5 ms·

Abstractions need not be approximations. Schroedinger's equation is an abstraction, but as far as we know it's exact.

by wyager 11y ago

ludamad 11y ago
Abstractions of social sciences do need to be approximations :-)
unabst 11y ago
The moment the theory is the reality, it's exact. Like cartoons. Like definitions. Like math. But physics and science is about reality. It's about the physical apple, not the word apple. A real apple is physical. There is no amount of theory or symbolism that will produce a real apple in the minds and systems that simulate it. That's the paradox.
- coldtea 11y ago
  >A real apple is physical. There is no amount of theory or symbolism that will produce a real apple in the minds and systems that simulate it. That's the paradox. Actually, I see two problems with this notion. First, there's no "paradox". That "no amount or theory or symbolism will produce a real apple" is not paradoxical. If anything, it's common sense. Second, this common sense might very well be wrong (and that would be a real paradox this time). In fact, what you call "real apple" might itself be a simulation (along with all the universe we know) -- created by higher order beings. Still, you might say, our theories, us being inhabitants of the (simulated) universe, won't produce a real apple for us. But who's to say that? It depends on the rules of the simulated universe. And we can't say with 100% certainty we know the rules of ours (if it's one such). E.g. the rules could very well allow the thoughts and symbolism of its inhabitants to create new objects in the universe. In that sense, the universe would be like Lisp (where data are code), or like using "reflection".
smaddox 11y ago
Schrodinger's equation doesn't even include special relativistic effects. It's not exact (at least not if you mean it exactly describes nature in general). Neither is Dirac's equation; it includes special relativistic effects for a single particle, but not general relativistic effects or multi-particle interactions (at least as far as I understand it).
- wyager 11y ago
  The general form using the unspecified Hamiltonian operator is compatible with relativity.
cyphar 11y ago
Schroedinger's equation isn't a theory. It's a law. And like other laws (F = ma) doesn't account for a bunch of other things. So yes, it still is an approximation.
Confusion 11y ago
What is Schroedinger's equation an abstraction of? What details does it abstract from? How can it be that the omission of those details does not result in an inexact representation of the unabstracted, more complete, situation? BTW, there are no exact solutions to the Schroedinger equation of most interesting systems: we only get numerical approximations to the values of interest from it.
- keithpeter 11y ago
  https://en.wikipedia.org/wiki/Hartree%E2%80%93Fock_method https://en.wikipedia.org/wiki/Hartree%E2%80%93Fock_method Some of those numerical solutions were really important historically and lead to the further development of numerical techniques. Back to main thread: I'm thinking of Lakatos' Proofs and Refutations, itself a play on Popper's Conjectures and Refutations, designed itself to escape from 'induction' based thinking, e.g. Hans Reichenbach Long time since I've thought of those, thanks.

Abstractions need not be approximations. Schroedinger's equation is an abstraction, but as far as we know it's exact.

by wyager 11y ago

Abstractions need not be approximations. Schroedinger's equation is an abstraction, but as far as we know it's exact.

ludamad 11y ago

Abstractions of social sciences do need to be approximations :-)

unabst 11y ago

The moment the theory is the reality, it's exact. Like cartoons. Like definitions. Like math. But physics and science is about reality. It's about the physical apple, not the word apple. A real apple is physical. There is no amount of theory or symbolism that will produce a real apple in the minds and systems that simulate it. That's the paradox.

coldtea 11y ago
>A real apple is physical. There is no amount of theory or symbolism that will produce a real apple in the minds and systems that simulate it. That's the paradox. Actually, I see two problems with this notion. First, there's no "paradox". That "no amount or theory or symbolism will produce a real apple" is not paradoxical. If anything, it's common sense. Second, this common sense might very well be wrong (and that would be a real paradox this time). In fact, what you call "real apple" might itself be a simulation (along with all the universe we know) -- created by higher order beings. Still, you might say, our theories, us being inhabitants of the (simulated) universe, won't produce a real apple for us. But who's to say that? It depends on the rules of the simulated universe. And we can't say with 100% certainty we know the rules of ours (if it's one such). E.g. the rules could very well allow the thoughts and symbolism of its inhabitants to create new objects in the universe. In that sense, the universe would be like Lisp (where data are code), or like using "reflection".

smaddox 11y ago

Schrodinger's equation doesn't even include special relativistic effects. It's not exact (at least not if you mean it exactly describes nature in general). Neither is Dirac's equation; it includes special relativistic effects for a single particle, but not general relativistic effects or multi-particle interactions (at least as far as I understand it).

wyager 11y ago
The general form using the unspecified Hamiltonian operator is compatible with relativity.

cyphar 11y ago

Schroedinger's equation isn't a theory. It's a law. And like other laws (F = ma) doesn't account for a bunch of other things. So yes, it still is an approximation.

Confusion 11y ago

What is Schroedinger's equation an abstraction of? What details does it abstract from? How can it be that the omission of those details does not result in an inexact representation of the unabstracted, more complete, situation? BTW, there are no exact solutions to the Schroedinger equation of most interesting systems: we only get numerical approximations to the values of interest from it.

keithpeter 11y ago
https://en.wikipedia.org/wiki/Hartree%E2%80%93Fock_method https://en.wikipedia.org/wiki/Hartree%E2%80%93Fock_method Some of those numerical solutions were really important historically and lead to the further development of numerical techniques. Back to main thread: I'm thinking of Lakatos' Proofs and Refutations, itself a play on Popper's Conjectures and Refutations, designed itself to escape from 'induction' based thinking, e.g. Hans Reichenbach Long time since I've thought of those, thanks.