Questions tagged [foundations]
Devoted to the conceptual bases of the fundamental theories of physics, to their philosophical and logical premises.
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Limits to the complexity of a fundamental theory
There are examples in physics in which a simple law results from an immeasurably more complicated set of underlying interactions. Consider Hooke's law, for instance: there is a very simple equation ...
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What is wrong with decoherence? [closed]
One possible explanation of the quantum to classical transition, or in other words of why we don't see macroscopic quantum effects naturally, is environment induced decoherence.
Basically, the system ...
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Self-study for quantum foundations and quantum gravitation
I want to study quantum foundations, and also quantum gravitation.
What is a starting point?
(Although I have a ph.D of physics but I don't have sufficient knowledge about those topics.)
good review ...
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Symmetries of a 1 qubit universe [closed]
I am studying an isolated 1 qubit system trying to find its symmetries. By that I mean see what I can change without changing the physics. But I am having problems understanding what is the physics of ...
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How are Gleason's and Kochen-Specker's theorems related?
If, on the one hand, I were to paraphrase Gleason's theorem, it would loosely state that
if one can assign a truth value $p_k$ to each basis vector $\vec{u}_k$
such that $\sum_k p_k = 1$, then that ...
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Is this strenghthening of Wigner's theorem on quantum symmetries true?
For every nonzero vector $\phi$ in a Hilbert space $\mathcal{H}$, let us denote $[\phi] := \mathbb{C}\phi$ the ray associated to $\phi$.
Let $S$ be the set of rays. For all non-zero $\phi,\psi$, $<[...
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On the correspondence rules between the physical world and mathematical frameworks (quantum mechanics)
At the start of Chapter 2 of his Quantum Mechanics: A modern development, Ballentine gives the framework which sets the stage for the questions I have:
Every physical theory involves some basic ...
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What is the most general mathematical structure for representing a state in QM?
In quantum mechanics textbooks which are a little more careful it is common to see it noted that a (pure) quantum state is not a vector $|\psi\rangle$ but rather a ray in Hilbert space, $c|\psi\rangle$...
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What is needed to base physics on iterated functions? [closed]
Iterated systems are considered candidates for the foundation of physics. Iterated functions have an even stronger claim:
Arnold and Avez (1968)
Let $M$ be a smooth manifold, $\mu$ a measure on $M$ ...
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Is this a Valid Axiomatization for a System of Particles in the formalism of Newtonian Mechanics?
I read an article proposing four axioms for a system of particles in the formalism of Newtonian Mechanics:
Inertial frames of reference
Conservation of Momentuum
Superposition of forces
Instantaneous ...
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What is the proof of Davies theorem: if a map on pure quantum states transforms equivalent ensembles to equivalent ones, then the map is unitary?
In the following paper (Dynamical Reduction Models by Bassi and Ghirardi), at the end of section 5.3, the following claim is made.
Consider a bijective(*) map on pure states (not necessarily unitary ...
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Why does GRW theory choose position as a 'special' basis in which to localize?
GRW theory attempts to solve the measurement problem by positing that 'localization' events, where a particle's position wavefunction becomes localized (effectively, measured), happen at random times ...
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Mackey's notation for "disjoint"
George W. Mackey uses this strange notation for "disjoint" in his book "Mathematical Foundations of Quantum Mechanics":
Or, in its context:
(see here)
What kind of symbol is this?...
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Non-distributivity of quantum logic according to C. Piron
I'm trying to understand this highlighted sentence in Piron's "Foundations of Quantum Physics" on p. 21:
I know that distributivity of a lattice means $a\land (b\lor c)=(a\land b)\lor(a\...
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Epistemic vs. ontological interpretations of QM
There are several posts under [quantum-interpretations] epistemic ontological, but I'm not seeing an answer to my question there (nor from google searches)...
I hadn't thought about it very much, ...
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Using De Broglie matter wave hypothesis for expressing the wave funtion of a macroscopic body
Consider a body formed for $N$ identical particles, that moves freely at constant velocity through a region of space without interacting significantly with anything else. According to De Broglie's ...
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Does string theory shed light on foundations of quantum theory?
It is well known that quantum theory is ridden with foundational problems such as the measurement problem, nonlocality, wavefunction collapse, etc. Moreover, it seems that all those problems continue ...
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To what extent does Hardy recover quantum mechanics?
In his 2001 paper, Hardy claims to recover quantum mechanics from five reasonable axioms. I am a mathematician and honestly admit that I don't understand the paper.
I would like to understand exactly ...
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Looking for proof/derivation for non-zero off-diagonal terms in density matrix as a characterization of interference
Is anyone capable of giving a rigorous derivation of why non-zero off-diagonal terms in the density matrix of a quantum system written in a spesific observable basis characterize the possibility of ...
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Quantum theory over the algebraic closure $\overline{\mathbb{Q}}$ of the rational numbers $\mathbb{Q}$
Consider classical quantum theory described through the København interpretation over the complex numbers.
Is there any need for transcendental numbers at all to describe state vectors ? I think I ...
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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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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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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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