Questions tagged [foundations]
Devoted to the conceptual bases of the fundamental theories of physics, to their philosophical and logical premises.
131
questions
0
votes
1answer
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 ...
0
votes
0answers
81 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 ...
1
vote
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 ...
0
votes
0answers
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 ...
6
votes
1answer
104 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 ...
-3
votes
3answers
130 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 ...
2
votes
0answers
74 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”?
0
votes
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 ...
3
votes
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 ...
35
votes
17answers
8k views
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 ...
11
votes
3answers
1k views
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 ...
0
votes
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 $ ....
0
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0answers
74 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 ...
5
votes
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, ...
-2
votes
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 ...
-2
votes
2answers
84 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 ...
0
votes
0answers
68 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 ...
1
vote
0answers
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
...
0
votes
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, ...
2
votes
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 ...
4
votes
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 ...
8
votes
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 ...
15
votes
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 ...
1
vote
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> +...
2
votes
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 ...
-1
votes
3answers
125 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 ...
0
votes
0answers
27 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 ...
0
votes
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 $\hat{\phi}(r)$ & $\hat{\pi}(r)$,...
4
votes
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 ...
3
votes
1answer
50 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 ...
2
votes
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 ...
2
votes
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 $|\...
1
vote
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 ...
1
vote
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 ...
1
vote
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:
...
2
votes
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 ...
2
votes
0answers
42 views
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 ...
2
votes
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 ...
-6
votes
1answer
137 views
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_{-\...
1
vote
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 ...
3
votes
0answers
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 ...
2
votes
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'...
1
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0answers
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 ...
145
votes
10answers
14k views
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 ...
asked Apr 4 '18 at 18:54
AccidentalFourierTransform
34.2k14 gold badges84 silver badges157 bronze badges
1
vote
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: ...
3
votes
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 ...
3
votes
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....
0
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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 \...
0
votes
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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0answers
101 views
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 ...
