Special Relativity question previously on HSC Physics Question Thread

[zhudiac]

Hi,
I was just going through the HSC Physics Question Thread (a post back in 2016, so I relocated it here), and I saw a question:
Two trains are moving at different but constant velocities. Are there any conditions under which they are in the same inertial reference frame?

The answer given by HPL was very thorough, but I am not sure if it answered the question. If it is my understanding which is in fact lacking, please correct me and help me understand.

HPL's answer basically stated the principle of relativity for IFOR- that it is impossible for an IFOR to know its velocity without reference to a stationary external point. Based on this, he said that thus; these two are the same IFOR's, as it is impossible for an observer on the two trains to know of their own velocities, thus based on their POV's, they are "the same".

However, my interpretation of the word "same" in this context is quite different. As the two trains are in relative motion to each other, this implies they must experience time etc. differently to the other, even if they don't know it (time dilation). This implies time is moving faster in one of the trains, and so they are not, strictly speaking, the same.

Please correct me if I'm wrong, and thanks for reading this much !!

[blasonduo]

Hi,

-snipped-

Hello! What Happy Physics Land says is absolutely correct. You cannot know your own velocity in an IFOR without an external view.

You are also correct in saying that time would pass differently in each reference frame.

Let's consider 2 brothers; Bill and Billy want to carry out an investigation to find the speed of a rolling ball in a 50m/s IFOR and a 30000000m/s IFOR to see if it affects the speed of the ball. Assuming they make all their variables correct, both Bill and Billy would come back with the exact results, concluding that the speed of the IFOR does not affect the overall motion of the ball.

They repeat the experiment to ensure reliability, however a third curious brother; Bob observes them both undertaking the experiment. Again Billy and Bill come back with the exact same results, but this time Bob speaks up and comments on how he got different readings for the ball when watching the experiment.

They key thing here is that yes, according to Billy and Bill, they consider their IFOR "the same"  as there was no variance in their results. BUT Bob, in this scenario is considered a stationary observer; "a stationary external point" in which allows Billy and Bill to distinguish the difference in their IFORs, which makes their frames "not the same".

So, I guess in both scenarios here, both are correct, because time can only be seen as dilating with another external reference frame, and it really depends if you include it or not. It really depends on who's perspective you want to look at.

I guess the vagueness in the term "the same" really makes this difficult to interpret, it did for me!

Hope this helps

If anyone else wants to add their input, I'd love to hear it!