John,
To continue -- "If 'the initial condition of your car's gearbox does determine its direction for an instant of the present,' then it would certainly determine what the future event would be, based on whatever prior event placed the gearbox in that condition."
You are assuming, as anti-realists also do, that history is determined conditioned on prior probabilities. How does one justify this assumption? -- by an infinite regress of probable acts that are also conditioned on prior probabilities. The novice driver who put the car in reverse and doesn't know it and thus wrongly predicts the future of the car (and her with it) pulling out of the garage, was conditioned by a whole lot of things prior -- the working condition of the gearbox, the fact that the car even has a reverse gear, the design of the gearbox that caused the driver to choose reverse instead of forward, etc., all the way back to the beginning of time.
"Is the past cause and the future effect?"
What is the past cause of the driver choosing the wrong gear? Assume anything you wish, to the beginning of time. You will have to calculate it based on the assumption of prior probabilities, and that calculation will depend on an aggregated history of events, *not* on the event in question. Actuaries will have a lookup table broken down to as many parameters as practical, for the number of drivers who mistakenly use reverse when they mean to go forward, according to such things as age, driving record, the make, model and year of the car, time of day, weather at the time of the event, etc. One might be able to say, e.g., that for every 1000 female drivers of this car age 18-22, 2 of them, or 1/10 of 2 percent, will have an accident involving the wrong choice of gear between forward and reverse, every year. Theoretically, one could assemble 1000 such drivers at the same time and place, instruct them to move forward on cue, and 2 of them will move in reverse.
We use this prior data for a lot of practical things, like insurance rates, and vehicle design. And it explains why statisticians such as Richard Gill and computer scientists such as Scott Aaronson are considered experts in quantum theory. The theory itself is based on the assumption that nature is fundamentally probabilistic.
In actual nature, though, there is no prior probability for the example of our *individual* 18-year-old female choosing forward or reverse. The choice is classically random; i.e., if there were no way of telling which gear is forward or reverse, the 50-50 random choice would apply. And in fact, at the foundation of nature, that is the only probability that physically exists, i.e., exists *because* nature exists (there is something rather than nothing).
"Which would make time asymmetric."
Time isn't asymmetric. Cause and effect are continuous.
I saw a TV show rerun the other night, with a nice problem in it. (Those of you who know the solution, please don't spoil it for the others and don't google it.) The problem is:
Imagine you are in a sealed room with sacks of coins -- three sacks filled with as many coins as you wish. All of these sacks except one are real gold coins of uniform weight. One sack is full of fake coins of uniform weight differing from the real coins by some slight measure -- any difference you choose, so long as it is slight enough to be undetectable by holding the bags in your hand.
The problem is, you have a penny scale -- and you have only one penny; you can therefore make only one weight measurement. How do you tell the real from the fake?
Best,
Tom
