Could Tesla-style batteries be used to power trains? [View all]

I'm having a discussion on FB about Caltrain vis-a-vis the dreaded Google buses. Someone pointed out that even diesel-powered trains are electric; the diesel engine is used to power a generator.

So could it work, at least for short hauls like SF to San Jose (45 miles)? The disadvantage to the diesels over catenary or third-rail trains like Metro-North is dwell time at the stations. The 45-mile ride can take an hour and a half with all local stops! With only a few (Baby Bullets), ti's cut down to an hour, but they only run about three of those each way in the morning and three in the afternoon.