PAllen's latest activity

Good afternoon, This is not Paul, but rather his son Robert. I am very sad to write here that my dad passed away on Saturday...

So am I.

You can, but many people have a hard time picturing how this is possible. My suggestion provides a way to picture this that was helpful...

(When I said it was a property of all spacetime, I didn't say it was a property of all spacetimes. We're talking specifically about an...

Actually, it is only a possible property of very special spacetimes. It is a feature of geometry that is hard to visualize in a 3x1...

I’ve used the following analogy to picture an infinite expanding universe. Consider the universe as an (countably) infinite collection...

I found an explicit statement in this section of MTW (13.6 bottom of p. 331 in my edition) that makes clear that they have the meaning I...

The wording “proper reference frame of an accelerated observer” implies, in ordinary English, the notion of proper reference frame of a...

Well, MTW calls it the proper reference frame of an accelerated observer, implying that a standard inertial frame is the proper...

No, that's not the issue I realized. You have a piece of ##E^2## embedded in ##S^3##, all embedded in ##E^4##. I was thinking that a...

What I was thinking of here was based on the 3-sphere embedded in ##E^4## being able to contain a surface that is metrically ##E^2##...

I am saying this is not necessarily true. True is that you can find a hypersurface containing it such it is a geodesic of the...

I am not sure that is always true. Consider, by analogy, a 3-sphere embedded in Euclidean 4 space. It can contain a geodesic of the...

Yes.

Actually, if you take any small part of the geodesic, and a small neighborhood around that part, then that geodesic segment is minimal -...