper I wrote, which you can find on the arxiv: quant-ph/0505059 I submitted it to the Royal Society, and I received a notification of rejection, with the following comments from the referees, might be of interest for those who participated in the...