The Effects of Special Relativity on impulse Consider a particle moving near the speed of light (let's say 90% of c). It collides with a wall of much higher mass and bounces back. How would relativity affect that impulse value? The two observers would have different values of time for the collision. Does that mean the average force differs between perspective? I understand that the speed at which the particle is travelling is arbitrary, since the effects of special relativity scale all the way to zero velocity. But what would it look like, considering that the effects are so exaggerated at 90% c? 
 A: Yes, indeed, three-force is frame dependent. Look up the Wikipedia article on four-vectors, for example: it gives you a list of quantities that transform in the same way as vectors joining events in Minkowski spacetime.
The four-momentum of a particle is
$$\mathbf{p}=(E,\,p_x,p_y,p_z)=m_0\,\gamma\,(1,\,v_x,\,v_y,\,v_z)$$
where $E$ is particle's total energy, $v_i$ the Cartesian three-velocity components and $\gamma = 1/\sqrt{1-v^2}$ the Lorentz factor (velocities are all normalized so that $c=1$ here).
If this four-momentum is changed by an impulse through an interaction, we get the four force, which is the rate of change of this momentum with respect to the particle's proper time:
$$\mathbf{F} = \mathrm{d}_\tau \mathbf{p}=\gamma\,(P,\,\mathbf{f})$$
where $\mathbf{f}$ is the "everyday" three force, or the laboratory rate of imparting of impulse to the particle and $P$ the laboratory power, or rate of working by the three force. The components of the vector $\gamma\,(P,\,\mathbf{f})$ transform exactly as event spacetime co-ordinates do, i.e. by the Lorentz transformation, so that the three force is frame dependent and gets mixed with the power of the three force when we observe it from different inertial frames. As you can see from the presence of the $\gamma$ factor, the laboratory impulse of the force varies a great deal under relativistic-speed boosts.
How would it look? Bad. Like: really, really BAD!
A: Quantum Theory (lab observation): It would perform the bounce as a particle if there was no observers, but as there are two like you said, the particle would perform as a wave.

https://www.sciencedaily.com/releases/1998/02/980227055013.htm

Being near of speed of light is not being at the speed of light.
Best regards,
