How does light always recede at c, and does gravity warp spacetime around Earth?

[aychamo]

Heya guys

I have a few general questions.

The first one is about Stephen Hawking. How does he express his ideas these days? I saw a thing about him on TV today and it seemed as though he has extremely limited motor function in his hand, and he can't speak, except for the text-to-speach thing he has. But how does he write the text? It must be a god-awful slow process for him.

The next is about Einstein. The program said according to Einstein if you ran next to a beam of light the beam of light would move away from you. I have a basic understanding of relativity (moving at a fraction of c gives time dialtion, etc), so how does that explain the light moving away from you? Is it because for you time would slow down but the light doesn't?

My next question also involves Einstein. It's about gravity not really being a force or whatever. According to the program the Earth revolved about the sun because the sun warps the space time around it. So if I drop my cell phone and it hits the earth, is this because the Earth warps the space time around it? I don't understand this part.

Thank you kindly
AYCHAMO

 

[aychamo]

You guys think this is the wrong subforum for this?

 

[HallsofIvy]

1. Quite frankly I don't know how Hawking is doing these days. If he were completely healthy I would be in awe of him. As it is just thinking about him makes me feel like a wimp!

2. Basically, the reason light "moves away from you" (at the SAME speed- that crucial part) is that the formula for finding relative speeds is not just v₁-₂ but the more complicated
(v₁- v₂)/(1+ (v₁v₂)/c²). In the case of "running after a beam of light, v₁ is c and v₂= v, your speed. The speed of the beam of light relative to you is (c- v)/(1-v/c)= (c-v)(c)/(c-v)= c.

3. Geometrically, any surface or "curved" 3 dimensional volume has "geodesics" that act like straight lines: they are the shortest distance between points. Gallilean relativity says things move in a straight line unless acted on by an external force. Einsteinian relativity says things move in a geodesic unless acted on by an external force. Since we are used to "thinking in straight lines", when we see things move on a geodesic that is not a straight line, we interpret it as a force. For normal experience it doesn't matter which "model" you use but very precise experiments indicate that the "curved geodesic" model works better than the "force" model.

You might get better answers by putting this in the "special and general relativity forum".