The Uncertainty Principle, and the Quantum Discontinuity.

What is the uncertainty principle?  Some people think of it as the "Observer Effect", the fact that any time you measure an object, you change something about it.  For example, to see where an object is you have to bounce photons of light off of it, and those photons change the object.

But that's not what the uncertainty principle really is.  The Heisenberg Uncertainty Principle (HUP) is defined as follows:

That is, the uncertainty in position times the uncertainty in momentum is greater than or equal to Plank's constant over two.  Plank's constant being 1.054571628(53)×10⁻³⁴ J·s

What this means is that you cannot know both the position and momentum of something.  To the extent you know one, the other is uncertain.  Of course Plank's constant is a very small number, so most of the time the uncertainty of our knowledge does not matter.  It only becomes significant over very short distances and very small changes in momentum.

To understand where this uncertainty comes from, we need to understand that all matter and all energy is composed of waves.  I know this is difficult to envision, but take it on faith for the moment because once you accept this fact the uncertainty principle suddenly makes a great deal of sense.

Imagine a circular pond of very still water.  The surface is like a mirror in all directions.  Hold a stick in your hand, and insert the tip into the water.  Move the stick up and down at a fixed frequency.  Waves will ripple away from the stick in all directions, completely filling the pond.  The waves have no certain position.  They are everywhere on the surface of the lake.  However, because the frequency is fixed, the waves have a very well defined energy (momentum).  That's the first half of the HUP, we know the energy but we cannot determine any position.

Now change the way you move the stick.  Shake it up and down randomly -- perfectly randomly!  Make sure you incorporate every frequency into your motion.  The surface of the lake will return to it's mirror sheen because all frequencies will integrate out. You will know where all the energy is, it's in the stick, but you won't know how much energy there is because it's all random.  And that's the second half of the HUP.  You know the position of the energy, but the quantity is purely random.

That's how photons work.  Photons are "particles" of light.  But does light really move as a spray of particles?  It sometimes seems to.  However, it also seems to move in waves like the waves of a pond.

Plank showed that the energy of a photon is equal to Plank's constant times the wavelength of the photon's frequency:

What this means is that we cannot measure energies that are not integral multiples of this quantity.  Indeed, no interaction between two particles can take place unless there is an exchange of an integral multiple of that quantity.  For example, an interaction that would require half that energy simply could not occur.

So now, imagine a light source that emits light at a fixed frequency at a rate exactly equal to one photon per second.  Is this light source emitting one photon per second?  Or is it filling the space around it with light waves.  The answer is both.  The space around the light source is filled with a field of waves.  However, those waves cannot interact with any other matter more than once per second.  And the position of that interaction is, by the Uncertainty Principle, random.  So if you set up a screen around the light source, you'd see tiny little sparks of light in random positions at roughly one second intervals.

The waves are all there, filling space like the waves on the pond, but the energy of those waves can only be deposited in fixed quantities, and the position of each one of those deposits is random.   If you put such a light source in the center of a room, it would "illuminate" that room.  However, your eyes would only register the photons that managed to randomly deposit their energy on your retina via a pathway that passed through your pupil after reflecting off the objects in the room.  And that would happen at a rate much less than once per second because most of the photons emitted by the light source would deposit their energy somewhere other than in your eye.

What is bouncing off the furniture in the room?  Photons?  No, it is the waves that are reflecting off the objects in the room and that are passing through your pupil, refracting through your cornea and lense, and "striking" your retina.  And then those waves deposit their energies as photons at uncertain locations. The waves determine the probability that the energy will be deposited at one uncertain place or another.  So in some very real sense the waves are waves of probability.  If an area of the room is in shadow, no waves will be present in that part of the room, and so the probability that the waves will deposit their energy as photons in that area is zero.

If you put a camera in the room and left the shutter open for a very long time, the camera would record a perfectly normal image of an illuminated room.  Over time the field of waves would deposit some of it's energy as photons in the camera's receptor.  The probability information carried by those waves would cause those photons to build up an image of the room.

Indeed, that's what's going on right now as you are looking at these words.  The field of waves leaving your computer screen carries probability information to your retina, causing photon's to be randomly deposited there.  It's just that the flux of photons is so huge, that we do not notice their randomness.

What does this have to do with software?

Nothing directly.