Why does the spacetime interval give zero for causally disconnected events?

[Fredrik]

As this interval separates events

As evidenced by the fact that S² can be positive, zero or negative, and the fact that it can be zero without the two events being equal, it's not a measure of how "big" the separation is.

Considering event A to be the take off and event B to be the deceleration, does the difference in duration between event A and event B, for the spacecraft (1 year) and the space station (2 years), hold any significance?

Yes. To see this clearly, have the spaceship do the same thing again, but in the opposite direction. When it gets back to the space station, everyone on the station have aged 4 years, and everyone on the ship has aged 2 years. This is because human bodies can be thought of as really crappy clocks, and a clock measures the proper time of the curve in spacetime that represents its motion. (Note that there are lots of threads about this scenario already. This is a recent one).

 

[calebhoilday]

I get the twins paradox. I was wondering if Lorentz transformations affect the co-ordinates. Event A say happens in 2010 to both the the spaceship and the space station, when does event B happen? Would the spacecraft consider it to be 2011 and the space station consider it to be 2012?

 

[Fredrik]

I get the twins paradox. I was wondering if Lorentz transformations affect the co-ordinates. Event A say happens in 2010 to both the the spaceship and the space station, when does event B happen? Would the spacecraft consider it to be 2011 and the space station consider it to be 2012?

The space station would. To the people on the spacecraft , 1 year has passed since 2010. If they would say that the year is 2011 is another matter. It wouldn't make much sense to say that, because then they should also say that it's 2012 when they get back home and meet all the people who live in 2014.