This question: physics.stackexchange.com/questions/3983/…, specifically the answer by user1504. From the looks of it, the applicability of Haag's Theorem seems to be a somewhat controversial point, so I'm not sure if this is mainstream
@ACuriousMind thanks for pointing that out. I think the "actual" world is the real-world we live in; while, "all possible" worlds are the abstractions math makes.
In mathematics, variation of parameters, also known as variation of constants, is a general method to solve inhomogeneous linear ordinary differential equations.
For first-order inhomogeneous linear differential equations it is usually possible to find solutions via integrating factors or undetermined coefficients with considerably less effort, although those methods leverage heuristics that involve guessing and do not work for all inhomogeneous linear differential equations.
Variation of parameters extends to linear partial differential equations as well, specifically to inhomogeneous problems...
If what the answer said makes sense, I guess it's just saying this math trick better not leave any lasting physical impact on the final answer (i.e. it only matters in the intermediate steps)
I think the point about asymptotics that Lubos makes is why all of this stuff is basically irrelevant
Hey, I thought I'd ask here first instead of posting as a question, but does anyone have any good resources for understanding multipartite entanglement? I'm well versed with bipartite measures but read this paper (arxiv.org/abs/1106.4774) and i couldn't even understand the first result about all tripartite states being of the form mentioned, so I was hoping for a more pedagogical intro to tis subject.
I often see statements that say Einstein's paper on photoelectric effect proves that light consists of particles. How does it prove or disprove that light is a wave?
My understanding is that the paper proposed a hypothesis to explain Hertz's observations but how does it actually "prove" that light is made up of particles even if the mathematics works out.
@Yashas It doesn't "prove" anything. It proposes a model of light as particles that explains the specific observations of the photoelectric effect that the classical electromagnetic wave model cannot explain.
in a physics context people often use "prove" when they really mean "provide a convincing explanation", they don't mean that it adheres to any mathematical standard of proof
is it correct to say that for a particle like $e^-$, time evolution can bring a $e^-_L$ in $e^-_R$ thanks to the fact that the particle is massive ? (i.e., the weyl equations for the weyl spinors $e^-_L $ and $ e^-_R $ are coupled). And I'd even say that if I imagine absurdly that a $e^-$ is massless than both the left / right chiral states exist but they don't get mixed up like before. (depending on if this is right or not maybe a question on the neutrino will follow)
thanks @ACuriousMind . I actually don't know much about netruino oscillations. My problem with the nuetrino is this, if I assume that it is massless, then there isn't any known process that can create $\nu_R$ ( I think), but conceptually it would be wrong to state that $\nu_R$ doesn't exist, simply for now i can't "see" it. It is kind of a philosofical question maybe, but I got confused about this by a sentence in a paper
@Ratman afaik, no one thinks the neutrino is part of a Dirac field. Even in models like seesaw mechanisms where you have right-handed Neutrinos, they carry Majorana masses, not Dirac masses
i.e. the $\nu_L$ and $\nu_R$ aren't coupled via the Weyl equations even when they're massive - the masses are Majorana masses that don't appear in the Weyl equations
ok, that's really interesting. And at the same time I see I need to study more about neutrinos to understand this. Thanks a lot @ACuriousMind, your help is being very usefull
@BioPhysicist @VincentThacker Regarding this migration, it's worth keeping in mind that migrations get blocked if the question's tags don't exist in the destination site
@ACuriousMind yeah, well, of course you wouldn't, Mr Exception Man
> A migration can be automatically blocked before it even gets migrated if any of the following conditions apply: > The question does not use any tags that exist on the destination site, with three exceptions: > - a moderator performs the migration
in larger sites there's a substantial problem of over-migration, i.e., folks migrating crap questions that don't fit the target site at all, just because they don't want them in the origin site
asking that the tags match is a good bare-minimum requirement to ensure this
I don't really envy the sites on the business end of the migration funnels coming out of SO
@EmilioPisanty because it requires the tags on both sites to be aligned but there's no system to align them - what if we have group-theory and it's called groups on math?
There is, as far as I'm aware, no way for regular users to see intrinsic tags*. Moderators can see intrinsic tags in the same place as blacklisted tags though (labelled as "Intrinsic Tag" on the Blacklisted User Input page, visible at /admin/blacklist).
