@alarge I've been booting and rebooting quite a bit for this Morrowind mod installer. From the moment the screen went black from the shut down to a 1080p YouTube video playing: 28 seconds.
I have to find a mathematical model for the temperature vs. time to study the temperature of the environment next to a lamp.
The lamp is very powerful, so heating a lot
When the lamp is started, a cooling starts with increasing efficiency and stabilisation after a short amount of time
When the ...
I'm watching MIT online lectures Quantum Physics I (roughly from one hour mark in the video). The lecturer explains wave functions that describe "Stationary States" that consist of a single energy eigenfunction then he points out that no such thing exists in real life. At some point a student ask...
Yeah, could be... I've understood the E-t uncertainty principle to be more of a heuristic saying that measuring energy to a certain precision requires a certain amount of time in which the system is coupled to the measuring device.
I'm quite surprised to see this highly upvoted on MO
user54412
@DavidZ Sure I guess it's on topic. I mean, it is modeling a physical system.
user54412
Of course, I don't know why such a simple task is being described in such an enormously complicated way. Is this what "data science" is?
@ChrisWhite I'm not sure anyone really knows what data science is :-P but seriously though: it appears to be focused on the extraction of patterns from data sets which can in general be very large. It's like the applied math version of phenomenology. And I think that's the focus of the question as it's currently written.
There's some physics in there, sure, but it seems to be buried.
@gonenc no argument there
> Big data is like teenage sex: everyone talks about it, nobody really knows how to do it, everyone thinks everyone else is doing it, so everyone claims they are doing it.
@DavidZ FWIW I would consider the Temperature modeling question off-topic for the Data Science SE. It's mostly physics, with some stats. Yeah, who knows what DS is, but based on my read of how people use the Data Science SE, you wouldn't get a good answer to this there.
Hmm, so tomorrow's chat session will be shortly after the New Horizons closest approach.
user54412
(+/- some hours -- no one's particularly clear on whether they're using physicist clocks-and-rulers-throughout-spacetime perspective or astronomer past-light-cone perspective)
Quick question : I've just started reading on SR, and was wondering : in 3D geometry, if we know all the pairwise distances between all the points of a set then we know how they are organized, modulo any rotation of the whole set around the origin. If likewise we know all the pairwise spacetime intervals between events of a set, they will be determined modulo ... ?
Asked another way, what is the practical equivalent of the rotation of an event in spacetime ?
In non-relativistic QM, the $\Delta E$ in the time-energy uncertainty principle is the limiting standard deviation of the set of energy measurements of $n$ identically prepared systems as $n$ goes to infinity. What does the $\Delta t$ mean, since $t$ is not even an observable?
@ACuriousMind do you have any particularly good way of learning them, this book that I have starts the deal with vector calculus and advances therefrom
Ugh I'm having a weird problem with spacetime intervals : if some spaceship travels from a point A to a point B at the speed of light, then in the frame of reference of A the spacetime interval would be $0$, but from the ship's interval it would be non zero since the time interval is non zero and the distance is zero...
In mathematics, the musical isomorphism (or canonical isomorphism) is an isomorphism between the tangent bundle TM and the cotangent bundle T∗M of a Riemannian manifold given by its metric. There are similar isomorphisms on symplectic manifolds. The term musical refers to the use of the symbols ♭ and ♯.
It is also known as raising and lowering indices.
== Discussion ==
Let (M, g) be a Riemannian manifold. Suppose {∂i} is a local frame for the tangent bundle TM with dual coframe {dxi}. Then, locally, we may express the Riemannian metric (which is a 2-covariant tensor field which is symmetric and...
In mathematics, the interior product or interior derivative is a degree −1 antiderivation on the exterior algebra of differential forms on a smooth manifold. The interior product, named in opposition to the exterior product, is also called interior or inner multiplication, or the inner derivative or derivation, but should not be confused with an inner product. The interior product ιXω is sometimes written as X ⨼ ω.
== Definition ==
The interior product is defined to be the contraction of a differential form with a vector field. Thus if X is a vector field on the manifold M, then
is the map which...
Ok basically to do the exercise above to first get the spacetime interval in the Earth frame we get the measured time between the two events $\Delta t_T=\frac{100}{95}c$, the measure distance between the two events in light years $\Delta l_T=4.3$ and that gives us a squared interval of $I^2=4.3^2(\frac{100^2}{95^2}-1)$ light years. Now if we do that from the ship's frame we'l just get $I_t^2=I_s^2=\Delta t_s^2>>0$. Then I wondered why we still had $I_s^2>>0$ but $I_t\to0$ when
the speed was tending to the speed of light. ($T$ is for earth, $s$ is for ship)
@ChrisWhite That's not what I'd call data science (going to the original question) because he's not looking through actual data sets to find relationships, he's simply modeling a physical scenario and using statistical techniques.
"*Reassert the twin paradox in a new light, leading to the conclusion that the theory of relativity is inconsistent with the physical reality*" ← sign of a big big bs
@gonenc Basically when the speed tends to $c$ we have $\tau\to0$ if we look from the earth's frame. However, if we look at the ship's frame, since $\dot{x}=0$, shouldn't we have $t=\tau\to0$ ? (that sounds very false to me)