I like Rob, but some of his ideas are a little off-kilter--and he definitely has to do his homework about Transcontinental Railroad history. Plans for a transcontinental railroad started in the 1830s (it certainly wasn't Judah's idea) and detailed studies for how to build it began not long after California became part of the Union. The driving force to build it came from the federal government, who wanted a way to economically connect California to the Union--and to get troops west quickly, in case California tried to secede (the project was approved and construction started during the Civil War, so it was a wartime/military project.)
Cost per mile for high speed rail is closer to $50 million per mile. Light rail construction cost is about $10 million per mile per track, assuming no special work like bridges or elevated tract structures. (Incidentally, it's also about the same cost for a mile of highway, so there is no financial advantage to building it as BRT instead of light rail, or just adding two more highway lanes.) Building a trestle across the Causeway would be the troublesome and expensive part. Figure $300 million plus the cost of a trestle--maybe $600-700 million.
Running Capitol Corridor at 15 minute intervals isn't exactly practical given that it's already a very busy freight route, but there are already plans afoot to increase frequency of Capitol Corridor and San Joaquin trains by building a new passenger service/maintenance facility here in Sacramento. If trains were hourly or so, running late enough to allow attendance of late-night classes at UCD and still provide a reliable ride home (or ride back to Davis after an evening in downtown Sacramento at club or concert) gives you the transportation capacity, plus it is also usable by anyone else going from San Jose to Roseville or any points in between.
You get students to ride by giving them a free pass. Set up a deal between UCD and Amtrak/Caltrans Capitol Corridor that lets UCD students and faculty ride free between Sacramento and Davis (or Roseville and Davis) and you'll see a bump in student commuter activity.
Instead of spending that $700 million on a new light rail line, spend it building the
proposed UCD satellite campus in the Railyards--conveniently located so students and faculty can walk over to the train station and catch the next Cap Corridor to the main campus or back to Sacramento. In this case, it's a lot easier to make the mountain come to Mohammed (or the campus to come to Sacramento) than to make the trip by light rail.