Questions tagged [foundations]

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

Filter by
Sorted by
Tagged with
3
votes
0answers
211 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
368 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
106 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 ...
147
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 ...
1
vote
1answer
64 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
288 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
351 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
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
121 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
102 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
186 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
330 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?
22
votes
1answer
1k 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
323 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
908 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
259 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
103 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
91 views

Defining Quantum Mechanics

Does Schrödinger's Equation (Operator form) $[\hat{X},\hat{P}]=i$ Born Rules define Quantum Mechanics?
0
votes
2answers
193 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
45 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
81 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
198 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
490 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
72 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
373 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
264 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 ...
13
votes
2answers
3k 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
1k 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
84 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}...
14
votes
2answers
1k views

The Origins of the Second Quantization

I've been studying quantum theory for a while now and have a number of closely related questions that are not giving me any peace. I am not sure if such a long format is appropriate here, but I'd like ...
1
vote
3answers
363 views

What Statistical Mechanics does in classical regime

In a book of Dipankar Home, "Foundations of Quantum Mechanics", he has mentioned that A newer theory should not only predict all the results that are already predicted by it's predecessor where it ...
5
votes
1answer
322 views

Help needed to understand “On the reality of the quantum state”

I am having trouble to understand the reasoning in the following paper, On the reality of the quantum state. MF Pusey, J Barret and T Rudolph. Nature Phys. 8, 475–478 (2012); arXiv:1111.3328. From ...
0
votes
2answers
328 views

Tensor product postulate [duplicate]

Non relativistic quantum mechanics assumes that a composite system should be described with the tensor product of the component systems. This is the tensor product postulate of quantum mechanics. I ...
1
vote
2answers
207 views

Relativistic probability amplitude of a particle to be in certain position

In the book “The story of spin” by Tomonaga on page 110, it says They insisted that a concept like "the probability of a particle to be at $x$ in space" is meaningless for relativistic particles—be ...
0
votes
2answers
277 views

Postulates of Relativistic Quantum Mechanics

I have been reading this Phys.SE answer in order to clarify my doubts. It seems to me that he claims that the postulates are the same no matter if it is QFT, QM or whatever. But some books tell us ...
8
votes
2answers
2k views

Is Einstein's characterization of “time” as “the position of the little hand of my watch” definitive and binding in the RT?

In Einstein's very first publication dealing with the Theory of Relativity, effectively as a preamble to all subsequent thought-experimental considerations and descriptions, Einsteín put the ...
1
vote
2answers
325 views

Is there any physical meaning for the inverse metric?

I've been wondering if we can attribute any physical meaning to the inverse metric. I mean when we talk about the metric itself, there are lots of insights we can have towards its role in spacetime, ...
0
votes
2answers
157 views

Does one *feel* the electrostatic force while not resisting it?

Suppose that I put lots of big magnets around me, or say, that I charge myself up to a macroscopic charge. Now, suppose that there's a huge magnet in front of me (or a huge object with opposite charge)...
0
votes
0answers
87 views

Derivable Concepts in Mechanics and Electromagnetism

In Classical Mechanics, one of the possible foundations is based on three concepts aka mass(equivalent to energy), length and time. This is a foundation because we can model everything ( pressure, ...
0
votes
0answers
73 views

finetuned quantum experiments by Murch lab, do any have dynamics outside of basic QM formalism/ axioms?

a series of very finetuned quantum experiments have been reported by the Murch lab eg in 2 articles in Nature & analysis there,[1][2][3] some leading to dramatic accounts in the media.[4] do ...
4
votes
2answers
543 views

Hilbert's sixth problem (current answers neglect the fact that $C_{U} \subseteq U $ ) [duplicate]

(current answers neglect the fact that the set of all concepts( $C_{U}$) is a subset of U as all of them are physically encoded( symbolically represented by the physical events themselves(brains, ...
7
votes
2answers
138 views

Is there a reason why the subset of our Hilbert space that corresponds to a particle is a vector subspace?

I'm trying to gain some intuition behind the definition that states a particle is an irreducible unitary representation of the restricted Poincare group (or more specifically, its double cover). Let'...
2
votes
0answers
226 views

The implications of Gödel's Second Incompleteness Theorem on Theoretical Physics models [duplicate]

Does Gödel's Second Incompleteness Theorem imply that no Theoretical Physics model of reality can be proved to be consistent using the laws of physics? I work partially in Quantum Information Theory ...
3
votes
5answers
695 views

On the foundations of quantum physics

Quantum physics has to be validated by experiments. But experiments are to be interpreted in the context of quantum physics. Isn'it like a snake biting its own tail? For example, using a scanning ...
0
votes
1answer
594 views

Why should we believe in clock hypothesis? [closed]

It is often assumed in special relativity that the rate of a clock in a non inertial frame does not depend on the proper acceleration of the observer. The point is, Rindler's observer shows us that ...
2
votes
2answers
174 views

The principles of statics without force

I'm a student of civil engineering and now my course is covering the basics of statics, such as the equations of equilibrium, etc. Trying to get a better basis on the subject, I started to search on ...
16
votes
5answers
315 views

How is anything *not* ultimately a position measurement?

Consider measuring the momentum of an electron. You pass it through some kind of electromagnetic field, it strikes a photodetector (e.g. a CCD), and you back-calculate out the momentum of the ...
40
votes
7answers
20k views

How can one derive Schrödinger equation?

The Schrödinger equation is the basis to understanding quantum mechanics, but how can one derive it? I asked my instructor but he told me that it came from the experience of Schrödinger and his ...
5
votes
0answers
261 views

Understanding the states in Quantum Field Theory

I am self-studying quantum field theory, and I've been struggling to understand the nature of the states that emerge in quantum field theories. After thinking about it, what I think one has in the ...