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Questions tagged [foundations]

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

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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 ...
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 ...
5k 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 ...
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 ...
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 (...
19k 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 ...
5k 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 $\phi ^2$ ...
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 ...
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 ...
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 ...
443 views

216 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 ...
100 views

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

Is Einstein's insight  that All our well-substantiated space-time propositions amount to the determination of space-time coincidences [such as] encounters between two or more [...] material ...
4k 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 ...
684 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 ...
5k 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 ...
161 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 ...
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 ...
2k views

The meaning of 'postulate' in physics? [duplicate]

What does postulate mean in physics? What is its role in physical theories? Is it possible to break physical postulates?
73 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 ...
277 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 ...
207 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 ...
338 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 ...
164 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 ...