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69
votes
6answers
2k 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 ...
38
votes
0answers
881 views

Experimental test of the non-statisticality theorem?

Context: The recent paper The quantum state cannot be interpreted statistically by Pusey, Barrett and Rudolph (now On the reality of the quantum state, Nature Physics 8, 475–478 (2012), ...
27
votes
14answers
2k 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 ...
17
votes
6answers
715 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 ...
13
votes
4answers
780 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 ...
13
votes
3answers
684 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 $\phi ^2$ ...
11
votes
3answers
620 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 ...
11
votes
3answers
362 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 ...
11
votes
3answers
201 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 ...
7
votes
1answer
179 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 ...
6
votes
2answers
511 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 ...
6
votes
5answers
714 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 ...
5
votes
2answers
212 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 ...
4
votes
3answers
949 views

Learn algebra and interpretation of QM

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 algebrically from some reasonable ...
3
votes
3answers
230 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 ...
3
votes
1answer
87 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 ...
3
votes
0answers
62 views

on 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, ...
2
votes
1answer
99 views

What aspect of quantum mechanics forces probabilities to be (conventionally, at least) central?

I understand how to compute probability distributions and expected values and such from quantum states, but a lot of treatments of QM make it look like this is what the wavefunction is essentially ...
1
vote
2answers
125 views

What are the practical applications of quantum foundations?

Many quantum foundation researchers keep emphasizing that For All Practical Purposes (FAPP), quantum foundations are irrelevant. They even invented an acronym for it! Does that mean that quantum ...
1
vote
2answers
79 views

How rigorous can conservation of energy be made?

The principle conservation of energy is often taken as an obvious fact, or law of nature. But it seems to me the definition of energy is far from obvious, or natural: ...
1
vote
3answers
488 views

Is the classical world an illusion?

In the paper Zeh, H. D. The Wave Function: It or Bit? In Science and Ultimate Reality, eds. J.D. Barrow, P.C.W. Davies, and C.L. Harper Jr. (Cambridge University Press, 2004), pp. 103-120. ...
1
vote
1answer
86 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 ...
1
vote
2answers
69 views

How are propositions concerning spacetime curvature constructed explicitly in terms of coincidences?

Is Einstein's insight [1] that All our well-substantiated space-time propositions amount to the determination of space-time coincidences [such as] encounters between two or more [...] material ...
1
vote
1answer
110 views

Questions about MTW's _“thousand” tests of the Einstein principle_ (Box 16.4)

In Misner, Thorne, Wheeler (henceforth written as "MTW"), "Gravitation", Box 16.4, there's an experimental setup construction (or method) presented by which "Each geodesic clock is constructed and ...
1
vote
0answers
28 views

Ontic state space from operational structures

Operationalism eschews a notion of system state in favour of the empirical behaviours of preparation and measurement. Abramsky has formalized operational structures as Chu spaces. It would be nice ...
1
vote
0answers
22 views

Does it make sense to speak of amplitudes of finite closed boundaries in QFT?

A example of amplitude in Relativistic Quantum Mechanics or specifically in QFT is the amplitude of a field configuration on a space-like hyper-surface of space-time to "lead" to another field ...
0
votes
1answer
113 views

How to go from Quantum World to Classical World? [duplicate]

Possible Duplicate: Is it possible to recover Classical Mechanics from Schrödinger’s equation? Classical Limit of the Feynman Path Integral In the quantum world we don't have ...
0
votes
0answers
109 views

Can quantum field theory be seen as an epistemic restriction on (quantum) causal structure

Suppose we take Vicary's quantum harmonic oscilator as a kind of "toy quantum field theory". Next, take the category of internal comonoids to not represent the background causal structure. We ...
-1
votes
1answer
92 views

Which “space-time coincidences” are described by a “co-ordinate system in which the gravitational field does not appear”?

In Einstein's exposition of the foundations of General Relativity (cmp. http://en.wikisource.org/wiki/The_Foundation_of_the_Generalised_Theory_of_Relativity , end of §3) there appears an emphasis on ...