Complex numbers and time

1. Dec 7, 2004

Rothiemurchus

The time independent schrodinger equation doesn't involve complex numbers.
The time-dependent equation does involve complex numbers.
When a complex number appears in an equation or expression can we assume that there is some underlying relation to time?
So if I had a probability such as 1/4 + i / 8 could this be a probability that
varies with time?

Last edited: Dec 7, 2004
2. Dec 7, 2004

matt grime

No. You cannot assume all complex numbers relate to time (they don't), and probabilities are defined to be real numbers (in the interval [0,1]

3. Dec 7, 2004

Rothiemurchus

Isn't it true though that everything exists in time?
Even a number.I could represent a number by 1 electron,2 electrons etc.
electrons exist in time.Also I could multiply 2 imaginary probabilities together
for two events occurring at the same time and get a real number (using the complex conjugate).If all particles are ultimately made from 2 smaller particles,this would seem a legitimate thing to do.

4. Dec 7, 2004

matt grime

If everything exists in time, then what do you care about the "time independent" equation for? If we accept that mathematical things have a physical existence and thus exist in time, then you've just answered your own question with a trivial answer. Moreover you seem to think that maths is (particle) physics

And for the second time: probabilities are real numbers in the interval [0,1], unless we're doing some very weird theoretical physics/maths.

Your last conclusion has some very large and unspecified assumuptions:

that particles can be modelled with complex numbers; that these elements in the model are probabilities; that when you multiply two arbitray complex numbers together you get something real; that taking the conjugate is meaningful phyisically and even permitted....

5. Feb 2, 2005

properphysicist

It might be useful to say here that although something may exist in time, it's properties may not be a 'function' of time.

For example, an isolated electron with a charge q may exist in time. But that charge remains constant for all time i.e. q it is not a function of time.

This applies generally, even to complex numbers.

6. Feb 3, 2005

matt grime

q(t) = q is a function of t, it is just a constant function, that is all (ie it satisfies every reasonable definition of function you care to write out).

7. Feb 3, 2005

jackle

I confess that my maths is more rusty than Mars but complex numbers don't seem to be anything that fundamental. I found that they seem to be slipped in when a physicist wants to add an extra variable, dimension or degree of freedom but wants to keep their equation looking similar and then they find that it makes the interpretation of the extra quantity or the maths easier, so they keep it.

I'd love to believe that it meant it had something to do with the special imaginary part of the universe where the soul exists, but I don't.

8. Feb 4, 2005

Tournesol

See Cramer's transactional interpretaion of QM.