I don't think there's a good answer to this question, at least not when it comes to the nature of particles and light, because we don't have a good answer to what movement and time are. We already know both light and particles are you moving relative to fields. Light is you moving relative to an electromagnetic field. If you move towards a magnetic field you would find it starts "glowing", in fact, that is what light is. But it's not like a magnetic field reacts to you because you start moving.
The issue is that movement and time are fundamental to the universe, yes, in the way relativity describes but also in a totally different unknown way. In some ways particles are "just" things moving relative to one another. Which, for one thing, brings the perspective question (if you accelerated to a "real" speed, would you see a different universe? Because you would disagree with us slowpokes here on earth on what particles exist at least in some cases. But would you see an entirely different universe?)
The issue is that movement and time are fundamental to the universe, yes, in the way relativity describes but also in a totally different unknown way. In some ways particles are "just" things moving relative to one another. Which, for one thing, brings the perspective question (if you accelerated to a "real" speed, would you see a different universe? Because you would disagree with us slowpokes here on earth on what particles exist at least in some cases. But would you see an entirely different universe?)