Questions tagged [foundations]

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

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Why are commutators the first choice in describing observables that cannot be measured simultaneously?

In quantum mechanics, we convert Poisson brackets to commutators for the observables to account for the uncertainty principle. However, I do not understand why do we do this. What motivates us to ...
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Are violations of realism the same thing as contextuality?

I am basically looking for a counter-example where we'd get contextuality but not violations of realism (and vice-versa). If no such counter-examples exist, then it seems to me that they're really one ...
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Gauge transformation in a frame bundle

Let $\pi:P\longrightarrow M$ be the orthogonanal frame bundel. A gauge transformation is an automorphism $f:P\longrightarrow P$ such that $\pi(p)=\pi(f(p))$ that is fiber preserving automorphism. Now ...
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5answers
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Why is time different between different inertial observers? [duplicate]

Suppose we have observer $A$ and observer $B$ that meet at a point $p$ when both of their clocks are zero. Why after that, the measure of their clocks would be different, since clocks depend on ...
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4answers
73 views

Is the set of spacetime manifold a set of event?

In general relativity spacetime is defined as manifold. Is this manifold the set of events? For example if our universe is constituted of only one non-interacting particle, should our manifold be a ...
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Rather technical question concerning Bell's Theorem (from 1964)

I'm trying to understand Bell's theorem as he published it in 1964 on a merely technical level. I refer to the version as it is provided in Bell's theorem: experimental tests and implications by ...
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1answer
74 views

Why isn't the variance of a quantum observable depend on how gently or roughly the measurement is carried out?

Consider an ensemble specified by a state $|\psi\rangle$ on which we decide to make measurements of an observable $A$. If the state $|\psi\rangle$ is not an eigenstate of $A$, there will be a scatter ...
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1answer
72 views

Does Kochen-Specker's theorem follow immediately from Gleason's one?

In Kochen-Specker's theorem, as presented e.g. in (Rajan 2017) or (Breuer 2002), we consider maps $\nu:\mathrm{Herm}(\mathcal H)\to\mathbb R$ that are algebra homomorphisms on compatible observables, ...
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1answer
44 views

Why must the gauge potential create negative norm states?

This question concerns the quantisation of the EM gauge potential $A_\mu$. When the Gupta-Bleuler formalism is introduced, it is usually stated that the creation/annihilation operators satisfy $\...
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2answers
147 views

Does this argument prove that all fermionic states have zero norm?

The following argument seems to show that all states created by a fermionic field have zero norm. This would surely cause problems in QFT, so I believe there must be an error somewhere, but I can't ...
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1answer
59 views

How can quantum mechanics describe the classical world when itself is a derivation out of ideas from the classical world of physics? [closed]

It dawned on me while revising the basics of quantum mechanics (the Schroedinger equation, de Broglie's matter waves, the quantum postulates etc. - essentially the basic first year undergrad schedule)....
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1answer
23 views

In the Kochen-Specker theorem, where does the assumption $v(-n)=v(n)$ come from?

I'm trying to get a better understanding of the Kochen-Specker theorem, reading the presentation in arXiv:1708.01380. In section (2) of the above paper, the authors introduce the two KS assumptions as:...
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2answers
63 views

Are self-consistency arguments logical/rigorous? An example with Pauli paramagnetism

I am never yet satisfied by arguments in physics that go along the lines of 'assume A is true', 'one way of making A true is for B to happen', 'we check that if B happens then A is indeed true ...
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2answers
140 views

Current texts on the foundation of quantum mechanics?

So I'm currently writing an article regarding a priori axiomatic systems and the nature of inference (I'm not a physicist but a philosopher doing philosophy of science), one of my main texts is "...
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49 views

Yet another question about Schrödinger's cat

I had always believed that the point of the (in)famous Schrödinger's cat thought experiment was pretty obvious: people, back then, were puzzled with the state space being (basically) a vector space. ...
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2answers
107 views

What would be a basic example of an axiomatic physical theory? (except Newton's Principia or Einstein's Special Relativity Theory) [closed]

If I were asked to give an example of an axiomatic mathematical theory, I'd be able to answer: set theory, probability theory, maybe group theory (assuming the elements of the definition of a group ...
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39 views

Can the narrative of spooky action at a distance be derived from the mathematics of quantum mechanics?

The usual popular (and also not so popular) science lore about entanglement goes about like this: Two particles enter into contact (or a single particle decays into two new particles) and hence get ...
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14 views

Does an accelerated lab defines an observer?

I have always been confused if an accelerated lab is an observer. Let us take an example, suppose we have an oscillating antenna due to the inertia of the electrons we will have a current in the ...
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2answers
109 views

How does relaxing counterfactual definiteness allows for CHSH inequality violation?

Scenario, I want to play a game with a group of students as a teacher, I ask two teachers to help. The students are from the central classroom, going to room A and room B where the teachers there asks ...
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1answer
30 views

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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3answers
54 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
36 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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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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25 views

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
266 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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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
79 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
112 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
371 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
113 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
303 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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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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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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28 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
149 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
46 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
133 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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0answers
50 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
124 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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1answer
90 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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94 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
73 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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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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215 views

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
178 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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0answers
140 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
83 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
138 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 ...