The Uncertainty Principle of Heisenberg
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2. Heisenberg's Uncertainty Principle

— Big Rules for Small Particles —


A scientific model or theory is supposed to be a cascade of certainties and whenever someone uses the word 'uncertainty' most scientists will run for the nearest airlock.

Great therefore was the consternation when uncertainty appeared to be one of the most characteristic qualities of quantum particles. Einstein even went as far as to boldly state: I don't believe that God plays dice!

But God did. Or so it seemed.

Heisenberg Uncertainty Principle
Werner Karl

The year was 1927 when a brilliant 26 year old German named Werner Karl Heisenberg postulated a principle that would go down in history as the Uncertainty Principle of Heisenberg. It goes like this:

A large object that moves along a trajectory has, at any point in time, a certain speed and a certain position. Both speed and position for any point along the track can be accurately calculated or measured. But of a quantum particle that zips through space the speed and position can not both be accurately known. Either the position of the particle is known or the speed. And when one of the two is known accurately, the other one is hidden. When we know the speed, we have no idea where the particle is situated. And when we know the position of the particle, we are oblivious to its speed. And that is not because we're not smart enough, or our instruments are not accurate enough. It simply does not exist!

Hold that thought (2a)

The Uncertainty Principle of Heisenberg: Of a quantum particle, speed and location can not be simultaneously known.

We like to think of speed and position as two separate things but in fact they are two sides of one thing. Just like space and time are really not two but one: space-time. Einstein was right when he said that God doesn't play dice. He doesn't. In stead He created the universe on a principle of sovereignty. Quantum particles are allowed to surround themselves with mere blurs of their intentions. No one is to know their true speed-position, not even God, because it does not exist.

The Famous Slot Experiment

Quantum-uncertainty has a very peculiar consequence. It can not be predicted where a particle will end up when we shoot it at a target. Particles are sovereign and can not be coerced.

Take a look at the following installation:

quantum slot experimentA particle canon shoots particles at a screen with a slot. Behind the first screen we place a recording screen that marks the place of particles impact with a black dot. We let the installation run for a couple of hours, or at least long enough to have fair coverage of possibilities.

If particles were regular objects they would have been easily directed through the slot and on to the same spot on the recording screen. But particles are not regular objects and our recording screen shows a blurred black smudge at the spot we were aiming at.

Obviously most particles hit the recording screen somewhere in the vicinity of our target. Particles can not be coerced but they seem nevertheless quite willing to join the fun.

But the black blur does not have a boundary. It smudges across the entire recording screen, graying out radially until at the edges hardly any impact shows. It appears that some particles chose to avoid the mainstream and steer for the edge. In fact, if we would have placed recording screens all around the canon, we would have seen impacts everywhere, even behind the canon! Some particles simply tear a U-turn and hit a wall 180 degrees opposite the one we were shooting at.

Erwin Schrödinger
Erwin Schrödinger

We decide to count the number of impacts directly behind the slot in an area with a certain small radius. Then we count again but cover a larger area. We count more hits of course because we've added surface to the first count. Then we count again, and again until we have a pretty accurate picture of the spread of particles. We plot the numbers in a graph and find a curve that never becomes zero (since particles hit everywhere). This curve was plotted for the first time in 1925 by an Austrian named Erwin Schrödinger and has been called the Schrödinger Wave ever since.

Schrödinger solved the troublesome particle/wave duality paradox that had plagued scientists for so long. The question whether things such as photons were waves or particles was answered with a loud negation across the board: they are neither, or rather: both! Quantum particles are particles that propagate through space by means of chance-waves. That is the wave some scientists had detected. This wave does not propagate through some kind of medium, like water or air, but emerges from the individual sovereignty of quantum particles. Before quantum theory waves always ran through a medium, like the ocean. Take away the wave and you still have water. A quantum wave does not use a medium; it uses chance. Take away the wave (which are the particles) and you'll be left with nothing.

The Famous Two Slots Experiment


If quantum particles that burst forth from their source behaving like a wave, we should be able to observe interference. Interference happens when two waves collide and some parts of both waves cancel out and other parts add up. (To construct a resultant-wave we add up the amplitudes of both waves for all points - above the gray line is positive, below is negative).

