There are 2 paradoxes in relativity

 This post is based on an interaction I had on Quora. When people discuss the twin paradox (like I did), they always discuss the difference in time, each twin experiences relative to the other; they don’t discuss the difference in distance they experience, which is a logical consequence of the same Lorenz transformation. 

However, someone on Quora conjectured that in reality, the clocks actually measure time at the exact same rate and it’s the distance that changes. Mathematically, there is nothing wrong with this argument, so why do I disagree with it?

 

The twin paradox, of course, is a thought experiment, but there is a real-life experiment where this happens, which I’ve also discussed in another post, and that is the half-life of muons in the Earth’s atmosphere. According to the scientists observing them on the Earth’s surface, there are too many of them, which means they took longer to decay (the half-life got longer). But, from the muon’s perspective, their half-life hasn’t changed, it’s just the distance to the Earth was shorter. Now, this creates a paradox, which is equally manifest in the twin paradox thought experiment. 

 

How can the distance change depending on whose perspective you take? I don’t believe it does. I contend that the moving observer ‘measures’ a shorter distance based on their clock slowing down. But, you’ll say, the whole point of relativity is that no one knows who is moving and who is stationary. Well, there is a reference point, which, in the case of the muons, is the gravitational field of Earth. A body in free fall experiences maximum ‘proper’ time and any deviation from that causes a clock to slow down. The fact is, because the muons are travelling at high fractional light speeds, their deviation from maximum proper time is greater than the observers on the ground. I believe this logic also applies to the travelling twin in the thought experiment.

 

If you take this to extremis, someone could hypothetically travel across the entire galaxy in their lifetime if they travelled fast enough (without exceeding the speed of light). From their perspective, the distance would shrink astronomically, but if they returned to Earth, eons would have passed in their absence. I should point out that science fiction writers (like myself) routinely ignore this fundamental consequence of relativity. We ‘imagine’ that humanity has discovered ‘new physics’ to overcome this ‘problem’

 

I’m not sure how heretical it is to argue this: that time changes but the distance doesn’t. if one goes back to the argument that started this rumination: when the twins reunite their respective clocks disagree and the space-faring twin is noticeably younger than their counterpart. However, they not only disagree on the elapsed time, since the space-faring twin’s departure, they also disagree on how far that particular twin travelled. BUT, now that the space-faring twin is back in the same frame of reference as their Earthbound twin, they concur on the distance, yet still disagree on the time elapsed, evidenced by their clocks and age difference.

 

 

Addendum: Ian Miller (PhD in Chemistry and a self-described 'theoretician' on Quora) argues that it's the ruler that changes relativistically and not the distance travelled. And I'd contend that the clock is effectively the ruler.