## Time dilation is like yacht racing

An explanation of time dilation by analogy with yacht racing

In yacht racing, unlike say motor racing, it is difficult to know which boat is in front when they have taken different paths. Consider the case of two-yachts, e.g. an America’s Cup type event. One boat might look closer to the finish line, but if it is substantially down-wind of the mark  then it will be moving slower than another boat upwind but further away. In addition, the boats might move into regions of the water space where the wind is faster (or slower), or coming from a different direction, and this will affect the outcome.

For a spectator, it is very difficult to see which boat is winning, or how the boats are doing against each other when they are on different parts of the water, unless that spectator has a lot of sailing knowledge him/herself. Plus the spectators are invariably far away and low to the water, so have very little ability to perceive the depth of the visual field. All this makes watching yachting a boring spectacle.

To improve the situation Virtual Eye, based in New Zealand, has developed a data acquisition, software, and rendering system to visually show spectators how the race is progressing. This is a  neat system as it shows the advantage between the boats, and avoids the need for the spectator to have specialised sailing knowledge…which of course is important in getting the wider public interested in the sport. Here for example is an image showing a red boat ahead of a black one. It would otherwise not be clear which one was leading.

Things start to get more complex when there are multiple boats, all taking very different paths across the water. In this next image, the white boat with the blue line is ahead of the black boat (Oracle). This would have been hard for a land-lubber to determine, as black looks ahead. The larger the physical space between the boats, the harder it is to see which boat is ahead. This also applies to the yachties on board their boats.

White leads black in this visualisation of a yacht race. Image from Visual Eye (http://virtualeye.tv/images/stories/sailing/large05.jpg)

By now you will probably be seeing where this discussion is heading. Yachting is done on a 2D course where there are an infinite many loci possible. The boat’s velocity depends on which part of that 2D space it travels through, how fast the wind flows in those spaces, and the relative orientation of boat and wind.

Now replace the flow of the wind with the flow of time, and the time dilation situation emerges. If two space craft were to take different paths through space, going through different regions of gravitational strength  and accelerating differently, then it would be difficult to determine from afar which was ahead in time. Hence the Andromeda Paradox.

Time dilation is often illustrated with the idea that ‘you’ stay on Earth and ‘your twin’ goes off in a spacecraft. In which case we are protagonists embedded within the time dilation, and like the yachties on their boats, find it difficult to comprehend our relative progress. Visual Eye’s software looks down on the yacht race from an independent third-party perspective, and worldlines do this for cosmology though not nearly so engagingly.

Time dilation only applies when two (or more) protagonists take different routes through space. One can never be totally sure which protagonist is ahead in time, because you don’t know what future choices they will make regarding the gravitational and acceleration regimes they will be exposed to. It is only when the protagonists are brought back together in the same location that you can see the time difference. In the case of time dilation this will show up as one clock indicating a later time or date, or a biological organism showing greater age. (This part may sound weird, and indeed it is still something of an open question as to how time occurs at the level of fundamental physics. You can just accept that the clocks will show a difference. There are many explanations of time-dilation on the internet. They invariably address the question of  what is is and how to formulate it mathematically. The much harder question is how it occurs. If you want the additional mental gymnastics, start by thinking about atomic clocks (i.e. like atomic vibrations), as this feels less weird.  Then you can ponder how atomic time scales up to the level of clockwork timepieces.  Then explain to yourself how this determines biological time at the cellular level.  Finally, work out the implication for yourself as a biological being. It is a interesting and rewarding personal gedanken experiment. The initial weirdness, which arises from the psychological incongruence between what physics and our own senses tell us of the *now*, becomes resolved and one gains an appreciation of time and the nature of the gift. Our own explanation of time is referenced below).

In the case of yachting, this time dilation shows up as one boat ahead of the other, i,e, one boat enters a region of 2D space before the second boat enters the same space. So whatever has happened before on the water, when the boats come together, heading in the same direction, then it is apparent who is in front, as the image shows. The finish line is one such 2D space, and the most important one. But there are also others where the precedence becomes visible, e.g. going around marker buoys.

White leads Black. Differences in time are definitively evident only when the boats are in the same space. Image source Virtual Eye. http://virtualeye.tv/images/stories/sailing/thumb06.jpg

So the outcomes of time dilation only become clearly evident when the protagonists are brought back to a common location in space. At this point the ambiguity of which one is ahead collapses. The Andromeda-type paradoxes exploit this ambiguity, but the ambiguity only exists when the protagonists are far away in space – bring them together again and the paradox collapses. Just like in yachting, all the ambiguity during the race collapses at the finish line: both boats have to cross the same region of 2D space, and the first one there is the winner.

References

PS: If you don’t like wet, then alternatively, time dilation is like hiking up a mountain where there are no paths and each hiker takes his/her own route. Some paths might look like a more direct route to the summit, but if they are steeper then progress may be slower. This is actually what I was thinking of first since I was hiking at the time and realised that hiking was just like yachting, and then realised both were like time dilation.

Dirk Pons 23 April 2014