# Q & A: time and distance in special relativity

Q:
I have recently been getting familiar with Einstein�s and Hawking�s work and theories, and I have a question that no one in my social circle can help me with. In Hawking�s theory about travel into the future, passengers board a train that circumvents the globe at near the speed of light. The passengers feel as though only a week has passed, but when the get out, a hundred years has passed for everyone else on earth. For ease of discussion, let�s say the train traversed the globe 100 times during this week for the travelers. (I know it would be a LOT more.) The onlookers from earth would have seen the train going very slowly, and only going around the earth once per year (in my dumbed down example). If something is traveling that slowly to the onlookers, is it really going near the speed of light? Is speed determined by the object traveling, or the on lookers? To add onto that thought, particles in the super collider that should extinguish themselves in one second, can last much longer when accelerated to near the speed of light (30 times longer according to the show I was watching), which proves that they are �time traveling�. My question above relates to this because if scientists, who are standing still, are tracking the speed of this time traveling particle in the super collider, then isn�t the particle itself actually moving much faster than we observe if it is also traveling through time? If we observe it traveling near the speed of light when we are static, could it in theory be moving faster than we think given that speed is determined as time vs. distance and it�s time is moving much slower, but it�s speed is close to the speed of light in the on lookers time? Or, is this a circular reference, for lack of a better term, because you are trying to find out speed, which takes time into account time (miles per hour for example) but �hour� is no longer a constant?
- Jacqueline Georges (age 35)
Millbury, MA, USA
A:

On the first part about going around the earth, actually everybody will agree about how many times the train (or, realistically, satellite) has gone around. An earth observer and a somebody going around just have to count how many times they wave as they go past each other, and they'll get the same count.

On your second question, the key point is that there is no such thing as one true answer to "how fast is it going?" Velocity depends on the reference frame, an the same laws of physics work in frames that are in motion with respect to each other. So there is no way to pick one answer as the right one. Different frames not only assign different time intervals to events but also different length intervals. They don't agree on which events are simultaneous, unless the events also happen at the same place. Basically they all agree on when things bump into each other, but use different coordinates to describe other pairs of events.

Mike W.

(published on 03/18/2019)