Questions tagged [foundations]
Devoted to the conceptual bases of the fundamental theories of physics, to their philosophical and logical premises.
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Books on the interpretations of Quantum Mechanics [duplicate]
I have a masters in theoretical physics, and throughout my studies I feel like the concept of 'interpretations of quantum mechanics' was never given any attention. All my quantum mechanics courses had ...
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Technical meaning of "no faster-than-light communication"?
I often read sentences like "relativity forbid faster-than-light communication" or "quantum entanglement cannot be used to convey information faster than light", but it seems to me ...
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Trouble understanding the math of the preferred basis problem
I've been trying to understand the preferred-basis problem in QM, specifally in the Everettian intepretation.
To quote an answer to another question which discusses this:
In my opinion, the situation ...
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Is the historically adopted 'bare' model of elementary particles causing the infinities problem and main reason to use re-normalization method?
I'm interested to know if the so called non-physical 'bare' model especially for massive elementary particles, which treats the particles as mathematical dimensionless points without any volume and ...
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Why doesn't Gleason's theorem imply the Born rule?
I know that the question "does Born's rule follow from Gleason's theorem" has already answers on the website: see here, and here. I am not satisfied with the answers given (one cannot rule ...
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Would a closed universe lead to violations of Heisenberg's uncertainty principle?
If the universe were finite it should mean that the position of a particle can't be uncertain beyond the universe's size itself. If that is true, then what stops the momentum from being in a perfectly ...
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On the Bell's Theorem / Bell-type Inequalities and the Kochen-Specker Theorem
It appears to me that the Kochen-Specker theorem, if not Gleason’s theorem already, seals the fate of realism / value definiteness (with possibly the additional assumption of non-contextuality, ...
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Quantifiers in physical theories vs reality
I understand a physical theory as a set of axioms/postulates like an axiomatic system in mathematics. When we use some theory to describe the physical world we assume that the axioms hold. In other ...
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Am I correct in saying "falsifiability is the feature of a scientific theory to be tested"?
Falsifiability is usually defined as "the extent to which a scientific theory can be proven wrong". Does this mean that falsifiability is basically the extent to which a scientific theory is ...
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What happens to linear terms like $\langle \psi| \hat{a}\cdot \vec{\sigma} | \psi \rangle$ in CHSH inequality?
The CHSH inequality is given by (e.g., 4.33 here)
$$\langle E_a E_b\rangle + \langle E_{a^\prime} E_b\rangle + \langle E_a E_{b^\prime}\rangle - \langle E_{a^\prime} E_{b^\prime}\rangle \le 2,$$
where ...
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Why is Norton's dome said to exhibit a non-deterministic behavior?
I have seen quite a few times the assertion "Norton's dome demonstrates non-determinism of ***" (replace *** by "Newtonian mechanics" or something else), cf. e.g. this Phys.SE post....
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Does Grete Hermann's thought experiment concerning the relative nature of QM stand valid?
In the 1930's, Grete Hermann argued of the relative nature of quantum systems. In her words (after translation),
Quantum-mechanical characterization is not, like the classical one,
attributed to the ...
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Does physical prediction depend on the topologies that we put in the space of smooth section of a vector bundle?
In the artice Properties of field functionals and characterization of local functionals, we have
Let $M$ be a manifold and $B \rightarrow M$ be a smooth vector bundle of $\operatorname{rank} r$ over $...
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What kind of phase it is when a photon gain a quantum phase, a dynamical one or a geometrical one?
It's known$^1$ that the phase factor in quantum mechanics can be divided into geometric phase and dynamical phase. Since in quantum optics, light is treated as a quantum object, i.e., the photon. So ...
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"Active quantum fluctuations" due to the quantization of the gravitational field?
This is a follow-up to the question In what sense is the word quantum fluctuation used here?
In arXiv:0710.3787 it is stated on page 7 that there are "active fluctuations in the intrinsic ...
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In what sense is the word "quantum fluctuation" used here?
I found this paper: On the origin of the LIGO "mystery" noise and the high energy particle physics desert, currently only published on arXiv as far as I can tell.
