Actually, the shape of the dot is unchanged by going faster. Since it isn't a real object, it isn't affected by relativistic contraction. If you emit a circle, it'll be a circle.
It is of course changed by what it gets reflected off of, but that's not special to this situation at all. If you're at the center of an enormous hollow sphere and shine an astronomically-bright laser circle around, it'll always be a circle to you no matter how fast you move it.
If the laser emits all photons constituting the dot at the same time, in pulses... I was thinking of the photons that make up the dot arriving at random intervals, but I'm probably making things too complicated.
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Actually, the shape of the dot is unchanged by going faster. Since it isn't a real object, it isn't affected by relativistic contraction. If you emit a circle, it'll be a circle.
It is of course changed by what it gets reflected off of, but that's not special to this situation at all. If you're at the center of an enormous hollow sphere and shine an astronomically-bright laser circle around, it'll always be a circle to you no matter how fast you move it.
If the laser emits all photons constituting the dot at the same time, in pulses... I was thinking of the photons that make up the dot arriving at random intervals, but I'm probably making things too complicated.