Time relative to someone moving at a high speed-equations for a layman?

[DyslexicHobo]

I know only the basics about relativity, and was explaining to my friend that as you travel at a speed that approaches c, you experience less time than an observer. I believed that it was explained in "A Brief History of Time" such that your 'velocity' vector can only have a magnitude of c, and if portions of that vector are are in the spatial dimensions rather than the time dimension then you won't experience as much time as an observer.

So then my friend asked "well, if I rode Kingda Ka for 50 years straight, would I age at least 1 second less than you?"

I have the feeling that it would have a negligible effect on his aging, and my prediction was that he would experience only millionths of a second less time than a relatively motionless observer would.

Is there any equations for the layman that I could use to calculate something like this?

 

[tiny-tim]

Hi DyslexicHobo!

… if I rode Kingda Ka for 50 years straight, would I age at least 1 second less than you? …

I have the feeling that it would have a negligible effect on his aging, and my prediction was that he would experience only millionths of a second less time than a relatively motionless observer would.

Is there any equations for the layman that I could use to calculate something like this?

easy -peasy!

the time dilation factor is exactly √(1 - v²/c²) …

which, for very small v (as on Kingda Ka), is practically 1 - v²/2c²

 

[DyslexicHobo]

Thanks!

This was much simpler than I expected. I calculated that if he rode Kingda Ka for 50 years nonstop at a constant velocity of 120mph (which is incorrect, because it only reaches 120mph for a few seconds), then he would experience about .0000253864 seconds less than myself.

I'll let him know that he'll need to try going on a concord jet for 50 years nonstop, instead. :)