Questions tagged [foundations]

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

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Diffeomorphism invariance in special relativity

Suppose space time is the manifold $M $ isomorphic $ \mathbb{R^4}$ whit the metric $-\eta_{00}=\eta_{11}=\eta_{22}=\eta_{33}=1$ in the Cartesian coordinates $\Psi(p)=(x^0,x^1,x^2,x^3)$ for $p \in M $ ....
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How do quantum field values combine?

I am interested in how quantum field values combine under superpositions of states in the case of free real scalar fields. I believe I understand the following: A fock basis of a free real scalar ...
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In what way do non-rigorous arguments make sense? [closed]

I specifically have in mind arguments made in QFT textbooks in mind. There are no rigorous foundations for QFT, at least not any that can reproduce the predictions of the Standard Model. In fact, ...
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What is the necessity to universalise a law? [closed]

What are the necessary conditions or observations that are required for universalisation of a law? I am not good at English so by universalise I mean to claim something to be universal. So how can ...
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What species of arguments are used in physics and science in general? [closed]

Arguments are needed to provide theories but I'm only used to deductive reasoning in physics and science, maybe due to their empirical nature. Does anyone know if other species of arguments have or ...
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Axiomatic Quantum Theory, and the complex numbers

In Lucien Hardy's influential paper "Quantum Theory from five reasonable axioms," Hardy states in the abstract: This work provides some insight into the reasons why quantum theory is the way it ...
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What is the role of metric transitivity in statistical mechanics?

I was reading a paper of E.T. Jaynes 'Information Theory and Statistical Mechanics'. There he mentions the following principle in the section 'Application to Statistical Mechanics': The link to paper ...
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Is there a theory on the creation and genesis of fields?

I do not intend to ask theological questions on PSE, so, you can interpret, if you want, this question on a purely physical basis. Almost everywhere, in classical and non-classical physical theories, ...
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If the only two empirical measurements we can make are change in length and passage of time, how are dimensions and units of quantities formulated?

So this is something really confusing to me. Recently a professor of mine gave a talk and said something that I thought was very interesting and kind of crazy. "The only two quantitative measurements ...
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Do observables only amount to computing functions of outcome probabilities?

It is well known that in quantum mechanics any Hermitian operator $A$ can be thought of as an observable. Given any (pure) state $\lvert\psi\rangle$, measuring such observable gives an average ...
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Are bubble chamber tracks inconsistent with quantum mechanics?

I am reading the book How Is Quantum Field Theory Possible? by Sunny Auyang, and he raises an interesting point in chapter 4 (p. 23): L. E. Ballentine argued that the projection postulate leads to ...
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Is there a proof that the set of real numbers can exactly represent distances? [duplicate]

Mathematicians define real numbers in an abstract way - as an 'ordered field' with 'the least upper bound property'. In physics, we use real numbers to represent distances. For us to be able to do ...
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Encoding infinite information in a qubit vs. classical system

In this Quantum Computing article by Michael Nielsen he argues about some of the limitations imposed by quantum measurement. In particular how the amplitude $\alpha$ of a single qubit $\alpha |0> +...
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What “determines” a specific quantum theory

I'm trying to give a bare bones description of non-relativistic quantum mechanics, for mathematicians. A description of the mathematical machinery. It is meant to answer to the questions: What makes ...
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Can bipartite mixed entangled states show Hardy nonlocality?

I understand that apart from maximally entangled states, all pure entangled states yield Hardy correlations for certain measurement settings. Can the same be told for mixed entangled states?
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Physics breaking down - is it logically consistent? [closed]

I was just reading a sci-fi novel where physics "breaks down". While of course fiction is fiction and I don't expect this to happen in real life, when I tired to contemplate the concept I find that I ...
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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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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 operator-valued distributions $\hat{\phi}(r)$ & $\hat{\pi}(r)$,...
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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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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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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 ...
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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
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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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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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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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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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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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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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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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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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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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299 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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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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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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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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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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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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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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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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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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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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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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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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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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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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Defining Quantum Mechanics

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