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Questions tagged [foundations]

Devoted to the conceptual bases of the fundamental theories of physics, to their philosophical and logical premises.

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Does the Yang Mills Mass Gap represent “Absolute Bottom”?

The question of the existence of a Yang Mills mass gap is a complex and technical one. In this paper Philip Gibbs asks "Is fundamentality then a relative concept with no absolute bottom, or is there ...
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1answer
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What is the content of an occupied QFT fermionic state?

A simple non-interacting quantum field is constructed by analogy to a harmonic oscillator, with $\hat{x}$ & $\hat{p}$ replaced by $\hat{ \phi}$ & $\hat{\pi}$ & with a separate oscillator ...
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1answer
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Frauchiger-Renner explanation in Many Worlds

In Frauchiger-Renner's paper, the authors propose a thought experiment which suggests that taking QM together with certain natural assumptions, one arrives at a contradiction. They go on to say that ...
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1answer
47 views

Theories, Corollaries, and Models

I apologize if this question seems overly basic. I was wondering how to recognize what a theory is really saying, as opposed to the explanation/corollaries that are drawn from it. As an example, take ...
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3answers
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Contravariant metric in Newton-Cartan spacetime

I'm interested in the geometrized newtonian gravitation or Newton Cartan theory. In every reference that I have found begins saying that a Newton-Cartan spacetime is a manifold M with some structures. ...
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0answers
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Is there an official list of the postulates of quantum mechanics?

Having been looking at lecture notes, online sources and books, the list of postulates of quantum mechanics seems to vary. For instance, some sources (my lecture notes, for instance) refer to $|\...
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1answer
79 views

Is photon interference really random? [closed]

I know that according to the many worlds interpretation, there is no randomness and rather there is a universal wave function that simulates an observer with a continuously branching timeline. My ...
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1answer
43 views

Quantum state space constructing operator

If I use British money the amounts I can have are isomorphic to $\mathbb{Z}_{\geq0}$ (in pennies). If I also use Australian money, if I want to think about the amount I have in total, I can use ...
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0answers
131 views

Local determinism vs. Local realism vs. Local causality

I found the following definitions for the three different terms. Do you find these definitions exhaustive, or can you suggest more precise formulations? Quoting the wikipedia page on Local realism: ...
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1answer
69 views

How much freedom is there in a quantum field?

Let's imagine we have a free scalar quantum field, and that it has 2 particles in a specific momentum eigenstate only. Does this information completely fix the quantum field, or is there additional ...
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0answers
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Spekken toy model: measurement of spin in any direction

Spekkens' toy model [1] can handle the measurement of a spin 1/2 along the directions $x$, $y$ and $z$. Unless I am missing something, it can't handle measurement in any direction. Would there be a ...
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1answer
85 views

What is “fundamental” in physics?

Sorry about the broad question. I'm still learning to frame the questions on Physics StackExchange. Currently researching the nature of interactions in philosophy. My question is: When physicists ...
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1answer
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Calculating Average Position in Quantum Mechanics [closed]

I know that $\begin{gather*} \langle x\rangle = \int_{-\infty}^{\infty} P(x)x\,\mathrm{d}x = \int_{-\infty}^{\infty}\psi^*(x)\psi(x)x\,\mathrm{d}x \end{gather*}$, however $\begin{gather*} \int_{-\...
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1answer
49 views

What is the difference between no-disturbance principle and non-contextuality?

The no-disturbance (ND) principle states that, for any three observables A, B, and C such that A and B are compatible, and A and C are compatible, the probabilities of outcomes of A do not depend on ...
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109 views

Modern axioms of quantum mechanics

Recently I have been learning a lot about what kind of axioms and mathematical formulations there are for non-relativistic quantum mechanics. Unfortunately, I am a little confused, because at first I ...
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1answer
208 views

All of the postulates of quantum mechanics without additional information [closed]

$\newcommand{\braket}[2]{\left<#1|#2\right>}% \newcommand{\bra}[1]{\left<#1\right|}% \newcommand{\ket}[1]{\left|#1\right>}% $As an undergraduate who's trying to learn quantum mechanics it'...
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0answers
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Causality in Quantum mechanics

If we consider a quantum preparation procedure on a system followed by a projection measurement as constituting two sequential events in space-time (which seems plausible ,given that the Copenhagen ...
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10answers
13k views

What makes a theory “Quantum”?

