Does Travelling at Light Speed Turn the Time Cone into a Cube?

[kokain]

Time is on the y-axis and distance is on the x-axis and z-axis. Depending upon your velocity the cone is formed. At, let's say 1/10c, you can reach point "A" in ten years and your cone is narrow, but at 1/5c point "A" is 5 years away and the cone is wider. At 1/2c you could be at point "A" in two years and the cone is extreamly wide. Now here is my question. I see that point "A" is one year away. Correct? Now if you could and if you were traveling at c would it take you one year to reach point "A"? I see the cone at c to be a cube encompassing all volume to the future. If so, you would arrive at point "A" immediatly as you left. Where am I wrong? Is c still a cone? Is infinity(c) the cube that I see. (That's poetry) Anyway, if so it would also encompass the past as well? Now I am more confused than when I started. HELP!

 

[LURCH]

Originally posted by kokain
Time is on the y-axis and distance is on the x-axis and z-axis. Depending upon your velocity the cone is formed. At, let's say 1/10c, you can reach point "A" in ten years and your cone is narrow, but at 1/5c point "A" is 5 years away and the cone is wider. At 1/2c you could be at point "A" in two years and the cone is extreamly wide. Now here is my question. I see that point "A" is one year away. Correct? Now if you could and if you were traveling at c would it take you one year to reach point "A"? I see the cone at c to be a cube encompassing all volume to the future. If so, you would arrive at point "A" immediatly as you left. Where am I wrong? Is c still a cone? Is infinity(c) the cube that I see. (That's poetry) Anyway, if so it would also encompass the past as well? Now I am more confused than when I started. HELP!

If I'm visualising your chart correctly, then it looks like what you've got there is a graph of length contraction (the flip-side of time dilation). To you, the time it takes to make the trip is indeed measured as 0, because the distance of the trip appears as 0 when you travel at lightspeed. However, to an outside observer, the distance was one lightyear, and the trip took you one year. But throughout that time and across that distance, you appear to them as frozen in time.