Questions tagged [foundations]
Devoted to the conceptual bases of the fundamental theories of physics, to their philosophical and logical premises.
308 questions
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Are fields and particles physically different entities? [closed]
Can a field in space-time be equivalently thought of as a sea of particles?
In fluid mechanics we usually switch to a field-like picture because of the large number of particles involved and the ...
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What makes Hardy's Paradox different from the Quantum Bomb Tester?
It seems both rely on the idea of interaction-free measurements; is the difference in the nature of what they are "measuring"? I understand that they are made to demonstrate different things,...
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Quantization conditions and uniqueness
In modern physics, classical theories are intuitively understood as approximations of an underlying quantum theory of some kind, I have essentially two questions about this:
Can every classical ...
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What happen with wavefunction immediately after a measurement?
One of the postulates of quantum mechanics, introduced by Dirac, says that immediately after a measurement of an observable $\hat A$ the wavefunction abruptly becomes an eigenfunction of $\hat A$. In ...
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Is analog data truly continuous, or ultimately discrete due to physical limitations?
I've been thinking about the physical nature of analog vs digital data. Analog data is often described as “continuous,” while digital data is “discrete.” However, I'm struggling to understand how true ...
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Physical Significance of Relative Quantities [closed]
One of the tenets of relativity lies in the fact that the form of any physical equation must not depend on a particular choice of a coordinate system
I was wondering if this implies the fact that some ...
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On deriving classical to modern physics using minimal axioms [closed]
I am not a physicist but was curious on the differentiation between classical and modern physics.
I keep hearing the physics before $1905$ was classical and usually classical physics is associated to ...
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What are the conceptual foundations of Lagrangian formulation? [duplicate]
When learning Lagrangian mechanics in a standard mechanics course, it is typically introduced as an alternative formulation of classical mechanics which can be derived from Newtonian mechanics. ...
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Is Quantum Mechanics Self-Consistent?
Quantum mechanics postulates the following (and please correct me if I'm wrong):
Every physical state of a system is uniquely identified with a ray in a Hilbert space $|\Psi\rangle \in \mathcal{H}$ ...
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The concept of speed in relativity [closed]
A point which is sometimes raised by people in the foundations of physics, is how to make sense of the concept of "velocity" in relativity, given that neither space nor time are coordinate-...
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Causality in the context of Quantum Information
It is very well known that in the context of quantum information, the simplest entanglement-generating circuit is the following one:
The state of the two Qbits right before the final measurement will ...
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How to intuitively understand the relation between an quantum mechanical operator and it's corresponding infinitesimal dynamic operator?
In quantum mechanics, we know that the generator of the infinitesimal time translation operator $$U(dt) = e^{-\frac{i}{\hbar}\hat{H}dt}$$ is the Hamiltonian $\hat{H}$.
Similarly, the generator of the ...
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Validity of EPR Argument and Causality
From my understanding, Bell's theorem rests on the EPR argument, where it is argued that either the quantum state does not completely specify a physical system, or the theory is non-local.
Because ...
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Am I right or wrong about Wheeler's mental retrocausality problem involving one remote star and gravitational lensing?
Tell me where I am wrong.
One of Wheeler’s supposed examples of retrocausality speaks of a remote star, a black hole or other gravitation lens in between it and earth, and astronomers on earth who can ...
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Has anyone constructed an explicit hidden-variable theory that reproduces the predictions of quantum mechanics for two separated qubits?
Consider the Hilbert space
$$\mathcal{H} = \mathrm{span}\left( \{ |0\rangle\ |0\rangle, |0\rangle\ |1\rangle, |1\rangle\ |0\rangle, |1\rangle\ |1\rangle \} \right) \cong \mathbb{C}^4$$
of (pure) ...
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Can Bell's formulation in his paper "Bertlmann's socks and the nature of reality" lead to an undecidable problem?
In J.S. Bell, Bertlmann’s socks and the nature of reality, CERN Ref.TH.2926-
CERN (1980) (PDF), consider Ineq.(9):
The probability of being able to pass at $0^\circ $ and not able at $90^\circ $ $\...
