Questions tagged [foundations]

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

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Finding the expectation value of a mixed function of both momenta and coordinates

I'm reading Merzbacher's Quantum mechanics. In Chapter 3, section 2, he tackles this question. For a function solely of coordinates, say $f(\mathbf r)$, he says that the expectation value is given by $...
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2answers
36 views

Why spacetime translations don't affect the physics of de Broglie plane waves?

I'm studying Merzbacher's Quantum Mechanics. In Chapter 2 Section 1, he "derives" the expression $\psi(x, t)=Ae^{i(kx-\omega t)}$ for the de Broglie plane waves for free particles. Basically ...
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1answer
28 views

Conway's and Kochen's SPIN axiom seems unphysical

In their "Free will theorem", Conway's and Kochen's states the "SPIN axiom": "A triple experiment for the frame (x, y, z) always yields the outcomes 1, 0, 1 in some order.&...
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65 views

Is there a mathematical model of the process of “getting entangled with”?

[Warning: I'm not a physicist] Let $A$ and $B$ be microscopic systems, with corresponding Hilbert spaces of state vectors given by $H_A$ and $H_B$ respectively. Let's say $A$ is in a state $\psi\in ...
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Physical states are primary and space-time is secondary

This is pure speculation. The title of the question is a quote from Zeidler's book on QFT p.141: In the setting of noncommutative geometry, physical states are primary and space-time is secondary. ...
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4answers
260 views

Why does a physical theory need to be testable? [closed]

We are generally not interested in physical theories that cannot be tested with the scientific method. This would seemingly apply even if the theory has other advantages, e.g. simpler, more general, ...
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36 views

Quantum Psuedo Telepathy vs. “Deterministic random seed” (piece of paper)

I'm trying to get a better understanding of "quantum psuedo telepathy." It seems as though all games that can be won with entanglement simply exploit coordination. In any of these games, ...
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1answer
74 views

Are there meaningful theories with both locality and “counterfactual definiteness” that are ruled out by Bell's Inequality?

Bell's Inequalities are a set of inequalities that establish that theories with "counterfactual definiteness" and "locality" require a set of inequalities (describing the ...
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1answer
84 views

Why is the assumption of free will important to physics [closed]

I have watched a few lectures and have heard in quite some places that free will is an important assumption in physics. For example Bell's theorem assumes that the two experimenters can freely choose ...
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2answers
240 views

What is the exact meaning of Lorentz invariance for a quantum scalar field?

In axiomatic QFT, the defining property of a scalar field $\phi$ is that it does not change under a Lorentz transformation: that is, "If $U(\Lambda)$ is the unitary representation of a Lorentz ...
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1answer
74 views

Difference between Phenomenal and Phenomenological in the Context of Physics

I was going through a conference presentation on System of Systems Engineering. In the presentation entitled "Macroscopic Quantum Mechanics and the SoSE Design Approach", I came across a ...
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4answers
271 views

Interpretation of Hilbert space in the Wightman Axioms for QFT

My confusion is about the different Hilbert spaces we meet in QFT. In a first introduction to QFT, the Hilbert space is often taken to consist of wavefunctionals on classical fields on $\mathbb{R}^3$. ...
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24 views

Unification of Forces

I was reading that unification of Forces is the most important task in the entirety of Physics. My question is why do the forces have to Unified. Why can't they be different forces what makes us think ...
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14 views

Predictability in decoherence theory to find the classical states: at which time must we evaluate?

I have read Decoherence, einselection, and the quantum origins of the classical, end a way to quantify the classicality of states is the following. We have the system $S$ and its environment $E$. The ...
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25 views

Decoherence: Does the environment must be a tensor product of two sub-systems to remove any ambiguity?

In decoherence theory, we describe the decoherence of a system $S$ by the mean of an interaction with an environment. In short, if I consider: $|\psi_S \rangle=a|0_S\rangle+b|1_S\rangle$, the system ...
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3answers
130 views

What is a probabilistic physical theory?

What do we mean when we say that we have a probabilistic theory of some phenomenon? Of course, we know from experience that probabilistic theories "work", in the sense that they can (somehow)...
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1answer
37 views

Quantum measurement limit of decoherence and scattering: why are position pointer said classical?

In decoherence theory, we explain the decoherence by hamiltonian evolutions between a system and its environment. Calling $H$ the total hamiltonian, I have: $$H=H_S + H_E + H_{SE} $$ A pointer state $|...
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33 views

Measurement outcomes of a “not totally decohered” system

In decoherence theory, the basic situation is the following (I illustrate with two level system for simplicity). I want to measure a system $S$ by the mean of an apparatus $A$. Around it there is the ...
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1answer
132 views

Decoherence theory: System+Apparatus+Environment correlated. What becomes the global state when I measure SA? Did it collapse?

In decoherence theory, the basic situation is the following (I illustrate with two level system for simplicity). I want to measure a system $S$ by the mean of an apparatus $A$. Around it there is the ...
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45 views

Decoherence and einselection model: Contradiction with two different explanations?

I am a little puzzled by einselection models. I followed those two papers (Environment-induced superselection rules Decoherence, einselection, and the quantum origins of the classical) to understand ...
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3answers
106 views

Why is it said that the physics is preserved when the equations of motion are invariant under a tranformation/Symmetry?

It is always said (and this is even how physicists motivate some theories instead of others) that the physics is preserved (by some transformation) whenever the equations of motion are left unchanged ...
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86 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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88 views

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
72 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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48 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
159 views

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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114 views

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
81 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
125 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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18answers
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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
191 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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76 views

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
141 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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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
87 views

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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72 views

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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1answer
61 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
31 views

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
185 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
272 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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11answers
1k views

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
315 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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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
131 views

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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29 views

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
108 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
173 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 ...