Confusion on 'proper time'

I am confused as to who reference frame 'proper time' and 'proper length' is. I thought that proper time and proper length was the time/length measured by a stationary observer.

However in my notes I have an example where there is a man on a train moving relative to a man on the platform. The man moving on the train has a light clock and is taken as T nought. whereas the man on the platform is taken as 't', in the formula

t=\frac{t_0}{\sqrt{1-\frac{v^2}{c^2}}}

This has really confused me as I thought the man on the platform should be taken as t nought as he should have the 'proper time' because he is stationary. On top of that, my teacher has given me a tip in calculations, she said that in a calculation you should always use either the proper time with the contracted length, or the proper length and the dilated time. ie. you should not find yourself using the dilated time, and the contracted length in the same reference frame.

But when I thought about it, it doesn't seem to make sense, if you are using the proper time, you should be stationary (supposedly), but if you are stationary you should be measuring the proper length, not the contracted length.

Can anyone help me out?
Thanks

(edited 11 years ago)

Reply 1

Fleming92

Haha, this can be pretty confusing at first, but reaaly the only problem with understanding the concept is what how you deifne the word "Stationary."

I guess this is best explained by using your example above.

"Proper time" Is the time which the observer perceives. Ie the clock which is being used on the train is stationary with respect to the observer.
Think of it another way, consider that the train is staionary, and that the man on the platform is running (usain bolt style lol) instead? The relative velocity is much the same.

Overall really the man on the train can be considered stationary, and the world is moving with respect to it!

Hope this helps!