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2
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2answers
163 views

Are the only observables in string theory the S-matrix?

Is the S-matrix the only observable in string theory? What about time varying spacetime backgrounds, or thermal states then?
1
vote
1answer
254 views

Conserved quantum observables from symmetries *with density matrix*

I’ve read Ballentine where he derives the conserved observable operators (momentum, energy, ...) from symmetries of space-time. Can I read up such a derivation in more detail somewhere else or even ...
4
votes
1answer
171 views

The difference between projection operators and field operators in QFT?

Is there a good reference for the distinction between projection operators in QFT, with an eigenvalue spectrum of $\{1,0\}$, representing yes/no measurements, the prototype of which is the Vacuum ...
5
votes
3answers
36 views

Constructing a CP map with some decaying property

Given some observable $\mathcal O \in \mathcal H$ it is simple to construct a CP (completely positive) map $\Phi:\mathcal{H}\mapsto \mathcal{H}$ that conserves this quantity. All one has to observe is ...
5
votes
3answers
362 views

Some questions on observables in QM

1-In QM every observable is described mathematically by a linear Hermitian operator. Does that mean every Hermitian linear operator can represent an observable? 2-What are the criteria to say whether ...
4
votes
1answer
2k views

Compatible Observables

My QM book says that when two observables are compatible, then the order in which we carry out measurements is irrelevant. When you carry out a measurement corresponding to an operator $A$, the ...
6
votes
9answers
1k views

What exactly is the 'observer' in physics and/or quantum mechanics? [duplicate]

Possible Duplicate: nature of an observer For instance, in the double slit experiment, what is exactly defined as an observer? I remember from somewhere, light is also an observer?
2
votes
1answer
612 views

“Completeness” of eigenvectors in a complete, commuting set

This question was originally the one below dashed line. Now after further discussions, it has boiled down to this question: Is the following construction possible? Suppose we have a 3 dimensional ket ...
4
votes
2answers
210 views

Uniqueness of eigenvector representation in a complete set of compatible observables [duplicate]

Possible Duplicate: Uniqueness of eigenvector representation in a complete set of compatible observables Sakurai states that if we have a complete, maximal set of compatible observables, ...
3
votes
2answers
376 views

Uniqueness of eigenvector representation in a complete set of compatible observables

Sakurai states that if we have a complete, maximal set of compatible observables, say $A,B,C...$ Then, an eigenvector represented by $|a,b,c....>$, where $a,b,c...$ are respective eigenvalues, is ...
8
votes
2answers
270 views

Observables with transcendental eigenvalues

Are there any "natural" physical observables which have non-empty point spectrum which consists of numbers which are not algebraic numbers?
16
votes
3answers
1k views

How does non-commutativity lead to uncertainty?

I read that the non-commutativity of the quantum operators leads to the uncertainty principle. What I don't understand is how both things hang together. Is it that when you measure one thing first ...
4
votes
4answers
521 views

Is the wave function objective or subjective?

Here is a question I am curious about. Is the wave function objective or subjective, or is such a question meaningless? Conventionally, subjectivity is as follows: if a quantity is subjective then ...
6
votes
6answers
824 views

What is an observer in quantum mechanics?

My question is not about (pseudo) philosophical debate; it concerns mathematical operations and experimental facts. What is an observer? What are the conditions required to be qualified of observer, ...
8
votes
5answers
9k views

What is the Physical Meaning of Commutation of Two Operators?

I understand the mathematics of commutation relations and anti-commutation relations, but what does it physically mean for an observable (self-adjoint operator) to commute with another observable ...
11
votes
3answers
388 views

Is it possible to define a “it went through two slits” observable?

This concerns the famous two-slit experiment. Electrons or photons or your favorite particle, doesn't matter. As we all know, the attempt to detect which slit the quanta pass through leads to loss ...
14
votes
2answers
2k views

Time as a Hermitian operator in QM?

In non-relativistic QM, on one hand we have the following relations: $$\langle x | P | \psi \rangle ~=~ -i \hbar \frac{\partial}{\partial x} \psi(x),$$ $$\langle p | X | \psi \rangle ~=~ i \hbar ...
4
votes
5answers
562 views

Eigenvalue Postulate and Experiment Outcomes in QM

In Nielsen and Chuang's text on Quantum Information and Computation, the measurement postulate is stated by using a collection of measurement operators and the outcomes are the indices of the ...
3
votes
2answers
367 views

Diff(M) and requirements on GR observables

This question is kind of inspired in this one: Diff(M) as a gauge group and local observables in theories with gravity The conundrum i'm trying to understand is how is derived the (quite) ...