SWaB: time isn't just another dimension

[notFritzArgelander]

https://www.forbes.com/sites/startswith ... 7293da47dc

[metastable]

re: "Here’s a question that most of us have been asked at some point in our lives, “what’s the shortest distance between two points?” By default, most of us will give the same answer that Archimedes gave more than 2,000 years ago: a straight line. If you take a flat sheet of paper and put two points down on it absolutely anywhere, you can connect those two points with any line, curve, or geometrical path you can imagine. So long as the paper remains flat, uncurved, and unbent in any way, the straight line connecting those two points will be the shortest way to connect them."

the shortest path through time between 2 points is often curved

[Lady Fraktor]

That is completely wrong.
The curved line shown is only faster due to the added momentum of the first drop off.
If the initial momentum did not change it would not reach the end faster.

[metastable]

Both balls have the same initial momentum, but the ball that takes the low path converts some gravitational potential energy to kinetic energy then back to potential energy, making it travel faster.

[Lady Fraktor]

Which changes the momentum which means the curved line is not faster.
If they travel at the same speed the curved line is the slower path.

[notFritzArgelander]

Which changes the momentum which means the curved line is not faster.
If they travel at the same speed the curved line is the slower path.

Yes. In addition to the ball for the curved track being dropped from a slightly greater height (more potential energy convertible to kinetic energy and higher speed) there is also the issue of rolling versus sliding friction to contend with. That could also result in the results as they are.