Can Hyperloop actually work?

The chances of Hyperloop actually working are nearly 100% as the science has already been proven. The chances of Hyperloop becoming a constructed reality is an entirely different concern.
There are several factors to take into account when answering this question. Thankfully, at the time of my writing Elon Musk has released the Hyperloop alpha plans as a 57 Page PDF whitepaper. His proposal appears to contain not only the expected alpha-stage technical specifications but a lot of project details as well, including proposed route and predicted cost. These details make it possible to answer this question.

Technology. Most of the technology described in Musk's paper exists today, much of it practically off the shelf. The most basic and brief description of the Hyperloop is that it mimics the pneumatic tubes used in banks and large buildings to send mail and other goods short distances. Of course, this can't be achieved without a little innovation. Perhaps the most important of the solutions described in the whitepaper is how the Hyperloop overcomes the Katrowitz Limit. Musk writes,
The approach that I believe would overcome the Kantrowitz limit is to mount an electric compressor fan on the nose of the pod that actively transfers high pressure air from the front to the rear of the vessel. This is like having a pump in the head of the syringe actively relieving pressure.

This solution allows the pod to be nearly the same size as its containing tube without being trapped having to push air through the tube. This in turn means that the Hyperloop would not require an evacuated (airless) tube to function, much like ETT (Evacuated Tube Transport) does. This brings the cost down, making the project much more realistic.

Cost. The paper claims that the proposed system could be built entirely for less than 6 billion USD, and in his press conference Musk said he might be able to bring that cost down even further. This is a mere fraction (11.3%) of the cost of the California High-Speed Rail project's Phase 1 which similarly links San Francisco with Los Angeles for a whopping $68 billion USD. The whitepaper Musk released also declares that "amortizing this capital cost over 20 years and adding daily operational costs gives a total of about $20 USD (in current year dollars) plus operating costs per one-way ticket on the passenger Hyperloop." Basically, the Hyperloop would not only be unbelievably inexpensive for a project of this scale but would pay itself back in 20 years, assuming a trip charge of just $20-- one third the price of a plane ticket.
Construction. The largest obstacles to large-scale construction projects like this are political. As a private company, obtaining the Right of Ways and eminent domain necessary to build on public and private property between San Francisco and Los Angeles will prove to be the most difficult part of this project. Certainly not impossible, but difficult. Musk was asked about this challenge during the Hyperloop press conference and said that having the Hyperloop on raised pillars helps mitigate this problem, though he was criticized for giving only a partial answer.

The technology exists, the capital exists, there's just a lot of paperwork to be done.
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