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I am trying to construct a Lorentz transform special relativity animated simulation, and am unclear about some aspects, please.

The simulation is as follows:

enter image description here

At time=0, the person at the center [0,0,0] coordinate throws a ball to the right.

In every frame (or time-step), we need to compute the location of the person (which always remain at [0,0,0] here), and also the coordinate of the ball, which gets further per frame. Without knowing this new location coordinates, we cannot draw the ball in subsequent frames.

Assuming unit speed of light c = 1, and speed of ball v_ball = 0.5, using standard non-relativistic calculations, I can compute the right coordinate of the ball easily for every frame:

t=0: ball is at [0, 0, 0]

t=1: ball is at [0.5, 0, 0]

t=2: ball is at [1 , 0, 0]

t=3: ball is at [1.5, 0, 0]

t=4: ball is at [2 , 0, 0]

t=5: ball is at [2.5, 0, 0]

My question is, what will be the right numbers for the coordinate of the ball, when taking into account the Lorentz transformation here, and what is the right formula to use in this case?

In other words, what are the final answers (explicit numbers) for ? to be used here as time progresses in this animation?

t=0: ball is at [0, 0, 0]

t=1: ball is at [?, 0, 0]

t=2: ball is at [?, 0, 0]

t=3: ball is at [?, 0, 0]

t=4: ball is at [?, 0, 0]

t=5: ball is at [?, 0, 0]

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The relativistic calculations are the same as the non relativistic calculations in this case. You are working in a single frame so there is no Lorentz transform involved. The Lorentz transform is used to transform between frames, so it is not needed when everything is in a single frame.

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  • $\begingroup$ @ Dale thank you, this clears up some confusion for me! I'm still a little unclear, in real implementation terms, what actions that i take (being the simulator) will constitute a "change of reference"? For example, if at t=6, I decide to recenter the frame, making the ball at coordinate [0,0,0] and its velocity [0,0,0], then what is the use of Lorentz transform in this new "frame of reference", to calculate the postiion of the man? Thank you. $\endgroup$
    – user315366
    Commented Oct 13, 2021 at 5:05
  • $\begingroup$ I wrote a new, expanded question after some more simulations on physics.stackexchange.com/questions/671378/… $\endgroup$
    – user315366
    Commented Oct 13, 2021 at 7:15
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    $\begingroup$ @James basically, if you describe something in one frame then you can use the Lorentz transform to obtain the description in another frame. If you want to describe everything from one frame then you don't need to do any transformations. $\endgroup$
    – Dale
    Commented Oct 13, 2021 at 14:32
  • $\begingroup$ @ Dale thank you, yes this point when to use Lorentz transform and when not to use is clear to me now, thank you for your help! $\endgroup$
    – user315366
    Commented Oct 13, 2021 at 14:48

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