Recent content by HackaB

87 percent of people who begin sentences with "Statistically..." are full of horse poo.

I think finding the eigenvectors of the individual matrices H1 and H2, as you were doing before, is the right way to go. Here are some things to keep in mind. Recap of what I said in the edit of my last post: since H1 and H2 are hermitian operators on a 3-d vector space, they each have a set...

When you say common set of eigenvectors, do you mean all eigenvectors in common or just some (like one in common, for instance)? edit: blanik: hermitian matrices always have a set of orthogonal eigenvectors that span the vector space they operate on. So you should have 3 different...

So there is more than one way to imbed a n-1 sphere in Euclidean n-space? I take it that Alexander's horned sphere is an example of such an embedding, since it provides a counterexample to the theorem. What is meant by "embedding". What structure does it preserve?

danai_pa: Did you get an answer to this problem? I don't believe you will need to solve any cubic equations. Do what robphy said...set up the equation E = (1/2)mv^2 + U(x), where v = dx/dt and solve for dt. Integrate from one turning point to the other. That's half a period. This...

how would you get k from that? Seems like you need to know what x is... :smile: Is that what you mean by "use some math"?

Is that the jordan curve theorem?

Don't worry. Your insights are much appreciated, even if most of them go way over my head.

Yes it is. It sort of relieves the tension in the room. Although it is possible to overdo it, too. One of my linear algebra teachers (we had different teachers for different semesters) was not so awesome. He was determined to fill up the lecture period with worked numerical examples, but...

Wow! Where did that come from? I'm sorry I participated in your little experiment. I'll let you continue trying to prove that everyone else besides you is an idiot. Good luck. edit: Why are you so angry?

He didn't give it, but I attempted to come up with one myself. Here are the axioms for vectors u,v,w in a vector space V and numbers a,b in a field K: 1) u + v = v + u 2) (u+v)+w = u+(v+w) 3) There is a zero vector O s.t v + O = v for all v 4) for every v and every O, there is an...

CarlB: It does make very good sense that the frame of the thrown watch should be considered the inertial frame and the held watch be should be the accelerated frame. But I don't understand why you insist that acceleration does not affect proper time. Sure, it doesn't appear explicitly in...

Okay, I'll repeat my question from post #18 since I'm still curious. Does anyone else find it surprising that you can prove that vector addition is commutative using the other 7 axioms that Sharipov gives (they seem to be the standard ones)? Or is this old hat? It was news to me. edit...

If you are just testing us to see if we can solve the problems you thought up, won't you at least tell us the right answer after we've given it a try?

Cool. Is it still the thrown watch that has less time elapsed, though? Seems like I remember reading that the elapsed proper time is maximized in free fall, so I was wondering if in GR it was the thrown watch that read a later time. He asked for the difference in elapsed time on the two...