One small but important nit-- you're not trying to move the most cars, but the most people.

In LA they most certainly do. They can't make drivers drive better, but they instrument the hell out of the roads and there are a number of ways for drivers to get detailed real time information. The whole region's freeway system is instrumented and you can get near real time updates of freeway speeds at sigalert.com as well as most of the popular mapping apps. It even gives the dispatch reports from incidents so you know which lanes are blocked. I glance at sigalert and replan my route in an instant due to a collision 15 miles away. The city of LA also just completed integration of city street sensors and lights system wide, and it does work. You can get street speed data on google maps, and there are also crowdsourced apps like waze (which I don't use since it put me on a dead stopped 405) or trapster, that integrate realtime data from drivers on the road.

but with a funny accent, nonetheless

I temporarily commute from the SGV to the south bay (I'd move if it was permanent), and my experience is consistent with your claim. Getting into DTLA is a mess-- I have a bunch of bailout points that I use (and know in part from biking around the same areas) to at least keep rolling. I basically get off the freeway and take surface streets through DTLA then get back on the 110 outbound, both north and south, and in the morning there's generally less traffic outbound than inbound. I also get to cheat a little because I have a transponder and get reimbursed for tolls-- it saves a lot of time and drive stress, and I'd probably stay overnight a couple nights a week rather than do the round trip every day without it.

It works well in LA, too, where the weather is nearly always ideal. Better station planning and car design could speed the boarding times. Or having more secure bike parking at the ends (shared use lockers or valet services-- there are a few stations in LA that have bike valets).

And treat the wide line between the carpool lane and the number 1 lane as their own lane when both of those are stopped.

Nothing actually relieves congestion-- you just move more people using less space or resources per person but the same congestion. There's a certain amount of congestion/delay/commute time that people are willing to tolerate, and people will keep saturating transportation modes back to that level no matter what you do to relieve it. New freeways or lanes rapidly return to the previous levels of congestion-- you can't pave your way out of it, but you can provide modes that are more pleasant or more efficient.

Transit being slower than driving in US cities is because most transit is buses that travel in the same lanes as auto traffic, but make more stops. Of course it's slower. Light rail can be quite fast, and in LA light rail plus bicycle can be much faster than driving at peak times. You also can do something like read while you're on the train, which you can't in the car. I live in the Pasadena area, and it's much faster to take the train to DTLA at peak hours than to drive. I temporarily have a commute several times a week to the south bay-- that's faster by car because I'd have to take 4 different trains or bus lines to do it. But traffic is so bad that I can get to Sunnyvale in about the same time it takes me to get to the south bay. Leaving early and coming home after peak make it tolerable for a little while (and it's usually only 3 days/week). I'd move if it was permanent.

My partner commutes (bike+train) sometimes to DTLA, and when she's late getting home it's because someone gave her a ride partway-- it's consistently slower than bike+train. Now that Metro lets you take a bike any time, there are a lot of people who do bike+train commutes. They should really consider a different style car, with bike hooks and flip up seats along one side, and regular seats along the other. It would make it easier to pack more people+bikes in. Shared use bike lockers (which are now available in the bay area) instead of long term rental lockers would also make bike commuting/shopping easier-- they work like parking meters, but keep people from stealing parts off your bike.

SpaceX is located smack in the center of the LA aerospace industry- there's a huge pool of experienced engineers to draw from who have been working around that area for ages.

His neighbors in Bel Air will complain about the noise.

I've seen an electric crotch rockets that will do at least 55 mph. They're not allowed to go faster than that on the indoor velodrome where we motorpace behind it (generally not nearly that fast). It uses some huge AGM batteries.

I just mapped it, and it comes up about 17-18, but you're still in the right ballpark.

His best bet is to move- as soon as the 405 is built out, it will return to the same congestion as before (that happens to freeways everywhere). The next best thing (and better for LA) would be to fund a rail line that essentially parallels the 405. And maybe throw in a bikeway-- LA has 330 days/year that are good biking weather, but having to do a long commute on city streets can be a pain. There are a few bikeways along the various rivers and/or freeways (SGRT, LARIO) that can make a bike commute competitive with driving, even for very long distances. Shorter than about 10 miles it's faster to bike, and even at 15-20 miles, the combination of bike and train is faster than driving at rush hour.

As a physicist who's known a few mathematicianns, I can assure you, y'all are an odd bunch.

University of Chicago used to have at least a few people doing it-- granular media experiments can be done pretty cheaply, and there was someone there doing theory and experiments on migration of suspensions in droplets as they evaporate that started out with a bunch of experiments using coffee droplets. Poke around 4 year colleges that have good physics departments and there's probably someone doing good physics on the cheap.

Try low temperature physics...

When I was in grad school I used to ride bikes with a guy who was a biology PhD-- I can't remember if he was a post-doc or staff somewhere. One time we were out and he asked "How many experiments do you do a week?" I almost fell off my bike laughing. I ran my experiment 3 times in 6 years (all in the last 1.5 years), and each time it ran for no less than 4 weeks (I think the longest run was 12 or 13 weeks). But up to the first successful run (as in all the engineering worked and it was possible to get data): design, build, test, fix (hardware, software, and electronics).

Funding?

There are areas of physics where the cycle time for proposals is 2 years (from announcement to release of funds) with a success rate of less than 10% for even senior people (NIH has an even lower funding rate, and an expectation that most things get proposed a couple times before being funded). Many, if not most, graduate students in science can easily get funding to cover their salary through fellowships/RA positions/TA positions, etc, but the chances of a grad student writing their own grant proposal in most subfields is pretty small. Sure, there are areas where you can do good science with dimestore materials (and a few places that specialize in that), but that's a pretty narrow slice of science in almost any field. Some of the most successful faculty I've known at one of the top science/engineering universities in the world are successful because they let their post-docs be PI on proposals (which is relatively uncommon). Then if the project is awarded the post-doc starts the work as a post-doc and manages to spin it into a faculty job.

Almost everybody I know who got both a masters and PhD in physics did it for one of two reasons-- 1) they started grad work at a smaller school that didn't have a PhD program (or not much of one) and switched to a larger/better program 2) they expected to work at large companies (e.g. 3M) where the pay scale gave you slightly more money if you had a masters+PhD than PhD alone, even if all you did for the masters was fill out a few extra forms and bind up some intermediate result (that you had anyway) into a thesis.