Complex Colors

[Purple]

Let us venture for a moment into the realm of "what if". Assume that mass can be a complex value. That in turn would mean that quantity can also be complex. Armed with these two facts we can conclude that in such a system there can be a complex as well as a regular quantity/ratio of color pigment(s) in a mixture. In other words there can be such a thing as a complex number color.

How would the existence of such colors effect our day to day lives as well as the physics of our universe?

[General Zod]

Exactly what do you mean by "complex"? This term is meaningless without more detail.

[Purple]

Exactly what do you mean by "complex"? This term is meaningless without more detail.

http://en.wikipedia.org/wiki/Complex_number

[Surlethe]

If mass can be complex, we should start by worrying about what that does to basic mechanics before we can figure out what it means for light's frequencies.

[Purple]

If mass can be complex, we should start by worrying about what that does to basic mechanics before we can figure out what it means for light's frequencies.

That works too. Go on.

[Blayne]

Doesn't linear algebra and calculus III at some point make these assumptions?

[Surlethe]

Make what assumptions? If you mean that they (more or less) work over fields other than the real numbers, yes, but that's not really related to what Purple is asking.

[Blayne]

I was just thinking that "This has to already exist." (As a field of study) While I do not know if there's a field of study (though I know some people I could ask) some googling does show that there is imaginary colours though possibly not what the OP was asking for admittedly. Maybe I'm misinterpreting?

[Simon_Jester]

Electromagnetic waves with complex number frequencies already exist.

They're called "waves that damp out and disappear."

As to what "complex number color" means, first Purple would have to quantify color in some mathematically meaningful way, not rely on someone else to do it for him.

If he thinks color depends on mass, then as Surlethe says, we'd have umpty jillion things to worry about before we even begin to consider "what's the color of this paint mix after I add 5i milliliters of yellow pigment?"

[Purple]

As to what "complex number color" means, first Purple would have to quantify color in some mathematically meaningful way, not rely on someone else to do it for him.

I thought I was very, very clear about that in my opening post. Hell some people here, you and S included figured it out but just seemed to discard the idea outright. *sigh*

Well to be sure there is no confusion any more, allow me to translate the opening post into its base most form:

RAR:
Assuming that for some reason complex mass (examples: 23+7i kg butter, 13.5+21i tons of coal etc.) and complex quantities of mater (examples: 23+5i hydrogen atoms, 13+72i battle tanks, 128+21i apples etc.) both exist how would that effect our universe and in particular the colors in it.

[Terralthra]

Complex mass does exist, as one way of handling decaying particles.

[Purple]

Complex mass does exist, as one way of handling decaying particles.

That's what prompted me to post this actually. I read that somewhere years ago and in the mean time, I forgot exactly where I read it and about what. But it came to me this morning in my sleep and when I woke up I fallowed the logic loop that was in my OP. As in, if I can get a complex mass of particles of paint pigment in a mix than I can get a color whose pigment ratios are complex as well. For example: 33+2i % Red, 22 +4i % Green, something Blue. (and yes, I am using RGB as an approximation) And I started thinking, what would that color look like?

[Simon_Jester]

You can't make paint out of decaying subatomic particles, or at least not paint that lasts long enough to be paint instead of "vaguely interesting lab sample."

I mean, the first order of business would be to come up with a theory of electromagnetism in which you can just tack an arbitrary imaginary mass of things. Let me ask you, Purple, could you fill a paint can with i kilograms of paint? Where would you find the imaginary atoms to make it from?

[Purple]

You can't make paint out of decaying subatomic particles, or at least not paint that lasts long enough to be paint instead of "vaguely interesting lab sample."

I mean, the first order of business would be to come up with a theory of electromagnetism in which you can just tack an arbitrary imaginary mass of things. Let me ask you, Purple, could you fill a paint can with i kilograms of paint? Where would you find the imaginary atoms to make it from?

Well the idea in this case is to start from the base assumption that somehow you just can and go from there.

[madd0ct0r]

hmmm.

we use imaginary numbers in structural calculations too (and frequently in the accounts, but I digress).

I'm trying to imagine a 500+100i deep I beam.

About the only mental model I can get is a universe with two types of matter, only one of which we can perceive. Mendeleev's chart looked more like a spiral, but has since stabalised into a simpler butterfly shaped periodic table. This isn't how imaginary numbers work though.

[Purple]

hmmm.

we use imaginary numbers in structural calculations too (and frequently in the accounts, but I digress).

I'm trying to imagine a 500+100i deep I beam.

About the only mental model I can get is a universe with two types of matter, only one of which we can perceive. Mendeleev's chart looked more like a spiral, but has since stabalised into a simpler butterfly shaped periodic table.

