73
votes
Why is it impossible to measure position and momentum at the same time with arbitrary precision?
When someone asks "Is it really impossible to simultaneously measure position and momentum with arbitrary precision in quantum theory?", the best preliminary answer one can give is another ...
- 3,833
42
votes
Accepted
The importance of the phase in quantum mechanics
When people say that the phase doesn't matter, they mean the overall, "global" phase. In other words, the state $|0 \rangle$ is equivalent to $e^{i \theta} |0 \rangle$, the state $|1\rangle$ is ...
- 105k
36
votes
Am I in a superposition?
This is a deceptively simple question, and I would like to answer it in the context of Condensed Matter Theory. We will start with the question: why do objects in our everyday life appear to be ...
- 1,253
36
votes
Accepted
Is my interpretation of the underlying idea behind this 2022 Nobel Prize story “How physicists proved the universe isn’t real” more or less accurate?
First, it's important to clarify two definitions.
The principle of locality loosely says that interactions occur at individual points in space. If you say that one charged particle at a point $\...
- 71.4k
31
votes
Accepted
Why do eigenvalues correspond to observable quantities?
Suppose we don't know quantum mechanics yet and we want to calculate the expecatation value of an observable $A$. Could be momentum, spin whatever. It is given by
$$\mathbb E(A)=\sum_i a_i\,p(a_i)$$
...
31
votes
Why are there no clear experiments describing the exact boundary between classical and quantum sizes?
Why are there no clear experiments describing the exact boundary between classical and quantum sizes ?
There are no clear experiments because there is no exact boundary.
Although we think of quantum ...
- 60.4k
27
votes
Accepted
Why are quantum effects of the apparatus ignored in quantum experiments?
And in all the experiments all these in-between steps are considered to be "magically perfect". Nobody pays them any more attention except to mention that they're there. All mirrors reflect ...
- 648
23
votes
Accepted
Why are wavefunction collapses instantaneous?
It’s important to remember that quantum mechanics is a tool that we use to describe the world — it is not the same as the world. For all that we love to talk about wavefunctions, it’s not clear at ...
rob♦
- 94.2k
22
votes
Accepted
Why are expectation values of an observable important in QM?
This is an important point which should be discussed.
What one obtains from experiments are frequencies of outcomes of given measured observables on an ensemble of identical quantum systems all ...
- 78.1k
21
votes
Accepted
Why do we use Eigenvalues to represent Observed Values in Quantum Mechanics?
One of the postulates of quantum mechanics is that for every observable A, there corresponds a linear Hermitian operator A^, and when we measure the observable A, we get an eigenvalue of A^ as the ...
- 71.4k
20
votes
Are observables in QFT actually observable?
A quantum mechanical secret kept very well in plain sight is that the word "observable" when defined as "self-adjoint operator on a Hilbert space" does not actually mean "you ...
- 129k
20
votes
Accepted
Does the collapse of the wave function depend on the observer?
The measurement problem is one of the most relevant open problems of quantum mechanics. What is a measurement? What constitutes an observer and what doesn't? Is the wavefunction a physical object (...
- 2,929
20
votes
Accepted
Are two states with the same measurement probabilities necessarily equal up to unitary equivalence?
Let $H$ denote a finite-dimensional complex Hilbert space, $\rho$ and $\rho^\prime$ be two density matrices, i.e. positive semi-definite operators with unit trace and $A$ an arbitrary hermitian ...
- 8,442
19
votes
Do we or do we not observe (measure) superpositions all the time?
To answer the question, you have to specify what observable’s eigenstates the “superpositions” you’re talking about are superpositions of.
If you measure the energy, you always get one single energy ...
- 52.2k
18
votes
Accepted
Why is it impossible to measure position and momentum at the same time with arbitrary precision?
You can't measure precise values at the same time because precise values for both don't exist at the same time.
All the properties of, say, an electron and be inferred from the electron's wave ...
