Questions tagged [foundations]

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

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28 views

Question regarding Wightman's “transformation law” axiom for QFT

On the Wightman axioms Wikipedia page, the W2 axiom describes the effect of Poincare transformations on the quantum field. It states: $$U(a,L)^\dagger A(x) U(a,L)=S(L)A(L^{-1}(x-a))$$ where A is the ...
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Is the commutator relation $[\hat{x}, \hat{p}_x]=i\hbar 1\!\!1$ an *assumption* in the quantum theory?

This question is somewhat related to (but not by any means the same as) the question I asked recently. In his Lectures on Quantum Theory, Isham essentially says (reference given below) that if an ...
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1answer
71 views

Can function-preserving quantisation be assumed even if it leads to contradictions?

Isham in his Lectures on Quantum Theory, Chapter 5, General Formalism of Quantum Theory, Section 5.2.1 makes states the following two assumptions for quantising a classical system. Q1 The ...
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45 views

Arguments for Feynman diagrams (or related) as Lagrangian tools, or “vice-versa”?

I know that the Feynman diagrams and perturbation series are used as computational tools to evaluate a specified Lagrangian for a QFT. This is usually used as an argument in itself to discourage ...
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Decoherence and quantum to classical limit: good resources?

I am looking for good references for decoherence theory. I mainly worked with "Decoherence, einselection, and the quantum origins of the classical" from Zurek, but some parts are a little bit ...
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3answers
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Calculus shouldn't work for describing physics [duplicate]

I am not crazy. Hear me out. I am not from a physics background but from maths. I have a really weird question in physics that is making me lose sleep. How can calculus describe physics? How is it ...
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Stephen Wolfram’s new class of models [closed]

Does the physics community have a consensus view on Stephen Wolfram’s “A Class of Models with the Potential to Represent Fundamental Physics”?
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1answer
79 views

Does the collapse of a state need to be necessarily included within the set of postulates of quantum mechanics?

When an operator is measured on a quantum state of a system, the state collapses into an eigenstate of the operator being measured. Should something of this sort be necessarily included within the ...
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1answer
115 views

How did Heisenberg come up with CCR?

Usually it is pointed out that the relation $[x,p]=i\hbar$ comes from the promoting the poisson bracket to commutator but as I know this process of quantization is called deformation quantization ...
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17answers
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Can a mathematical proof replace experimentation?

I know that this is very similar to How important is mathematical proof in physics? as well as Is physics rigorous in the mathematical sense? and The Role of Rigor. However, none of the answers to ...
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3answers
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Does spacetime structure in GR break time symmetry?

In Frederic Schuller's GR lectures, he states as a postulate of GR that spacetime comes equipped with a time orientation that distinguishes the "past" direction from the "future" direction, vaguely ...
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1answer
180 views

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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1answer
118 views

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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3answers
70 views

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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2answers
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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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32 views

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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1answer
57 views

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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1answer
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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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1answer
180 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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3answers
240 views

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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3answers
271 views

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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0answers
88 views

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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3answers
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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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1answer
101 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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1answer
163 views

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
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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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3answers
222 views

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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0answers
102 views

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
85 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
57 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
295 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
77 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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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
102 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
84 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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210 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
362 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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105 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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10answers
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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
63 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
284 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
329 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
102 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
120 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 ...