John Carlos Baez on Nostr: The problem is not dropping assumptions: that's easy to do. The problem is coming up ...
The problem is not dropping assumptions: that's easy to do. The problem is coming up with new, better assumptions.
For example, it's easy to *say* spacetime is not a continuum. Just say it's a lattice made out of little cubes with sides having length whatever you want! But then you need to make up a theory based on this idea. It had better fit all the existing data, yet make new predictions.
It's pretty easy to fit the particle physics data: just take our existing theories and 'discretize' them by putting them on a lattice where the cubes are so tiny we wouldn't have noticed them. Then the new prediction is that when our particle accelerators get good enough, we'll notice those little cubes. Namely, we'll see some directions in spacetime are different than others, and also there's a preferred 'rest frame' - two predictions that go against special relativity.
Great! Then you wait for someone to see this stuff so you can collect your Nobel. But in the meantime you're not making progress on solving any mysteries we want solved.
It's also easy to *say* you don't want a renormalizable quantum field theory. In fact you can work with the very simplest theory of quantum gravity, which is not renormalizable, and make a lot of progress. It makes precise predictions, like deviations from the inverse square force law at short distances. All this is very nice, and smart people have been working on it. But it only goes so far.
In short we've got a chess game here, and the experts know how the first 10 or 20 moves go.
(2/n)
For example, it's easy to *say* spacetime is not a continuum. Just say it's a lattice made out of little cubes with sides having length whatever you want! But then you need to make up a theory based on this idea. It had better fit all the existing data, yet make new predictions.
It's pretty easy to fit the particle physics data: just take our existing theories and 'discretize' them by putting them on a lattice where the cubes are so tiny we wouldn't have noticed them. Then the new prediction is that when our particle accelerators get good enough, we'll notice those little cubes. Namely, we'll see some directions in spacetime are different than others, and also there's a preferred 'rest frame' - two predictions that go against special relativity.
Great! Then you wait for someone to see this stuff so you can collect your Nobel. But in the meantime you're not making progress on solving any mysteries we want solved.
It's also easy to *say* you don't want a renormalizable quantum field theory. In fact you can work with the very simplest theory of quantum gravity, which is not renormalizable, and make a lot of progress. It makes precise predictions, like deviations from the inverse square force law at short distances. All this is very nice, and smart people have been working on it. But it only goes so far.
In short we've got a chess game here, and the experts know how the first 10 or 20 moves go.
(2/n)