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Measure of the failure of Stone-von Neumann theorem
The Stone-von Neumann theorem says that all pairs $\{U(a), V(b)\}$ of strongly-continuous unitary irreducible representations $U: \mathbb{R} \to \mathcal{U}(\mathcal{H})$ that satisfy
$$U(a)V(b) = V(b)...
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Is the uncertainty principle a consequence of classical reference frame?
Consider a quantum particle in a box (everything one dimensional, for simplicity). The box is isolated from everything else. We could not measure simultaneously the particle's position and momentum, ...
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What does it mean when folks say that universe is not "Locally real"?
I've read somewhat about the matter but can't quite picture it. Is this a property that only applies at the quantum level and not the classical level like us?
So far I've seen some rather strange ...
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Creation and annihilation operators in complex projective space
Note 1: The Hilbert space $\mathcal{H}$ of a quantum system cannot possibly be the genuine space of states in quantum mechanics. In particular, $\vec{0} \in \mathcal{H}$, which is not a valid state. ...
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Time non-locality in quantum mechanics [closed]
In non-relativistic quantum mechanics, the spectrum of a particle in a 1D closed box is $E_{n} = \frac{n^{2}\pi^{2}\hbar^{2}}{2mL^{2}}$, in order to get this result one has to consider boundary ...
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What is currently the currently understood relationship between classical and quantum world?
Which of these is understood to be the relationship between classical and quantum mechanics? Or is it a mixture of these, or something else entirely?
The classical world comprises of measurement ...
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Relativity and Page-Wooters (PW) Mechanism
In the Page-Wooters formalism, time is treated as a position observable of a reference clock system, so that states are double-kets $|\Psi\rangle\rangle \in \mathcal{H}_{t} \otimes \mathcal{H}_{S}$ ...
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Why charge can be positive or negative but mass is always positive? [duplicate]
This question may sound silly but think about it.
It is fair to say that nobody knows the nature of either mass or charge. That is, nobody can answer the question what mass or charge is, even though ...
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Is measurement in quantum mechanics a CPT-symmetric process?
As I understand it, physicists believe that all the laws of physics are CPT-symmetric. That is, if you change a particle to an antiparticle, mirror everything, and then reverse time, the laws of ...
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Non-Local Causality - The Piston
A free particle is inside a box of length $L$ with a movable piston at the end. The piston is attached to two plates facing each other and a ball is fired at the first plate.
Now assume that all ...
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What does an ontic hidden variable quantum model achieve?
Is it only to show that maybe, preparations can be depicted in a form other than the density matrix and measurements other than POVMs? Or does it also introduce realism in the sense that all ...
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If a system is found to be in a degenerate energy level, which specific eigenstate is it in and at what probability?
Let's say we measure a system's energy and find that it is in a degenerate energy level. Which specific eigenstate of that eigenenergy should we find it in? My first thought was that, since we did not ...
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Soft question: MWI and localization
According to the many worlds interpretation when an electron passes through a diffraction slit we would approximately have a superposition of states.
For each place where the electron wave and the ...
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What is Configuration Space as described in Bohmian Mechanics?
Are the configuration spaces necessary in Bohmian mechanics simply a mathematical abstraction that is not directly related to any set of dimensions "classically" experienced? Can they be ...
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Interaction-free measurement and energy and momentum transfer
I was reading an article by Lev Vaidman, who helped create the quantum bomb tester thought experiment which inspired much work on quantum interaction-free measurements (IFMs), that was analyzing the ...
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Classical electromagnetism with matter particles and electromagnetic fields
In the seemingly standard treatment of classical electromagnetism (cf. Qmechanic's answer here) we decide to work entirely within the framework of classical field theory. In particular, we define our ...
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Joint measurability in quantum mechanics
Two POVMs $E= \{E_i\}$ and $F= \{F_j\}$ are said to be jointly measurable if there exists a POVM $G= \{G_{ij}\}$ such that $$E_i=\sum_j G_{ij}\quad \text{and}\quad F_j =\sum_i G_{ij}$$
From this ...
