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
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 ...
104
votes
6answers
6k views

What are the justifying foundations of statistical mechanics without appealing to the ergodic hypothesis?

This question was listed as one of the questions in the proposal (see here), and I didn't know the answer. I don't know the ethics on blatantly stealing such a question, so if it should be deleted or ...
99
votes
0answers
5k views

Experimental test of the non-statisticality theorem?

Context: The paper On the reality of the quantum state (Nature Physics 8, 475–478 (2012) or arXiv:1111.3328) shows under suitable assumptions that the quantum state cannot be interpreted as a ...
82
votes
15answers
11k views

Why quantum mechanics?

Imagine you're teaching a first course on quantum mechanics in which your students are well-versed in classical mechanics, but have never seen any quantum before. How would you motivate the subject ...
64
votes
8answers
6k views

Why is the application of probability in QM fundamentally different from application of probability in other areas?

Why is the application of probability in quantum mechanics (QM) fundamentally different from its application in other areas? QM applies probability according to the same probability axioms as in other ...
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 ...
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 ...
32
votes
6answers
3k views

Reason for the discreteness arising in quantum mechanics?

What is the most essential reason that actually leads to the quantization. I am reading the book on quantum mechanics by Griffiths. The quanta in the infinite potential well for e.g. arise due to the ...
31
votes
3answers
6k views

The interpretation of mass in quantum field theories

Consider a free theory with one real scalar field: $$ \mathcal{L}:=-\frac{1}{2}\partial _\mu \phi \partial ^\mu \phi -\frac{1}{2}m^2\phi ^2. $$ We write this positive coefficient in front of $\phi ^2$ ...
28
votes
6answers
2k views

Is the density operator a mathematical convenience or a 'fundamental' aspect of quantum mechanics?

In quantum mechanics, one makes the distinction between mixed states and pure states. A classic example of a mixed state is a beam of photons in which 50% have spin in the positive $z$-direction and ...
28
votes
3answers
1k views

Why are only linear representations of the Lorentz group considered as fundamental quantum fields?

As described in many Q&As around here, fundamental quantum fields are expressed as irreducible representations of the Lorentz group. This argument is entirely clear - we live in a Lorentz-...
25
votes
2answers
2k views

Why am I wrong about how to view gauge theory?

Edit: I know there have been some similar questions but I don't think any had quite articulated my particular confusion. If gauge symmetries are really just redundancies in our description accounting ...
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)...
20
votes
5answers
3k views

What happened with Hilbert's sixth problem (the axiomatization of physics) after Gödel's work?

I'll write the question but I'm not fully confident of the premises I'm making here. I'm sorry if my proposal is too silly. Hilbert's sixth problem consisted roughly about finding axioms for physics (...
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 ...
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 ...
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 ...
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? ...
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 ...
11
votes
3answers
425 views

POVMs that do not require enlargement of the Hilbert space

The usual justification for regarding POVMs as fundamental measurements is via Neumark's theorem, i.e., by showing that they can always be realized by a projective measurement in a larger Hilbert ...
9
votes
3answers
4k views

Learn QM algebraic formulations and interpretations

I have a good undergrad knowledge of quantum mechanics, and I'm interesting in reading up more about interpretation and in particular things related to how QM emerges algebraically from some ...
9
votes
4answers
684 views

What fundamental principles or theories are required by modern physics? [closed]

We have been taught that speed of light is insurmountable but as we know an experiment recently tried to show otherwise. If the experiment did turn out to be correct and confirmed by others, would ...
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 ...
8
votes
5answers
2k views

General relativity and the microscopic/macroscopic distinction

Here is Wikipedia's diagram of the stress-energy tensor in general relativity: I notice that all of its elements are what would be termed "macroscopic" quantities in thermodynamics. That is, in ...
8
votes
1answer
702 views

Are identity types interpreted physically in an infinity-topos formulation of equations of motion?

In reference to Urs Schreibers paper/book on foundations of field theory Differential cohomology in a cohesive infinity-topos I wonder: are identity types there used "only" for the computations, or ...
8
votes
2answers
1k views

In the topos-theoretic interpretation of Physics by Isham & Doering what role does intuitionistic logic play?

Isham & Doering have written a series of papers exploring how to ground physics in topoi. Now the internal logic of topoi is higher order typed intuitionistic logic. In their theory what role is ...
8
votes
3answers
247 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 ...
8
votes
3answers
1k views

What makes General Relativity conformal variant?

I have a question regarding the well known fact that General Relativity is not a conformal invariant theory or to put it in other words about the fact that it is conformal variant: What are the ...
7
votes
7answers
1k views

Why should a (physical) principle be applicable to different systems in different positions in space and time?

This is a question with a philosophical, as well as physical, flavor. Why should a physical principle (or a description of one), be applicable to different systems that can be in different positions ...
7
votes
2answers
6k views

How important is mathematical proof in physics?

How important are proofs in physics? If something is mathematically proven to follow from something we know is true, does it still require experimental verification? Are there examples of things that ...
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, ...
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'...
7
votes
1answer
199 views

Quantum Logic and Quantum Field Theory

Quantum Logic is a very interesting and powerful answer to the problem of Quantum Mechanics foundations. Nevertheless this approach is usually developed in a non-relativistic framework. Is it still ...
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 ...
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
3answers
2k views

What is the difference between realism in locality, and counterfactual definiteness?

I understand the EPR-experiment and the Bell inequalities. I can see how dropping 'locality' solves the issue, and how dropping 'realism' solves the issue (e.g. there are really no hidden variables ...
6
votes
1answer
121 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 ...
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 ...
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 ...
5
votes
1answer
129 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, ...
5
votes
3answers
871 views

Banach Space representations of physical systems

I think most physicists mostly model physical systems as some kind of Hilbert space. Hilbert spaces are a strict subset of Banach spaces. Questions: Can physical systems really have non-compact ...
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 $...
5
votes
0answers
260 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 ...
5
votes
0answers
243 views

What is meant by “quantum steering”?

I have become interested in quantum steering after listening a talk and tried to read more about it. I think I am more confused now. My understanding is as follows: Sharing a (entangled) state, Bob ...
4
votes
1answer
775 views

Time evolution in QFT

Standard quantum mechanics postulates that, for an isolated system, time evolution is ruled by unitary operators, then one can prove Schrodinger equation (SE), which is not Lorentz invariant. If we ...
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, ...
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 ...
4
votes
1answer
165 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 ...
4
votes
1answer
348 views

What are type system examples of local gauge transformation- and field strength-like objects?

This is essentially a follow up motivated by this answer to my question about the gauge transformation interpretation of identity types. A field $$\psi:\mathcal M\to\mathbb C^n$$ is a section of the ...
4
votes
0answers
68 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 $\mathbb{R}^3$. ...