The Uncertainty Principle of Heisenberg And to make two waves in order for them to interfere we take out the slotted screen of our previous experiment and insert a screen with two slots. We fire at will and wouldn't you know... interference! Indeed many particles ride the wave of their identity.

But! we're not happy so fast. We decide to fire off one particle at a time with an interval of one minute between particles. Quantum particles are those things that can not be divided. Particles must go through one of the two slots, our intuition dictates. Firing off particles one at a time should not produce an interference pattern, we think.
A few hours later we return, and find the recording screen adorned with yep! an interference pattern. How is this possible?
Well, apparently we have stumbled upon the heart of quantum weirdness. The rule is easily derived, but not easily swallowed. We'll have to choke it down: Quantum particles are per definition indivisible, but they travel through space according to all the many possibilities that they have to choose from. They are not compelled to choose one specific trajectory, but are allowed to travel all of them, according to the chance that they will.

groovy party

Particles will travel everywhere from source to target, like a smear, thick where the particle is most likely to be, and thin where it is most likely not to be. The smear by which they travel is called a path integral: the total area covered by all possible trajectories.

Interpretation of the Slots Experiments

In the two-slots experiment the following is true:

The chance that the particle goes through slot 1 is x%. The chance that the particle goes through slot 2 is y%. Chance x and chance y are both Schrödinger-waves and they will engage each other to form an interference pattern behind the two slots.

Quantum particles are indivisible but will interfere with themselves to form complex patterns when they encounter obstacles. When we repeat the experiment we will find the same results. Approximately the same number of particles hit in certain areas. Uncertainty appears to have its certainties after all. Or...doesn't it?

What if we shoot one hundred particles at a target and the first ninety nine of them 'choose' to fit the pattern. Then, if certainty existed, the hundredth particle would be forced to land in the only spot left by its predecessors. No way Jose. There's no way of telling where the hundredth particle will go. The last one's freedom will always infringe ultimate certainty.

The more particles we fire off the more accurate we can predict how the spread of particles will be. If we shoot off a million particles, we can quite accurately predict the percentage of hits per area. If we shoot of a hundred particles we can still predict how the spread will be but not very accurately. And if we shoot off one particle we can not make any sound prediction where it will end up. All we can talk about is the chance that our particle will end up in a certain area.

If 95% of one million particles ends up in a radius of 50 centimeter from the projected heart of the slot we can say that there is a 95% chance that particle number one-million-and-one will end up in the same area. But this says nothing about the actual destination of the particle.

Hold that thought (2b)


A quantum particle can not be coerced. If it chooses to do so it will end up there where only 1% of the particles ended up. It might even boldly go where no particle has gone before. Nothing is certain. Everything is possible.

Which brings us to another phenomenon: quantum tunneling, which allows a quantum to simply up and leave and show up somewhere else. In fact, there is a very real yet astronomically small chance that all particles that make up you and your computer suddenly decide to zip to Mars. The chance that this happens naturally is so small that we don't incorporate it in our daily experience of reality. But it is certainly not zero. Quantum tunneling is a very real thing, like say electricity.

Before electricity was comprehended and harnessed by man, all natural manifestation of it (lightning, static electricity, magnetism) must have seemed miraculous and magical, but nowadays we don't look up from a illuminating light bulb. Same with quantum tunneling. If the principle is understood and a pact is sealed with the world of the small, large objects such as a human being may be freely transported instantaneously over great distances. Like Philip in Acts 8:39, or the disciples in John 6:21. No magic. No super natural goings on. Just a utilization of one of nature's freely available principles.

Still, even sovereignty is limited. Freedom seems to be something that exists between borders. Freedom has its parameters after all.

Find out in the next chapter:
The Atom

Summary 2: The Uncertainty Principle of Heisenberg

  • Freedom is the most fundamental principle of the universe.
  • The Uncertainty Principle: Speed and position of a quantum can not be simultaneously known.
  • Quanta move along according to the chance that they do, and can interfere with themselves.
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