Time Dilation: Object slowing down vs Subject speeding up

Goosington

Hi people, I'm in the same boat as coktail trying to understand Time Dilation. I'll have a crack at explaining in my own words where I am coming up short.

Firstly we have the scene at the train station with two subjects, one located on the train moving at a set velocity, and the other on the platform. Both subjects have clocks at rest relative to them observable by the other. Now subject 1 (platform) observes that subject 2 (train)'s clock is moving slower relative to subject 1 abiding by the two axioms of Einstein's theory -light travels at the same speed regardless, and there is no identifying absolute motion.
Ok, this is nothing new and I can grasp that. Now here is my dilemma.
Relative to subject 2, is subject 1 not also moving, therefore causing subject 2 to observe subject 1's clock as slowing down also, while his clock at rest relative to him is moving "normally"? And if not, what determines which point the movement is relative to? I know it has been proven in experiment with muons to be true but I don't understand how it doesn't work both ways and cancel itself out?
Thanks a lot for your help and sorry for the lengthy question.

ghwellsjr

As I pointed out in post #15, your question is about Relativistic Doppler, not Time Dilation. As the train is approaching the station, both subjects will see the other ones clock ticking faster than their own and by exactly the same amount. When they pass each other, they will then see each others clock ticking slower than their own.

Now if we want to apply SR to the scenario so that we can talk about Time Dilation, we have to first decide on an Inertial Reference Frame. If we pick the station as the IRF, then subject 1 (platform) is stationary and has no time dilation while all of it falls on subject 2 (train). Subject 2's clock is running at a constant slow rate, even while the train is approaching and after it has passed. If we choose the train as the IRF then subject 2 (train) is stationary and has no time dilation while all of it falls on subject 1 (platform), even while the train is approaching and after it has passed.

Goosington

Thanks George for you help. That has cleared it up a bit. I am only new to the subject so it is hard to refrain from using my instinctual interpretation of motion. I will be sure to ask if something else comes up.

[edit]: Okay, I understand now what you mean by the Relativistic Doppler. Just one question. Is that the effect that is being described by Einstein when he is using the Lorentz transformation? I keep hearing that speed of motion affects time with weird examples such as, if you were to travel at 99% of the speed of light and then return millions of years would have passed. That clearly can't be a Doppler effect, can it?

ghwellsjr

No, Relativistic Doppler is an effect that can be explained purely on the Principle of Relativity which is Einstein's first postulate. It doesn't require his second postulate which is the basis for his Theory of Special Relativity which includes the concept of a 4-coordinate Inertial Reference Frame and in which he derives the Lorentz Transformation which leads to the concept of Time Dilation.
Yes, it is. Or more precisely, the Doppler effect and the example of time passing differently for a traveler and one who remains inertial are both direct results of the Principle of Relativity and don't require Einstein's Special Relativity to explain or understand them. Here is a thread where I develop this concept. There are a lot of side tracks but it eventually gets to the point.