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Is the zero vector necessary to do quantum mechanics?
Textbook quantum mechanics describes systems as Hilbert spaces $\mathcal{H}$, states as unit vectors $\psi \in \mathcal{H}$, and observables as operators $O: \mathcal{H} \to \mathcal{H}$. Ultimately, ...
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Why are measurements considered irreversible?
In quantum mechanics, every interaction is described by a unitary Hamiltonian operator. We expect that a measurement is no different from any other interaction, yet in the standard way of treating QM ...
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Is there a resolution to the "Wigner's Friend" paradox?
Suppose that two observers $A$ and $B$ are mutually isolated, observer $A$ measures the state $|0\rangle + |1\rangle$ and concludes that the result is $|0\rangle$.
However, observer $B$ concludes that ...
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Physical interpretation of reducible but indecomposable reps of the Poincaré group?
As I understand it, there are representations (reps) of the Poincaré group that are reducible but still indecomposable (i.e., cannot be expressed as a direct sum of two subreps). This would be ...
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What are the distinct mathematical formalisms of quantum mechanics?
Consider the physical theory called non-relativistic quantum mechanics. What are the distinct mathematical formalisms for this physical theory? That is, different mathematical frameworks for this ...
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What is Decoherence? [duplicate]
What precisely is decoherence? Assume familiarity with the density matrix formalism of quantum mechanics.
I read this related question, but I am looking for a more precise answer than the one given. I ...
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Non-orientable time
Consider the following toy classical physical theory.
Let the theory take place on a fiber bundle $(E, M, \pi, F)$ such that $M$ is a one dimensional manifold interpreted as time. Define an action $S[...
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Can we set up an experiment in which Schrodinger's cat is hidden?
Here is a thought experiment that I would like to turn into reality.
An electron is prepared in a superposition of up and down
The electron passes through a hole into a box that is completely ...
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Is the spontaneous flow of heat to thermal equilibrium an explicit law or is it implicitly assumed in thermodynamics?
This sounds like a really daft question, but I am trying to clarify details on foundations on thermodynamics to myself, which will involve asking really (seemingly) basic things.
When you have two ...
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Is Heisenberg Uncertainty Principle (HUP) actually epistemic and not physical? [closed]
Is HUP just a way the physicists found to correct the unnatural concept and mathematical formalism of dimensionless-point elementary particles? Making these points more fuzzy and therefore giving ...
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How do we arrive at the Bell polytope constructed starting from definition of behaviours?
While reading Valerio Scarani's book ; Bell Nonlocality I came across section 2.4 where the author tries to represent the set $\mathcal{L}$, of all local behaviours as a polytope. The term behavior ...
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Conjugate variable measurement and superluminal signaling
In the hard/soft vs white/black experiment from David Alberts book, used in Allan Adams MIT YouTube vid,
the removal of the barrier enables 100 percent measurement of the conjugate variable but "...
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Axiomatic Treatment of Quantum Probability Theory
Define quantum probability theory to be an axiomatic mathematical theory which appropriately generalizes classical (Kolmogorov) probability theory to provide the precise probabilistic framework ...
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Quality Undergraduate Physics Resources in French [closed]
Context: I am embarking on my journey into physics as a beginner. Four years ago, I completed my Baccalaureate (high school diploma) and subsequently pursued software engineering independently. It's ...
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Path Integrals for entangled states
Is there a way of characterizing entanglement between states in a path integral formalism? If so, does this shed some light on the apparently non-local effects of quantum mechanics?
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On the Measurement Problem
In the orthodox interpretation of quantum mechanics, the following three assumptions are made (please correct me if I am wrong):
Every physical system is completely specified by a state $\lvert\psi\...
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Kraus Decomposition of Orthogonal Projections
More specific, short form of my question:
POVMs assign expectation values of positive operators (summing to identity) to probabilities of events, but not a particular measurement scheme, leading to no ...
