Utopia and Time Travel

[The Greater Fool]

It's going to break down here because instant wouldn't be well defined. Unless you want to make it so by fiat.



Sure, so long as we bear in mind the above.



Same real chain.



No.



Each person may measure the "10 seconds later" differently. Otherwise, no.



Pretty much. The elephant doesn't change, the measurements made on it do. But even those can be recast to the "correct" measurements providing we know the state of motion of everything relative to everything else.

Here is a funny version...

In your example, everyone is in the same inertial reference frame. Here's the other key thing to remember about relativity, and especially space/time. While the speed of light is a finite limit, you can (theoretically) accelerate forever. So when we see a light cone:

[qimg]http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/spacetime/terminology.gif[/qimg]

(Taken from http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/spacetime/ which explains these concepts very well)

Remember that while straight up means zero velocity, and 45 degrees means light speed, every inertial reference frame's light cone will look identical, with the speed of light always being 45 degrees away. No matter how much you accelerate, things look the same, there is no preferred velocity:

[qimg]http://www-bcf.usc.edu/~fbonahon/Images/FareyPoincareMovie.gif[/qimg]

This is an example of a poincare. An infinite plane represented in a single disk, with distance getting infinitely smaller as you reach the edge. You can imagine that the center is zero velocity and the edge is lightspeed. Picking a reference frame in reality to choose a "now" is like choosing a point on this disk. There are infinite points to choose from and the disk looks the same no matter what point you choose.

I like this image much better, but it's too large for the thread http://www-bcf.usc.edu/~fbonahon/Images/FareyPoincareMovie.gif

I understand the hurdle better now, though I don't see a way around or over it. I'll have to ponder a path from here to there.

Thanks again for the interesting and educational discussion.

 

[marplots]

I understand the hurdle better now, though I don't see a way around or over it. I'll have to ponder a path from here to there.

Thanks again for the interesting and educational discussion.

It's a good idea. Thank you for introducing it.

I'm still stuck on part, but my instinct tells me the part I don't grok gets into topology and the way dimensions are mapped. I doubt I'll make any progress because I lacks the larnin'.

As an aside, your idea reminded me of something from complex numbers. That one couldn't order complex numbers in a greater than/less than way, at least not in the way you do it with real numbers. I always thought that was weird.

 

[The Greater Fool]

It's a good idea. Thank you for introducing it.

I'm still stuck on part, but my instinct tells me the part I don't grok gets into topology and the way dimensions are mapped. I doubt I'll make any progress because I lacks the larnin'.

As an aside, your idea reminded me of something from complex numbers. That one couldn't order complex numbers in a greater than/less than way, at least not in the way you do it with real numbers. I always thought that was weird.

Sure you can...

 

[Dancing David]

In your example, everyone is in the same inertial reference frame. Here's the other key thing to remember about relativity, and especially space/time. While the speed of light is a finite limit, you can (theoretically) accelerate forever. So when we see a light cone:

[qimg]http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/spacetime/terminology.gif[/qimg]

(Taken from http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/spacetime/ which explains these concepts very well)

Remember that while straight up means zero velocity, and 45 degrees means light speed, every inertial reference frame's light cone will look identical, with the speed of light always being 45 degrees away. No matter how much you accelerate, things look the same, there is no preferred velocity:

[qimg]http://www-bcf.usc.edu/~fbonahon/Images/FareyPoincareMovie.gif[/qimg]

This is an example of a poincare. An infinite plane represented in a single disk, with distance getting infinitely smaller as you reach the edge. You can imagine that the center is zero velocity and the edge is lightspeed. Picking a reference frame in reality to choose a "now" is like choosing a point on this disk. There are infinite points to choose from and the disk looks the same no matter what point you choose.

I like this image much better, but it's too large for the thread http://www-bcf.usc.edu/~fbonahon/Images/FareyPoincareMovie.gif

Super cool!