# I Attempt at Disproving Velocity Curving Space-Time

1. Feb 17, 2017

### stevedgarcia

For the past few weeks, I've been struggling with the idea that velocity must curve space-time because of phenomena such as time dilation. Initially, I believed that because time is a component of space-time, through the phenomena of time dilation, velocity must curve space-time. I think I reasoned my way out though. Let me know if I fouled up somewhere.

1) Travelling at relativistic speeds contracts space by a speed dependent factor (namely, the Lorentz factor)
2) Travelling at relativistic speeds dilates time by a speed dependent factor (namely, the Lorentz factor)
3) Therefore, travelling at relativistic speeds contracts space and time by the same factor
4) Thus, space-time does not curve with increased velocity, but instead, it compresses in all 4 dimensions equally in a way

Furthermore, time dilation occurs only to objects within the object travelling at relativistic speeds. So, there is no (1/r^2) or any such field parameter felt by surrounding objects. Therefore, there is no curving of space-time induced by increased velocity.

"Now here is an interesting thought experiment. Imagine a train on a long straight horizontal monorail that is suspended from springs that directly measure the weight of the train and the rail. When the train is accelerated to the same velocity as the bullet in the OP [relativistic velocity] will the track scales directly measure the train to be 7 time heavier?"

I believe the answer is no for the reasons stated above. Also, it's interesting to consider whether, due to contraction and all, would the train even be able to stay on the track. I think not.

2. Feb 17, 2017

### Staff: Mentor

You are correct that spacetime does not curve due to velocity. This is actually part of the meaning of the principle of relativity. Straight lines in one inertial frame map to straight lines in another inertial frame, not curved lines.

However, the Lorentz transform is not a compression, but rather a shear. A unit cube of spacetime is not mapped to a smaller or larger cube, but a rhomboid.