Why does the traveling twin age less if both see each other's clock slow?

[Hurkyl]

The metric of spacetime defines the distance between two events. This metric is well defined (ignoring for the moment if this space is actually Hausdorff) for both flat (Minkowski) and curved (Lorentzian) spacetimes.

http://en.wikipedia.org/wiki/Metric_(mathematics )

First off, you've cited the definition of the wrong word: see Metric tensor. Secondly, see proper length and proper time.

 

[MeJennifer]

Every serious book on relativity writes about distances between events in spacetime.

What I write seems to fall on deaf ears, so I won't respond anymore to this.

 

[Al68]

Hello Al68.

I think you are wrong. However i would rather let someone decide this for us rather than continue disagreeing.

It's 4AM here so i will be disappearg soon.

Matheinste.

I don't understand why there's a disagreement. In the twins paradox, the ship's twin measures the distance traveled to be less than that measured by the Earth twin. If I'm right, that would mean that the ship's twin would age less. I thought we all agreed on which twin aged less. I thought the only disagreement was why.

Al

 

[matheinste]

Hello Al68.

I have no disagreement about which twin ages less. I only disagree about the spactime distance. Tomorrow i will consult my textbooks and then can hopefully quote some relevant passages.

Matheinste.

 

[Al68]

Hello Al68.

I have no disagreement about which twin ages less. I only disagree about the spactime distance. Tomorrow i will consult my textbooks and then can hopefully quote some relevant passages.

Matheinste.

Well, there's the problem, I was referring to spatial distance, not spacetime length.

Al