1,102 reputation
320
bio website
location
age
visits member for 3 years, 4 months
seen 8 hours ago

Nov
15
comment What is a tensor?
"A (rank 2 contravariant) tensor is a vector of vectors": I like this picture! From the three numbers of a vector, we construct its length which is an invariant to rotations. Does something analogous exist for a rank 2 contravariant tensor wrt rotations?
Nov
12
comment Will a ball slide down a lumpy hill over the same path it rolls down the hill?
The difficult part is showing that the constraint for no slipping and its angular momentum doesn't affect the path taken by the center of mass when it's allowed to slip.
Nov
10
comment Will a ball slide down a lumpy hill over the same path it rolls down the hill?
@RonMaimon I've done a search on Amazon.com for that reference in your answer, but I can't find it; is it an old rare book?
Oct
27
comment Reading the Feynman lectures in 2012
@ArtBrown I've seen the book on Amazon.com and after looking at the contents, I'm still scratching my head over the whole point of it: Physicists use QED, engineers use CED and both models are brilliantly served by main stream text books.
Oct
13
comment Should the eigenkets be weighted in $|P\rangle = \sum\limits_{r}|\xi^r\rangle$?
every ket-vector can be expressed as a sum of a set of unity weighted eigenvectors? I find this hard to believe.
Oct
5
comment Why does Dirac write $\langle\xi'|\overline{f(\xi)} = \overline f(\xi ')\langle\xi'|$?
@KyleKanos Why doesn't Dirac just substitute $\xi'$ into $\overline{f(\xi)}$ as for (34)?
Oct
5
comment Why does Dirac write $\langle\xi'|\overline{f(\xi)} = \overline f(\xi ')\langle\xi'|$?
@KyleKanos Dirac uses $\xi$ for a real linear operator, ' to label objects connected with eigenvalues-- $\xi'$ for an eigenvalue, $\langle\xi'|$ for an eigenbra
Sep
23
comment How does Dirac form this conjugate imaginary equation?
@ACuriousMind This is page 30 of his book where the basic mathematical framework is based around there being a function of a ket, amongst other things. You really need to have a look at the book to see what I mean.
Sep
20
comment What axiomatizations exist for special relativity?
Nowadays, we'd say there is a universal speed limit c that light happens to travel at, making its measurement convenient.
Sep
18
comment How can (in Dirac's terminology) the product of two “real” linear operators be “not real”?
This answers my question. It would help if you could put $\alpha = \bar\alpha$ in brackets after Hermitian.
Sep
3
comment How does Dirac show that $\langle B|\bar{\bar{\alpha}}|P\rangle\;=\; \overline{\langle P|{\bar{\alpha}}|B\rangle}\;=\; \langle B|{\alpha}|P\rangle$?
Indeed; I assumed that the adjoint of an adjoint cancelled like the inverse operator. It seems obvious now that the adjoint of an adjoint should initially be assumed to give a different linear operator since its still just a linear operator.
Aug
25
comment Explanation for $E~$ not falling off at $1/r^2$ for infinite line and sheet charges?
@RonMaimon now that you've had a long rest, does this answer still make sense to you honestly?
Aug
24
comment Is there a “forwards” and “backwards” in one dimension?
So a magnitude can be negative?
Aug
24
comment Is there a “forwards” and “backwards” in one dimension?
@HDE226868 sure you can. But maybe that isn't a true one dimensional space as defined by a physicist or mathematician, and a direction paramaterized by two discrete symbols +,- has been added.
Aug
24
comment Physical reason for Lorentz Transformation
You're only looking at a light-like interval; you need to show how invariance of this implies invariance of space-like and time-like intervals also.
Aug
20
comment Rotation axis of a rigid body
+1 all this work, and just one lousy up-vote?
Aug
19
comment Why should multiplication of a ket vector by a complex number change only its “direction”?
@ACuriousMind A vector multiplied by a negative real number changes its direction, yes? How are we to interpret multiplying it by a complex number?
Aug
19
comment Why should multiplication of a ket vector by a complex number change only its “direction”?
@Nathan I'm looking for an answer in the spirit of Dirac talking vaguely about vectors in an infinite dimensional space up to this point. I guess this will become clearer later on in the book, but Dirac seems to suggest this statement is obvious for physical/mathematical reasons.
Aug
19
comment When is it useful to distinguish between vectors and pseudovectors in experimental & theoretical physics?
Cool, is there a book you can recommend which goes into this in more detail?
Jul
23
comment What is a tensor?
A tensor is a geometrical object whose components transform like that of a tensor.