Say you cook up a model about a physical system. Such a model consists of, say, a system of differential equations. What criterion decides whether the model is classical or quantum-mechanical? None ...
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1answer
59 views

Statistical error with large number of particles in weak measurements

Consider a measurement process. If $\Delta \pi$ and $\Delta x_n$ is the uncertainty in momentum and position of the measuring device. Aharonov, Albert, et al. ask us to consider the opposite limit: ...
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1answer
193 views

Are certain fields of physics axiomatized?

Everything from Quantum mechanics can be derived from six (?) postulates. Similarly classical electrodynamics can be reduced to Maxwell's equations and Lorentz force law, and special relativity is ...
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1answer
111 views

What is a quantum “state preparation procedure” and what isn't

The term "state preparation procedure" is widely used in quantum mechanics without clear explanation of what it is or isn't. Sometimes it's suggested that it is a controlled procedure in a laboratory....
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2answers
82 views

EPR-Bohm paradox and Robertson uncertainty relation [closed]

Consider Bohm's version of the EPR paradox, where spin-1/2 are used. The bipartite system is in the state $$ \vert \Psi\rangle = \dfrac{1}{\sqrt{2}} \left( \vert \uparrow_x \rangle_A \vert \...
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1answer
115 views

Non-negotiable laws in physics [closed]

Are there laws (axioms / principles / equations / inequalities) in physics that cannot be violated, no matter how slightly, by hand without leading to absurdities (singularities, inconsistencies)?
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Interpretation of quantum superposition and classical Brownian motion

In the standard, Copenhagen interpretation of quantum mechanics, the usual ontology assigned to the phenomenon that repeated measurements of a quantum mechanical observable yielding different results ...
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3answers
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How can we certify that the randomness in the measurement outcomes is not due to randomness in the state preparation?

According to the theory of quantum mechanics, if a spin state is prepared along axis "x", and then measured along axis "z", then the result of the spin projection is probabilistic: half of the times ...
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2answers
221 views

Is Bells inequality always violated? [closed]

Is Bell inequality always violated by a quantum system? Can it ever be violated by a classical system?
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1answer
736 views

How does QFT predict the probability density to find a particle at x?

In quantum mechanics, the probability density of a particle's position is $$\rho(x)=|\langle x|\psi\rangle|^2$$ What is the corresponding expression in QFT to predict this distribution? Since $\rho(x)...
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Experiments are monads (I think), but are they comonads too?

Quantum theory is equally an epistemic (ie about information) and ontic theory (see "reality of the wavefunction" on Google Scholar). My question is about a theory that aligns with this, ie, the ...
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3answers
840 views

Why is the word 'simultaneously' important in stating Heisenberg's uncertainty principle?

The Heisenberg's uncertainty principle states that a particle cannot have a precise value of its position and conjugate momentum simultaneously. If these uncertainties are intrinsic properties of a ...
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2answers
199 views

Implication of Born's rule on the superposition principle

BACKGROUND Born's rule quantifies the interference pattern of a single quantum particle going through two possibles paths A and B as $P = |A|^2 + |B|^2 + ⟨A|B⟩ + ⟨B|A⟩$. The standard interpretation ...
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2answers
84 views

Proving the orthogonaity property by using using the reality condition

I am reading Modern Quantum Mechanics by Sakuria and Napolitano. Background Information from the Textbook a' and a'' are eigenvalues of A. A is a Hermitian operator. The symbol, * , implies ...
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1answer
90 views

Defining Quantum Mechanics

Does Schrödinger's Equation (Operator form) $[\hat{X},\hat{P}]=i$ Born Rules define Quantum Mechanics?
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2answers
143 views

Is the one-dimensional string actually a real string, with some diameter to its cross section — just as a rope has some thickness?

