A Bitcoin split doesn't create more Bitcoin, it just creates another currency.
A Bitcoin split doesn't create more Bitcoin, it just creates another currency.
Another way of looking at this is to observe the market cap of both currencies after a fork; in theory you'd expect the total market cap to remain unchanged, since the newly forked currency is presumably either worthless OR has worth only to the extent that it removes value from the original currency. In practice, this doesn't seem to be occurring.
Sounds like nonsense to me. Practically nobody accepts BCH.
(...which is to say, precisely 0 vendors accept either, of course. Most people are not picking a crypto currency based on their ability to conveniently buy a coffee with it just yet.)
Otherwise the value of a jstanleytoken will remain at 0 and the value of a dollar will be unaffected.
Let's say that the corner store arbitrarily decides that they'll accept jstanleytokens at 10% the value of a dollar. I can go buy my soda for 20 jstanleytokens, or whatever it would be, instead of $2. That decreases the demand for dollars, and thus the value of a dollar.
I think that "unless you were lending dollars" bit is a really important aspect of this, though. Lending happens a lot. This is true even in the Bitcoin world. We don't normally call it "lending," but that's what people do whenever they store coins on an exchange.
This has been a major problem with these forks, too. You deposit some Bitcoin with an exchange, then there's a fork... do they owe you the forked currency as well, or not? There's no obvious answer to that.
But that's not what's happening!
It's closer to everyone getting 1 jstanleytoken for each dollar they hold.