Is Nature uncertain?

In my Digital Transformation Masterclass I have two provocative slides, which I use to support my evocative call to action:

“Embrace uncertainty”

because – I say – even the two most precise of all human knowledge domains, mathematics and physics, are fraught with it.

The mere mentions of their names is enough to inculcate a healthy sense of awe and respect, so I never have to explain in more detail the depth of these discoveries.

So I cannot claim that this post serves a business purpose: it serves, however, my vanity in explaining what I believe are two incredibly profound (and overlooked) achievements by geniuses who graced my time: who knows, after the movies on Turing and Nash, these two might be next, because Science is sexy, after all.

Heisenberg’s indetermination principle

I’ll start here because, while Gödel’s Theorem deals with the logic of formal systems, Heisenberg’s Principle has much closer consequences on our everyday life even though it seems to violate what our senses tell us.

In one of its many expressions, the principle states that:

Δx × Δp ≥ h/2π

in plain English: “the uncertainty in the position of an object multiplied by the uncertainty in that object’ momentum is always greater than the reduced Planck’s constant”

I do not have to explain “position”, “momentum” is the product of the object’ mass times its velocity and “h” is the proportionality constant between energy and frequency of a radiation (6.62 × 10-34 J s or kg ms) which had been calculated by Max Planck at the beginning of the century.

This looks counter-intuitive: if I put a ping-pong ball with a mass of 1g on the kitchen table, I know exactly its position (Δx = 0) and its momentum (Δp = 0 because v = 0), no?

Well, not really: the mistake lies exactly in the sloppiness of our senses; when I say that I know the position of the ping-pong ball, I omit to add “as well as my eyes can”. Let’s make an assumption on this precision: what will it be? A tenth of a millimeter? a hundredth? Let’s assume we know the position of the ball with a 1 μm (= 10-6 m) precision. Werner is then telling us that the we know the velocity of the ball with a precision of ±10-25 m/s).

Our impression that the ball was at rest was indeed justified, since to travel 1 cm at the maximum velocity error, the ball would take longer than the age of the Universe.

But see what happens if we consider an electron, whose mass is 9 × 10-31 kg; if we know it’s inside an hydrogen atom (Δx = 5 × 10-11 m), its velocity cannot be determined with a precision of more than 10m/s: therefore it could be standing still or it could be traveling at thousands of kilometers per second.

If, however, we know with good accuracy its velocity (for example because we apply an electrical field), then there is a non-zero probability that the electron is not in the atom at all (or on our planet, for that matter), an effect which made possible to build devices such Scanning Tunnelling Microscopes who are capable of taking images of actual atoms.

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