- 45.7k
17
votes
Accepted
Confusion about the description of the uncertainty principle
The first one is correct, the second is not.
The second definition1 is actually describing the observer effect. Explanations written by non-experts often mix the two up. But one key difference is ...
- 77.3k
17
votes
Accepted
What is the Hamiltonian of a Measurement?
The following argument is very vague and hand-wavey - as is inevitable when discussing measurement apparatus with on the order of $10^{23}$ particles. It is intended only to illustrate the idea. We ...
- 186
16
votes
The importance of the phase in quantum mechanics
The global phase does not matter. In your example
$\lambda(\vert\psi_1\rangle+\vert\psi_2\rangle)$ has the same physical contents as $\vert\psi_1\rangle+\vert\psi_2\rangle$ but this will be in ...
- 47.8k
15
votes
Accepted
Can the collapse of the wave function be modelled as a quantum system on its own?
To model the act of measurement itself as an interaction of the measurement apparatus and the measured system as quantum systems is a perfectly standard thing to do, though you might get disagreements ...
- 129k
14
votes
Proof that you can't disentangle two parties if you only operate on one
If there was some unitary operator factorized as $\mathbb I_A \otimes U_B$ that would send the entangled state $|\psi\rangle$ to a factorized state $|\phi_A\rangle\otimes |\phi_B\rangle$, ie :
$$|\...
- 6,119
13
votes
Accepted
Are there any theoretical reasons why we cannot measure the position of a particle with zero error?
Continuous variables can't be measured with zero error in principle, already due to them being real numbers, nothing to do with quantum theory. It would take infinite number of digits to write down ...
- 41.2k
12
votes
Why do eigenvalues correspond to observable quantities?
I think the conceptual issue is that you've got it backwards. Given any set of eigenfunctions, you can have operators with those eigenfunctions, whose corresponding eigenvalues are anything you want. ...
- 105k
12
votes
How is it that a particle's wave function is not a real thing, yet we can still observe it?
Plenty of things in physics are mathematical objects/models that we use to describe the world around us and can also use to guide our measurements and observations. For example, when you are walking ...
- 58.5k
11
votes
A question regarding the commutators of operators
I think that the misunderstanding follows from the following fact. Given that $[A,B]=0$ then we can build a simultaneous eigenbasis for $A$ and $B$, call it $\mathcal{B}_1$.
On the other hand we have ...
- 4,130
11
votes
Are observables in QFT actually observable?
As emphasized in the excellent answer by ACuriousMind, some of the operators that we usually call "observables" might not be feasibly measurable through any physical process that the theory ...
- 55k
11
votes
Am I in a superposition?
TL;DR Your position is not well-defined... but for more mundane reasons.
Quantum mechanical view
You are not in a pure state - that is you are not an object, that can be described by a wave function, ...
- 65k
11
votes
Accepted
Which experiments confirm that the Born rule is $|\psi|^2$ rather than $|\psi|$?
I might be missing the depth somewhere, but I would suggest the electron double-slit experiment first: $|\sin(kx)|$ clearly looks different as compared to $\sin^2(kx)$.
The second example is the Malus'...
- 4,193
11
votes
Accepted
What is the physical significance of projectors vs. Pauli matrices in spin measurements?
The projection operator $|u\rangle\langle u|$ corresponds to the experimental question "Does the spin point in the positive $z$-direction - yes or no?" The outcome "yes" ...
- 7,298
10
votes
Why do we use Eigenvalues to represent Observed Values in Quantum Mechanics?
The Stern-Gerlach experiment and similar experiments show
A system has a state.
The states of a system form a Hilbert space. You can choose a set of basis states and represent the system's current ...
- 45.7k
10
votes
Am I in a superposition?
The question 'where am I', taken at a microscopic level, is hardly meaningful.
A human body, as a physical system, is overwhelmingly complex. It certainly cannot be described as a quantum system in ...
- 3,811
Only top scored, non community-wiki answers of a minimum length are eligible