"All that we see or seem is but a dream within a dream."
- Edgar Allan Poe


My latest entry concerns a principle which I find is vaguely known by many one way or another but not really understood or appreciated fully. What I intend to describe in this entry is a consequence of the most important physical theory of the 20th century, that being Heisenberg's Uncertain Principle. It is not an understatement to state that this principle really opens your eyes as to the nature of our existence and its implication on how it is we experience the universe we live in. What we observe with our 5 senses really is nothing more than an illusion, a gross over-simplification designed by our brains to make sense of the world as much as possible when in reality something far stranger and mysterious is going on behind the scenes.

I am motivated to write this after having a discussion on this issue where I felt some of the fundamental ideas behind the uncertainty principle were not well understood. It's not unusual that I find people confuse the uncertainty principle for being some philosophy or idea that says that when we observe something, we change the outcome of what we observe in an unpredictable way. This actually is radically different from what the principle states itself, although I can understand why people would make this mistake.

Unfortunately to really understand why this is can't just be laid out all in laymens terms and it does require having some understanding of the physics behind it. I am virtually baffled as to how to begin approaching this topic, and so perhaps some motivation and would help, let's imagine we're physicists embarking on a new field of study. We'll start with the simple question, is light made up of tiny particles, or is it instead a wave like sound?

Think about what it means to be a particle, usually a particle is some ball of mass that occupies a region of space. A wave, on the other hand is something that sort of vibrates up and down as it travels along a path. When two particles collide they bounce off of one another, whereas when waves collide they just temporarily merge and then travel through one another without a problem. Simple stuff right...

So, in general, how can we determine if light is a wave or a particle? Well how can we determine if any arbitrary entity is a wave or a particle? Let's come up with an experiment, in fact the name of this experiment is the double-slit experiment.

What we will do is have a machine that emits something repetedly over and over again and we will follow the path that it takes as it passes through a barrier with two slits in it.

If what we emit is a wave, then when it hits the barrier two new waves are generated whose origins are the slits, and since we have 2 waves they are free to pass through one another and merge together.

When two waves merge one of two things happens, either the waves cancel one another out and it appears as though the wave disappeared (destructive interference), or the two waves boost one another and you get like a super-wave (constructive interference).




(example of a single wave splitting into two)

As such, if we emit a wave we expect that when the single wave splits into two waves, that those two waves will sometimes interfere and disappear, or interfere and become a superwave.

However, if I take a pellet gun and start shooting bullets, there's no chance that a bullet will magically split into two identical bullets and either cancel one another out and remerge to create a super bullet. That makes no sense at all and clearly is an absurd notion... a particle can't just split and be at two places at once only to either re-emerge as a super particle, or to just vanish off the face of the earth.



(example of path of a particle)

So, let's take our experiment and apply it to light, if it's a wave then we will notice the wave of light split into two waves and these two waves will interfere with one another blah blah blah you get the idea... if it's a particle no such weirdness will occur.

Well after conducting this experiment, it turns out we notice that light DOES interfere with one another. Voila, light must thus be a wave and this century old debate is now over...


And now comes the Uncertainty Principle. Without diving too much into the math, it turns out that a physicist by the name of Heisenberg managed to derive, purely mathematically, an equation that relates position and momentum together. The problem is that the equation states that the more you know the position of a particle, the less you can know about its momentum. This equation has nothing to do with the fact that our measuring tools are inprecise, or that when we observe something we change the outcome, it has to do strictly with the definitions of position and of momentum and it is something that is derived entirely mathematically. This is IMPORTANT since many people seem to think that the problem is simply that when you observe something you change the outcome, that couldn't be further from the truth.

Well if this is the case, then something is really wrong here. See it turns out that waves in general have momentum, and if you don't know what momentum is, it doesn't matter, just recognize that light does have such a property. So this uncertainty principle says we can't know both position and momentum accurately, there's some kind of trade-off. Well let's cheat the system. By examining the way that the waves interfere with one another, I can actually determine as accurately as I desire what its momentum will be. To determine what the position of the wave will be, well that can also be done, I will just place a position detector at each slit and wait for the wave to pass through it, when it does I can use the detector to record its precise position. By making better and better position detectors I can also record the position of the wave as accurately as I desire.

So in doing this I will now proceed to cheat the system and measure BOTH the position and momentum of light as it passes through my slit with arbitrary accuracy thus violating this mathematical proof of Heisenberg's.

But alas, something very weird happens when you perform this experiment! Whereas before light behaved as a wave, when you try and measure its position, it now behaves like a particle and so it's not possible to measure its momentum since no interference occurs! What the heck is going on? When light was allowed to pass unobserved, it behaves like a wave, but when you observe it passing, it behaves like a particle.

Okay fine... light is weird, let's ignore it. Let's use our experiment on something we know to be a particle, the good ol electron. An electron is a particle everyone knows that right? It's a particle that orbits a nucleus at the centre of an atom in much the same way that planets orbit the sun. The trusty ol electron surely won't have any crazy behaviour like light does.

But indeed, when you perform this exact same experiment with the electron you will also notice that when you don't observe the electron, it BEHAVES LIKE A WAVE! The electron somehow manages to be in two places at once at the same time! But when you try and observe the path the electron takes, then it behaves like a particle.

That's the weirdness of the uncertainty principle, it's not that if you observe an electron you change its position or you change its momentum, it's that until you actually observe the electron, it doesn't have any actual position or any actual momentum. An objects position or momentum does not exist, period, until something observes it.

Position is just some concept that our brain uses to make sense of the universe, this notion that you're position is way off over there and that my position is over here, and the sun is out some billions of kilometers away are but illusions, they exist only in so far as something is there to observe its existence. But when left alone an object is free to occupy many positions all at once and it will do so and it will interfere with itself sometimes disappearing and producing really weird side effects. In our example I simplified it and told you the electron splits into two, this is technically false, the electron technically is in an infinite number of positions all at once and it isn't until you observe it that you force it to be in one of those infinity of positions. This is why an electron left unobserved produces this wave like behaviour, it is in so many positions at once travelling that it interferes with itself, it bounces off of its own self sometimes disappearing, sometimes reappearing.

But position and momentum aren't the only two physical quantities that are a product of our own observations... quantum mechanics actually has several such pairs, and perhaps the one that might strike you as being the weirdest is that both time and energy are also subject to this same weirdness.

The universe, in reality, is typically denoted by U. The universe we observe, is typically denoted by R. Since R is a simplification of U, there are many possible ways that U can be converted into R so that we human beings can observe it. Because of these many possibilities, physicists have to resort to using probabilistic models of physics to describe the observable universe. They use something known as Schrodinger's equation to describe the behaviour of an object as it exists in the universe U, but there is a special procedure known as the wave-function collapse which describes how to take the universe U and convert it into one of the many possibilities for R. This wave-function collapse occurs when someone tries to observe U and thus make a simplification of it.

And there you have it, the uncertainty principle in as close to laymans terms as I could possibly make it, but also staying true to what the uncertainty principle really says. This really is only touching the surface of course, since now that we know that what we observe is different from what really happens, the question is, how do we reconcile this difference? How do we interpret this result? What are the implications?

I will save this for another post.