Can two objects moving parallel relative to a ground meet?

[Lotto]

Homework Statement

Can two objects moving paralell relative to a ground meet when we move properly?

Relevant Equations

I think that yes.

I think that yes but how to explain it when someone standing on a ground sees them moving paralell? If I move properly, I can see two cars moving paralell ralative to the ground crashing, while someone on the ground do not see them crashing. Is it consistent?

 

[PeroK]

I've no idea what you mean!

 

[haruspex]

What do you mean by "moving properly"?

 

[kuruman]

You don't really mean crashing do you? Crashing implies a collision in which metal is bent, glass is broken and people are often hurt. These will occur no matter how an observer moves relative to the cars. By "crashing" did you mean that a moving observer can see the cars being at the same spot at the same time whereas another observer sees the cars at different positions at that same time?

 

[jbriggs444]

Homework Statement:: Can two objects moving paralell relative to a ground meet when we move properly?
Relevant Equations:: I think that yes.

I think that yes but how to explain it when someone standing on a ground sees them moving paralell? If I move properly, I can see two cars moving paralell ralative to the ground crashing, while someone on the ground do not see them crashing. Is it consistent?

Guessing at what you mean...

You are thinking about special relativity. You know that how fast things move and what direction they move can change if you shift which frame of reference you are using.

So you adopt a frame in which the ground is at rest. In this frame you have two cars moving on parallel trajectories. Both cars are moving in the exact same direction and never collide.

Now you shift to a different frame of reference. Now the cars are moving in a new direction. If the cars were moving at different speeds, the new trajectories traced out by these cars in three-space may not be parallel any longer. But the fact will remain that no collision ever occurs.

[If the cars were moving at different speeds, their trajectories in four dimensional space-time were not parallel to start with either, but we can stick with the familiar three dimensional vectors and not try to think about four-vectors]

When you change frames of reference, you are changing the coordinates assigned to every physical thing in your scenario. You are not changing any of those physical things. If there is a collision event then that collision event will have a time coordinate and a location coordiate in every frame. Those numeric coordinates will differ from frame to frame. But there will be a collision event in every frame.

Similarly if no collision occurs. If no collision occurs in one frame then no collision occurs in any frame.

The collision or lack thereof is an "invariant" fact of the matter. Changing frames does not change it.

Invariance is a useful concept. It means that a fact or a measured or computed quantity is true in all reverence frames. As above, one "invariant" thing is the fact of the matter about whether a collision occurs.

In relativity, another invariant quantity is the "squared interval" between two events: $(\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2 - (\Delta t)^2$

 

[Mister T]

Homework Statement:: Can two objects moving paralell relative to a ground meet when we move properly?

If they are moving towards each other?

 

[Lotto]

You don't really mean crashing do you? Crashing implies a collision in which metal is bent, glass is broken and people are often hurt. These will occur no matter how an observer moves relative to the cars. By "crashing" did you mean that a moving observer can see the cars being at the same spot at the same time whereas another observer sees the cars at different positions at that same time?

Yes, that is exactly what I meant.