Problem with understanding of relative motion.

[withoutn]

Hi everyone,
I have a problem with understanding a few lines from the book on Relativity I am using. Let me first quote my troubles,

"Let us express these facts algebraically, for two observers, K and K', who are moving with uniform velocity relatively to each other, thus:
K writes x = ct,
and K' writes x' = ct',
both using the same value for the velocity of light, namely, c, and each using his own measurements of length, x and x',
and time, t and t', respectively.

It is assumed that at the instant when the rays of light start on their path, K and K' are at the same place, and the rays of light radiate out from that place in all directions.

Now according to equation x = ct, K who is unaware of his motion through the ether (Since he cannot measure it), may claim that he is at rest and that in time, t, K' mus have moved to the right and [vice versa (K' thinks same about K)"

My question is, if K and K' are in the same place at an instant, how come either of them moves while the other stays in place? As is written, K thinks that K' moved, while K' thinks K moved, but wait a minute, since they're at the same place, don't they both move or stay?

 

[George Jones]

My question is, if K and K' are in the same place at an instant, how come either of them moves while the other stays in place? As is written, K thinks that K' moved, while K' thinks K moved, but wait a sminute, since they're at the same place, don't they both move or stay?

Consider a traffic accident, but a non-violent one in which the two cars are able to move through each other. The cars are only together at the instant of the collision; before and after the colliion, the cars are separated.

 

[withoutn]

Hey, thanks
However, I can't quite imagine a guy standing on a piece of matter, and another passing right through him - Wouldn't that result in a colission? I need somewhat a better explanation. If these two guys are in spacecraft s, and let's say K passes by Point O where K' is parking at that moment and emitting a ray of light too, then, These two as long as they are in the same medium and same working spacecraft s, then I'm pretty sure it'd be possible to calculate the velocity of either one based on how far they recede from one another in time t, but on the other hand it's condradictory to experimental data which A. Einstein proposed (according to the book) where velocity of moving object cannot be measured.
Case 2, if they're not in Spacecrafts but for example at some distant planets, each moving through space with unknown velocity v (since it cannot be measured according to the data), Wouldn't the two fall into each others' gravitational fields while passing by? I don't know... It's so confusing and I suck in physics, Help Me...

 

[Doc Al]

If these two guys are in spacecraft s, and let's say K passes by Point O where K' is parking at that moment and emitting a ray of light too, then, These two as long as they are in the same medium and same working spacecraft s, then I'm pretty sure it'd be possible to calculate the velocity of either one based on how far they recede from one another in time t, but on the other hand it's condradictory to experimental data which A. Einstein proposed (according to the book) where velocity of moving object cannot be measured.

There's no problem with either observer measuring their relative velocity. But an "absolute" velocity has no meaning; velocity is always with respect to something.

 

[robphy]

Can you draw a position vs. time graph [a spacetime diagram] of two objects traveling with different constant velocities?

 

[JesseM]

Hey, thanks
However, I can't quite imagine a guy standing on a piece of matter, and another passing right through him - Wouldn't that result in a colission? I need somewhat a better explanation. If these two guys are in spacecraft s, and let's say K passes by Point O where K' is parking at that moment and emitting a ray of light too, then, These two as long as they are in the same medium and same working spacecraft s, then I'm pretty sure it'd be possible to calculate the velocity of either one based on how far they recede from one another in time t, but on the other hand it's condradictory to experimental data which A. Einstein proposed (according to the book) where velocity of moving object cannot be measured.
Case 2, if they're not in Spacecrafts but for example at some distant planets, each moving through space with unknown velocity v (since it cannot be measured according to the data), Wouldn't the two fall into each others' gravitational fields while passing by? I don't know... It's so confusing and I suck in physics, Help Me...

Usually in physics when you talk about two observers passing next to each other, for convenience you're treating the observers as mathematical points, so their paths are just 1-dimensional lines, and the point where the lines intersect is where they pass. Of course this is an idealization, but if the scale of the problem is in light-years and the two ships pass within a few meters of each other, the error in treating them as points which pass at a single point is negligible.