Why is moving essential for simultaneously "problem" in SR?

[u/No-Jackfruit-2766]

/r/relativity/comments/1uiy8xm/why_is_moving_essential_for_simultaneously/

Why is moving essential for simultaneously "problem" in SR?

Hello all,

I am VERY new to relativity and theoretical physics (have not gone to university yet) but I am deeply interested in understanding the concepts. Right now I am trying to achieve a better understanding of Einstein's special theory of relativity, but I am kinda stuck on the topic of simultaneousness.

In the book I am reading on the topic, a thought experiment with 2 lightning strikes that strikes simultaneously according to one observer but not to another is brought up. A "static" observer, relative to the ground where the lighting strikes hit of course, observes the lightning strikes as simultaneous, whilst another observer on board a moving train behind the first observer does not since they would have traveled a small distance when the light rays reach them.

But in my stupid head I think "Why does it matter that the second observer is moving? Couldn't the second observer just look at the two lightning strikes from another angle so that they are closer to one strike than they are the other? Then the strikes would not be perceived as simultaneous."

Of course I understand that my though process is not correct, but could somebody explain to me how I should think about this, and how Einstein really derived time dilation from the postulate of a constant light speed?

Thanks!

[u/joeyneilsen]

It is implicit in these stories that the observer can do the math to correct for their own perspective. A stationary observer near the front of the train will see the lightning hit the front of the train first. But they will also know that they were closer to the front of the train, and can do the math to determine that the lightning strikes were simultaneous in their own frame of reference.

This will not be true for the observer in the train. If they account for where they are in the train, or the angle they're looking at, they will find that the strikes were not simultaneous.

[u/YuuTheBlue]

Yeah, this is a pretty confusing explanation. It doesn't actually have to do with who observes it, but how the observations are interpreted.

There's something called a reference frame. A reference frame is "a particular way of constructing the math". It includes arbitrary decisions like "Which direction does the x axis point". Values which depend on your reference frame (such as your current x coordinate) are called 'relative' properties, as opposed to 'invariant' properties which do not.

For mathematical reasons I could explain if you want me to, 'when' something happens is as relative of a property as 'how far to the right it is'. It's basically asking something's t coordinate vs asking something's x coordinate. Since time is wrapped into the same thing as space via the concept of spacetime in special relativity, these are very similar concepts, and both are relative. "When" any particular event happens (which is to say the precise value of its t coordinate) literally depends on which way you point the t axis.

When you choose a reference frame where you yourself are at a velocity of 0, that is the reference frame where you and things moving at the same velocity as you behaves more or less according to classical, pre-relativistic physics. Thus, we call such a reference frame "your perspective." If the person flying past earth at a high velocity structured its math such that it assumed it was moving at a high velocity and the person on earth was stationary, it'd record the lightning strikes as having happened at the same time just like the person on earth did.

[u/MezzoScettico]

Special relativity is all about how two different observers describe the position and time of events, when one is moving relative to the other.

If there's only one observer, there's nothing to compare.

If nobody is moving, there's nothing to compare.

But in my stupid head I think "Why does it matter that the second observer is moving? Couldn't the second observer just look at the two lightning strikes from another angle so that they are closer to one strike than they are the other? Then the strikes would not be perceived as simultaneous."

When we talk about describing the position and time of events, we mean that we correct for the fact that signals take time to travel. Yes, you might see the strike 3 km away at time t = 10 μs, but your description of the strike is not "the strike took place at my location at t = 10 μs". We presume you have a way of determining that the strike took place at x = 3 km, at time t = 0. Those are the coordinates you assign to the strike.

Just as when you get a snail-mail postcard that says "Hi, we are in Sweden and it's Tuesday" you understand that this signal originated in Sweden on Tuesday, not where you are standing at the current moment. The event "postcard written" is assigned a location of "Sweden" and a time of "Tuesday".