Why Do Different Observers Measure Varying Directions in Particle Motion?

[fusi0n]

Hi all. I just started a modern physics course and I am having a difficult time conceptualizing the material right from the beginning. No homework yet..., but a question from the text reads:

Q. Since the velocity components of a moving particle are different in relatively moving frames, the directions of the velocity vectors are also different, in general. Explain why the fact that observers in S and S' measure different directions for a particle's motion is not an inconsistency in their observations.

I feel like if someone worked through this I could grasp the material better. As of right now I would say both observations are correct because the particle is being measured relative to each observer.

Thanks

 

[Doc Al]

You should try to think this through for yourself. I'm sure you are learning these facts: that measurements of length and time depend on the velocity of the frame doing the measuring. But there is a key difference between those two kinds of measurements. Hint: A moving clock will be measured to run slow no matter what direction it moves, but the length a moving object will only be measured differently in the direction of its motion.

 

[teclo]

what is velocity in differential form? the change of what with respect to what?

what kind of strange things are byproducts of the lorentz transformations?

i'm just learning special relativity too, hope that helps?

 

[schattenjaeger]

Q. Since the velocity components of a moving particle are different in relatively moving frames, the directions of the velocity vectors are also different, in general. Explain why the fact that observers in S and S' measure different directions for a particle's motion is not an inconsistency in their observations.

Now note they're saying in general. Mathematically speaking and usually, you try to set it up so the two frames have parallel x-axis' which means they do in fact have the same direction, but in general if S' is moving up or down at all, they won't. As for why it's not an inconsistency, I'm betting your book has a diagram with the lights and mirror clock thing, and if the mirror and light are moving you get that zigzag that forms the triangle that you can use to get the formula for time dilation. Well, in the moving frame they just see a light going back and forth like normal, in the stationary frame they see that zigzagging triangle, looking at the same thing, they see two different things(heh, that's so not worded right but you know what I mean)yet there is no inconsistency in their observations. See?

 

[lightgrav]

FusiOn,

you know the principle that
absolute velocity cannot be measured.
So now you realize what this implies: that
different observers don't have to agree
on the results of direction measurement either.
(but if needed, these can be "converted")

Would you feel better if they assigned a HW
where you practice converting a direction angle?
Even if the direction is not important?