Philosophers could discuss the metaphysical implications of the candela and the radian, but physicists are better than that! That's why we shut up and calculate :P
I agree. I just remembered that mol was in the list of fundamental dimensions. But I'm not really sure why it's in there. Probably just for convenience and a historical remnant
Remember that dimensional analysis is a tool. Regardless of the philosophy over how correct it is to do so, it's often useful to include amount as a dimension; which is why people do it.
And one radian is absolutely not equal to one mole. They're really quite different things, as you know.
A measurement isn't the same thing as a dimension.
Dimensions are some kind of equivalence classes of measurements, where the equivalence relation is defined by saying that two measurements are in the same equivalence class if their ratio is unitless.
@LegionMammal978 Decibels can have different "starting points", say, 1 millivolt (dBmV) or 1 volt (dBV). The decibel does not care whether you're comparing electric potential or whatever, but the starting point matters.
OK, but Legion's comments indicate that he/she is confused over the distinction between a measurement and a dimension. If he/she is a mathematician, he/she will understand my comment. If not, I can elaborate. But the starting point is .... "a measurement is not the same thing as a dimension".
@LegionMammal978 Yes, it's like saying 1 truckload of potatoes is the same thing as 1 bag of potatoes. Of course, "truckload" and "bag" are defined differently, maybe a tonne and a kilogram. The only thing in common is that both ratios are 1/1 relative to a constant. But that constant is different on each case.
For example, I can separate these measurements - 3kg, 500g, 50km, 1cm, 2cm into two equivalence classes. Formally, I'd define those classes in such a way that two things in the same class have the same dimension.
Now do the same thing to the set of all possible measurements. Then the equivalence classes are the dimensions themselves.
I'm a Sr. front-end dev, coding in Babel ES6. Part of our app makes an API call, and based on the data model we get back from the API call, certain forms need to be filled out.
Those forms are stored in a doubly-linked list (if the back-end says some of the data is invalid, we can quickly get...
The irony of the question is that the first snippet looks like something a fairly experienced developer might write. The second snippet looks like it was written by a novice programmer who's just learnt a new technique.
I suspect that if you've heard or read "linear mass", the speaker/writer meant to say/write "linear mass density" but was just being careless. Knowing the context in which you heard or read it will confirm that (or not confirm it).
[Random] What if energy is really not conserved in cosmological scales where the curvature of spacetime is significant, but only conserve at the tangent spaces of the spacetime manifold
If so, then theoretically if we parallel transport from one tangent space to a neightbouring one, the change in energy will be consistent with the change in the curvature of spacetime?
I mean, as the light ray passed through a gravitationally dense region, it gains energy, but that is really because space is contracted relative to regions outside the gravitationally dense object.
But time should be dilated also relative to said frame, thus won't that cancel out the apparent gain in energy due to space looks contracted from that frame?
it should typically be open, otherwise you won't gonna get soundwaves in from the top. (Well you can, with something like closed jar and then send soundwave in by pressing a sound device on top of the lid, which is why for safety I will calculate both cases)
Exam questions are usually more clear through, though I am not sure about JEE because it is well known to be full of ambigurious questions
Is it for a generic fiber bundle on its vertical space
Or is it for vector bundles
Or is it that, for vector bundles, the vertical space is isomorphic to itself
"However, for a vector bundle there is a canonical isomorphism between the vertical space at the origin and the fibre VoE ≈ E. Making this identification, the solder form is specified by a linear isomorphism"
Hey does someone know a link to a derivation of $dQ/T = dS$? I only found questions here on SE about what entropy is in general but no derivation of this formula
In my physics book Tipler&Mosca there is kinda a derivation but as often in physicists literature it's written sloppy and not understandable for a learner
ok but about it being a definition, we know $dQ_{rev}$ is a inexact differential and it's stated often that $1/T$ is something called a integrating factor making $dQ_{rev}/T$ an exact differential how is that so?
@Slereah I understand that $dQ_{rev}$ is not an exact differential since Q_{rev} not a state function hence path dependant as you said, but why would dividing it by T making that better? Entropy is a state function but from first law of thermo we know work and heat are somewhat equivalent so how could integrating $dQ_{rev}/T$ give us the change of the system? We don't consider work here do we?
@Sanya Well, you'll see some people saying alternating multilinear forms $V \times V \cdots V \to \Bbb R$ on vector spaces as "k-forms". But I generally use that terminology when $V$ is a (varying) tangent space $T_pM$ of a differentiable manifold $M$ (well, tangent bundle, but whatever man)
So, if I am understanding this correctly, $1~\text{mol}=6.022141...\times 10^{23}$ (where the RHS dimensionless) in the same way that $1~\text{lb}=0.45359237~\text{kg}$. Correct?
Hey guys, if anyone is free could you take a minute to tell me what exactly is wrong with my question. why isn't it getting any answers or even comments? I read many related posts on meta, etc. but i still couldnt figure what was wrong. some suggested asking on the h bar.... [heres the question]physics.stackexchange.com/questions/334421/…)
I'm a Sr. front-end dev, coding in Babel ES6. Part of our app makes an API call, and based on the data model we get back from the API call, certain forms need to be filled out.
Those forms are stored in a doubly-linked list (if the back-end says some of the data is invalid, we can quickly get...
