But I think there's an alternative view.

In two dimensions, we can move left/right or forward/backwards. If we elect to move left/right we do not move any distance forwards or backwards at all. Or we can decide to move in both dimensions at once: two steps to the left and one forward, say.

In three dimesions the same thing applies. We can choose to go in any one given direction without moving at all through the other two. We can go three steps to the left. Or Three steps forward. Or climb three steps upwards. Or we can do a combination. Three steps upwards and one to the left, for example.

In the four dimensions of space-time, the same principles apply. We should be able to move through time alone, or through time and space in any given proportions.

Imagine we decide to move through time alone.

Where we end up at may not actually be where we started from spatially. This is because while we have been traversing the time dimension, the earth (or whatever is our starting point) has itself moved spatially. As well as the earth's rotation, there is also the earth's orbit around the sun to consider. And the sun's orbit around the galactic centre. And the galaxy's acceleration towards the so-called Great Attractor. And the entire universe's expansion to boot. All in all, we are whizzing about the universe along multiple trajectories at phenomenal rates.

So the question is: when we rematerialise at the different time, will we be somewhere in outer space, the earth having now moved thousands of kilometers around the galaxy?

Or will our current momentum through space have caused us to "keep up" while we were moving through time?

In the former case, where we effectively step off this moving universe without retaining spatial momentum and then reembark at a different time (and place), we might wonder whether we have violated the law of conservation of momentum. But I don't tyhink we would have. From the universe's perspective, upon rematerialisation at the new time coordinate, we retain the same spatial momentum we had previously but now it is being exerted at different spatial coordinates.

So such a scenario opens up the interesting possibility that time-travel would be exploitable as travel through space. If time travel could be achieved at low-cost then we have simultaneously developed a low-cost means of normal travel.

Thoughts?

2old