1 Shady black market weapons dealer: {showing off an imposing looking heavy weapon} This plasma cannon is a quantum leap ahead of its competitors! 2 Iki Piki: That little difference, huh? 2 Shady black market weapons dealer: What? 3 Iki Piki: A quantum is the smallest possible unit of change. It's impossible to be any more similar without being identical. 3 Shady black market weapons dealer: What are you saying? 4 Iki Piki: Never mind. Your brain is clearly a quantum leap above primordial protoplasm. 4 Shady black market weapons dealer: Flattery ain't gonna get you a better deal, bub.

The word quantum is derived from quantity, as it describes a fundamental indivisible unit of energy in modern physics theory.

In our everyday macroscopic world, we are used to energy being pretty much divisible as far as we care to play with it. As a concrete example, we can adjust the brightness of a light source continuously from painfully bright to so dim that it starts to be difficult, or even impossible, for us to see it. We don't see discrete steps at any point - the amount of light varies gradually and smoothly (assuming we have decent dimming circuitry).

Light behaves kind of like a fluid in this way, a stream of water if you will. We can vary a flow of water from a torrent to a trickle, setting it to any rate of flow we like in between. We aren't restricted to particular rates of water flow, because we can divide the water up as finely as we like and it's still basically water with the same properties.

Except that's not actually true when we get down to a submicroscopic level. Water is made of molecules (each one made of one oxygen atom and two hydrogen atoms, but that's an annotation in itself for another time). Each molecule is a discrete particle of water, which it is impossible to divide further (without becoming something other than water). So if we reduce the water flow enough, we eventually get to a point where we are letting a fairly small number of water molecules go by. We can imagine reducing the flow so much that we only let one molecule of water go per second. Or per minute, or even per hour.

There is still a flow of water, but it's no longer the smooth, rippling, infinitely divisible thing we are familiar with. It's like lumps of rock flowing past. Water is quantised - exists as discrete chunks of water - and the quantum of water is a water molecule. Water is grainy, but at a scale so small that we don't notice it.

It's the same thing with light. Light looks smooth and even and infinitely controllable to us. But it too is quantised, in tiny packets which we call photons. If you dim a light far enough (and not actually very far beyond the level where we can still see it), the light starts to look no longer like a continuous stream, but becomes detectable discrete chunks. Again, like the water, these chunks of light are so small that in our everyday life we never notice them. But they are there. Light is grainy, just like water.

And that's what a quantum is - the smallest possible unit of difference. So when advertising people say something is a quantum leap better than something else, they really mean it's so similar that you can't tell the difference.

The other point of view is that when studying a quantum system, the jump from one quantum state to another is often a significant change. It kind of has to be, because it's a "jump", in the sense that it doesn't go through any intermediate stages.

For example, the lowest energy state of an electron in a hydrogen atom is -13.6 electronvolts (eV).[1] The next lowest energy state is -3.4 eV. States of energy between -13.6 eV and -3.4 eV are not available, by the laws of quantum mechanics. It's not possible for an electron to be bound in a hydrogen atom with an energy of -9.7 eV.

So rather than going from -13.6 eV to just -13.5 eV, the quantum leap takes it all the way to -3.4 eV. So, looking at this way, the quantum leap is actually much bigger than an amount of change that you might otherwise think you could take.

But, in the big scheme of things (i.e. from our macroscopic point of view), 10 eV is actually a piddlingly small amount of energy. It would run a typical mid-sized car for approximately 10-22 of a second. The energy you use to blink your eyes once would run your car for roughly 1017 (a hundred thousand trillion) times longer than that.

[1] The energy states of an electron bound to a hydrogen atom have negative energies because as you pull the electron further away it gains electrical potential energy (in the same way that if you raise a mass above the surface of the Earth it gains gravitational potential energy). The zero level of energy is defined to be when the electron is not bound to the hydrogen atom. So when it becomes bound to the atom, the electron loses potential energy from this zero starting point, resulting in a negative energy.