Quantum mechanics describes the microscopic properties of nature in a regime where classical mechanics no longer applies. It explains phenomena such as the wave-particle duality, quantization of energy and the uncertainty principle and is generally used in single body systems. Use the ...
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Is Angular Momentum truly fundamental?
This may seem like a slightly trite question, but it is one that has long intrigued me.
Since I formally learned classical (Newtonian) mechanics, it has often struck me that angular momentum (and ...
36
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7answers
5k views
Why do people categorically dismiss some simple quantum models?
Deterministic models. Clarification of the question:
The problem with these blogs is that people are inclined to start yelling at each other (I admit, I got infected and it's difficult not to raise ...
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16answers
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Quantum mechanics and everyday nature
Is there a phenomenon visible to the naked eye that requires quantum mechanics to be satisfactorily explained? I am looking for a sort of quantic Newtonian apple.
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2answers
220 views
Physical interpretation of different selfadjoint extensions
Given a symmetric (densely defined) operator in a Hilbert space, there might be quite a lot of selfadjoint extensions to it. This might be the case for a Schrödinger operator with a "bad" potential. ...
30
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3answers
333 views
What is the use of a Universal-NOT gate?
The universal-NOT gate in quantum computing is an operation which maps every point on the Bloch sphere to its antipodal point (see Buzek et al, Phys. Rev. A 60, R2626–R2629). In general, a single ...
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7answers
2k views
Quantum Entanglement - What's the big deal?
Bearing in mind I am a layman - with no background in physics - please could someone explain what the "big deal" is with quantum entanglement?
I used to think I understood it - that 2 particles, say ...
27
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5answers
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Path integral vs. measure on infinite dimensional space
Coming from a mathematical background, I'm trying to get a handle on the path integral formulation of quantum mechanics.
According to Feynman, if you want to figure out the probability amplitude for ...
26
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8answers
4k views
Why quantum entanglement is considered to be active link between particles?
From everything I've read about quantum mechanics and quantum entanglement phenomena it's unobvious for me, why quantum entanglement is considered to be active link. I.e. it's stated every time that ...
26
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4answers
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Trace of a commutator is zero - but what about the commutator of $x$ and $p$?
Operators can be cyclically interchanged inside a trace:
$${\rm Tr} (AB)~=~{\rm Tr} (BA).$$
This means the trace of a commutator of any two operators is zero:
$${\rm Tr} ([A,B])~=~0.$$
But what about ...
26
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4answers
2k views
What is spin as it relates to subatomic particles?
I often hear about subatomic particles having a property called "spin" but also that it doesn't actually relate to spinning about an axis like you would think. Which particles have spin? What does ...
26
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0answers
452 views
Experimental test of the non-statisticality theorem?
Context: The recent paper The quantum state cannot be interpreted statistically by Pusey, Barrett and Rudolph shows under suitable assumptions that the quantum state cannot be interpreted as a ...
23
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7answers
908 views
Are these two quantum systems distinguishable?
Suppose Stanford Research Systems starts selling a two-level atom factory. Your grad student pushes a button, and bang, he gets a two level atom. Half the time the atom is produced in the ground ...
23
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5answers
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A list of inconveniences between quantum mechanics and relativity?
It is well known that quantum mechanics and (special and/or general) relativity do not fit well. I am wondering whether it is possible to make a list of contradictions or problems between them?
E.g. ...
23
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11answers
885 views
Negative probabilities in quantum physics
Negative probabilities are naturally found in the Wigner function (both the original one and its discrete variants), the Klein paradox (where it is an artifact of using a one-particle theory) and the ...
22
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10answers
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Discreteness and Determinism in Superstrings?
So Gerard 't Hooft has a brand new paper (thanks to Mitchell Porter for making me aware of it) so this is somewhat of a expansion to the question I posed on this site a month or so ago regarding 't ...
21
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5answers
2k views
Hamilton's Principle
Hamilton's principle states that a dynamic system always follows a path such that its action integral is stationary (that is, maximum or minimum).
Why should the action integral be stationary? On ...
21
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4answers
2k views
What is the usefulness of the Wigner-Eckart theorem?
