3 ms·

Anyone whose ever studied vibrations (e.g. spring mass dampers) already knew this. This is a cool example but it’s not really any more “essential” than macro-le

by elil17 6y ago

Anyone whose ever studied vibrations (e.g. spring mass dampers) already knew this. This is a cool example but it’s not really any more “essential” than macro-level phenomena.

Armisael16 6y ago
Half the article is explicitly talking about how this fundamentally is different than the phenomena you’re talking about. Imaginary numbers are merely convenient in the cases you’re describing; you can get the same results without using them. The paper this article is about is claiming that in QM this is fundamentally untrue, and models that don’t use complex numbers cannot match those that do.
- pfortuny 6y ago
  They do match. The thing is that the description is much more complex, nothing else. What I see from the preprint (notice that the authors have not discussed it with Quanta, because it is under peer-review) and bothers me is that they "add a real qubit" (...) which should be done very carefully because the two real qubits are not independent (they are linked by the hamiltonian). I have not read the whole preprint, though.
- Enginerrrd 6y ago
  To a certain extent, you could probably say the same about the time term in the flat spacetime metric in relativity. There might be ways around it, but I'd wager that anything you come up with can be massaged a bit to make it look like time is an imaginary dimension of space where it's contribution to distance along the spacetime manifold is negative when squared.
CyberRabbi 6y ago
Was going to comment this. Complex numbers are a natural consequence of the basic math axioms and the fact that they are two dimensional (and not 3,4,etc.) is not arbitrary.
ihunter2839 6y ago
Not a physicist, so maybe I took the wrong gist away from the article, but - it seems like what they are saying is that systems that are generally modeled by complex equations have always had real valued equivalents that were known. So it's not that the complex representation isn't a useful mathematical tool, but that it was an alternate representation that was easier to work with. Can you represent a spring mass dampening with all real valued quantities, even if it's a real piece to work with?
- pfortuny 6y ago
  Sorry because I do not understand your wording very well (English is not my FL), so the answer to your question is yes, you can: e^(-at)*(A cos(bt) + C sin(bt)) where b is the frequency and a the dampening. (But you might not be asking for an answer).

by elil17 6y ago

Anyone whose ever studied vibrations (e.g. spring mass dampers) already knew this. This is a cool example but it’s not really any more “essential” than macro-level phenomena.

Armisael16 6y ago

Half the article is explicitly talking about how this fundamentally is different than the phenomena you’re talking about. Imaginary numbers are merely convenient in the cases you’re describing; you can get the same results without using them. The paper this article is about is claiming that in QM this is fundamentally untrue, and models that don’t use complex numbers cannot match those that do.

pfortuny 6y ago
They do match. The thing is that the description is much more complex, nothing else. What I see from the preprint (notice that the authors have not discussed it with Quanta, because it is under peer-review) and bothers me is that they "add a real qubit" (...) which should be done very carefully because the two real qubits are not independent (they are linked by the hamiltonian). I have not read the whole preprint, though.
Enginerrrd 6y ago
To a certain extent, you could probably say the same about the time term in the flat spacetime metric in relativity. There might be ways around it, but I'd wager that anything you come up with can be massaged a bit to make it look like time is an imaginary dimension of space where it's contribution to distance along the spacetime manifold is negative when squared.

CyberRabbi 6y ago

Was going to comment this. Complex numbers are a natural consequence of the basic math axioms and the fact that they are two dimensional (and not 3,4,etc.) is not arbitrary.

ihunter2839 6y ago

Not a physicist, so maybe I took the wrong gist away from the article, but - it seems like what they are saying is that systems that are generally modeled by complex equations have always had real valued equivalents that were known. So it's not that the complex representation isn't a useful mathematical tool, but that it was an alternate representation that was easier to work with. Can you represent a spring mass dampening with all real valued quantities, even if it's a real piece to work with?

pfortuny 6y ago
Sorry because I do not understand your wording very well (English is not my FL), so the answer to your question is yes, you can: e^(-at)*(A cos(bt) + C sin(bt)) where b is the frequency and a the dampening. (But you might not be asking for an answer).