Questions tagged [foundations]
Devoted to the conceptual bases of the fundamental theories of physics, to their philosophical and logical premises.
8
votes
3answers
166 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 ...
16
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
79 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
87 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 ...
0
votes
0answers
12 views
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?
-1
votes
3answers
115 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
17 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
73 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 $\hat{
\phi}$ & $\hat{\pi}$ & with a separate oscillator ...
4
votes
1answer
115 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
48 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
4answers
103 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
80 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
83 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 ...
0
votes
1answer
44 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
155 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
69 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
36 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
85 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
83 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
54 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
127 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 ...
1
vote
1answer
228 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
vote
0answers
97 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 ...
139
votes
10answers
13k 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 ...
1
vote
1answer
61 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: ...
2
votes
1answer
202 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
126 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
votes
2answers
85 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
$$
\vert \Psi\rangle = \dfrac{1}{\sqrt{2}} \left( \vert \uparrow_x \rangle_A \vert \...
0
votes
1answer
115 views
Non-negotiable laws in physics [closed]
Are there laws (axioms / principles / equations / inequalities) in physics that cannot be violated, no matter how slightly, by hand without leading to absurdities (singularities, inconsistencies)?
1
vote
0answers
76 views
Interpretation of quantum superposition and classical Brownian motion
In the standard, Copenhagen interpretation of quantum mechanics, the usual ontology assigned to the phenomenon that repeated measurements of a quantum mechanical observable yielding different results ...
3
votes
3answers
154 views
How can we certify that the randomness in the measurement outcomes is not due to randomness in the state preparation?
According to the theory of quantum mechanics, if a spin state is prepared along axis "x", and then measured along axis "z", then the result of the spin projection is probabilistic: half of the times ...
0
votes
2answers
245 views
Is Bells inequality always violated? [closed]
Is Bell inequality always violated by a quantum system? Can it ever be violated by a classical system?
16
votes
1answer
786 views
How does QFT predict the probability density to find a particle at x?
In quantum mechanics, the probability density of a particle's position is $$\rho(x)=|\langle x|\psi\rangle|^2$$
What is the corresponding expression in QFT to predict this distribution? Since $\rho(x)...
0
votes
0answers
288 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 ...
6
votes
3answers
844 views
Why is the word 'simultaneously' important in stating Heisenberg's uncertainty principle?
The Heisenberg's uncertainty principle states that a particle cannot have a precise value of its position and conjugate momentum simultaneously.
If these uncertainties are intrinsic properties of a ...
6
votes
2answers
222 views
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 ...
0
votes
2answers
85 views
Proving the orthogonaity property by using using the reality condition
I am reading Modern Quantum Mechanics by Sakuria and Napolitano.
Background Information from the Textbook
a' and a'' are eigenvalues of A.
A is a Hermitian operator.
The symbol, * , implies ...
0
votes
1answer
90 views
Defining Quantum Mechanics
Does
Schrödinger's Equation (Operator form)
$[\hat{X},\hat{P}]=i$
Born Rules
define Quantum Mechanics?
0
votes
2answers
152 views
Is the one-dimensional string actually a real string, with some diameter to its cross section — just as a rope has some thickness?
Would not a one-dimensional string be just a Platonic idea, and not actually physical? Because if physical, the one dimensional string would comprise a line of point particles, each point particle ...
0
votes
0answers
44 views
On explaining QM by modeling the observation mechanism using a density operator
I just have some elementary thoughts on the foundations of QM, based on modeling the observation mechanism by a density operator. A density operator is a weighted sum of orthogonal projections on the ...
-1
votes
1answer
75 views
Do physical laws require 2nd derivatives [duplicate]
Is it a happy coincidence that second degree differential equations approximate reality or a necessity? They describe how a system will evolve from one state to the next, but surely the ultimate laws ...
1
vote
0answers
182 views
Improvement of Von Neumann's measurement scheme [closed]
I would like to know some references on possible improvements of Von Neumann's measurement scheme beyond the use of POVMs.
Specifically, I am interested in the possibility of implementing a sort of ...
5
votes
1answer
354 views
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 $...
0
votes
2answers
60 views
How non-conservative fields emerged in the universe?
I know all of the fundamental forces/fields(Gravitational, Electromagnetic, Strong and Weak) of the nature are conservative and we know every other derived force/field in the nature is just produced ...
0
votes
1answer
307 views
Dispersion relation of QM in the presence of a potential
Correct me if I'm wrong, but equations in QM are quite always obtained by looking at the energy dependance of the problem of interest. For example, for Schrodinger's equation one just uses
$E = \...
7
votes
4answers
1k views
Circular definitions in Special Relativity?
Standard textbooks introduce Special Relativity in this way:
They introduce two postulates, the second being something like that
The speed of light in a vacuum is the same for all observers, ...
0
votes
3answers
226 views
What is the program of quantum field theory? What is its derivation?
Paraphrasing Griffith's: For some particle of mass m constrained to the x-axis subject to some force $F(x,t)=-∂V/∂x$, the program of classical mechanics is to determine the particle's position at any ...
7
votes
2answers
2k views
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?
...
6
votes
6answers
965 views
What things in our universe can be considered uncountable? [closed]
I am taking a course in mathematics that covers countability. The trick with the uncountability of the real line is that no matter how many times you divide up an interval, there would still be a real ...
1
vote
0answers
80 views
Why not measure the velocity of a quantum particle by $\frac{\Delta \vec{x}}{\Delta t}$
Why is it not possible in quantum mechanics to measure the velocity (and thus momentum) of a particle just by two position and time measurements and get it approximately by
$$
\vec{v} = \frac{\vec{x}...