I am doing some self-study in between undergrad and grad school and I came across the beastly Wigner-Eckart theorem in Sakurai's Modern Quantum Mechanics. I was wondering if someone could tell me why ...
20
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5answers
85 views
Which symmetric pure qudit states can be reached within local operations?
There are two pure symmetric states $|\psi\rangle$ and $|\phi\rangle$ of $n$ qudits. Is there any known set of invariants $\{I_i:i\in\{1,\ldots,k\}\}$ which is equal for both states iff ...
20
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4answers
764 views
In quantum mechanics, given certain energy spectrum can one generate the corresponding potential?
A typical problem in quantum mechanics is to calculate the spectrum that corresponds to a given potential.
Is there a one to one correspondence between the potential and its spectrum?
If the ...
20
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6answers
3k views
Why don't electrons crash into the nuclei they “orbit”?
I'm having trouble understanding the simple "planetary" model of the atom that I'm being taught in my basic chemistry course.
In particular,
I can't see how a negatively charged electron can stay ...
19
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4answers
1k views
Is Stephen Wolfram's NKS, an attempt to explain the universe with cellular automata, in conflict with Bell's Theorem?
Stephen Wolfram's A New Kind of Science (NKS) hit the bookstores in 2002 with maximum hype.
His thesis is that the laws of physics can be generated by various cellular automata--simple programs ...
19
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10answers
892 views
What is the difference between a measurement and any other interaction in quantum mechanics?
We've learned that the wave function of a particle collapses when we measure a particle's location. If it is found, it becomes more probable to find it a again in the same area, and if not the ...
19
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2answers
46 views
Bell polytopes with nontrivial symmetries
Take $N$ parties, each of which receives an input $s_i \in {1, \dots, m_i}$ and produces an output $r_i \in {1, \dots, v_i}$, possibly in a nondeterministic manner. We are interested in joint ...
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5answers
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Does Heisenberg's uncertainty under time evolution always grow?
Recently there have been some interesting questions on standard QM and especially on uncertainty principle and I enjoyed reviewing these basic concepts. And I came to realize I have an interesting ...
18
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3answers
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Why are von Neumann Algebras important in quantum physics?
At the moment I am studying operator algebras from a mathematical point of view. Up to now I have read and heard of many remarks and side notes that von Neumann algebras ($W^*$ algebras) are important ...
18
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2answers
970 views
Rigorous justification for rotating wave approximation
Whenever I have encountered the rotating wave approximation, I have seen "the terms that we are neglecting correspond to rapid oscillations in the interaction Hamiltonian, so they will average to 0 in ...
18
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1answer
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In 't Hooft beable models, do measurements keep states classical?
This is a questions on 't Hooft's beable models (see here: Discreteness and Determinism in Superstrings?) for quantum mechanics, and the goal is to understand to what extent these succeed in ...
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10answers
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What is spontaneous symmetry breaking in QUANTUM systems?
Most descriptions of spontaneous symmetry breaking, even for spontaneous symmetry breaking in quantum systems, actually only give a classical picture.
According to the classical picture, spontaneous ...
17
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7answers
651 views
Is there a symmetry associated to the conservation of information?
Conservation of information seems to be a deep physical principle.
For instance, Unitarity is a key concept in Quantum Mechanics and Quantum Field Theory.
We may wonder if there is an underlying ...
16
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9answers
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About the complex nature of the wave function?
1.
Why is the wave function complex? I've collected some layman explanations but they are incomplete and unsatisfactory. However in the book by Merzbacher in the initial few pages he provides an ...
16
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3answers
159 views
Quantum computing and quantum control
In 2009, Bernard Chazelle published a famous algorithms paper, "Natural Algorithms," in which he applied computational complexity techniques to a control theory model of bird flocking. Control theory ...
16
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7answers
2k views
Is mass quantized?
I learned today in class that photons and light are quantized. I also remember that electric charge is quantized as well. I was thinking about these implications, and I was wondering if mass was ...
16
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5answers
478 views
Is it really a particle?
Forgive the stupid question but when colliding particles together, how does one know that a particle is actually a new form of sub-atomic matter and not simply just some shattered fragment of the ...
