Special Relativity - Events and Frames of Reference

[Pezz]

Hello everyone :). I'm new here and wasn't sure where to post my physics question so here I am in the homework help section as my question is homework related...

The problem I'm having is of very basic nature however I might have some trouble wording it. I understand an event is something that happens independent of frame of reference. Let's say we have two frames S and S' with a relative speed of v along the x axis. If an event occurs at some point x, and we figure out x', when looking separately at each frame of reference the event would be at a fixed point in each frame correct? I mean if S is looking at S' and an event occurs at x = 10, S sees S' moving toward the event. When we figure out x' for S', would the event be fixed in that frame at x' or would there be any movement between the frame and the event in the S' frame... I hope I got across my question and thank you in advance for any attempts at an answer :P...

 

[Simon Bridge]

Welcome to PF;

The trick here is to be very careful about your wording.
Events do not occur only at a particular position, but also at a particular time.
The event that something occurs a distance x from S (the S-frame observer) also occurs at time t.
S' is moving towards x.

According to S', the event occurs at position x' and at time t', and S is moving away from x'.

The point x is stationary in S and x' is stationary in S' - the cause of the event need not be stationary in either.

Later you will be using the word "event" to mean the point in space-time rather than the thing that happens there ... the thing that happens just becomes a handy label for the point.

 

[mfb]

Every frame can assign specific coordinates to the event, sure. Everyone has a birthday in every system ;).

 

[Pezz]

Thanks for the responses, it clears some stuff up.

I think I'm overthinking the whole thing but it's only been a week since I've been introduced to all of these concepts of length contraction, time dilation etc. I hope it becomes clearer with time, I guess I'm just not used to thinking "relatively". I've lived all my life thinking in Galilean transformations haha...

Are there any tips that you guys could give me in how to approach this whole thing. I want to understand the equations and the concepts from a more intuitive standpoint. I know how to formally derive the Lorentz transformation equations and use them, but I wish to actually understand them and the whole concept of special relativity intuitively.

 

[Simon Bridge]

You basically have to get used to it by doing examples.
There was a time when Galilean relativity and vectors were weird.
You may like to try: http://www.physicsguy.com/ftl/html/FTL_intro.html
... that's just the intro - there are 4 parts which concentrate on the concepts and how they fit.

 

[Pezz]

Thanks for the link. I will definitely start reading it tomorrow as it's getting late here and I'm about to go to sleep. Before I go off, I thought of one thing that doesn't make sense to me and I know that there is an error in my thought process but I just can't seem to find it...

Say a lightning bolt strikes at x in the S frame, and x just happens to be a location on top of a very fast moving train with an observer S' inside of it. Observer S determines that the distance between the mark the lightning bolt leaves and the observer S' is a distance d. Using Lorentz transformations we would get an x' that is larger than d. Shouldn't x' = d? Would S' see the lightning bolt hit a different part of the train?

The only answer I can think of is that S sees the train as shorter and thus measures a shorter distance...

 

[Simon Bridge]

If the train is stationary in S', then it is moving in S.
A way to make the situation clear is to say that there are two lightning strikes, one at each end of the train, and they strike so that they leave a burn mark on the train, and also on the tracks.
The key to understanding what each party measures is to realize that events which are simultaneous in one frame are not simultaneous in all frames.
The reading I gave you covers several such situations.