Devoted to the conceptual bases of the fundamental theories of physics, to their philosophical and logical premises.
Questions tagged [foundations]
285 questions
169
votes
11 answers
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 of the following criteria are valid:
Partial…
AccidentalFourierTransform
- 56,647
124
votes
1 answer
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 probability distribution over hidden variables.
In the…
Chris Ferrie
- 2,908
120
votes
6 answers
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 be changed to CW then I'll let the mods change…
Logan M
- 4,614
111
votes
15 answers
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 and convince your students that in fact classical…
Jonathan Gleason
- 8,834
93
votes
8 answers
Why is the application of probability in Quantum Mechanics 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 areas of physics, engineering, etc.
Why is there…
Nikos M.
- 5,302
49
votes
9 answers
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 experiments. My question is, can one derive the…
A.khalaf
- 852
41
votes
7 answers
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 boundary conditions, and the quanta in harmonic…
user7757
40
votes
5 answers
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 $\phi ^2$ as $\frac{1}{2}m^2$, and then start calling $m$…
Jonathan Gleason
- 8,834
34
votes
18 answers
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 those questions really resolved my own question :…
34
votes
6 answers
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 50% have spin in the positive $x$-direction. …
Jonathan Gleason
- 8,834
31
votes
3 answers
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-invariant world and those elements of an observed system that…
Void
- 21,331
29
votes
1 answer
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 $\rho(x)$ can be measured (at least to some accuracy) in…
spinachflakes
- 7,318
26
votes
2 answers
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 to seize this opportunity and share my questions…
mavzolej
- 3,093
26
votes
8 answers
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 particle by how much it curved from a straight-line…
Nick
- 3,039
26
votes
2 answers
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 for nonphysical degrees of freedom, then how does…
gn0m0n
- 562