https://en.wikipedia.org/wiki/Vactrain

That, using magnetic stabilization, and the "Gravity tunnels" idea seems plausible. I agree it is a science fiction approach, but I'm more interested in a mathematical perspective over a current technology one. Basic math says it is possible, but I would love input from someone on the more advanced side of physics. Also, reading back the idea of essentially making the capsule propel itself seems asinine, so ignore that aspect.

Also, correct me if I'm wrong, be would the vacuum help solve the heat problems?