I do not understand any of ...
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Relation between quantum and classical mass gaps
We say a QFT has a mass gap if the spectrum of the mass operator $M:=\sqrt{P_\mu P^\mu}$ is bounded below by some $\Delta >0$.
I will define a $\textit{classical}$ field theory to have a mass gap ...
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Modern interpretation of "Heisenberg's microscope" heuristic [duplicate]
If I understand it correctly, the "Heisenberg's microscope" was a heuristic introduced by Heisenberg in order to explain the eponymous uncertainty principle. The idea would be that, when ...
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A Different Type of a "Measurement" Process?
In my understanding, a measurement process for the measurement of an observable $\hat{A}=\sum_i a_i\vert a_i\rangle\langle a_i\vert$ over a system that lives in $\mathcal{H}_1$ (when unentangled) by a ...
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Can a theory contain postulates of other theories?
I was reading about kinetic theory of gases and its postulates (assumptions). What I can't understand is for example in the derivation of:
$$PV=\frac{2}{3}K$$
It uses the fact that:
$$F =\frac{ΔP}{Δt}$...
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Vector spaces without a basis and observables in quantum theory
In Zermelo-Fraenkel set theory without the Axiom of Choice (AC), there exist models in which not all vector spaces have a basis.
Suppose $V$ is a Hilbert space (over the complex numbers), and assume ...
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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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First order logic of complex quantum theory
Suppose we describe quantum theory through the København interpretation, that is, through unitary linear algebra of complex Hilbert spaces.
Can quantum theory in this description (the part that ...
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Reference Request: Mathematical Foundations of Physics
I am looking for reading on examples, or preferably a comprehensive summary on how the foundations of mathematics are related to physical theory. I would like to know whether basic set-theoretic and ...
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Is there a foundation of mathematical logic? [duplicate]
As Mathematics has its foundations in logic and set theory in the sense that you can derive all of mathematics from such theories, does mathematical physics have such foundations? A theory or theories ...
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Is incompatibility required for contextuality?
A preprint just came out claiming that incompatibilty is not requried to demonstrate generalized contextuality. My question isn't about generalized contextuality---which I don't quite understand---but ...
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Understand Heisenberg's uncertainty principle in a statistical way?
In the proof of Heisenberg's uncertainty principle (HUP), it doesn't constrict the observables in only one object(one particle for example). So if I can have two particles have the same observable, ...
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Are objective collapse theories (GRW) noncontextual?
The contradiction of the Kochen Specker Theorem can be traced back to either one (or both) of two assumptions: outcome determinism and measurement noncontextuality (see e.g. Leifer, Appendix C, Def. C....
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Active vs passive transformation in parity violation
I am no familiar with electroweak force so I will pose this scenario.
Suppose we have a positive charge at rest and an electric field pointing to the right than the particle would accelerate ...
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Why are commutators the first choice in describing observables that cannot be measured simultaneously?
In quantum mechanics, we convert Poisson brackets to commutators for the observables to account for the uncertainty principle. However, I do not understand why do we do this.
What motivates us to ...
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Are violations of realism the same thing as contextuality?
I am basically looking for a counter-example where we'd get contextuality but not violations of realism (and vice-versa). If no such counter-examples exist, then it seems to me that they're really one ...
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Why is time different between different inertial observers? [duplicate]
Suppose we have observer $A$ and observer $B$ that meet at a point $p$ when both of their clocks are zero. Why after that, the measure of their clocks would be different, since clocks depend on ...
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Is the set of spacetime manifold a set of event?
In general relativity spacetime is defined as manifold.
Is this manifold the set of events? For example if our universe is constituted of only one non-interacting particle, should our manifold be a ...
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Why isn't the variance of a quantum observable depend on how gently or roughly the measurement is carried out?
Consider an ensemble specified by a state $|\psi\rangle$ on which we decide to make measurements of an observable $A$. If the state $|\psi\rangle$ is not an eigenstate of $A$, there will be a scatter ...
