Questions tagged [foundations]

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

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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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95 views

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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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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Why are only linear representations of the Lorentz group considered as fundamental quantum fields?

As described in many Q&As around here, fundamental quantum fields are expressed as irreducible representations of the Lorentz group. This argument is entirely clear - we live in a Lorentz-...
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1answer
156 views

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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Why is the application of probability in QM fundamentally different from application of probability in other areas?

Why is the application of probability in quantum mechanics (QM) fundamentally different from its application in other areas? QM applies probability according to the same probability axioms as in other ...
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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 ...
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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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184 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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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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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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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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What are the justifying foundations of statistical mechanics without appealing to the ergodic hypothesis?

This question was listed as one of the questions in the proposal (see here), and I didn't know the answer. I don't know the ethics on blatantly stealing such a question, so if it should be deleted or ...
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What is meant by “quantum steering”?

I have become interested in quantum steering after listening a talk and tried to read more about it. I think I am more confused now. My understanding is as follows: Sharing a (entangled) state, Bob ...
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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
49 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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What is the difference between realism in locality, and counterfactual definiteness?

I understand the EPR-experiment and the Bell inequalities. I can see how dropping 'locality' solves the issue, and how dropping 'realism' solves the issue (e.g. there are really no hidden variables ...
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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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84 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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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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Why quantum mechanics?

Imagine you're teaching a first course on quantum mechanics in which your students are well-versed in classical mechanics, but have never seen any quantum before. How would you motivate the subject ...
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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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Learn QM algebraic formulations and interpretations

I have a good undergrad knowledge of quantum mechanics, and I'm interesting in reading up more about interpretation and in particular things related to how QM emerges algebraically from some ...
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1answer
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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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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
62 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
59 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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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
88 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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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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157 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
271 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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100 views

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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1answer
207 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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163 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
92 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
116 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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277 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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Reason for the discreteness arising in quantum mechanics?

What is the most essential reason that actually leads to the quantization. I am reading the book on quantum mechanics by Griffiths. The quanta in the infinite potential well for e.g. arise due to the ...
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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
157 views

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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854 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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297 views

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 ...