Even though there are much better standards for it
user228700
@JohnR: Oh. My. God. They've created a server especially for Harry Potter (for the members of the Nerdfighteria Scavenger Hunt community) and I am positively freaking out.
apparently, reference frames are not obligated to use a coordinate system, but then what other options could you use to specify say the position of an object?
A reference frame is a point of view. A coordinate system is an agreement on how to measure position and time.
You can have a point of view without specifying how to measure stuff, thought it makes a hash of all the mathematical tools we use in introductory physics.
Which means that you need a rather high-level view of physics and some abstract mathematical tooling to do coordinate-free physics.
I really struggled with the course on the subject I took in grad school.
Note that the definition of "reference frame" I gave includes both inertial and non-intertial frames. But for the introductory course you want to stick with inertial frames. Really.
Why do you think I was disrespectful? I simply can't understand it... I'm looking for someone with a certain degree of experience...why would that make me a phallus waving around?
no sense at all
Now, callin' me a phallus?! Isn't that also an insult?
in my opinion, if you got offended because I was looking for someone with a certain degree of expertise it's because you're not humble enough to admit that experience counts
As a workaround while this request is pending, there exist several client-side workarounds that can be used to enable LaTeX rendering in chat, including:
ChatJax, a set of bookmarklets by robjohn to enable dynamic MathJax support in chat. Commonly used in the Mathematics chat room.
An altern...
Steenrod builds the metric as a bundle of $S_{n,k}$, the set of symmetric invertible matrices of signature $k$, but it seems weird to not make it a subset of the tensor (0,2) bundle
"Any complex non-singular matrix $\tau$ can be factored in one and only one way into a product $\tau = \sigma \alpha$ where $\sigma$ is unitary and $\alpha$ is positive definite hermitian"
It occurred to me today that I don't know what a good approach is for providing hints to homework-like questions.
I cannot find any clear policy on how this should work. The example that brought it to my attention is this question.
My initial reaction was to comment with a question to help poi...
I mean that sounds very reasonable, but usually when I inquire about this I get the impression that no bc classification of manifolds
Or maybe not all triangulable manifolds are classifiable?
Maybe you require a nice triangulation
"It follows that every topological m-manifold, m≥7 (or m≥6 if ∂M=∅), can be triangulated if and only if there exists a PL homology 3-sphere H3 with Rohlin invariant one such that H3#H3 bounds a PL acyclic 4-manifold."
"Hence the set of all hermitian matrices is homeomorphic to $R^n \times C^{n(n-1)/2}$, ie also to $R^{n^2}$."
I'm not sure how this relates exactly
Oh wait, no, it's actually the next theorem
"Any regular matrix $\tau$ may be written in one and only one way as the product $\tau = \sigma \alpha$ of a unitary matrix $\sigma$ and a positive definite hermitian matrix $\alpha$"
Now the thing to prove is that if the retraction of a bundle admits a global section, the bundle admits one too
> My master’s thesis research focused on the metric structure of Lorentzian manifolds, including a simplified linear-algebraic version of the proof that a Riemannian manifold admits a Lorentzian metric if and only if it admits a smooth one-dimensional distribution.
So, based on the suggestions by @dmckee, here's my attempt to summarize the differences between a coordinate system and a frame of reference. Please, make me know if this definition is wrong or inconsistent with something that you know about. Also, if it's lacking of info, make me know.
Roughly speaking, a reference frame is a “point of view” and a coordinate system is an “agreement” on how to specify points, which, in a frame of reference, can assume different meanings (like position or velocity), depending on the context. {CONT}
{CONT} We can have a point of view (i.e. frame of reference) without specifying how to measure (i.e. without specifying a coordinate system) what we want to measure, but it would probably not be too useful. Hence a frame of reference (a “perspective”) can use different “agreements” (i.e. coordinate systems) on how to specify the properties of the objects
In a comment on the accepted answer to this question about non-mainstream physics, @jdm said:
+1, I'd add two things: 1) Questions about non-mainstream physics should be ok, e.g. ("Have Podkletnov's antigravity experiments been independently reproduced?", "Why do we believe cold fusion can't ...
As a workaround while this request is pending, there exist several client-side workarounds that can be used to enable LaTeX rendering in chat, including:
ChatJax, a set of bookmarklets by robjohn to enable dynamic MathJax support in chat. Commonly used in the Mathematics chat room.
An altern...
It occurred to me today that I don't know what a good approach is for providing hints to homework-like questions.
I cannot find any clear policy on how this should work. The example that brought it to my attention is this question.
My initial reaction was to comment with a question to help poi...
In a comment on the accepted answer to this question about non-mainstream physics, @jdm said:
+1, I'd add two things: 1) Questions about non-mainstream physics should be ok, e.g. ("Have Podkletnov's antigravity experiments been independently reproduced?", "Why do we believe cold fusion can't ...
