@ACuriousMind Looks like I dozed off right before you sent that. My text is using the tensor product definition $(f\otimes w)(v,h) \equiv v(f)h(w) = f(v)h(w)$ for $v\in V, f\in V^*, w\in W$, and $h\in W^*,$ mapping $V\times W^* \rightarrow \mathcal{C}$.
Seems like an extremely nice definition, because if $W = V$ then $V^*\otimes V: V\times V^*\rightarrow \mathcal{C}$ lives in the same vector space as $(1,1)$ tensors, so any $(1,1)$ can be written with the $\{e^i\otimes e_j\}$ basis, generalizing to $\mathcal{T^r_s}\in\text{span}\{e^{i_1}\otimes\cdot\cdot\cdot e^{i_r}\otimes e_{j_1}\otimes\cdot\cdot\cdot e_{j_s}\}$
Any element of $\mathcal{T}^r_s$ is in that span, I mean.
Maybe I'm being a bit sloppy; by $V^*\otimes V$ in that mapping I'm denoting any element of that vector space, not the space itself.
@Slereah Just worked out the connection, and now what you're saying on "not quite a curry" makes so much sense. $(e^i\otimes e_j)(v,f) = v^k\delta_k^if_\ell\delta_j^\ell = v^if_j$, and just a "partial" on $v$ as $(e^i\otimes e_j)(v) = v^k\delta_k^ie_j = v^ie_j = E_{ji}v$, where $E_{ji}$ is the matrix with a $1$ $(ji)^{\text{th}}$ position, $0$ in all others. So they are connected by
Yeah man, thanks a lot! I just realized how that nicely shows the different ways of viewing the moment of inertia tensor, either as returning the kinetic energy from a $(2,0)$ or the angular momentum from a $(1,1)$:
Two cats are sitting on a slanted tin roof. Which one falls off first? I've tried to figure it out, but I can't figure out any way to tell which cat falls off first.
@KyleKanos This is an interesting theoretical problem. I suggest trialing it with an experiment that may or may not involve dropping cats off of roofs.
You're failing to incorporate the coefficient of friction, which could be different between the cats and, thus, could provide an answer. In fact, I believe the resolution to this problem is commonly stated as the cat having the smaller coefficient of kinetic friction will slide off first. — Jim15 mins ago
I don't get it. This guy admits his answer is wrong, but has done nothing to fix it.
I went back over the paper and saw their reasoning. I was wrong with my answer. I would recommend checking out the book Gravity by J.B. Hartle for more information, which can be found here: archive.org/details/… — Guthrie Douglas Prenticeyesterday
Two cats are sitting on a slanted tin roof. Which one falls off first? I've tried to figure it out, but I can't figure out any way to tell which cat falls off first.
@AbhasKumarSinha In English, the sound a cat makes is usually spelt "mew", and some people pronounce the Greek letter "mu" the same way. $\mu$ is commonly used for the coefficient of friction.
Because a low-frequency beam at a high intensity could not build up the energy required to produce photoelectrons like it would have if light's energy were continuous like a wave, Einstein proposed that a beam of light is not a wave propagating through space, but rather a collection of discrete wave packets(photons).
I would like to discuss the policy around asking questions which are intended as setups for a joke. I searched through the meta, and didn't see anything about this directly, so I would like to gauge the community opinion on this.
For an example of what I am talking about, see today's question T...
This question. Until recent interface changes, I could see that the close reason stated that the question is about engineering, and hence is off topic, but an inquiry I made has shown that this reason is wrong, and a suggestion that it is, rather, too broad, was given instead.
As I can see, the ...
I would like to know how is the form of the electromagnetic energy-momentum tensor for a tetrad frame. I mean for a perfect fluid we have then that the tensor is defined as $T_{ab}= (\rho + p)u_{a}u_{b} + pg_{ab}$ but for a observer moving with the fluid (a comoving tetrad) the matrix have the form of $T_{ab} = Diag(\rho, p_{1},p_{2},p_{3}) $ I would like to know for electromagnetic energy-momentum tensor.
how has there been so much discussion about this meta post? Honestly, I'm disappointed in everybody. I'm going to have to ask you guys to turn in your scientist cards
@Jim You seem to imply (based on your answer) that just because we see a possible experiment, we should do the experiment. That seems like a dangerous road for scientists to take. First it's good to figure out if the experiment will lead to any damage, which is presumably why they polled the community first.
@JMac I agree, but given that we have another "published paper" from Stack Overflow that presents successful data from their own conducting of the experiment, we have good reason to believe the experiment is not prohibitively dangerous
@Jim Sure, but the SE communities are different. Asking and confirming before actually doing it makes a lot more sense than just assuming it will work the same on Physics as other SE's. That's how we wind up with our close reasons hidden from new users, because it's not a big deal on SO so they just went ahead and did it network wide without consulting us. I like this way better.
No, it's good that they asked us first. That isn't what surprises me. It's the amount of discussion, some of the resistance, and their surprise over a quick uptake that gets to me
@AaronStevens I got lost too, just like on the first thread OP made. They have a really strange way of wording things that I have trouble following the intended meaning of what they are saying.
@JMac Exactly how I feel too. They had a comment that has been deleted (not sure by who) that claimed I was slandering their good name, and that I am bound by my honor to keep talking to them.
I've asked a several questions (for example, one about gravity waves (3k views) in the two last days With more than 2k views. So not too long ago. There is another question (I don't want with say who asked it because I think this ain't fair) with almost 100 views, that is marked as hot.
Why the...
I would like to discuss the policy around asking questions which are intended as setups for a joke. I searched through the meta, and didn't see anything about this directly, so I would like to gauge the community opinion on this.
For an example of what I am talking about, see today's question T...
I've asked a several questions (for example, one about gravity waves (3k views) in the two last days With more than 2k views. So not too long ago. There is another question (I don't want with say who asked it because I think this ain't fair) with almost 100 views, that is marked as hot.
Why the...