That is strangely similar to how I imagined it.

This isn't how imaginary numbers work though.

No, of course not. But why should that stop us?

[Magis]

Hold on, people.

No physical quantity is ever complex. Not the mass of unstable particles, and not the frequencies of signals, either. Whenever imaginary components are introduced for the sake of some analysis, it is only for mathematical convenience - the final result is always a real value, such as the real component, or the modulus, or the phase, etc. The idea is that introducing an imaginary component can simplify some equations, but they had better cancel out with other imaginary components later on, or be worked on by a function that returns only real values.

Frequencies for example are always real-valued. However, for mathematical convenience when time-domain signals are put through a Laplace transformation, imaginary components appear but the only relevancy they have is that the phase angle of the complex number represents the phase shift of the signal. So in that sense Laplace transforms involve quantities in the complex frequency domain, but that doesn't imply that the signal itself has any imaginary components.

Similarly, unstable particles having complex mass is only a mathematical formalism. The actual mass of those particles - meaning the traditional concept of mass and not some abstract quality - is still a real value and the imaginary component just represents the decay rate. That's a big leap away from saying that some particles actually have complex mass. It would screw up all the laws of mechanics for starters, just as a previous poster eluded to.

[EDIT] That doesn't mean that the thought experiment proposed by the OP isn't an interesting one, I was just mainly just addressing some of the posts that claim complex physical quantities are already known to exist. Because that's not true.

[Surlethe]

No physical quantity is ever complex.

I disagree. Check out the Aharonov-Bohm effect. I think the correct interpretation is that the complex wavefunction of the electron is a meaningful physical quantity, not an abstraction, and that potential is more physically meaningful than a field.

[Starglider]

Complex numbers are not just 2-vectors, they have a specific relationship between the real and imaginary parts that only really makes sense in the context of negative numbers. As such 'imaginary mass' is not a sensible even as a concept unless you already have 'negative mass', which is already physically dubious. Similarly you can't have 'complex RGB values' without negative RGB values, and there is no such thing as negative light (there is phase cancellation, but you can't un-excite electrons by shining negative light on atoms). You can specify a colour as six numbers, but that's just a way of approximating the true spectral distribution (which is the 'real' colour) that is half as lossy as RGB.

[Surlethe]

Complex numbers are not just 2-vectors, they have a specific relationship between the real and imaginary parts that only really makes sense in the context of negative numbers.

I'm not following here. Do you mean multiplication?

[Purple]

Complex numbers are not just 2-vectors, they have a specific relationship between the real and imaginary parts that only really makes sense in the context of negative numbers. As such 'imaginary mass' is not a sensible even as a concept unless you already have 'negative mass', which is already physically dubious. Similarly you can't have 'complex RGB values' without negative RGB values, and there is no such thing as negative light (there is phase cancellation, but you can't un-excite electrons by shining negative light on atoms). You can specify a colour as six numbers, but that's just a way of approximating the true spectral distribution (which is the 'real' colour) that is half as lossy as RGB.

Since the start assumption is that complex mass and complex quantity do indeed exist and as you have said that would require negative mass and quantity to exist as well we can only conclude that under the conditions as given they do. And yes, as it seems in my scenario you can indeed un-excite electrons the way you described.

[Magis]

No physical quantity is ever complex.

I disagree. Check out the Aharonov-Bohm effect. I think the correct interpretation is that the complex wavefunction of the electron is a meaningful physical quantity, not an abstraction, and that potential is more physically meaningful than a field.

It was clumsy of me to say "physical quantity", since that isn't formal terminology. What I really had in mind was that observables (and I'm using that word in its physics context) are always real-valued - I can provide references for this if someone asks. A quantum wavefunction is not an observable, whereas the the square of the modulus of the wavefunction is an observable, and is also always real-valued.

[Surlethe]

Ok, I see. No need for references -- I am well aware that quadratic forms associated to self-adjoint operators on Hilbert spaces adopt real values I'd argue that the wavefunction is physically meaningful even though it cannot be directly "observed" insofar as it is an elegant piece of formalism which makes many useful predictions.

[Simon_Jester]

Since the start assumption is that complex mass and complex quantity do indeed exist and as you have said that would require negative mass and quantity to exist as well we can only conclude that under the conditions as given they do. And yes, as it seems in my scenario you can indeed un-excite electrons the way you described.

Purple, the problem is that your question boils down to:

"Assume two plus two equals five, and pi equals three. What would be the effects on my favorite pastry recipe?"

The final question is trivial, and the starting assumptions so dodgy that no one can say anything meaningful about them.

What would happen if two plus two equaled five? Who the hell knows?

[Purple]

Thats actually not a bad idea. I am tempted to start a new thread for it.