What (physically) would be required for a 3rd dimension in electronic signals?

[soccerballtux]

Resistance is linear; capacitance/inductance operate in the 'imaginary' plane.
What would a third plane be to a signal?

 

[repoman0]

An electronic signal is just a voltage or current or both changing over time. The complex numbers that represent resistance and capacitance/inductance are just convenient ways to compute the frequency response of a circuit in the Fourier domain, i.e. without solving differential equations -- algebra is usually easier than calculus, in this case.

Despite all the fancy complex number math, it's still some 1D signal s(t) going through a circuit, you can watch it on an oscilloscope over time.

 

[polarmystery]

Temperature.

Normally temperature changes result in increased/decreased resistance, but I'm referring to a full temperature range of 0K up to something much higher (1000 K?) electrons behave much differently at extreme temperatures. The "third" plane for temperature would most likely have to be exponentially logarithmic.

 

[soccerballtux]

Temperature is interesting idea.

I was thinking about the memristor's role

 

[Mand]

An electronic signal is just a voltage or current or both changing over time. The complex numbers that represent resistance and capacitance/inductance are just convenient ways to compute the frequency response of a circuit in the Fourier domain, i.e. without solving differential equations -- algebra is usually easier than calculus, in this case.

Despite all the fancy complex number math, it's still some 1D signal s(t) going through a circuit, you can watch it on an oscilloscope over time.

This.

There are no dimensions involved, it's just math to make the calculations simpler. The imaginary numbers involved are used to track the phase of the components of a signal, but all you have is V(t) and I(t) once you get right down to it.

To get a "third" component you'd have to change the nature of the universe so that waves, in general, are no longer defined by amplitude and phase, but by something else as well.

 

[KWiklund]

Not really. In recent years, hyper-complex numbers have been found to be a useful way of representing polarization.

 

[Abwx]

Resistance is linear; capacitance/inductance operate in the 'imaginary' plane.
What would a third plane be to a signal?

Resistance also operate in the imaginary plane, it s just that the value of the imaginary part is 0, and zero is not nothing when we speak physics, it s bigger than a negative number, for exemple, also Ohm s law is not linear and not a real law , it s an empirical law whose validity is limited to a given range, past a voltage threshold the current in a conductor increase exponentialy with said voltage.

Not really. In recent years, hyper-complex numbers have been found to be a useful way of representing polarization.

Quaternions are just that, a mathematical modelisation that allow accurate description of the nuclear force (force whose bosons are the gluons), an exemple is the spin of a particle, to get a given particle in its initial state you have to rotate it twice by 360°.

 

[inachu]

To the OP...

Your question reminds me of future trends where the CPU will no longer be flat but in the future the pc cpu will start to build up and out and will quite possible look like a borg cube from star trek. Just an idea to think of...

 

[Savatar]

I think quantum entanglement and non-locality has pretty much shown that there is what can essentially be thought of as another dimension lingering about that is not well understood yet.