Activity

I want to put something we discussed in my own words to see if I understand it.

Suppose we have a vector V in Cartesian coordinates, and we want to transform it to Polar coordinates.
We denote its Polar version with
V ¯ α

[𝑣𝛼]

I want to put something we discussed in my own words to see if I understand it.

Suppose we have a vector V in Cartesian coordinates, and we want to transform it to Polar coordinates.
We denote its Polar version with

[𝑣𝛼]

Yes! And then those magnitudes xx, xy specifically point in the direction of the basis (one-forms) ex, ey

1. Thanks.

Skipping to 3,

3. D’oh! Of course.

Back to 2,

2. So is it correct (assume Cartesian) that we’re identifying points in space with x, y, and we’re identifying magnitudes at those points with xx, xy?

1.

d

dx

tan
-1

x

=

1

1
+

x
2

So, using the chain rule

∂
θ…[Read more]

Questions:

1. In the One Form Transformation document, can someone help me understand how

∂
θ

∂
y

=

1

(
1
+

(

y
x

)…[Read more]

Questions:

1. In the One Form Transformation document, can someone help me understand how

∂
θ

∂
y

=

1

(
1
+

(

y
x

)…[Read more]

I’ve considered my issue with identifying what we mean by gravitational redshift more, and there are two specific statements that I’m having issue reconciling.

1. Gravitational redshift occurs as light escapes a gravitational field and loses energy
2. By the equivalence principle, an observer in inertial motion will not detect the redshift.

I am…[Read more]

As we get ready to look at the Equivalence Principle, a note of warning, because I think the terminology in Collier’s write-up is confusing and it starts off with a major typo.

(1) The write-up starts on page 163 (of the orange edition). There two bullet points early on. The first one says:

* The weak equivalence principle states that ……[Read more]

The little “spacetime creed” above is supposed to provide a little (humorous) commentary on the flowchart used in the meeting.

Solutions updated and corrected