# This is a thought experiment in relativity, can you try to solve this

Consider two guys A & B who are separated by a distance of 1 light hour (they are at rest to eachother)
Then A decides to fire a bullet at B. He took his gun and fires.
The bullet moves with a velocity of 90% speed of light (here the bullet is hypothetical therefore it moves at that speed at the instant it is fired)
The observer B calculates its time of arrival by using Distance/Speed therefore B predicts the bullet will reach when HIS CLOCK reads 1hr and 6 minutes.
I hope you don't have any doubt in this.
(IT IS CLEAR THAT BULLET HIT HIM WHEN IT RED 1HR & 6MTS ON B’s CLOCK )
Now imagine everything from the bullets point of view
Bullet thinks it is at rest and the whole system ’that its A & B’ is moving pass by. So the B guy will reach at bullet when Bullets clock read 1hr and 6mts.
Since moving objects slow down in time by relativity, bullet calculates the time of B to be slowed down
Therefore bullet uses his equation of time dilation and finds out that when B reached bullet, B’s clock will only read 26.15 minutes
I hope it is clear for you
(IT IS CLEAR THAT "B" HIT THE BULLET WHEN B’s CLOCK RED ONLY 26.15 MINUTES)

both the results does not match eachother, what is the solution of this paradox

mfb
Mentor
1h/0.9 = 66.666... minutes, not 66 minutes. Well, does not matter.

The bullet will not agree on the clock synchronization - when it is at A, the clock of A is at 0 (all agree on that), but the clock of B (as seen by the bullet frame) is already somewhere at ~50 minutes (did not calculate it) at that point. This is relativity of simultaneity.

Sorry i didn't understand. can you explain it once more? lets assume that the Two clocks of A & B are synchronised, when the it ticks 12 on A he fires the bullet and bullet reaches at B’s clock at 1hr 6 mts.
Now from bullets point of view, it starts from at 12:00 and the bullet too has a clock in it & its time was also 12 when it was fired
Now at what time of B will bullet reach?

Ibix
2020 Award
The clocks are only synchronised according to observers at rest with respect to the clocks. In moving frames, the clocks tick at a slower rate and do not show the same time as each other. This is the "relativity of simultaneity" that mfb referenced.

mfb
Mentor
lets assume that the Two clocks of A & B are synchronised
In which frame?
If they are synchronized for A and B, they are out of sync for the bullet, and vice versa.

Now at what time of B will bullet reach?
At the clock of B: 1:06:40
At the bullet clock: 66.666... minutes divided by the gamma factor, roughly 0:29:04.

In the frame of the bullet, the distance between A and B is reduced by a factor of 2.29. In the frame of A and B, the clock of the bullet is slower by the same factor. Both frames can analyze the setup and get the same calculated value for the clock of the bullet.

The clock of B is more interesting. In the frame of B, this is easy to see, but in the bullet frame, we have to consider that the bullet will see the clocks of A and B running out of sync. For the bullet, the clock of B is at 0:54:00 when it leaves A. B then travels a distance of 1/2.29 light hours, with a clock slowed by a factor of 2.29, and B arrives at the bullet with a clock reading of 1:06:40.

so here in bullets frame of reference it the observer B who is moving towards it so Bs time will slow with respect to bullet, am i right?

mfb
Mentor
Sure.

so when B reach Bullet, B’s clock will read only about 12:26 or 12:29
While bullets clock read 1:06mts. am i right?

mfb
Mentor
Right, see post #5.

thanks to all, that helped a lot

In addition to what was posted above, also note that the distance between A and B will be Lorentz contacted in the bullet reference frame so their distance is only about 26 light minutes and it takes about 29 minutes for the bullet to reach B in its own ref frame.

Doc Al
Mentor
This is the third thread you've started on what amounts to essentially the same issue. Once is enough!

ghwellsjr
Gold Member
Consider two guys A & B who are separated by a distance of 1 light hour (they are at rest to eachother)
Then A decides to fire a bullet at B. He took his gun and fires.
The bullet moves with a velocity of 90% speed of light (here the bullet is hypothetical therefore it moves at that speed at the instant it is fired)
The observer B calculates its time of arrival by using Distance/Speed therefore B predicts the bullet will reach when HIS CLOCK reads 1hr and 6 minutes.
I hope you don't have any doubt in this.
The only problem is that observer B will not have an hour and 6 minutes to dodge that bullet, he won't even be aware that observer A has fired a bullet in his direction until the image of the gunblast propagates to him at the speed of light so he won't see it until an hour has gone by leaving him just over six minutes to figure out its speed and get out of its way.

Here is a spacetime diagram depicting your scenario. Observer A is in blue, observer B is in red and the bullet is in black with a thin black light signal propagating from the firing event to observer B one hour later:

(IT IS CLEAR THAT BULLET HIT HIM WHEN IT RED 1HR & 6MTS ON B’s CLOCK )
Now imagine everything from the bullets point of view
Bullet thinks it is at rest and the whole system ’that its A & B’ is moving pass by. So the B guy will reach at bullet when Bullets clock read 1hr and 6mts.
Since moving objects slow down in time by relativity, bullet calculates the time of B to be slowed down
Therefore bullet uses his equation of time dilation and finds out that when B reached bullet, B’s clock will only read 26.15 minutes
I hope it is clear for you
(IT IS CLEAR THAT "B" HIT THE BULLET WHEN B’s CLOCK RED ONLY 26.15 MINUTES)

both the results does not match eachother, what is the solution of this paradox
Your results have already been corrected by others but here is a diagram transformed from the first one showing the bullet's rest frame:

Now you can see what mfb said in post #5 that in the bullet's rest frame, observer B's clock is at 54 minutes when the bullet is fired, but remember that B doesn't see that until his clock is at 60 minutes.

Here is another diagram zoomed in around the events of interest:

Now you can see what dauto said in post #11 that the distance between the two observers is 26 light-minutes. (Look at when A's clock is 0 and B's clock is at 54.)