Concepts explained
Not Unknown but Absent — The Uncertainty Principle
A very short sound has no pitch — not because the instrument is poor, but because pitch is not in it. Position and momentum are like that for an electron. The uncertainty principle is not about measurement but about what exists.
This is the same story as an electron's position and speed. Here is how they become the same story.
A short sound has no pitch
Pitch is how many times something vibrates per second (). Four hundred and forty times a second is an A.
But to count how many times per second, you have to hear it vibrate several times. If it vibrates once and a half and stops, there is nothing to count.
One thing must be said plainly here: this is not quantum mechanics. Sound, ripples, radio — anything that is a obeys it. It is pure mathematics, known a century before quantum mechanics existed.
But if the electron is a wave
The second article gave us two things: the electron is a , and its wavelength is its . Shorter wavelength, larger momentum.
Then the trade above carries straight over to the electron.
You cannot draw a round square, and that is not a failure of draughtsmanship. No amount of practice will produce one, because there is none.
A little further in
The man who first stated the principle did not explain it this way.
Heisenberg's microscope
Copenhagen, February 1927. Werner Heisenberg, twenty-five, opened with a thought experiment.
To see where an electron is you must shine on it and catch what comes back. But light is granular too (article one), so it kicks the electron. To pin the position more precisely you need shorter wavelengths, and a short-wavelength grain kicks harder. The better you see it, the harder it is kicked.
Intuitive and memorable, which is why it remains the most widely repeated account. It also has a problem.
Measuring disturbs the thing measured, as a thermometer slightly changes the water's temperature. Gentler measurement reduces it, and it happens in the classical world too.
The state does not exist before any measurement. No amount of care reduces it. It follows from being a wave, not from measuring.
Bohr was the one who pressed the point. The two argued bitterly for weeks, and Heisenberg had to add a qualifying note to his paper at proof stage.
Bohr's answer
What Bohr offered instead was : the wave picture and the particle picture are both needed, and cannot be used together in one experiment.
The double slit of the third article is exactly that. See the stripes, or see which slit — one or the other. How the apparatus is arranged decides what can be seen, and there is no way to lay the two pictures over each other.
The Copenhagen interpretation
In October 1927 twenty-nine physicists gathered at the Solvay conference in Brussels. The position that settled there came to be called the — a name applied afterwards to the views of Bohr, Heisenberg and Born, not to any single document.
- The wave function is not a real thing but a ledger of what can be predicted.
- Before measurement there is no value. At measurement one value settles.
- Why it settles is not asked.
The second is called the of the wave function: what was spread through space is described as folding to a point the moment it is measured.
What collapsed was determinism
In 1814 Laplace imagined an intellect that knew the position and momentum of every particle at this instant. It could compute every future and every past of the universe.
What uncertainty destroyed was not the computation but its starting point. No such state exists in nature — every particle with a position and a momentum together. The ledger is not incomplete; there is no such ledger.
Empty space is not empty
The principle has a second form: over very short intervals, is not fixed either.
So a pair of particles may briefly appear in empty space and vanish again. If they do not last, the books still balance. The vacuum is not a still emptiness but a seething one.
This is not speculation. Two metal plates placed very close together are pushed by these fluctuations, and the force has been measured. A slight discrepancy in hydrogen's energy levels has the same cause.
- 1814Laplace — know everything and you can compute the future
- 1927.2Heisenberg — uncertainty, argued through a microscope
- 1927.9Bohr — complementarity: both pictures needed, neither at once
- 1927.10The Solvay conference — what will later be called Copenhagen
- 1935Two letters of objection arrive
Those who would not accept it
Copenhagen's answer was this. Before measurement there is no value. At measurement it settles. Do not ask why.
Two men would not have it. One of them was the man who, in the first article, pushed hardest for quanta being real. The other was the man who, in the third, could not bear his own equation being read as a table of odds.
Both wrote objections in 1935. One was about two particles far apart. The other was about a cat in a box.
The question that remainsIf a value settles at the moment of measurement, how far does that moment reach? To the detector? To the person reading it? And to the other electron, sent to the far side of the world as its partner?