Would not a one-dimensional string be just a Platonic idea, and not actually physical? Because if physical, the one dimensional string would comprise a line of point particles, each point particle ...
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On explaining QM by modeling the observation mechanism using a density operator

I just have some elementary thoughts on the foundations of QM, based on modeling the observation mechanism by a density operator. A density operator is a weighted sum of orthogonal projections on the ...
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1answer
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Do physical laws require 2nd derivatives [duplicate]

Is it a happy coincidence that second degree differential equations approximate reality or a necessity? They describe how a system will evolve from one state to the next, but surely the ultimate laws ...
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0answers
180 views

Improvement of Von Neumann's measurement scheme [closed]

I would like to know some references on possible improvements of Von Neumann's measurement scheme beyond the use of POVMs. Specifically, I am interested in the possibility of implementing a sort of ...
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1answer
343 views

Why is time-evolution unitary (the sequel)?

One foundational postulate of QM is that a closed physical system at one instant of time, say $t$, is completely described by a wavefunction $\psi \in S^1\subset H$ (where $H$ is a Hilbert space and $...
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2answers
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How non-conservative fields emerged in the universe?

I know all of the fundamental forces/fields(Gravitational, Electromagnetic, Strong and Weak) of the nature are conservative and we know every other derived force/field in the nature is just produced ...
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1answer
269 views

Dispersion relation of QM in the presence of a potential

Correct me if I'm wrong, but equations in QM are quite always obtained by looking at the energy dependance of the problem of interest. For example, for Schrodinger's equation one just uses $E = \...
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4answers
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Circular definitions in Special Relativity?

Standard textbooks introduce Special Relativity in this way: They introduce two postulates, the second being something like that The speed of light in a vacuum is the same for all observers, ...
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3answers
219 views

What is the program of quantum field theory? What is its derivation?

Paraphrasing Griffith's: For some particle of mass m constrained to the x-axis subject to some force $F(x,t)=-∂V/∂x$, the program of classical mechanics is to determine the particle's position at any ...
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2answers
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Why hermitian, after all? [duplicate]

This question is going to look a lot like a duplicate, but I've read dozens of related posts and they don't touch the subject. Here we go. Why are observables represented by hermitian operators? ...
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6answers
950 views

What things in our universe can be considered uncountable? [closed]

I am taking a course in mathematics that covers countability. The trick with the uncountability of the real line is that no matter how many times you divide up an interval, there would still be a real ...
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0answers
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Why not measure the velocity of a quantum particle by $\frac{\Delta \vec{x}}{\Delta t}$

Why is it not possible in quantum mechanics to measure the velocity (and thus momentum) of a particle just by two position and time measurements and get it approximately by $$ \vec{v} = \frac{\vec{x}...
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2answers
1k views

The Origins of the Second Quantization

I've been studying quantum theory for a while now and have a number of closely related questions that are not giving me any peace. I am not sure if such a long format is appropriate here, but I'd like ...
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3answers
301 views

What Statistical Mechanics does in classical regime

In a book of Dipankar Home, "Foundations of Quantum Mechanics", he has mentioned that A newer theory should not only predict all the results that are already predicted by it's predecessor where it ...
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1answer
280 views

Help needed to understand “On the reality of the quantum state”

I am having trouble to understand the reasoning in the following paper, On the reality of the quantum state. MF Pusey, J Barret and T Rudolph. Nature Phys. 8, 475–478 (2012); arXiv:1111.3328. From ...
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2answers
242 views

Tensor product postulate [duplicate]

Non relativistic quantum mechanics assumes that a composite system should be described with the tensor product of the component systems. This is the tensor product postulate of quantum mechanics. I ...
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2answers
162 views

Relativistic probability amplitude of a particle to be in certain position

In the book “The story of spin” by Tomonaga on page 110, it says They insisted that a concept like "the probability of a particle to be at $x$ in space" is meaningless for relativistic particles—be ...
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2answers
236 views

Postulates of Relativistic Quantum Mechanics

I have been reading this Phys.SE answer in order to clarify my doubts. It seems to me that he claims that the postulates are the same no matter if it is QFT, QM or whatever. But some books tell us ...