We can not conceive of other matrices through which to perceive the world, which makes inventing aliens based on that practically impossible. We can, however, conceive of the matrices being ordered differently. We have space and time as relative to the speed of light, because that is as fast as we can perceive things. What if we perceived things more through some other matrix?
Suppose an alien whose reason makes the world appear to him primarily causally, rather than spatially.Here is how such a being might try to explain his perceptual world:
I don’t see as humans see. I see cause, effect. You see events, one, two, three, and so on. I see this causes that, causes the other. For you, everything is displayed as changing spatial dimensions. For me, it is changing causal dimensions. I can see far ahead what will come, just as you can see into the next room. If I am standing in a room, and there is a switch, I can see what happens if I switch it. I don’t see by light, either, but instantaneously, as far as your dimensions are concerned, by particles which you cannot perceive, nor will you ever be able to, apart from special structures. Because I “see” instantaneously, rather than by light, I perceive no relativistic effects.
Because I see causally, rather than spatially, I can see where every particle which has mass is. Each one has an effect on my own mass, pulling it in various directions, and I can see that. I can’t see each particle all that clearly, though, it is just as if you were to look out onto a field: you would see each blade of grass, but not at all clearly. What you could see clearly is where the grass was thick, and where it was thin, at least the extremes.
I don’t move in time in the same way as you. You are pulled along as if by a current. Because I pass through causality the way you pass through space-time, I can go backwards in certain ways. You can walk into and out of a room, but the room has changed due to time. I can walk into and out of an event, in the same way, but the event has changed in the meantime. For me, everything that could happen, does. I just don’t necessarily go to where it is. If I walk into a room, as far as you see, then I see many different directions I could go: where I knock a vase over, where I don’t. Both events happen as much for me as your kitchen and living room exist for you when you are in the dining room. You don’t experience your kitchen when you are in your dining room, and neither do I experience knocking over a vase when I don’t, but I can see it and what comes of it. Even when I do experience it, I can step back in time. I can knock over a vase, then rewind, by walking back through the choices, and then walk through what happens if I do not knock over the vase, or what happens if I knock it over differently.
What are, to you, alternate worlds, are, to me, akin to the future and the past. You measure time by changes in spatial objects. I measure time by changes in causal objects. Spatial objects are like boxes and wardrobes and stuff. Causal objects are openings and closings and knockings and such. I don’t actually see a vase, I see various possible actions tied to a vase, like you see various objects tied to knockings, rather than the knockings themselves. I just have it the other way from you.