Is The Twin Paradox Still a Paradox?
By Jon Therkildsen, MSc MBA from University of Århus (2004)
THIS ARTICLE WILL ADDRESS AND ANSWER THE FOLLOWING:
WHAT IS THE TWIN PARADOX?
WHAT IS THE ANSWER TO THE TWIN PARADOX?
No. The Twin Paradox is no longer a paradox. Where Einstein’s “Special Theory of Relativity” gave birth to the paradox, his “General Theory of Relativity” laid it to rest.
The infamous Twin Paradox is often incorrectly referred to in the popular media to be about a change in aging. This is not correct. Time dilation is easy, and fun and I suppose this is why this version is often used. But that is not the puzzle.
“Special Theory of Relativity” (1905) taught us that time is a function of speed. We call the phenomena: “Velocity Time Dilation,” and it has been verified beyond any doubt.
Anyone speeding relatively to someone not speeding, will experience time dilation (aka a different flow of time). And this goes for any speed - be it a stroll in the park or a spaceship whooshing away. Wave your hand, and it experiences time slightly slower than your shoulder. Your circulating blood cells age slower than your stationary heart. Etc. Etc. Everything is relative.
The popular media often mentions that this is only possible near the speed of light. This is false. Naturally, the difference is more noticeable the closer to the speed of light one travels, but the effect appears at any speed. You can read more about it here.
And if we imagine a pair of twins, where one travels in, for example, a spaceship, and another stays back on Earth. Well, according to “Velocity Time Dilation,” the moving twin will age slower because her time is ticking slower.
This is correct, and the phenomenon has been verified beyond any doubt. But…
That is not the Twin Paradox.
The Twin Paradox is asking who of the two twins moved?
This is the Twin Paradox.
Seemingly, an easy question and so perhaps not a paradox? Obviously, it is the one in the spaceship. However, it is not that simple in a world of science. You see, how do we experimentally determine and calculate if it is the spaceship that moves or if it is the planet that moves?
In scientific terms, when we are analyzing from a different point of view (standing still as opposed to moving), it is called; "from different frames of reference." The theories of relativity are tied up to this, which is why it is called "relativity." It can only ever be determined if compared to another frame of reference. No matter how fast or slow you move, you - the mover - will never experience any difference yourself. It is only when you will compare it to another frame of reference that this relativity difference becomes apparent.
In other words, we need to determine if it is the Earth moving (and the whole universe with it) or the spaceship. Only then do we know who aged less. We can compare their clocks and the number of gray hairs on their return, but how can we calculate it prior? And this is the core of the infamous paradox.
A cardinal rule in science is that if we cannot calculate, measure, or determine a difference, there is no difference. And therefore, to solve this puzzle, we need to figure out a way to determine where the difference is (without counting gray hairs upon arrival).
When two frames cannot measure who moves, we call this “symmetrical relativity” or “relativity symmetry.” And Velocity Time Dilation is symmetrical - until the two frames compare, we won’t know who moved. When you are sitting on a train and looking at another train outside, you can get confused about which of the two trains are moving. Is it your train, the other train or both? Look out the window, and only when you can compare your own frame of reference to another third point, like a tree in the background, can you determine this. Scientifically, this is inadequate. The tree might be moving in its own frame of reference as well. How can we ever be sure?
Let us go back to the twins: When they meet again, they will clearly see that it was the one on board the spaceship that aged less. Something in this frame of reference must have been different. And as it turns out, Einstein’s second theory of relativity shows us how.
The “General Theory of Relativity” included gravity to the equations. And gravity, Einstein found, is equal to constant acceleration. Imagine that you are standing inside an elevator in deep space, and it is being pulled at a fixed rate of acceleration. In this scenario, you would have no way to figure out if you were on a planet with stable gravity or if you were being pulled in space. This is what Einstein meant when he equated the two. Now imagine this acceleration is changing. You will feel a difference inside the elevator, and you will realize you are moving - even if you have no windows or other points of reference to compare to.
Any change in acceleration can determine who moves. And so, this is where we will find the solution to our paradox.
Earth has constant acceleration; there is no significant change in its orbit around the Sun or even in relation to a potentially moving spaceship. Earth's gravity is constant, and so is its acceleration. You (we) can only deduce Earth is moving by comparing to other planets and stars. Without any points of reference, we would never know.
The spaceship, on the other hand, has to accelerate to a faster speed, decelerate to make a turn at one point, accelerate again back to the original speed. Once it reaches Earth, it has to stop completely: Acceleration -> deceleration -> acceleration -> Then, it finally decelerates to a full halt. And all these changes in acceleration will make it apparent that movement occurs - even if there is no point of reference to compare with.
This is the solution to the Twin Paradox.
The twin that experiences a change in acceleration, within its own frame of reference, is the one that experiences relative speed. And so will be the one that experiences time dilation.
But how can each twin do an experiment to see if she is the one moving?
Easy, look at a cup of water:
The one on Earth will have a cup of water that looks like the left cup, the whole time. The one in the Spaceship will have a cup like the one on the right side of the illustration - you get the picture; mass react to a change in acceleration and a cup of water is an easy to way to record how. No change in acceleration and the water is leveled and calm. Change in acceleration and the water will rise to one side, away from the direction of motion.
So one more time, in case you skipped to the end:
The Twin Paradox is not about a change in age.
The mechanics behind the time dilation phenomenon has never been a paradox.
The twin paradox is determining who it is that moves?
The solution is to invoke acceleration into consideration. The twin that will experience relative acceleration and relative deceleration will be the one who ages less.
Puzzle solved.
There is no paradox
Photos via Google