Addition of velocities at speeds near C - any differences?

[PeroK]

Good evening,

If a ship is moving at 0.5C east in a gravity free environment, and fires a bullet perpendicular at 0.5c, is it just the hypotenuse (a squared + b squared)/c squared that we use for the speed?

Or is there more to it since we are at great speed?

View attachment 219082

As mentioned in the posts above, you have been helped with some calculations, but the serious, fundamental conceptual problems with the way you asked the question have not been addressed. This ties in with some of your other posts, where it is clear that you have not yet grasped the importance of measured quantities being given in a particular reference frame.

In this question, I believe, you have in your mind a general reference frame where things like "travelling North" and "perpendicular" are absolute. This is not the case. You must define in which reference frame these velocities are measured.

The most natural interpretation of your question is that in the reference frame of the observer, the paths fo the ship and the bullet are as shown. In this case, the velocity and speed of the bullet are given by normal vector addition. I.e. in this reference frame, the bullet is moving at about $0.7c$ North-East.

In fact, special relativity has nothing to say about this. As all velocites are given in a single reference frame.

The interpretation you may have intended is:

The bullet is fired at $0.5c$ north in the ship's reference frame. And, you want to know the velocity and speed of the bullet in the observer's reference frame. In this case, you must apply relativistic velocity addition, as the two velocities you are giving are measured in different reference frames.

The most important thing for you, in my opinion, is to begin conceptalising these problems differently. And to think clearly about the frame of reference in which measurements are made and velocities are specified.

For example. You could and should have said:

If a ship is moving at 0.5c east relative to an observer, and, in the the ship's reference frame, fires a bullet at 0.5c north, what is the velocity of the bullet relative to the observer?

Note that in this case, the bullet and the observer have perpendicular velocities in the ship's frame. But, the ship and the bullet do not have perpendicular velocities in the observer frame.

Finally, your post #6, I believe is loaded with similar misconceptions and implicitly involves a general absolute frame of reference.

 

[PeroK]

So, the observer on the ship still sees the bullet moving at 0.5c, even though the ship is moving 0.3.
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The observer on the ship sees the bullet moving at the velocity they fired it. The ship is not moving - only relative to the other obsever. The other observer could start running and turning cartwheels and it will have no effect on the relative motion of the ship, bullet and target.

 

[Alex Pavel]

As mentioned in the posts above, you have been helped with some calculations, but the serious, fundamental conceptual problems with the way you asked the question have not been addressed. This ties in with some of your other posts, where it is clear that you have not yet grasped the importance of measured quantities being given in a particular reference frame.

In this question, I believe, you have in your mind a general reference frame where things like "travelling North" and "perpendicular" are absolute. This is not the case. You must define in which reference frame these velocities are measured.

The most natural interpretation of your question is that in the reference frame of the observer, the paths fo the ship and the bullet are as shown. In this case, the velocity and speed of the bullet are given by normal vector addition. I.e. in this reference frame, the bullet is moving at about $0.7c$ North-East.

In fact, special relativity has nothing to say about this. As all velocites are given in a single reference frame.

The interpretation you may have intended is:

The bullet is fired at $0.5c$ north in the ship's reference frame. And, you want to know the velocity and speed of the bullet in the observer's reference frame. In this case, you must apply relativistic velocity addition, as the two velocities you are giving are measured in different reference frames.

The most important thing for you, in my opinion, is to begin conceptalising these problems differently. And to think clearly about the frame of reference in which measurements are made and velocities are specified.

For example. You could and should have said:

If a ship is moving at 0.5c east relative to an observer, and, in the the ship's reference frame, fires a bullet at 0.5c north, what is the velocity of the bullet relative to the observer?

Note that in this case, the bullet and the observer have perpendicular velocities in the ship's frame. But, the ship and the bullet do not have perpendicular velocities in the observer frame.

Finally, your post #6, I believe is loaded with similar misconceptions and implicitly involves a general absolute frame of reference.

Actually I have grasped considerably more than what seems apparent here. I will follow up with another question this weekend.

 

[Alex Pavel]

Ultimately, the bullet hits the same target regardless of the motion of the ship.

Observer on the ship perceives no difference in speed or direction.

Observer outside the ship sees bullet move at .6614 c.

 

[PeroK]

Ultimately, the bullet hits the same target regardless of the motion of the ship.

Regardless of the motion of the observer.

Observer on the ship perceives no difference in speed or direction.

No difference between what scenarios? There is definitely no difference caused by the shot being observed, nor by the motion of the observer.

There is only one scenario here. Assuming the target is not moving relative to the ship: e.g. the target is on the ship. What are your two scenarios?