Recent content by D.S.Beyer

Thanks for all the wonderful responses to this question. It sounds like, no matter if the geodesic is hyperbolic, highly elliptical, or circular, Twin A will elapse more time. One of the things that I wanted to get out of this question was if 'local acceleration' matters. Such that Twin B...

This is great. Thank you. How does one determine the maximal geodesic? I'm not to keen on the hard math, so if you have a geometric example, I'd love to see it.

I guess I was trying to get the meeting point even as far out into 'Minkowski' flat spacetime as I could, such that Twin A could basically be stationary. As PAllen says an 'asymptotically flat' spacetime. But, I guess it really doesn't change the outcome in the end.

~ Shower Thoughts ~ Twin A is in a spaceship, Twin B is in a spaceship. Both in 'deep space'. B follows a highly elliptical geodesic which goes around a planet (or black hole) with strong gravity, very far away. When they meet again, who is younger and why? I genuinely don't know what this...

Okay this is making more sense. I'm beginning to see some of my weird assumptions in here. I think the thing that is giving me trouble is the 're-embedment' of the lengths on the curve, back onto the ##(r,\varphi)## plane. This produces these varying ##r## values, which are not actual lengths...

I'd love have a little discussion about the Interior Schwarzschild Solution. Here's a diagram I slapped together to illustrate the key points. (I assume everyone reading this familiar with embedding diagrams, and using an axis to 'project' a value, in this case the spatial z-axis is replaced by...

This blows my mind that this is such a difficult question, but in a good way. Why is the exchange of signals important? Can't it just be a one way thing? For example (and in wild hypothetical land), if I take a telescope in my backyard and zoom in on a clock that is strapped to the body of a...

Wow. I'm going to have to take a moment or two to get through this thread, but it does get to the heart of a lot of what I'm interested in.

Did some searches through these forums but didn't find this exact question. I'm sure it's already been asked, but I just missed it, my apologies. Please link. I’ll try and ask this question in 3 different ways, and maybe the idea behind it will become apparent. I know that semantics can really...

This is awesome! Thank you for this helpful link.

@PeterDonis "The GR phenomenon you are describing is not "length contraction"." Then, how do talk about this visual phenomena? This came up in a previous post about Christmas Lights into a black hole. From the perspective of an outside observer, the light got 'squished' together near the horizon.

The 2 Bowling Balls Ball(a) & Ball(b) (a) is in acceleration of 10m/s^2 (b) is in at fixed position in a gravitational field where g=10m/s^2 In both cases the observer is: - perpendicular to the vector of acceleration - distant enough to be in empty flat space Question : In an instantaneous...

Awesome. I am a little shaky on the difference between length contraction in SR vs length contraction in GR. I am, most likely mistakingly, working under the assumption that the gravitational field in GR acts like the acceleration of an object in SR, to produce the length contracted effects...

@PeterDonis thanks for bearing with me on this. I am essentially trying to setup a scenario where a visual ruler (of time ie blinking lights and space ie length) extends from a relativity low spacetime curvature (Minkowski) to a relatively high spacetime curvature (Schwarzschild black hole). I...

I am open to suggestions. Maybe we calculate how fast Santa needs to travel to get toys to everyone?