FYI: While doing some cleaning around here, the mods found some socks behind the dryer. Please brace yourself for possible lost reputation points. Although it should be much less than previous clean-up.
@ACuriousMind I thought the last chapter of the book "Bosonic String Theory" would be a bit more physical than the rest of the book, but it's just 30 pages of Riemann surface geometry.
@ACuriousMind I was being sarcastic. (Perhaps you knew that.)
@Danu Consider then a hypothetical system of 'justice' that, when a man is convicted of kidnapping and murdering a child, puts the parents in jail and gives their belongings to the kidnapper thus punishing the innocent.
@0celo7 This isn't difficult to understand and I'm frankly surprised at how such intelligent people here seem to be tripping over this. On the other hand, this a physics site, not a philosophy site so maybe I shouldn't be surprised.
@Icosahedron I'm afraid you've missed the point too. Honestly, I did not anticipate that it would be this difficult to make. In the example I give, the system explicitly and objectively punishes the innocent parents by design. Whether or not some consider the kidnapping a crime is irrelevant. Whether or not judicial laws don't always hold is irrelevant.
@AlfredCentauri But to say that such a system is unjust is a value judgement - you proclaim that it is unjust to punish "innocents". Others might proclaim it just to punish the parents since they failed to protect their kid. If there are possible personal beliefs that might lead to a situation be called just and unjust by people holding different beliefs, then it follows that just and unjust are not objective criteria.
@ACuriousMind The parents in my hypothetical are not being punished because they failed to protect their kids. This is important and crucial. The parents are being punished instead of the kidnapper for the actions of the kidnapper.
@AlfredCentauri But it is not even universal (hence not objective) that that should matter. For example, consequentialists do not acknowledge that reasons matter at all.
@ACuriousMind I do not wish to take a tangent here with competing ethical theories (though that would be fun if I had the time). To get back to the subject, I initially wrote that "punishing the innocent is unjust". Two responses were that innocence is subjective. I've given a counter-example. Further, I hold that any theory of justice that finds the hypothetical situation given to be just is necessarily false.
@ACuriousMind "Now the total measure is written as $J\sqrt{\operatorname{det}(\Phi_r,\Phi_s)}\mathrm{d}^nt \mathcal{D} \delta\phi\mathcal{D}\delta\tilde v \mathrm{d}^k\delta a\mathcal{D} \delta\tilde X$"
@AlfredCentauri Ah, then I think the "issue" might be that there are different levels of "objective/subjective" floating around. You hold an ethical theory within which there is an objective conception of justice. I'd interpret that the objections to you were more in the vein of pointing out that yours is not the only ethical theory, and perhaps not the only one to have objective justice, and that one thus cannot consider "justice" to be an objective concept (on a meta-ethical level).
@Icosahedron The problem is that schematically, when calculating the string amplitude, we have to sum over topologies and metrics. The topologies part is easy. The metrics part is harder, because we have to worry about double counting and orientations in spacetime.
If you want a detailed analysis, simply solve Laplace's tidal equations. These are not easy to do. If you're curious, I can get you part of the way to what might be an answer. Also, I'm curious as to what the math will turn up.
Achille Hui has a very helpful spoiler (regular ones don't work for ...
That "Click to Show Math" thing is pretty nifty. Could be useful around here sometimes if there's long stretches of equations
@AlfredCentauri As @ACuriousMind already pointed out, I think we are/were simply talking past each other. Even if there exists an ethical system that one may objectively call unjust (which I'm not saying), this would not mean that all ethical systems (or notions of innocence) can be classified as either just or unjust in an objective way. No number of examples can prove such a "for all"-type statement, as you surely know.
In other news, a post on Physics Forums about askers who don't thank answerers and whether this constitutes rudeness. Something for us to always have in the back of the mind as well.
@DavidZ I think the accept is like a thank you right? I mean, i thought we were supposed to dispense with all salutations, thanks, etc. and the "thanks" comes from upvotes and acceptance, ie recognition and confirmation that an answerer's answer is valuable, which is a sort of implicit thanks
@ACuriousMind I dunno... they certainly can't see the collision, but there might be some kind of realtime status display of detector activity... the OP seems to have added in a link
@DavidZ I think the image that is visible there is not a real-time display, but an image of the jets generated from the recorded data afterwards, but...well, I don't know
@0celo7 Yeah. It might be a "real-time" display of the traced back trajectories, but I don't think we can calculate that fast enough to be real-time in any sense.
@ACuriousMind Ahhh, I think I found it. When we write $\delta\Phi=[\epsilon^*Q+\epsilon Q^\dagger,\Phi]$, $\epsilon$ is fermionic, so it produces a minus when moved past the fermionic superderivative. Maybe.
::turns to OP, puts on Jack Nicholson voice:: You can't handle the answer!
2
@ACuriousMind Er ... for many experiments, the "online" reconstruction and event display can show you the events a few seconds or minutes later. Details vary from experiment to experiment, but this is considered a high priority tool as it helps shifters detect problems fairly early.
@ACuriousMind Why does a(n) (anti)self-dual antisymmetric tensor form a $3$? I know that an antisymmetric tensor is a $6$, how does the duality condition half this?
I guess the duality condition matches up a component of the dual to a component of the tensor, right? How do we know that this exactly halves the $6$?
@0celo7 How do we know? By inspection - write down what the dual is, and observe that you get half the d.o.f. as independent equations for a tensor that must be self-dual
@ACuriousMind What is a physical situation in which the identities $(\frac{1}{2},0)\otimes(\frac{1}{2},0)=(0,0)\oplus(1,0)$ and $(\frac{1}{2},0)\otimes(0,\frac{1}{2})=(\frac{1}{2},\frac{1}{2})$ appear? I know how to get them, but I don't have a feel for what they mean.
@0celo7 First one: The combined system of two (non-relativistic) spin-1/2 particles decomposes into a singlet and three triplet states. Second one: A Dirac spinor consists of two Weyl spinors.
And the latter should have $\oplus$ instead of $\otimes$.
@ACuriousMind Ah, Wald uses that identity to motivate writing two spinor indices on vectors I think. (I only skimmed his spinor chapter, so I'm not completely sure.)
@0celo7 $\Phi = \int B ◦ n dA$ $\Phi = \int Bncos\theta dA$, the magnetic field and angle is constant so $\Phi = Bcos\Theta \int n dA$ I'm not sure how to interpret $\int n dA$
Ah right, right. If I actually wrote this correctly and written the dot product with the magnitudes, I think I would've gotten it. I should end up with $B\cos\theta \int dA = BA\cos\theta$ right?