After reading many books out of interest I thought I understood the basics of relativity, but a few extracts from a book I am studying from have confused me.
I shall copy them.
'Imagine a 22nd century rocket race over a distance of 30 million kilometres. Light takes 100 seconds to travel this distance so you would expect a rocket travelling at half the speed of light to take 200 seconds. The rocket crew and the race officials would also expect a time of 200s if, like Newton and Galileo, they thought in terms of absolute motion. However, according to Einstein's theory of special relativity, the rocket crew's on-board 'clock' would show they arrive at the finishing line 173 seconds after passing the starting line. The race officials at the starting or finishing line would still record 200 seconds on their clocks.'
'A moving clock runs more slowly than a stationary clock.'
I am also aware of the formula for time dilation, which seems to tell me that the faster a person moves relative to an observer at rest, the longer the time recorded is for the person who is moving compared to the time measured by the person at rest.
Now the first extract says the time recorded by the rocket which moves relative to the people at rest is shorter. Surely this isn't consistent with the formula, which shows that as the person who is moving has a larger speed, the ratio of v/c is larger so 1-(this ratio)^2 becomes smaller. So dividing the time measured by the person at rest by 1-(this ratio)^2 gives a larger measured time for the mover. Nor can I see how the second extract is consistent with the formula, as a slow clock would record a smaller time between two events. The first two extracts seem consistent to me.
I am aware that you would age more slowly if you travelled faster, which is consistent with the first two extracts.
So why can I not piece together the equation with the explanations in writing. This annoys me. The seem to be saying the exact opposite... Thankyou if anybody can see what I am getting at.