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Does Kochen-Specker's theorem follow trivially from Gleason's one?
In Kochen-Specker's theorem, as presented e.g. in (Rajan 2017) or (Breuer 2002), we consider maps $\nu:\mathrm{Herm}(\mathcal H)\to\mathbb R$ that are algebra homomorphisms on compatible observables, ...
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Why must the gauge potential create negative norm states?
This question concerns the quantisation of the EM gauge potential $A_\mu$. When the Gupta-Bleuler formalism is introduced, it is usually stated that the creation/annihilation operators satisfy $\...
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Does this argument prove that all fermionic states have zero norm?
The following argument seems to show that all states created by a fermionic field have zero norm. This would surely cause problems in QFT, so I believe there must be an error somewhere, but I can't ...
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How can quantum mechanics describe the classical world when itself is a derivation out of ideas from the classical world of physics? [closed]
It dawned on me while revising the basics of quantum mechanics (the Schroedinger equation, de Broglie's matter waves, the quantum postulates etc. - essentially the basic first year undergrad schedule)....
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In the Kochen-Specker theorem, where does the assumption $v(-n)=v(n)$ come from?
I'm trying to get a better understanding of the Kochen-Specker theorem, reading the presentation in arXiv:1708.01380.
In section (2) of the above paper, the authors introduce the two KS assumptions as:...
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How does quantum contextuality relate to realism?
According to Spekkens contextuality can be defined as follows:
Suppose A, B and C are Hermitian operators such that A and B commute,
A and C commute, but B and C do not commute. Then the assumption ...
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Are self-consistency arguments logical/rigorous? An example with Pauli paramagnetism
I am never yet satisfied by arguments in physics that go along the lines of 'assume A is true', 'one way of making A true is for B to happen', 'we check that if B happens then A is indeed true ...
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Current texts on the foundation of quantum mechanics?
So I'm currently writing an article regarding a priori axiomatic systems and the nature of inference (I'm not a physicist but a philosopher doing philosophy of science), one of my main texts is "...
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Yet another question about Schrödinger's cat
I had always believed that the point of the (in)famous Schrödinger's cat thought experiment was pretty obvious: people, back then, were puzzled with the state space being (basically) a vector space. ...
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What would be a basic example of an axiomatic physical theory? (except Newton's Principia or Einstein's Special Relativity Theory) [closed]
If I were asked to give an example of an axiomatic mathematical theory, I'd be able to answer: set theory, probability theory, maybe group theory (assuming the elements of the definition of a group ...
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How does relaxing counterfactual definiteness allows for CHSH inequality violation?
Scenario, I want to play a game with a group of students as a teacher, I ask two teachers to help.
The students are from the central classroom, going to room A and room B where the teachers there asks ...
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Finding the expectation value of a mixed function of both momenta and coordinates
I'm reading Merzbacher's Quantum mechanics. In Chapter 3, section 2, he tackles this question. For a function solely of coordinates, say $f(\mathbf r)$, he says that the expectation value is given by
$...
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Why spacetime translations don't affect the physics of de Broglie plane waves?
I'm studying Merzbacher's Quantum Mechanics. In Chapter 2 Section 1, he "derives" the expression $\psi(x, t)=Ae^{i(kx-\omega t)}$ for the de Broglie plane waves for free particles. Basically ...
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Conway's and Kochen's SPIN axiom seems unphysical
In their "Free will theorem", Conway's and Kochen's states the "SPIN axiom":
"A triple experiment for the frame (x, y, z) always yields
the outcomes 1, 0, 1 in some order.&...
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Is there a mathematical model of the process of "getting entangled with"?
[Warning: I'm not a physicist]
Let $A$ and $B$ be microscopic systems, with corresponding Hilbert spaces of state vectors given by $H_A$ and $H_B$ respectively.
Let's say $A$ is in a state $\psi\in ...
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Physical states are primary and space-time is secondary
This is pure speculation. The title of the question is a quote from Zeidler's book on QFT p.141:
In the setting of noncommutative geometry, physical states are primary and space-time is secondary.
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