[LG Optimus 2x] erups:
So you want the real explanation.

Here goes.

But first an historial note: during the time Intel was selling the Pentium 4, it obviously had mobile versions.

But a mobile version until very recently (until Sandy Bridge) has been not much different from a desktop processor.

When processors are manufactured the Heisenberg Law guarantees that not two of them are identical. So on the same slice of silicon from which a 3.2GHz version comes out, a more measly 1.8GHz comes out too.

Each die is tested in the fab, and only at this point it is clearly determined what kind of processor it will be. More complex operations may follow (like cache burning: all cpus are born the same, cache modules are just burned to make them unavailable and sell the cpu as a lower model).

So given this brief introduction: at the point in time in which Intel was selling the Pentium 4 as its mainstream processor, it had both mobile and desktop versions.

Still AMD with the Athlon product had a much better energy efficiency.

The super-pipeline employed on the P4 simply didn't pay out: it was really fast only in some occasions; while AMD's approach had less raw throughtput, it was much more efficient (if you go have a look at the P4 super-pipeline you'll see why, it's not that difficult).

Why did I cite this? Because everything's connected even if you don't see why.

Now onto the real explanation.

Electrical power, in its simples form, is current by voltage (V*A = W).

Now this is valid only for continous current, in the case of alternating current you'd have to bring in the Power Factor, keeping account of the varying alignement between the current wave and the voltage wave. But this is not our case.

So how does anything electronic really do its calculations?

By flipping state to lots and lots of transistors in different configuration.

It is inessential to know how this is really done, it's sufficient to know that we're talking 1,2,..10,..1000 million transistors.

But the flipping is not really instantaneous.

What does the flip do? It changes the voltage and current at the terminals of the transistor.

At logic zero we have 0V and nA (the actual number is not important), at logic one we have VCC (again the actual number is not important) and 0A.

During the flipping there are both a voltage and a current passing through the transistor, this is the switching power loss.

This explains what I've just said.

The lower peaks (triangular shapes on the violet line) represent the power that is wasted (dispersed as heat) during the transition.

Now this is theory: in reality things are not that neat, energies depend on time too. In fact the representation of a square wave is the sum of infinite sines (Forurier theory).

Since the number of frequencies we can create is limited, our representation is never a real square wave, rather an approximation.

Here you can see a still quite neat real switching wave.

The peaks represent the power spikes which are inevitable.

They are there in every switching thing: from the switch in your bedroom, to your vacuumcleaner, to the Ipad power button.

So what does Fourier have to do with this?

The lower the frequency, the larger the square wave, the lower the number of sines required for correct representation.

The higher the frequency, the smaller the square wave, the higher the number of sines required for correct representation.

Each sine element of the square wave brings energy, so to have a certain square wave at 100Hz requires some energy, to have the same (in terms of tolerance, of precision of the edges) at 100KHz requires much more energy.

Add to this that the spikes are greater (they are in effect the energy stored in the precedent state that has to be reconfigured to reach the new state) and the switching power losses, and you may finally understand why running the exact same thing faster will not yield a better result.

I may add: otherwise why ever downclocking?

Hope this satisfies you.