First I want to point out that SPICE is for simulating, not for proving.

Second, SPICE is not aware of the electric and magnetic fields. SPICE is for solving circuits using Kirchhoff, and it can work only

**after** you, the SPICE user, converts the geometry of a real circuit into a

*lumped* circuit, with equivalent coils and capacitors. You, the user, have the responsibility to take the real circuit where Kirchhoff might fail, and convert it into an equivalent lumped circuit with all kinds of coils and capacitors and transformers, and transmission lines, so SPICE can crunch the numbers using only Kirchhoff and no Maxwell. It is the SPICE user who must take into considerations not only the geometric size and shapes, but also the permeability and the dielectric properties of the surrounding materials. That is a lot left outside SPICE, and even more, the topology of the lumped circuit needs to be changed when the external conditions change.

A lumped circuit is an equivalent circuit, where you, the user, are responsible for finding the correct topology of coils and capacitors and their values in such a way that Kirchhoff's law can be applied.

https://en.wikipedia.org/wiki/Lumped_element_modelSpice is solving its I/V matrix equations based on Kirchhoff and lumped circuits. That is why

**in SPICE you won't find any circuit that does not obey Kirchhoff**.

In real circuits, any piece of wire is a capacitor, a coil and a resistor in the same time. This is crazy, and makes it almost impossible to calculate a lumped equivalent that holds with the real world. We have some dedicated shapes for capacitors and coils where the formulas for L and C are well known, but that's all. For a random piece of wire there is no clear formula without fields and material constants, and Maxwell. If we go into transmission lines or antennas, things goes even more complicated. There are no antennas in SPICE. There is no causality in SPICE. Propagation in lumped circuits is considered instantaneous, which in the real world is not true.

If we go further, let's say to calculate the beam of a particles accelerator, SPICE can not help. Spice does not know Maxwell, and does not know relative speeds and Special Relativity, SPICE knows only Kirchhoff.

If we go even further, for satellites working in different gravitational fields, SPICE is again unaware of General Relativity. It is us who need to take Special or General Relativity into consideration, and invent a lumped circuit in such a way that we capture all these effects into our imaginary lumped circuit.

Maxwell's equations stand no matter what. That is why they are so praised. Maxwell's equations does not need inductors and capacitors. Kirchhoff does. Again, Kirchhoff is great for static fields (AKA conservative), but can not be applied for non-conservative fields. It was not meant for such non-conservative fields.

In order to use Kirchhoff for non-conservative (loosely speaking "variable" fields), we found a workaround, a trick. We stuff the real circuit with all kinds of imaginary parts, and not only we add those imaginary parts, but the values and the

*topology *of the lumped circuit keeps changing based on external fields and external surrounding of the real circuit, yet our real circuit never changed during this, only the surroundings changed. We call this stuffed imaginary circuit a lumped equivalent circuit of the real thing.

This fake stuffing we do in order to obtain a lumped circuit is very, very fake and unnatural thing to do, yet we considered it NORMAL, because we are used to it, and because it makes our calculations easier.

In fact, we did it so often that the lumped circuit became to us a second nature, while the real circuit is looked rather as a fussy oddity that needs a lot of care (like electric and magnetic shielding) for it in order to work as expected. We got so used with our imaginary fake lumped circuits that we now consider reality an anomaly. We call reality parasitic hum, parasitic inductance coupling, parasitic capacitive coupling, parasitic ground loops, parasitic antennas, parasitic transmission lines, parasitic everything.

Suddenly, reality become for us just a parasitic effect, and we like to consider it that way just to accommodate our distorted lumped circuits with the cruel reality. That has a lot to do with how human mind works, and from here we are in the realm of human psychology and philosophy.

"A fake repeated over and over becomes reality" <- just an old saying.

Peace!