It occured to me that time could just be another spacial dimension and the reason we can't go back and forth through time like we do in space is because we've been flattened.

 

The best explanation I can think of is a flipbook with a 3D picture on it. Every page represents a slice of the fourth dimension. A fourth dimensional object would take up space on multiple pages, while we are just stuck on one, constantly traveling to the other pages.

 

Does this idea hold any water at all? I'm sure I'm not the only one who's thought of it.

The best I've heard it described as, is that there are four dimensions (think of them as spatial for the moment) and the sum total of our motion in those four dimensions adds up to the speed of light. Ex: You are moving at 10m/s in one direction, then you are also moving at 299,999,990m/s in the time dimension. Since there is no such thing as "negative speed" it is impossible to move backwards in the time dimension.

The best I've heard it described as, is that there are four dimensions (think of them as spatial for the moment) and the sum total of our motion in those four dimensions adds up to the speed of light. Ex: You are moving at 10m/s in one direction, then you are also moving at 299,999,990m/s in the time dimension. Since there is no such thing as "negative speed" it is impossible to move backwards in the time dimension.

 

That's close, except it follows vector maths, not scalar maths. Vector sums work differently.

Time is not a spatial dimension. And I don't think the flip book is a great analogy, because according to special relativity objects experience time at different rates, depending on their relative speed to one another. You should read up on world lines if you want an accurate visualization of it.

There is a way to go back into time but only in a limited way using SR. I did this before but will repeat myself. Say we had a room full of friends. One friend leaves the room and the rest are given SR velocity (the room gets SR) so there is time dilation. Just for numbers 10 years go by for the person who leaves the room and remains stationary. For the rest only 10 minutes goes by.

 

The room then returns. The stationary person then enters the room and it is exactly the way he remembers it from ten years ago, since only 10 minutes had gone by in the room. Even his half drank beer is still cold and has bubbles in it. In that microcosm of the room, he can go back into time and carry on the same conversation he had begun. Time was preserved in that room relative to the stationary person. It become a frozen snapshot of time, relative to the stationary reference. We could museum time snap shots with SR and go back to that point on demand. It would take a lot of energy but energy can be used to museum time.

There is a way to go back into time but only in a limited way using SR.

That is not actually going back in time. What it is, is that the people in the room experience time slower than the one who left. Time is still moving forward for all of them, so there is no going backwards in time.

Let us assume we are dealing with general relativity or some variant of it. Then, intrinsically there is no difference between space and time directions. The only "place" we see any difference is in the signature of the metric. This does not give an invariant notion of splitting space-time into space and time.

 

However, in practice one may need to make a distinction. This in general is difficult and puts restrictions on the kinds of space-times we can do this. (Globally Hyperbolic)