Understanding Einstein's Theory of Relativity: Laser Technique Questions

[Manfredthethird]

I just found out what relativity is and got some questions:
Actually, only one:

So, according to einstein,
1. Light travels the same speed independent of the source speed.
2. Its not possible to tell which object is moving compared to an other object.

I got that if one object A is moving faster than a object B, and fires a laser vertical to the direction it moves, from B perspective the laser will travel a longer distance. Ok.

As we can't even tell which object is moving, i could say that object B is moving and A is not. So, in the same situation, if object B fires a laser vertical to object A moving direction, from object A perspective the laser would travel a longer distance too.

So, in the same situation, if booth fire the laser i could say that time for object A slows down compared to object B, and time for object B slows down compared to object A?
Wouldnt it cancel the time dilation and nothing would happen?
Where am i wrong?
I am not trying to discuss about how the theory is wrong, I am trying to figure out how it works.

 

[Khashishi]

That's the crux of time dilation. Object A is slower in object B's reference frame and object B is slower in object A's reference frame. If you have two people moving relative to each other, they both think the other's clock is slow.

 

[Orodruin]

It is unclear what you mean when you say "travel a longer distance". By "vertical" you probably also mean "orthogonal to the direction of relative motion".

That being said: Most apparent paradoxes that appear when using time dilation arguments are based on a misconception about what is meant when we talk about it. In the end, it stems from events being simultaneous in one frame not (necessarily) being simultaneous in another.

 

[Nugatory]

To make sense out of the way that time dilation is symmetrical (A says that B's moving clock is slow; B says he's the stationary one and A's moving clock is slow) you have to understand relativity of simultaneity first. Google for "Einstein train simultaneity" to find Einstein's thought experiment showing how this works.

Once you have relativity of simultaneity down, you can make sense of the time dilation. You and I are in relative motion and I say that your clock is slow because at the same time that my clock reads 1:00 PM yours reads only 12:59 PM. It does not follow that you will also say that at the same time your clock reads 12:59 mine will read 1:00; because of the relativity of simultaneity we have different notions of "at the same time" and in fact my clock will read something less than 12:59 according to you.

 

[georgir]

A "light clock" with bouncing light rays orthogonal to the direction of motion between two fixed-distance mirrors is exactly how Lorentz transformations are derived in the SR intro textbooks I've seen. Pretty close to your setup. You may soon be able to derive SR yourself. Though you may still want to save some time and effort and get a textbook.

 

[Dale]

Im not trying to discuss about how the theory is wrong, I am trying to figure out how it works.

In general, one of the best ways to figure out how relativity works is to think geometrically.

Draw a spacetime diagram, use t as your vertical axis and use x as your horizontal axis. Draw a few horizontal lines for t=0 years, t=1 years, etc. Draw a few vertical lines for x=0 light years, x=1 light year, etc.

Then use the Lorentz transform formulas to draw t' and x' lines on the diagram. Use v=0.6c as a convenient speed.

Then using those lines you will be able to see geometrically how the unprimed clocks are slow in the primed frame and the primed clocks are slow in the unprimed frame.

 

[Manfredthethird]

I think i can make a image about it based on the replies.
I see it depends on the point of view.
But seeing the event from a diferent point of view, someoe who is not at object A nor at object B. What will he be able to tell about the time dilation on these two objects?

And a other question:
Someone placed a camera here on Earth with a huge cable to transfer the images, and then enters and leaves in a spaceship flying near the speed of light carring the other side of the cable and a monitor attached to it.
Imagining that the cable would have no resistance so that the data sended by the camera would travel as fast as possible, would the person in the spaceship see on the monitor how everything on Earth moves rapidly?

...And one last question to feel better about myself:
My friend enters a spaceship at my side and starts flying at near speed of light. Ok. As we know, if a millisecond passes in the spaceship, hours pass where i am and we can say that time at the spaceship is slower.
So according to this, why don't i see my friend fly really slow?

And yes, by "vertical" i mean "orthogonal to the direction of relative motion".

 

[Khashishi]

What another observer C sees depends on how they is moving relative to A and B. If C moves at the same velocity as A, they sees B is slow, just like A, and vice versa.

2nd question:
No. The spaceship occupant would see the video on Earth slowed down, since Earth is moving near the speed of light and experiences time dilation. Earth would similarly see the spaceship video slowed down, if the video is two-way, since in the Earth's frame of reference, the Earth is standing still and the spaceship is moving near the speed of light.

3rd question:
The premise of your question is wrong. You aren't understanding the relativity of time, instead thinking in absolute terms.