The earth is rotating, which is a non-inertial reference frame. Fido simply uses its own reference frame, which following the command is now inertial. The result is that Fido is no longer affected by gravity, and slowly floats away just as in the comic
"but Stephen, there are no fixed points in space. Space is relative, meaning you can only define positions relative to other things. You demand the fundamentally physically impossible of me, Stephen."
Is it tho? Assuming there was a big bang, isnt it fair to call that origin point 0 0 0 in 3D space? Subjective space is relative, but that doesnt mean space itself is relative.
the big bang wasn't an explosion from a point, it was an explosion of a point in space. That one point is still expanding to this day. Everything is moving away from everything else, which wouldn't be the case in an "ordinary" explosion. We are all still in that one point, it's just that that point has expanded. The center of the universe is, in the literal sense of the word "literally", everywhere.
that's not how the big bang works, the whole thing about the big bang is that it was a singularity containing all of space in a single point.
The standard analog is to take a small balloon with dots painted on it, then inflating it. The surface of the balloon is spacetime, and as it shows there is no origin, everything just gets more distant from everything else.
So from wherever you look, the universe is expanding away from you (I.e., other things in it move away from you).
Therefore, you can see that the universe doesn't have a centre. From this and some other a bit more complicated things, one can see that the Big Bang never had a single point but rather expanded everywhere at once when it happend. Although often called expansion from one point that is wrong.
Also technically you would need to give a time dimension as we live in 4D space.
the 0 0 0 0 (spacetime) orientation system would be possible if the universe was a minkowski space and thus flat, but spacetime is curvy due to relativistic effects, which prevents any sort of flat orientation like that
I'm just going to jump on the bandwagon and helpfully say; think of the universe as a large expanding paper bag.
Initially it was flat, but then the bagger expanded it in the third dimension and put bananas in it. Imagine now that you are one of those bananas, but oh no, here comes the 2L Pepsi bottle ready to crush us. Thankfully the bagger takes us out of the bag first, puts the cola bottle in, and then puts us back in on top.
Proper time is only defined along a timelike world line, e.g. the timeline of a specific reference point / object. It's "objective" in the sense that is true for the reference point, but other reference points may (for example) perceive distant events in a different order
Also, it's a little inaccurate as the dog would be moving at hundreds of thousands of kilometers per hour, either burning up in the Earth's atmosphere or plowing through its surface. Also, I don't think dogs have the ability to do this, so there's that.
because fixed points in space (stationary reference frames) fall inwards into gravity wells as time progresses, Fido, would need to burrow into the center of the earth. Fido should shoot into space like that if told to stay at a fixed point relative to the cosmic microwave background