> James Clerk Maxwell united electricity and magnetism with a pen and paper. Einstein discovered special and general relativity in the same way.
> Has theoretical physics advanced enough now that such pen and paper discoveries are all but over, and the only way to continue making progress is to dedicate an ever larger share of the global economy's productive capacity to building larger and more expensive experiments?
That's a bit disingenuous. At the time, GR was an unconfirmed theory not unlike, say, String Theory is today. Except it only took a couple of years to confirm by experiment.
Particle theorists and cosmologists have plenty of theories. But deciding which one describes reality best can only be done by data, no two ways about it. And yes, since most low hanging fruits have been found, experiments become harder and harder. Not to say more and more expensive.
Your conclusion is correct though, that at some point a society has to decide whether they can afford further progress.
Perhaps we also haven't found a theory as convincing as Einstein's GR because the math isn't there yet. GR was discovered shortly after differential geometry was formulated, and without it it would have been impossible. Similarly with Newton's theory and calculus.
So maybe what we need is the right breakthrough in math?
>So maybe what we need is the right breakthrough in math?
Funny you mention that, only recently I was reading a review paper on the state of constructive quantum field theory [0]. In the outlook section the author writes
>Why haven’t these models of greatest physical interest been constructed yet (in any mathematically rigorous sense which preserves the basic principles constantly evoked in heuristic QFT and does not satisfy itself with an uncontrolled approximation)? Certainly, one can point to the practical fact that only a few dozen people have worked in CQFT. This should be compared with the many hundreds working in string theory and the thousands who have worked in elementary particle physics. Progress is necessarily slow if only a few are working on extremely difficult problems
But they also say
> It may also be the case that a completely new approach is required
This kind of mathematical physics is generally considered a part of mathematics rather than physics, and this paper is talking about formulating a rigorous mathematical framework and elucidating conceptual ideas rather than about making new predictions, but the idea that new mathematics is required is certainly not a crazy one.
Apparently the next-gen LHC replacement will cost on the order of $100 billion. As a society (US, EU, or global), we can certainly 'afford it', but no-one is going to be writing that check anytime soon.
Yet Musk was prepared to spend $42B on the twitter purchase which would almost have been a null-op for the world in comparison to funding basically any kind of venture or experiment with the same amount of money... If only Musk was more interested in the universe's structure :)
>Yet Musk was prepared to spend $42B on the twitter purchase
Musk wasn't donating $42B to Twitter. He raised capital to purchase Twitter with the aim of actually making a return on that money.
A better example is someone like Warren Buffet donating ~$50B dollars to charity instead of building another particle collider. If only Buffet was more interested in the universe's structure eh.
> Has theoretical physics advanced enough now that such pen and paper discoveries are all but over, and the only way to continue making progress is to dedicate an ever larger share of the global economy's productive capacity to building larger and more expensive experiments?
That's a bit disingenuous. At the time, GR was an unconfirmed theory not unlike, say, String Theory is today. Except it only took a couple of years to confirm by experiment.
Particle theorists and cosmologists have plenty of theories. But deciding which one describes reality best can only be done by data, no two ways about it. And yes, since most low hanging fruits have been found, experiments become harder and harder. Not to say more and more expensive.
Your conclusion is correct though, that at some point a society has to decide whether they can afford further progress.
Perhaps we also haven't found a theory as convincing as Einstein's GR because the math isn't there yet. GR was discovered shortly after differential geometry was formulated, and without it it would have been impossible. Similarly with Newton's theory and calculus.
So maybe what we need is the right breakthrough in math?