# Questions tagged [observables]

A quantum observable is a measurable operator whose corresponding property of the state can be determined by some sequence of physical operations ("observation"), such as submitting the system to various electromagnetic fields and eventually reading a value. In systems governed by classical mechanics, any experimentally observable value can be shown to be given by a real-valued function on the set of all possible system states.

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### Is there a physical significance to non-normal states of the algebra of observables?

Quantum theory may be formalized in several different ways. Generally, the physical discussion of different states of a quantum system distinguishes pure and mixed states, and then subsumes both in a ...
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### The sum of two observables: Can its interpretation depend on more than just those two observables?

In the context of quantum theory, suppose we have two models $M_1$ and $M_2$ formulated on the same Hilbert space. Suppose that the operator $A$ is an observable in both models, with the "same" ...
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### Measurement formalisms - POVM formalism vs Hermitian observables

I am thinking in following way of thinking about measurements in quantum mechanics. Please correct any false statements I may be making below. We start with POVMs. Let our POVM be a set of positive ...
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### Measuring the Dirac field

If the Dirac field $\psi(x)$ is to the electron as the Electromagnetic field is to the photon, why is it that we can measure the Electromagnetic field, whereas the Dirac field we cannot?
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### Observables and local observations in quantum field theory

I have recently taken a quantum field theory course at my university but it focused heavily on the mathematics of the theory and not the physics. So I am left with a few questions on observables and ...
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### What is the set of observables of a quantum system?

This is a question I am wondering about because the answer to it seems to have some interesting - but perhaps already long considered and dismissed because it's been settled - implications for the ...
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### Breakdown of quantum mechanical observables in cosmology

In several different contexts, I've heard the claim that quantum gravity in an accelerating universe messes with our ability to define precise quantum observables.* One version of the argument goes ...
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### Does spin entanglement imply position entanglement?

My question is whether two electrons can be entangled only with respect to their spins but not with respect to some other observable, such as position. I initially believed that spin-entanglement ...
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### Derivation of the Heisenberg EOM in the most general case

I'm currently reading chapter 2.2 of Sakurai where the Heisenberg picture is detailed. However, in the text Sakurai doesn't treat the most general case of a time-dependent hamiltonian $\mathcal{H}(t)$,...
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### Confusion regarding the interpretation of simultaneity in the uncertainty principle

After studying the derivation of the generalised uncertainty principle, what I understand is: Suppose we have two operators associated with observables $\hat{A}$ and $\hat{B}$. If I prepare a large ...
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### Can local supersymmetry be characterized entirely in terms of observables?

Global symmetries can be defined through their effect on observables. In contrast, quantum theories are often constructed with the help of symmetries that leave observables invariant, like the ...
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### What quantities in Schwarzchild spacetime correspond to those we measure?

There are many classical tests of general relativity such as gravitational red shift, motion of particles, etc. In those calculations, we compare the result under general relativity with that under ...
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### Does the Kalman filter incorporate a Heisenberg-like uncertainty principle?

In the case of mechanical systems, applying the Kalman filter involves combining model based prediction (using an apriori known dynamical model) with real-world noisy observations of the positions and ...
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### Measuring momentum

I'm new here, possibly my apologies for misplacing. After a measurement in quantum mechanics, the wavefunction collapses to an eigenstate corresponding to the outcome of the measurement. Thus if we ...
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### Was the notion of observable really necessary before quantum physics?

I'm a mathematician who's been struggling with the search of connections between physics theories and $C^*$-algebras. The most known connection I found was that the observables in quantum mechanics ...
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### Observables of Dirac equation

So I learned about the Dirac equation which describes a relativistic free particle with spin $\frac{1}{2}$. I get the mathematics but what i can't find nowhere: What are the observables of this ...
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### Maximally uncorrelated observables as a consequence of unbiasedness relation

In the case of a fully correlated scenario of $A$ and $B$, which are descirbed in mutually unbiased bases, why do the other observables have to be maximally uncorrelated. How does this follow from the ...
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### What significance do field-operators have, if they don't correspond to observables because of non-hermicity?

Since field-operators are not always hermitian (for example in case of a complex scalar field, or the dirac-field), they don't (in the quantum-mechanical sense) correspond to observables. Does that ...
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### How to define an Operator Product Expansion (OPE) on arbitrary Riemann surface for a CFT?

Whenever we define the OPE of a 2D CFT, we do so (at least in the literature that I have come across) on the complex plane. Similarly, the commutation relations between conformal generators $L_n$ and ...
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### Quantum Observation

Bear with me if I present a lack of knowledge - QM is not my field. There's a common notion in QM that until a particle is observed (measured), its properties are not definite, but rather are spread ...
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### What does "contextuality" mean in the context of partial rather than complete quantum measurements?

The Kochen-Specker theorem is often described as ruling out "noncontextual" classical hidden variable theories. I understand the math behind the theorem, but I'm a little unclear on the exact, ...
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### What happens when one "observes' a quantum field, and how do particles get involved?

I've recently begun my journey to understand QFT. I apologize in advance for the length of the post, but there are gaps in my understanding of how I, as an experiementalist, interact with fields to ...
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### Is really hermiticity necessary to be a physical observable? What about larger class of operators like PT invariant operators or pseudo hermitian one?

It's really necessary for an observable represented by an operator acting in a Hilbert space to be hermitian? It's known that not only hermitian operators have real eigenvalues and that also normal ...
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