Twin Paradox

Why is the Twin Paradox a ‘paradox’? That time dilation would make one twin, travelling near the speed of light, age more slowly than his brother who stayed on Earth does not seem to be contraditory.

When I think of a pradox, I think of a time traveller who goes back in time and prevents his parents from ever meeting. If he did, then he would not have been born – and so he couldn’t have gone back in time to prevent his birth, so he would be born.

It’s called the twin paradox because somebody named it that and the name stuck.

If Alanis Morissette can have a huge hit with a song called “Ironic” whose examples are not irony, then why not a twin paradox that isn’t a true logical paradox?

Go blame the English language for not having rules.

The “paradox” is not really a paradox. Just seems like it at first glance.

The issue with the twins is theoretically there is no way to say which twin is actually moving. Common sense tells us of course the twin in the rocketship is the one jetting off at near light speed while the one on the earth is not moving (in any significant fashion anyway). Relativity tells us this is a wrong assumption. Anyone can say they are at rest and it is the other people who are moving. Those same people could likewise say they are standing still and it is you who is moving. Both are correct and no experiement will solve the problem. If it makes it easier consider a universe with just you and Spaceman Spiff in it. You are approaching Spaceman Spiff at 0.75c. Which of you is moving? Or if both of you are moving who has what speed? No way to tell.

So, our twins seem to be in a paradox because the twin in the spaceship is supposed to take the position that he is standing still and it is the twin on the earth jetting away at near lightspeed. When he gets back to earth he should be older than the earthbound twin but of course that is not the case. The twin in the spaceship is the younger of the two after the trip.

The paradox, IIRC, is explained by acceleration. While at a constant speed the two twins could not say who is moving the reality is the twin on the spaceship experienced an acceleration that the twin on earth did not. This makes it clear who is the moving one and who is the standing still one and we can say who will be the younger when the spaceship returns.

I remember reading (sorry, no cite handy, but I’ll google) that at the time when the Twin Paradox was proposed for the first time*, it actually was widely regarded as a paradox. Einstein’s equations of special relativity were known already, but the thought of two twins ending up at different ages struck many people as so unbelievable that some even thought it disproved the special theory of relativity.
[sub]*): Apparently by Einstein itself, in 1911, accoding to Wikipedia. [/sub]

The two twins are supposed to be a different age after the trip. While doubtless many people had trouble believing this Einstein for one was pretty clear on what should happen and had no trouble with it. As mentioned the presumed paradox was that each twin should be able to consider themself at rest in regard to the other one so how is it one would be younger after the trip? Again, the answer is the twin that experiences acceleration is the “moving” one thus the paradox is not a paradox and all is well with the universe.

Yes, this is it exactly. The common misperception is that the paradox is merely a counterintuitive result, mostly because so few people see a proper workup of the problem.

The first consideration is that since “everything is relative”, each twin can see himself as being at rest and so the other one will come back younger. But once they’re back together, they’ll both agree as to who’s older. The setup seems symmetric, but the end result can’t be. The resolution is that the twins differ in their experienced accelerations, which breaks the symmetry.

A year or so ago I watched a program on the news related to this subject.

Some scientist put an atomic clock on a jet and another atomic clock on the ground. They synchronized the two clocks and the jet took off. After some period of time (I don’t recall) the jet returned to earth. The clock on jet showed less time had elapsed relative to its earthbound counterpart. If I recall it was in the billionths of a second but still enough to prove Einstein’s theory correct.

I’ll try and find the original story for this. If I do I’ll post back.


There have been many experiments done regarding time dilation when moving…the jet being just one such example. In another they took two hyper accurate clocks and put one on top of a water tower and the other at the base. Over the course of a few months the clocks’ results diverged (the clock at the bottom is deeper in earth’s gravity well affecting its passage through time). I also read somewhere that cosmonauts aboard the Mir spacestation for six months came back to earth ~3 minutes “younger” then everyone left behind on earth (not sure if that was an experiment or a calculation but still fun trivia).

Time dilation seems to be a fact of the universe. So far every experiment confirms it and the results are right in line with predictions drawn from Relativity.

Whoops…I may have misunderstood what you were getting at in your post. It seems like your quote from me and your post is to suggest there are experiements to determine who is moving.

As mentioned many experiements have been done to confirm time dilation. The issue I was on about is you cannot determine a preferred reference frame. Essentially, two people moving towards each other in space (assume nothing else exists to keep it simple) can have absolutely no way to decide which of the two are moving (or any combination of speed the two have that adds up to their closure rate). Both people could decide they are standing still and it is the other person who is moving and they would both be right from their own perspective. There is no experiment either one could perform (or both in tandem) that would resolve this for them.

The science is pretty clear here, but the word “paradox” is being used in some odd ways. For something to be a paradox, it only has to have the appearance of a logical contradiction. Even though there is a perfectly sensible explanation of the Twin Paradox, it has not stopped being a paradox. There is no such thing as an “apparent” or “former” paradox - once you call something a paradox, you always refer to it as a paradox regardless of subsequent explanations.

Your footnote refers to a Wikipedia article, but the article does not say that that was the first instance, just that their quote was first stated by Einstein in 1911.

The essentials of the paradox (even that quote at wikipedia does not mention “twins”) was first presented, and analyzed, in Einstein’s original paper on special relativity, in 1905 (see the discussion about a “peculiar consequence” at the end of 1-4).

If one of the twins is and MD, and the other is a PhD, there’s your pair o’ docs. :smiley:


I think the Twin Paradox fits definition 1 quite nicely.

But they can locally measure tidal forces and find differences, which is what distinguishes the twins. They can tell which one is being accelerated and which one isn’t.

It’s not necessary to accelerate anything to present the paradox. Take three clocks, One being passed by Two headed for Three, and Three far away but headed towards One. As Two and One pass, they set their clocks together. When Two meets (passes) Three, Three adopts the time on Two. When Three arrives at One, it shows less elapsed time.

I believe that when first posited, most would have assumed that the twins would age equally fast. It would have seemed like a paradox… a nifty way to layman-ize it.

I’m not entirely sure what you mean without a diagram, but I think it’s this.

One path is One between One-meets-Two and One-meets-Three (points in spacetime labelled by events). The other path is Two between One-meets-Two and Two-meets-Three, followed by Three between Two-meets-Three and One-meets-Three.

These are two paths in spacetime between One-meets-Two and One-meets-Three, and only one is geodesic, and that one will show a longer elapsed time. Okay, so it’s not an acceleration of any one observer, but the path you’re considering does accelerate as it jumps from Two to Three.

When it was first posited, it was immediately solved, by Einstein. It’s in his first paper, on special relativity.

Yes. That is the way I was intending the paths. My point is that it is not the physical acceleration of a clock that causes the effect. It is a function of the paths in spacetime. That same analysis is exactly the way Einstein analyzed it in his paper.

Ah. I tend to look at SR as a mathematical model, so I use “accelerated” as a property of a world-line, and I’d say that the composite world-line is “accelerated”, in that it isn’t a constant 4-velocity.