imaginary numbers

[CPL.Luke]

how do you deal with an object that has imaginary energy (a particle moving faster than light)

 

in the theoretical context of course

[ydoaPs]

ftl isn't the only thing with imaginaryness. i appears in the schrodinger equation for a free particle as well.

[CPL.Luke]

anywbody care for a detailed explanation of what that means. I am not fully able to wrap my head around an imaginary number in a real world situation

[mtong]

Imaginary numbers do not occur in the real world (they are very useful mathematical tools, like negative numbers), they do however arise in relativistic calculations dealing with a velocity faster that light........beta will become greater than 1 and therefore gamma will be the root of some negative number.

[swansont]

Imaginary numbers do not occur in the real world (they are very useful mathematical tools, like negative numbers), they do however arise in relativistic calculations dealing with a velocity faster that light........beta will become greater than 1 and therefore gamma will be the root of some negative number.

 

And that's the problem.

 

Even though there is a mathematical solution, it is unphysical.

[ydoaPs]

i already said that it occurs other than ftl.

 

ur not 1 of those that think relativity is crap because it is counterintuitive, are you?

[Tom Mattson]

Imaginary numbers do not occur in the real world

 

Yes, but neither do the so-called "real numbers".

 

And that's the problem.

 

Even though there is a mathematical solution' date=' it is unphysical.

[/quote']

 

I don't think it can be concluded that a quantity is unphysical just because it is imaginary. Is the impedance of a circuit "unphysical" because it is complex? Of course not. And getting more to the topic at hand: tachyon's are not regarded as unphysical either. There is credible research going on regarding tachyons.

 

Unfortunately I don't know much about them, so I am not able to answer the question in the opening post.

[CPL.Luke]

you could expand on the impedance bit though...

[Tom Mattson]

you could expand on the impedance bit though...

 

It's just an example of a complex quantity that is also observable. In circuit theory it is possible to transform the modeling equations into something called the frequency domain. When this is done all energy storing elements can be modeled as resistors, if you generalize the concept of resistance to the complex quantity called impedance.

 

This is just a specific example of a more general idea: That if you have two observables A and B that take on real values a and b, then there is no sense in saying that the linear combination A+iB is not also observable, despite the fact that it takes on complex values a+ib.

[Klaynos]

Yes' date=' but neither do the so-called "real numbers".

 

 

 

I don't think it can be concluded that a quantity is unphysical just because it is imaginary. Is the impedance of a circuit "unphysical" because it is complex? Of course not.[/quote']

 

Not all of the impedance in a circuite is imaginary, there is indeed an imaginary part, but if you take the magnitude of the impedance you get a real part only.

[Tom Mattson]

Not all of the impedance in a circuite is imaginary, there is indeed an imaginary part, but if you take the magnitude of the impedance you get a real part only.

 

Ugh. I did not mean for this impedance thing to digress into a tangent of its own, and I am now sorry I mentioned it.

 

Yes, I know that not all of the impedance is imaginary. I am just pointing out that in some situations, people have no problem associating imaginary (or complex) values with physical quantities, while in situations the same people automatically reject such quantities.

 

I've just started my own thread (Observables in Quantum Mechanics) along this line (not about impedance though) in the Quantum forum.

[Johnny5]

Hey what happened to all my work????

 

It's too much so I'm not going to repeat it.