For me, I tend to do things as symbolically as possible, thus I plug $\pi$ into my calculator (or computing software) and then it spits out the number (usually in terms of $\pi$)
If I need an approximation, then 3.14 is usually suffice for me
Seriously it is rare to have data good to more than five or so digits. I use 3.14159 when I want to feel swanky; Or more likely double pi = 4.0 * atan(1.0); the traditional incantation of the the guild of numericists (of which I am all but the lowliest novice).
It is easy to conceptualise what non orientable space mean (basically chirality of the object was reversed after going around in a circle once
But what does time non orientability mean, does it mean that after completing a loop, we have effectively applied a time reversal operator on the system in question (e.g. electrons become positrons after the loop?
@Slereah Looks like a moebius stripe version of minkowski spacetime
So if there is no global definition of past and future, does it mean the initial value problem of any equations of motion not well defined at all points in the manifold?
So much reading to do before I can watch how a field propagate in such spacetimes (by doing the maths and then get mathematica to simulate the results)
I guess I should go back to my quantum chem reading for now and think about this next year
@theNamesCross no, not really. If a revision really needs to be purged (e.g. because it contains sensitive information, strictly defined), we can request that the SE team do that, but it's an involved process. In general there's nothing we can do about edits after the fact.
You don't seem to have created much of a mess anyway. Long comment threads are not so bad on meta.
But if you do want to start a side discussion, create a new chat room and post a link in the comments. Or sometimes you can have the discussion here.
@DavidZ Thanks. Do I need a certain rep to do that? I thought I might post a link in the comments where we could agree on a rollback or something. JohnDuffield wasnt too happy about my edits. Before it detracts from the question as a whole, I thought I might try to address it.
If an answer depends on some particular wording in the question, it should quote that wording so that the meaning is still clear if the question is edited later.
Ok. So he keeps his answer based on the earlier edit, but the edit is acceptable? Thats how it stands currently. I gave him a heads up that I edited thinking he would just 'requote'
Well sort of like that in the real world: A man cheated death twice: at 9/11 & at 13/11. This is luck. He was present at both places & each time, he flummoxed death!!
@JohnRennie : That sounds like the rating 3. Will require therapy after viewing on Mr.Cranky's rating scale. On a positive note, it is at least better than 4. As good as a poke in the eye with a sharp stick;5. So godawful that it ruptured the very fabric of space and time with the sheer overpowering force of its mediocrity; and 6. Proof that Jesus died in vain. :D
@Secret : secret there is a "global definition of past and future" implicit to the motion. You have to move from A to B to be able to move from B to C. Then you have to move from C to D to be able to move from D to E. You can't move from B to C then A to B then D to E then C to D.
@JohnDuffield I think what Slereah describe is sort of like moving from A to B then B to C then C to D then D to E and then E back to A. And we did this cycle twice but the two cycles of motion differ in some way
I have not have time to gone through the details yet, perhaps the lagrangian will tell me more about it
That is the motion ABCDE forms a loop. But it seems it cannot be the same again unless it cycle around twice
how it differs I am not sure, but Slereah said it is not as simple as a time reversal
@theNamesCross : I don't think anybody would mind if you added something, marked with an Edit:. But I imagine most people will say it isn't acceptable to make major structural changes to a question in response to their answers. Especially if it's a "political" question pushing for a change.
@Secret : Adrian Rossiter's torus animations maybe help. You can start with this:
@Secret: each torus has two orthogonal rotations. If two complete "steering-wheel" rotations occurred whilst one "smoke ring" rotation occurred, the rotation would have a spin ½ nature. Note that the two tori have the opposite chirality, and because we reversed the gif, each is time-reversed version of the other.
Amazon just suggested a book for me: Quantum Physics Without Quantum Philosophy. I was intrigued, until I realized it was nothing but philosophy written by a bunch of Bohmians with an axe to grind.
3
user54412
... and now Amazon is recommending the entire corpus of Bohmian mechanics books :(
