Straight Line Case. My paradox. Sorry if I rewrite and start a new post.

[ppppppp]

1. Suppose, a fast moving train (600,000 km long) running on straight line at speed 0.999c, perpendicular to A.
2. A is at point P. B stands in center of train. M point. Distance P to M is 300,000 km. C stands at end of train. D stands in head of train.
3. Now B flash light. According to B, the light reaches C, D same time, in one second in their reference frame. According to A, the light reaches C first, then 22 seconds later in A’s reference frame, reaches D.
4. Now suppose, as soon as light reaches C (now C shall be at M point), C shoot a super fast bullet, at speed 30,000 km per second, at A. D shoots a laser beam to destroy C's bullet as soon as light reaches D.

Now I ask, will A die or not? According to A's reference frame, he is dead. Because the bullet travel time travel from C to A is only 10 seconds, D's laser is fired 22 seconds later, too late to save A.
But according to B , C, or D, A is saved. Because when light reaches C, D at same time, D's laser takes just a bit over 2 seconds to intercept the bullet. (just a bit over 2 seconds is very simple geometry).

Please find out the problem or solve this of my paradox.

 

[PAllen]

1. Suppose, a fast moving train (600,000 km long) running on straight line at speed 0.999c, perpendicular to A.
2. A is at point P. B stands in center of train. M point. Distance P to M is 300,000 km. C stands at end of train. D stands in head of train.
3. Now B flash light. According to B, the light reaches C, D same time, in one second in their reference frame. According to A, the light reaches C first, then 22 seconds later in A’s reference frame, reaches D.
4. Now suppose, as soon as light reaches C (now C shall be at M point), C shoot a super fast bullet, at speed 30,000 km per second, at A. D shoots a laser beam to destroy C's bullet as soon as light reaches D.

Now I ask, will A die or not? According to A's reference frame, he is dead. Because the bullet travel time travel from C to A is only 10 seconds, D's laser is fired 22 seconds later, too late to save A.
But according to B , C, or D, A is saved. Because when light reaches C, D at same time, D's laser takes just a bit over 2 seconds to intercept the bullet. (just a bit over 2 seconds is very simple geometry).

Please find out the problem or solve this of my paradox.

You may not realize it, but there are still many features of your scenario that are not specified. Doing so might nudge you to solving the pseudo-paradox. Picking one ambiguity at random, in whose frame is the speed of the bullet specified? It will be very different in A's frame versus the train frame, and the difference will not be determined by vector addition as in non-relativistic mechanics. Further, this difference has a lot to do with the apparent paradox. You should also realize the directions of bullet and laser are different for the two frames.

 

[ppppppp]

Thanks for attention. I would say, bullet speed in A's frame.

 

[PAllen]

Thanks for attention. I would say, bullet speed in A's frame. Laser also in A's frame.

Next question: In A's frame you propose bullet kill's A before D shoots laser. In what direction (in A's frame) does D fire the laser? As I said, you have many unspecified features.

Step back: If you have a complete description in A's frame, then apply Lorentz transform, you will have complete description in BCD frame. By Lorentz invariance of physical laws, all physical facts will be the same in B frame (distances, times, order of non-causally connected events will be different; but order of causally connected events, and what collides with what, will be the same). This is what Dalespam has been encouraging you to do. It requires only algebra. No one else can do it for you because you have not actually specified a problem (though you think you have). The exercise of working it out will lead you to the conclusion that there is no paradox.

 

[ppppppp]

D fires towards the bullet in D's frame (that can be calculated with a slight angle 5.7391705041579 (out of 360) degree downwards , tang=0.100503782, so it takes a 2.010075631 seconds to intercept the bullet in D's frame.)

please give numbers and math to show it is NOT paradox. I need see numbers or math! Thanks ahead!

 

[vilas]

1. Suppose, a fast moving train (600,000 km long) running on straight line at speed 0.999c, perpendicular to A.

Yes! Solve it as PAllen said. I am interested in knowing the result. Use space-time diagram and let me and others know.

 

[PAllen]

D fires towards the bullet in D's frame (that can be calculated with a slight angle 5.7391705041579 (out of 360) degree downwards , tang=0.100503782, so it takes a 2.010075631 seconds to intercept the bullet in D's frame.)

please give numbers and math to show it is NOT paradox. I need see numbers or math! Thanks ahead!

Ok, so laser information given in D frame, bullet in A frame. Translate A frame information to train frame. In that frame, A is moving .999c in direction from D to C. Bullet is moving almost horizontally (*not* vertically) in the DC direction at slightly more than .999c. The laser at your specified angle won't come anywhere near the bullet.

You are mixing up frames all over the place. It would be simpler to describe everything precisely in one frame.

 

[ppppppp]

thanks, i get your point.

 

[Dale]

If you want help analyzing the problem I would be glad to help, but you have to work through it yourself if you want to really understand. Since you have specified the bullet speed in A's frame, the best approach will be to examine the problem in complete detail in the A frame. The first step is to specify the equations of motion for A, B, C, and D. For example:
$$(x_B(t),y_B(t))=(.99 t, 0)$$
$$(x_A(t),y_A(t))=(0, 1)$$
Where distance is measured in light-seconds and time is measured in seconds.

The next steps are to specify the equations of motion for C and D. After that, write the equation for the spacetime interval between an arbitrary point on C's worldline and the light flash, set that equal to 0 and solve for when the light flash reaches C. Repeat for D. Then you need to write the equation of motion for the bullet from C. Once you have that you determine if A lives by writing the expression for the spacetime interval between the flash arriving at D and the worldline of the bullet, set that equal to 0 and try to solve. If there is a solution then A lives, otherwise A dies.

Then, you simply transform everything to the train frame to get the story there.