B Does everything in space have or inherit inertia?

[phinds]

I can fix that.

Before you bother with that, answer me this: do you understand relativistic velocity addition? If not, you should study it before you go any further.

 

[DeckSmeck]

Before you bother with that, answer me this: do you understand relativistic velocity addition? If not, you should study it before you go any further.

Thanks for the advice but I think I need something simpler.

 

[PeroK]

Let's talk about a rock instead. I shoot a rock off my spaceship directly to the right. How do I calculate the resulting vector of the rock if the final speed is 100. What does the equation look like.

Suppose your spaceship is traveling at velocity $(v, 0)$ is some reference frame. This means velocity $v$ in the x-direction and $0$ in the y-direction.

Suppose you fire a rock with velocity $(0, u)$ relative to your ship. Then the velocity of the rock in the frame in which your ship is moving is simply $(v, u)$.

This is just geometry. You could draw a diagram to imagine the situation. Try this for visualisation:

You are standing at a crossroads. A car approaches from the West. When it reaches you someone in the car throws a rock out of the car in such a way that it moves directly up the road to the North. To the people in the car, however, the rock is not moving North. They must have thrown it out at a backwards angle.

Now imagine that the rock is thrown North to the people in the car. That means that as the car moves East the rock stays to the North of the car (until it lands anyway). To you, at the crossroads, the rock is not moving up the North road, but at an angle between the East and North roads.

Try drawing a diagram of this.

Light is similar to this, at least geometrically. A beam of light can moves in a physical direction. E.g. up the North Road or diagonally between the North and East roads. The observers at the crossroads and in the car must agree about this.

Some people have a weird idea that, to the person at the crossroads, the light noves up the North road; but, to the people in the car it moves North of the car. But, it phsyically cannot do both. It must be one or the other.

Note that the get the light going up the North road, the laser in the car must be pointing slightly backwards. The same is true is you fired a gun or through a rock. If you want to hit a target from a moving car, you must aim behind the target. This is another concept that many people struggle with.

Try drawing some diagrams to see what happens.

 

[jbriggs444]

Some people have a weird idea that, to the person at the crossroads, the light noves up the North road; but, to the people in the car it moves North of the car. But, it phsyically cannot do both. It must be one or the other.

Why can it not physically do both?

From the crossroads guy point of view, you have a vertical beam of light that is sweeping from west to east. At the instant the car passes the crossroad, all of the North road is briefly and simultaneously illuminated. Prior to that instant, the vertical beam was illuminating wheat fields to the west of the crossroad. After that instant the vertical beam was illuminating corn fields to the east of the crossroad.

From the car point of view, you still have a stationary vertical beam of light. At the instant the crossroad passes the car all of the North road is briefly and simultaneously illuminated. Prior to that instant, the beam was illuminating wheat fields to the west of the crossroad. After that instant, the vertical beam was illuminating corn fields to the east of the crossroad.

If you want to hit a crow sitting on a stop sign at the next crossroads to the north, you have to shoot early.

From the crossroad guy's point of view, the car shoots early and a pulse of light begins moving diagonally to the east of due north. The beam is vertical, but the beam contents are moving. The pulses are moving diagonally in lock step. The intercept is made and the crow loses some feathers from its tail.

From the car's point of view, car shoots early and a pulse of light begins moving vertically due north. Meanwhile the crow is moving westward into the path of the beam. The intercept is made and the crow loses some feathers from its tail.

The question may arise: "how can a mechanism composed of pieces that both car driver and crossroads guy agree are composed of nice pure 90 degree angles succeed in emitting a collimated beam whose pulses move diagonally according to one observer and vertically according to another?"

One way is to imagine the collimator as a series of rings (like the barrel of a gun) through which the light must pass before it emerges. To the car guy, these rings are stationary and lined up, so the sequence of pulses all move vertically north on the same path. To the crossroads guy, these rings are moving. In order to pass through all of them, each pulse in the sequence must be moving diagonally, following a path a little offset from the previous diagonal path.

Another way is to imagine the flat polished surface of a laser. The coherent wave form egresses from the surface and propagates normal to that flat surface -- or does it?

From the car point of view, the wave pulse is planar, parallel to the polished face and propagates due north.

From the crossroads point of view, the relativity of simultaneity kicks in. The wave front is cockeyed, not parallel to the polished face. It emerges at an angle east of north.