Questions tagged [foundations]
Devoted to the conceptual bases of the fundamental theories of physics, to their philosophical and logical premises.
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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 ...
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On the notion of Local Causality
In 1976, John Bell proved that any locally causal theory can't account for certain observed correlations, he formulated the local causality hypotesis in terms of "local beables".
In ...
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On the Double-Slit Experiment
In the double slit experiment, a source of particles is pointed towards a wall with two thin slits, the state of the particle before a dot appears on the screen is represented by a linear ...
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Significance of Pusey-Barrett-Rudolph (PBR) Theorem
I recently read the PBR Theorem and from what I understand it addresses one of the old problems regarding quantum state completeness, one for which there are three possibilities (correct me if am ...
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Relation between Locality and Determinism
In a previous question I asked, I was confused about how can you refuse determinism/realism in Bell's theorem without also refusing relativistic locality. I would like to understand where my following ...
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Why is $\lambda$-sufficiency necessary for No-Go Theorems?
In a talk given by Spekkens (Why I Am Not a Psi-ontologist) at 4:00 he talks about an assumption called $\lambda$-sufficiency which is part of any no-go theorem of quantum mechanics. It is described ...
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How would the Pusey-Barrett-Rudolph (PBR) theorem work in an $\psi$-ontic model?
In the PBR-Theorem they try to prove that $\psi$-epistemic models of quantum theory are impossible. The argument goes something like this:
Suppose we have two nonorthogonal states
\begin{equation}|\...
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Confusion around Bell's Theorem and Locality
I recently got interested in foundational aspects of quantum mechanics and I have some questions:
Bell's theorem proves that any local, deterministic theory with statistical independence can't account ...
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If we accelerate experimental apparatus and the object to be measured at the same acceleration, do we obtain the same measurement as we do in rest?
It is a fact of nature that measurement it is the same in all inertial frames.
But if we accelerate experimental apparatus and the object to be measured at the same acceleration, do we obtain the same ...
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How can the Copenhagen and Everett interpretations of quantum mechanics make the same predictions?
Suppose we have a spin $\frac{1}{2}$ particle in the spin-up state along the $z$-axis, $\lvert \uparrow \rangle$, and after $t$ seconds of evolution under the Schrodinger equation it is in state $\...
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Since simultaneity (or not) of A's flashing and of B's flashing is to be judged by the middle between A and B, should all others adopt this judgement? [closed]
In Einstein's thought experimental description illustrating the definition of (how to measure) "simultaneity" (1917), we're given to consider two "places, A and B, of the rails of our ...
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Train-and-Track thought experiment in Taylor & Wheeler: A plain initial difficulty
The book Spacetime Physics by E. F. Taylor and J. A. Wheeler belongs to the recommended sources on the topic of the special theory of relativity. (Also, meanwhile, some of its editions are readily ...
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In Einstein's thought experiment does each one event consist of one part taking place on the embankment and a distinct part taking place on the train? [closed]
In Einstein's original thought experiment involving "a (very long) train running along a [straight] railway embankment", of essential importance appears the prescription that
"[E]very ...
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Can not-conformally-flat spacetimes be partitioned into timelike worldlines where any two of them are subsets of at least one common photon 2-surface?
In flat spacetime it is straightforward to find and describe various sets of timelike worldlines such that
the worldlines belonging to any one such set $\mathcal P$ partition the spacetime,
any two ...
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Partitioning flat spacetime into timelike geodesics, where any two define a photon plane, are they a shear-, expansion- and vorticity-free congruence?
3+1 dimensional flat spacetime, as a set of events (with certain geometric properties), can be partitioned in various ways into (necessarily non-intersecting) timelike geodesic worldlines.
Some, but ...
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In a flat spacetime region, is any timelike worldline segment guaranteed geodesic if it belongs to at least three distinct photon 2-surfaces?
Photon surfaces have been recognized as intuitive and significant concept in the description of spacetimes.
All photon 2-surfaces in flat spacetime can be concisely classified
(cmp. "Inertial ...
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QM from the uncertainty principle?
In a book Quantum Mechanics with Applications (1970) by D.B. Beard and G.B. Beard, the authors wrote on page 34:
"By methods beyond the scope of this text, one could state the uncertainty ...
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Questions about E. Minguzzi's article on Synchronization (arXiv:1009.3005)
Only recently I learned of E. Minguzzi's article
"Clocks' synchronization without round-trip conditions", [gr-qc: arXiv:1009.3005] ...
(Notably, the article available for download is dated ...
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Consistent histories vs. relational interpretation and Qbism
I hope that my question will be suitable for this forum: I would like to understand the difference between the so called consistent history approach to QM and several other interpretations. In this ...
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Does quantum mechanics need projective representations only due to the Born rule?
In quantum mechanics, physical states don't live in the Hilbert space, but rather on the equivalence class of rays on the Hilbert space. This is called a projective space. This is the reason why when ...
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What's the difference between observable and unobservable objects in a physical theory?
Both can help explain physical effects, but I'm looking for a rigorous definition of “observable” and “unobservable.”
For example, how is the experimental evidence for the existence of particles such ...
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Does classical mechanics implicitly assume short-range forces?
If you take an axiomatic view of Classical Mechanics and the concept mass as primitive in this context, you could derive from Newton's laws an operational way of determining masses simply by ...
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What are the implications of entanglement swapping for the Pusey-Barrett-Rudolph (PBR) theorem?
The derivation of the PBR theorem makes an assumption that "systems that are prepared independently have independent physical states". However, it is known that it is possible to entangle ...
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System in thermal equilibrium with reservoir
Let's say I was trying to build Statistical Mechanics from scratch. I had studied the microcanonical ensemble and made the following definitions:
$$\frac{\partial S}{\partial E} = \frac{1}{T},$$
$$\...
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What is the definition of bound state in quantum field theory?
I asked a question a while a go what is a bound state and the question was closed because there is a similar question.
Now since best description we have to describe nature in quantum field theory
How ...
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What is the mathematical definition of bound state? [duplicate]
While searching why poles of Green’s function corresponds to bound states I came across that I don't know what bound state is. Intuitivaly I know that bound
State should be a state that the ...
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Can mass be defined using projective Hilbert space formalism instead of Hilbert space formalism?
The origin of mass in quantum mechanics was clarified by Bargmann in his famous paper, On Unitary Ray Representations of Continuous Groups (Annals of Mathematics, Second Series, Vol. 59, No. 1 (Jan., ...
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A local explanation of the CHSH game
I have read lots of papers claiming that we can get rid of nonlocality in QM using some interpretations like consistent histories. For example, Griffiths deduces the same violation of Bell's ...
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Average Time since the Big Bang
Can we define an average time for the entire universe relative to the Big Bang and call this the universal time since the beginning of the universe? (time, averaged relative to all possible reference ...
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Quantum Measurement and the law of thermodynamics
When discussing the conceptual issues of quantum mechanics, concepts like Bell's inequality, non-locality, and the Kochen-Specker theorem are often brought up. Many physicists have dedicated time to ...
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Why does the path integral formulation not provide an ontological basis for quantum theory?
I have looked at several books on the foundations of quantum theory and found that the path integral formulation is hardly ever discussed in detail. I find this surprising because this formulation of ...
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Is all change movement? [closed]
Is there a change in the universe that cannot be reduced to movement? One counter-example should be enough. :)
Heat is a type of change that was once thought to be qualitative, but is now realized to ...
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