16
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4answers
538 views
Particles for all forces: how do they know where to go, and what to avoid?
Here's an intuitive problem which I can't get around, can someone please explain it?
Consider a proton P and an electron E moving through the electromagnetic field (or other particles for other ...
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5answers
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Does a photon interfere only with itself?
I sometimes hear statements like that:
Quantum-mechanically, interference pattern occurs due to quantum interference of wavefunction of a photon. Wavefunction of a single photon only interferes ...
16
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1answer
146 views
What proof techniques have failed for solving the SIC-POVM problem and what new insights have been gleaned from them?
The SIC-POVM problem is remarkably easy to state given that it has not yet been solved. It goes like this. With dim($\mathcal H$) $=d$, find states $|\psi_k\rangle\in\mathcal H$, $k=1,\ldots,d^2$ ...
16
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4answers
305 views
Is every quantum measurement reducible to measurements of position and time?
I am currently studying Path Integrals and was unable to resolve the following problem. In the famous book Quantum Mechanics and Path Integrals, written by Feynman and Hibbs, it says (at the beginning ...
16
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3answers
540 views
Is there a thought experiment which brings to light the contradiction between General Relativity and Quantum Mechanics?
I've been told that GR and QM are not compatible, is there an intuitive reason/thought experiment which demonstrates the issue? (Or one of the issues?)
16
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0answers
279 views
What is the current state of research into $v$-representability?
In their proof, Hohenberg and Kohn (Phys Rev 136 (1964) B864) established that the ground state density, $\rho_\text{gs}$, uniquely determines the Hamiltonian. This had the effect of establishing an ...
15
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10answers
878 views
Why can't the outcome of a QM measurement be calculated a-priori?
Quantum Mechanics is very successful in determining the overall statistical distribution of many measurements of the same process.
On the other hand, it is completely clueless in determining the ...
15
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3answers
118 views
Information Retrieval
This question is motivated by the issue of information retrieval from black holes, but it is essentially a question about quantum information.
It is widely believed (in certain circles) that the ...
15
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7answers
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Is the wave-particle duality a real duality?
I often hear about the wave-particle duality, and how particles exhibit properties of both particles and waves. I most recently heard this in this video. However, I wonder; is this actually a duality? ...
15
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3answers
72 views
Is there a Majorana-like representation for singlet states?
I mean the Majorana representation of symmetric states, i.e., states of $n$ qubits invariant under a permutation of the qudits. See, for example, D. Markham, "Entanglement and symmetry in permutation ...
15
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7answers
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Does Quantum Mechanics assume space and time are continuous?
I was confused when I was listening to a Quantum Mechanics lecture online. Are space and time assumed to be continuous or discrete in Quantum Mechanics?
I can see the question is vague, but this is ...
15
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11answers
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Why quantum mechanics?
Imagine you're teaching a first course on quantum mechanics in which your students are well-versed in classical mechanics, but have never seen any quantum before. How would you motivate the subject ...
15
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5answers
673 views
Is there a difference between observing a particle and hitting it with another particle?
First, let me state that I'm a lot less experienced with physics than most people here. Quantum mechanics was as far as I got and that was about 9 years ago, with no use in the meantime.
A lot of ...
15
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2answers
127 views
Relevance of SIC-POVMs to quantum information
What is the real relevance of SIC-POVMs (symmetric informationally complete POVMs) to concrete tasks in quantum information theory? A lot of work has been put into giving explicit constructions, and ...
14
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5answers
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The transactional interpretation of quantum mechanics
John Cramer’s transactional interpretation of quantum mechanics (TIQM) is billed as resolving the fuzzy agnosticism of the Copenhagen interpretation while avoiding the alleged ontological excesses of ...
14
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3answers
844 views
Amplitude of an electromagnetic wave containing a single photon
Given a light pulse in vacuum containing a single photon with an energy $E=h\nu$, what is the peak value of the electric / magnetic field?
14
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4answers
59 views
Why can't noncontextual ontological theories have stronger correlations than commutative theories?
EDIT: I found both answers to my question to be unsatisfactory. But I think this is because the question itself is unsatisfactory, so I reworded it in order to allow a good answer.
One take on ...
