Lesson 16: The Heisenberg Uncertainty Principle

The Heisenberg Uncertainty Principle

Heisenberg’s Uncertainty Principle shows we do not live in a deterministic universe.  There are going to be things that we can never know for sure.  This is because, as we have discussed, the subatomic world comes in discreet units.  It is quantized. There is a minimum size we can use when trying to figure out how the world works.  We become part of the world.  We can’t observe something without affecting it.

This led German physicist Werner Heisenberg to develop The Uncertainty Principle in 1927.  Heisenberg’s Principle says that at the microscopic level, position and velocity cannot both be measured exactly at the same time.  

This seems very weird to us. Consider a car. Obviously, we can tell where a car is and how fast it is going and where it is going. With subatomic particles such as electrons, that is not possible.  There is a trade-off.   The more you know about the position of the electron, the less you know about its momentum, and the more you know about its momentum, the less you know about its position.

To understand this better, let’s do a quick review on waves.

The red wave has a long wavelength and, therefore, low frequency and low energy.

This blue wave has a shorter wavelength than the red, and therefore it has a higher frequency and more energy.

We also know that just about everything we see in the world can be a particle and wave.

Particles are like BBs or billiard balls.  Waves have no physical substance.  Waves can move through walls.

We have already learned when you look at something. Your eye is taking in light waves of the object.

To see something, we need to have light.

Now let’s say we want to find an electron.  We have to hit it with a photon of light to determine where it is at.  But the problem is a photon is a particle and a wave, so we don’t really know where the photon is either.  So we don’t know where the electron is, and to find it, we need to use a photon, but we don’t really know where the photon is at either.

The best we can do is send out a wave of light, known as a wave packet, to try and detect the electron. 
 

Look at the wave packet above.  It is a narrow wave and therefore has a shorter wavelength and high frequency and energy.

Now, look at the second wave packet above.  The wave is broader than the first therefore, it has a longer wavelength and lower frequency and energy. 

So we send out the wave packet in the direction we think the electron is.  We can say we are shooting a photon at the electron to try and determine where the electron is but the only thing we can say about the photon is that it is somewhere in the wave packet.  Look at both wave packets. It is easy to see the first has a smaller area than the second.  So if we detect an electron using the first wave packet, we are going to better know its location than if we detect it within the second wave packet, which has a bigger area. 

Think of it like you are trying to capture an invisible animal with a net.  If you catch it in a smaller net, you are going to know its location a lot better than if you catch it in a bigger net.

But getting back to waves, there is a problem. The problem is the compact wave packet has a high frequency and high energy, so when the photon hits the electron, it is going to be like hitting a billiard ball very hard.  The electron is going to shoot off in some direction at high speed, so we can’t know what the momentum of the electron was before we hit it.

So let’s use a lower frequency photon with less energy so the electron doesn’t shoot off away from us.  But remember, when using a lower frequency, the wave is now broader taking up more area. Now we can’t determine where the electron is as well as we could before.  Now we know its momentum better, but we are not quite as sure where its position is.

There is a trade-off.  The more you know about the position, the less you know about the momentum.  The more you know about the momentum, the less you know about the position.

Heisenberg’s Uncertainty principle says you can never have complete certainty.  And guess what determines that uncertainty? Plank’s constant (h).  Again it all comes back to Plank’s discovery.  Remember, Plank’s number is very small. So this is why we only have this trade-off with very small subatomic particles and not with things like cars and houses and us.  We can easily see where a car is and how it is moving.

Now here is where it gets weird again. We have been saying the photon is somewhere in the wave, but the photon is not really in the wave.  It is, and it isn’t. I know it’s so strange.  No one can really grasp it intuitively.  

Remember Niels Bohr?  He came up with what is called The Copenhagen interpretation to try and explain as best as possible all of this uncertainty stuff.  He said if you can’t measure both position and momentum, there is no sense in which to say it has either. It doesn’t exist.  The atom you see in school books is incorrect.  The atom doesn’t really have electrons circling around it. The electron is only a fuzzy probability of what might be.

And what determines what might be?

Are you ready for this?

You do!

We are going to stop here.  This is something you need to contemplate for a while. 

In the next lesson, we are going to discuss Schrodinger’s Equation and see if we can’t make a little more sense of all of this.  We are actually going to try to make sense of the senseless.

So go out there again and tell someone about this.  Make your drawing.