Recent content by guhan

Yup, I get it - that is your belief. And per my belief, when I refer to Newtonian mechanics I am also referring to the boundaries of its validity. As for GR, Iike we agreed, its status at event horizon is known to be unknown. So per my belief, when I refer to GR I am also referring to these...

We can say for sure that you won't see any stuff inside the horizon from your position just outside of it - so no, you won't see any thing inside, even if it is glowing brightly, however close that thing is from the horizon. In fact, you won't even be able to live long enough to watch your...

I am sure neither of us is keen on prolonging this over pedantics! :) I believe the definition of 'mathematics of a theory' also includes those statements on no-go domains, where we know** that the physics is unknown or not established. It is absolutely ok if you believe otherwise. **as you...

I don't think one can apply a theory beyond its domains of validity and call it factual. It would have been ok before the limitations of classical theory came up, by virtue of it being an 'unknown unknown' problem, but not anymore since it is a 'known unknown'. On firewalls etc, sure they are...

Another misconception: An in-falling person will not experience anything abnormal at the exact moment she is crossing the event horizon. Truth: It is a popular hypothesis, but not a fact (and continues to be challenged as in firewall etc). In fact, any statement on what happens at or within the...

@ zetafunction I don't think you can assume linearity of divergent series, but I could be wrong. If I am right, that leaves with only one value for your last example. On the other hand, I would be interested to know if you arrived at F(s) and G(s) through continuation of (two different)...

You are right, but I think the appearance of conformal symmetries comes because of one subtlety. The gauge fixing of the worldsheet metric to an euclidean metric using reparametrization and weyl symmetries leaves behind some more residual symmetries (which are roughly transformation of one...

I thought I would give this thread a proper burial... The formulation of QM is through a homomorphism of Lie algebras from the poisson bracket in classical hamiltonian mech to commutation relationships in QM. This is to handle the correspondence principle used in physics, in a more general way...

@Hurkyl: Sorry, I didnt get the sarcasm (or a genuine question/pointer?). I don't find anything wrong with generating functions per se. It is the analytic continuations that give results like 1+1+1+... = -1/2 that is bothering me. Maybe one reason I didnt get a full clarification from your...

Sorry for this bad behavior of bumping up my thread, but this thing is driving me crazy and I don't understand why it is not driving number theorists (or mathematicians, in general) the same way. I have read writings on this (age old) problem from Euler to Hardy, but I don't find them...

@CompuChip: I would call analytical extension more of a 'rearrangement' within the series definition of a function than a totally different function altogether. Also, wasn't the equivalence of this extended function to the original series established by number theorists? So, is it really a...

Sometimes, analytic continuation of some functions (like zeta) gives bizarre summation values for series like the one in the title or for 1+1+1+... = -1/2 etc... and they are also used quite often in physics. Are mathematicians really comfortable with such values for such series? Whats the...

Also read Baez book "Gauge fields, knots and gravity". He gives elementary intuitive introductions to forms (and other topics).

How do you get the V^i_{,j} and W^i_{,j} terms? And, if you are using the structure constants C^i_{jk}, then why not use the bilinear property of lie brackets and directly say that [V,W]=V^jW^k[e_j,e_k]=V^jW^kC^i_{jk}e_i?

In the case of non-commuting bases, I think there is no reason to believe that we can even find dual bases \{\omega^i\} such that \omega^i(e_j) = \delta^i_j and so modifying the lie bracket formula may not be as direct since we would be left with [X,Y]=[X^ie_i,Y^je_j]=X^ie_iY^je_j-Y^je_jX^ie_i...