How do we explain this new take on the old Twins Paradox? Here's a new take on the age old Twins Paradox that I have not been able to figure out.
We have two twins in two separate space ships at the same place and time. Twin A fires his thrusters for 1 year (proper time) of acceleration at 1 g, followed by 2 years of reverse acceleration at 1 g, followed by 1 year of acceleration at 1 g in the original direction, thus returning to his original position and inertial reference frame with twin B. During that time, Twin B went nowhere, but spent the time in a centrifuge, experiencing 1 g of acceleration, just like Twin A (albeit in different directions).
Both twins experienced 1 g of acceleration for 4 years (of Twin A's life), but analysis indicates that Twin B would have aged more than 4 years. Even if we treated the time in the centrifuge under 1 g as equivalent to 1 g of gravity on Earth, the gravitational time dilation is nowhere near the time dilation caused by Twin A's travel. Can someone explain where my analysis might be off?
Edit:
Just to clarify the paradox of this new scenario:
Both twins experience 1 g of acceleration for the entire interval.
Twin A experienced linear acceleration.
Twin B experienced centrifugal acceleration.
How does this only difference cause time-dilation between them?
Edit:
Sorry to have compared this scenario to the Twins Paradox, because that is not really what it is about. The answers to the Twins Paradox were accurate, but not the point.
Let's take 3 persons all staring at the same place and same time with no velocity with respect to each other. Person A experiences linear acceleration only. Person B experiences centrifugal acceleration only. Person C experiences gravitational acceleration only. There is no experiment that any of the 3 could do to determine the type of acceleration they are experiencing (in a black-box scenario). After an interval, they all return to the same position, each one having experienced the exact same magnitude (but not direction) of acceleration for the whole time. How is it that Person A experiences Lorentz time-dilation with respect to Person B, and Person C experiences gravitational time-dilation with respect to Person B? The appropriate analysis and formulas indicate that this is the case, but I would appreciate someone trying to explain the conceptual difference.
 A: The traveling twin ages less, and the acceleration doesn't resolve the paradox. In the standard version, the paradox is resolved when the traveling twin (who's name is traditionally "B") turns around. This turn around can take $\epsilon \rightarrow 0\ $ seconds in the Earth frame, so it cannot account for "lost" time. The change in the definition of the hyper-plane of simultaneity at the turn around event resolves the paradox--so that each twin can observed the other's clock going slower for the duration of the journey (which is a paradox with or without different total aging).
A: The twin paradox is purely special relativity. You don't need the general relativity tag.
The twin paradox can be resolved without acceleration by using three or more observers. 

The first one, A, sits at home with no acceleration. The second, B, starts out at t=0, x=0, right next to A, with speed v. The third, C, starts out at x=D, t=T, speed negative v as observed by A. C is arranged such that he passes B at the point we will call the "turn around."
So you've got a little triangle with three observers. It's possible to synchronize the clocks of B and C at the point they pass. Then you wait for C to return to A. Then you can compare the clock of A and C when they just pass.
Then by symmetry, the time B observes from being beside a to beside C has to be the same as the time C observes from being beside B to beside A. 
Then you can have comparison of clocks only at the points two observers are at the same location. And you can do it with no acceleration. You don't have to worry about confusion over synchronizing clocks at a distance.
No acceleration. No synchronization except for clocks right beside each other. You will still get the Lorentz transform.