For example, on Graphic Design I see (reda...
but the way to learn about edge cases it to have them pointed out when one runs into them ;-)
If anything, [limit] should be [limits] and [group-ring] should be [group-rings] on MSE as well. — Asaf Karagila ♦Jan 2 '14 at 7:50
@AsafKaragila Then there are [definite-integral], [indefinite-integral], [extension-field]... where is Atwood's giant $\Huge{S}$? — Post No BullsJan 2 '14 at 8:03
Integrals seem better in singular form; but [extension-fields] does sound better. I only know where is Riemann's giant $\huge S$: $$\Huge\int$$ — Asaf Karagila ♦Jan 2 '14 at 8:06
@PrateekMourya while I was making a joke I was trying to point out that this seems like a chicken-and-egg question to me where the relevance of the answer is unclear
Uh could I double check I've got something right, a "something"-valued p-form (eg. a vector valued p-form) just means we are defining a tensor $\vec v\otimes \tilde\alpha^p$ where $\tilde\alpha^p$ is a p-form, whose output is a vector if we "partly fill" its arguments with enough vectors to "contract" the p-form, leaving a vector (or something else)?
note in particular that the term "angular momentum" itself only seems to have come into common usage around ~1850, whereas there's substantial useful understanding towards that term in Newton's Principia form 150 years earlier
the concept of angular momentum did not emerge fully-formed in one single fell swoop
it was built piece by piece over several centuries
I am trying to understand the conceptual development of the "torque". I saw that Archimedes was the one from whom this idea took birth. I wanted to know from whom the torque got its mathematical form.
I will also be happy to know further reading materials and sources.
Momentum and energy play very similar roles in mechanics, each being changed by the application of force over a interval. For energy the interval is in space and for momentum it is in time. Both have associated conservation laws.
Yet, energy units are named in many systems and momentum units gen...
anyways, it is possible to think about QM strictly in operationalist terms, as described here, where wavefunctions are just descriptors of preparation procedures and "observable" operators are just descriptors of measurement procedures
I don't know how common this view is in practice out in the wild
the classic is this survey, and I don't recognize any of the interpretations listed there as purely operationalist (but then again I don't fully understand all the options in the survey)
@NiharKarve yeah, it sounds bonkers at first sight
if you want to get in on the ground floor, I'd recommend this paper
The PBR theorem is a no-go theorem in quantum foundations due to Matthew Pusey, Jonathan Barrett, and Terry Rudolph (for whom the theorem is named). It has particular significance for how one may interpret the nature of the quantum state.
With respect to certain realist hidden variable theories that attempt to explain the predictions of quantum mechanics, the theorem rules that pure quantum states must be "ontic" in the sense that they correspond directly to states of reality, rather than "epistemic" in the sense that they represent probabilistic or incomplete states of knowledge about reality...
@NiharKarve (but if I wanted to pull your chain a bit, I'd remark that those terms are only relevant within realist theories, i.e., when you've already committed to there being something real, and not everybody agrees with that =P)
Growing up I used to enjoy reading Halliday and Resnick questions in Principles of Physics. But now I realise that Physics currently cannot represent reality accurately. This seems to me because the subject is hitting a wall which is physical. This wall is the inability of computers to operate on real numbers.
there's lots of problems with the implementation details of numerical algorithms, but rounding errors due to floating point representations are usually rather low on that list, so I'm not sure why you would think that
also, an approximate representation of reality is still better than no representation of reality, so what's the issue?
Hi, an isometry of a semi-riemannian $f:\Bbb R^{1,1}\to \Bbb R^{1,1}$ is different than an isometry for a Riemannian manifold right? In the Riemannian case distances must be exactly preserved, but for an isometry of a semi-riemannian manifold, the spacetime interval just needs to be preserved?
(btw, $\Bbb R^{1,1} from the textbook is a 2-dim. semi-riemannian manifold)
there's no difference between the notions of isometry for Riemannian and pseudo-Riemannian manifolds, "distance" and "spacetime interval" are just two different names for the metric on such a manifold
we don't call it a "distance" in the pseudo-Riemannian case because it can be zero and negative, which doesn't play well with our intuitive notions of "distance"
okay yeah that makes much more sense now. So, I'm trying to work through a proof and show that a nonlinear mapping (a sort of dilation I think) from Minkowski to Minkowski, preserves a "strongly equivalent metric"
because it cannot be a isometry, I now know
Looking at the definition I'm pretty sure it's not even "strongly equivalent" lol
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Let qA and qB represent unit, orientation quaternions of grain A and grain B of a grain boundary in the lab reference frame, respectively. Let qm be the misorientation quaternion of qA and qB. Quaternion inversion (qinv) and quaternion multiplication (qmult) are discussed in Quaternion...
I have a quick q about the "choice of connection 1-form". I've seen in the construction of a connection on a principal bundle $P$, the choice of connection comes down to the choice of a 1-form on $P$, this is roughly where the lecture I followed finished. On the other hand a connection on a rank-k vector bundle $E$ involves defining an $E$-valued 1-form such that a connection is a map: $$\nabla:\Gamma(E)\rightarrow \Gamma(E\otimes \Omega^1(M)),$$ so we more or less take a section...
... act with the connection on it, then contract the result with another section (this process amounts to "taking the covariant derivative" of one section wrt. the other) and get a third section. I'm wondering if this "choice of connection on $P$" in the principal bundle is essentially the equivalent of the choice of 1-form in $\Omega^1(M)$ for the vector bundle.