The twin’s paradox revisited
I’m writing this article after reading a very unsatisfying discussion of the twin’s paradox. So here goes:
The twin’s paradox is not about relative speeds (special relativity), it’s about the effect of acceleration (general relativity). You can travel forward in time simply by vibrating in place (Flash anyone?).
The twin paradox:
The twin paradox has one twin travel on a round trip in a rocket ship and comes back older than the twin that has stayed home. The effect is explained by the theory of relativity and has been verified using synchronized atomic clocks where one clock travels around the earth on a jet plane while the other doesn’t.
According to special relativity, if someone has a different speed than yours, then you will see them age slower than you and vice-versa. Yes, it’s symmetric. Each sees the other aging slower. How strong the effect depends on the relative speeds.
This state of affairs is only paradoxical if you think of time as ‘flowing’ but if you think of all space-time as being in one piece then the interpretation is simple. While you’re looking at her ‘past’ unfolding in slow-motion, she’s looking at your ‘past’ unfolding in slow-motion.
In any case, relative constant velocity does not hold the key to the twin’s paradox.
Acceleration breaks the symmetry. If one twin accelerates while the other doesn’t, then the twin who accelerates will see the other as aging faster. The other twin will agree that the accelerating twin is aging slower. Here is then the key to a change in age between the twins. Of course, as always, each twin views their own time-flow as ‘normal’.
So, if a twin accelerates long enough and then decelerates to again continuously match the speed of the other twin, then both twins will agree that the accelerating twin has aged slower. After the process, when they match speeds again, they will be traveling in time at the same rate, or in other words, they will be aging at the same rate again.
In terms of the geometry, whoever accelerates has actually been traveling in time, specifically to the future. If all space-time is already ‘there’ then the net effect is of one twin moving to the other’s future at the same space coordinates. So the twin that accelerates and decelerates is a time traveler into the other twin’s future where past and future are already there to ‘visit’.
So what does the rocket ship have to do with the twins? Well, a good way to accelerate is to use a rocket. So one twin takes a rocket and the other stays home. Now, there’s the complication of both special and general relativity at the same time.
As the rocket moves away, it picks up speed. The speed differential causes the twins to occupy different inertial frames where they each see the other’s past unfolding in slow-motion. However, the one who accelerates has this added boost that breaks the symmetry. Which effect is stronger depends on the relative speeds and on the acceleration.
In the end, the rocket turns around (a complex acceleration maneuver) and moves back to the twin at home. As the speeds get closer to matching, the rate of time ‘flow’, or stretching when viewed as a dimension, starts to re-align and when the twins finally meet, they resume aging at the same rate. However, because one of the twins has accelerated, then that one has also travelled forward in time.
And I think it’s gonna be a long, long time …:
Well, can we separate the effect of special and general relativity and also have one twin travel in time?
Sure. Just have one twin accelerate and decelerate in short bursts so that the twin comes back to the same spot without developing any appreciable speed. In other words, let one twin vibrate (albeit very violently and in short bursts)!
By vibrating with tremendous but very short acceleration and deceleration bursts, we get the effect we need from general relativity without having to travel much. So, one twin can vibrate intensely like the flash (or quicksilver if you’re a Marvel fan) and can thus travel to the future without developing a significant mismatch in speed with the other twin.
So to vibrate is to time-travel!