I How can time only have one direction?

[Nugatory]

As is the procedure, we give both rocks' worldlines the time axis. Which Worldline gets the time axis?

It doesn't matter as far as counting dimensions is concerned. Up/down on the sheet of graph paper is forwards/backwards in the time dimension, left/right is the space dimension.

 

[student34]

"Time axis" is a property of frames, not objects. So this question is unanswerable as you ask it.

This was from your other post to the ultimate question of this thread, "Using the example in the OP, the object in the middle would calculate the time axis, of the objects moving away from it, pointing in different directions, no?"

I think I have narrowed down closer to my confusion. Here is my conclusion from my premise.

P1: Either rock can claim to be travelling through only time and no space.
Conclusion: Then it would seem to be true to say that both are travelling through only time and no space.

Of course my conclusion must be wrong, but I don't know why. I don't know how it can be either, but not both.

No, that is not "the procedure". A given inertial frame can only have one time axis. So you have to pick one. You can't draw a single diagram with both rocks' worldlines as the time axis.

I meant that each gets its own time axis in its own diagram.

How a length looks in a spacetime diagram does not always correspond to the actual length.

The lengths along worldlines are invariant. No spacetime diagram can make all lengths "look" like their actual lengths, because the piece of paper you are drawing the diagram on has Euclidean geometry, but spacetime itself has Minkowski geometry. So any diagram will distort some lengths.

And with all that said, your actual description of what the V will look like (leaving aside that how it looks is distorted compared to actual lengths) is wrong. If you just go by what each arm of the V looks like, and we assume that the actual lengths of the arms are equal (i.e., we mark the ends of each arm by the same elapsed proper time of the rock whose worldline is along that arm), then the arm corresponding to the time axis will look shorter than the other, not longer.

Oh right, I made a mistake. The point that I am trying to make is that the structure changes depending on which rock gets the time axis.

 

[PeterDonis]

I don't know how it can be either, but not both.

Because "traveling through time and not space" is frame-dependent. Each one, to make his claim that he is only traveling through time and not space, has to choose his own rest frame. But those frames are different. There is no frame in which they are both traveling through time and not space.

The point that I am trying to make is that the structure changes depending on which rock gets the time axis.

How the V looks changes. But the actual, physical lengths of its arms do not.

 

[jbriggs444]

The point that I am trying to make is that the structure changes depending on which rock gets the time axis.

The structure does not change. The description changes. One can describe all three rocks from the point of view of the inertial rest frame of any of the three rocks. Or from any other inertial frame not associated with any of the rocks.

There is a three dimensional space from which one can choose inertial frames that all correctly describe the three rock system.

All of the descriptions work. None of these descriptions are any more correct than any other.

 

[PeterDonis]

Thread closed for moderation.

 

[Dale]

After a brief discussion this thread will remain closed