Schrodinger’s Cat

Erwin Schrodinger

You can’t really look in the general direction of quantum mechanics without hearing the name Erwin Schrodinger.  Remember how we discovered that as long as a particle isn’t being observed it exists only as a wave?  Well Schrodinger’s equation is a partial differential equation describing how the state of a system changes over time.  Though there are lots of derivatives of it including time-independent one dimensional forms such as this one:

Schrodinger Equation

Essentially what Schrodinger’s equation tells us is that when the wave function of a particle isn’t being observed the wave function changes and evolves in a very deterministic manner.  In other words, (in a time dependent form) we can determine a wave function’s state in the future or in the past given its current state.  Once an observation causes collapse however, the wave function is changed, so this only holds true without observation.  Anyway, there’s no need for our purposes to get into the complexities of the math, other than to say that it’s a mathematical object that describes a specific state of an isolated system.  Instead we’ll focus on it’s focus, which is a wave function.  It’s important to note however that a wave function describes an entire system, meaning it covers all of the particles in it all at once though in our examples for simplicity we’re just going to talk about single particles.

So let’s talk more about a wave function.  When not being observed a particle is a wave function.  But what exactly does that mean?  Aside from the obvious implications that it doesn’t exist as a “thing” in our reality?  We can think of a wave function as a “wave of possibility.”  A wave function contains the probability of every possible observation. What do we mean by this.  Suppose we fire an electron off across the room with our eyes closed.  The wave function of this electron (know as Psi) describes every possible location we could find this electron as a probability.  Places where this wave function have a higher amplitude means a much higher probability of finding the electron there in that location.  Places where this wave function have 0 amplitude means we will not find the electron in that location.  In a proverbial sense we can say that as long as your eyes are closed it exists only as a wave.  That wave describes the “possibilities” of where that electron might be located.  As soon as we open our eyes and observe where the electron actually is, that’s when the wave function collapses and the electron “pops” into existence.

Now let’s be very clear about one thing.  When we say “observe” we don’t mean that you or I or anyone actually “sees” the electron.  What we mean by “observe” is that it interacts with something that then gives us, you or I, the ability to be able to “know” it’s position.  An electron is too small to be seen in the first place, but there are lots of ways we can figure out where an electron is.  But to elaborate this “observation” simply means we know “where” it is, by whatever means.  If we set up a screen that is excited by an electron hitting it (generating an electrical impulse), amplify that signal and record it to display on a screen, this is observation.  In other words, the universe now has “knowledge” about that particle.  Even if we haven’t looked at the data yet, the data still exists and therefore it has been observed.  There are some out there that would argue that since a non-consciousness (i.e. a detector) can cause a wave function to collapse, then it has nothing to do with consciousness.  That’s not true though since the eraser experiments (which we’ll get into later) clearly show that it’s rather or not we HAVE this information available to us that determines rather or not the wave function collapses, not rather or not it’s been observed directly in real time by a conscious mind.  But for now, let’s get back to our wave functions.

What is amazing about this wave function is that it describes the probability that the electron will be in a specific position once it pops into existence.  I couldn’t find a very good image so I had to draw one myself, so please forgive my graphic artist skills.

Probability Wave

Now a true probability wave wouldn’t look like this (or at least hopefully not!) but I’ve made a representation just to help illustrate my point.  So you’ve just fired your electron off from the left of this chart.  You open your eyes and observe it.  What position will it actually be at when it becomes “real”?  We can’t know for sure, but the probability wave gives us a lot of information about what is most likely.  We can see that it might be in one of the three lower probability areas.  It’s very possible that could happen.  On the other hand, it’s much more likely that it will be in one of the two high probability areas.

Remember our double-slit experiment?

Wave Function

Notice how the more intense peaks of the probability wave are in the center and they fade out in bands as they spread outward?  Does that remind you of anything?  Have a look at our interference pattern again.

Large Interference Pattern

Do you see it now?  The probability wave simply describes how likely the particle is to be in a certain position once it’s observed.  Because there is higher probability in the certain bands (due to the wave interfering with itself) when the particles actually pop into existence, they hit in the areas of high probability much more often than the areas of low probability.

Let’s try to imagine this in our minds.  Suppose we have a sealed box with walls that will just bounce an electron off.  Into this box we fire an electron.  We can’t see inside the box, which means the electron can’t be observed.  As long as that box remains closed, there is no electron.  Instead what’s inside the box is a wave of possibility which is spread out to fill the entire box.  If we were somehow watching the electron then we would see that it only took up a small portion of the interior of the box at any one time, a ridiculously small point, just bouncing around like crazy.  Instead, since we aren’t watching, we have this wave function.  Instead of taking up just one tiny point, it spreads out and fills up the entire box.  This wave will have peaks much like above, and those peaks determine the probability of where that electron might pop into existence once it’s observed.

Now suppose this box has a special partition that can be slid into place dividing the box in half.  Traditionally we might think that once in place the electron MUST be in one half of the box or the other.  That’s really not the case at all.  Instead you have to understand that it wasn’t an electron, but rather a wave function that was inside the box.  So when the partition divided the box in half, half of that wave function was trapped in one side of the box and the other half of the wave function was trapped in the other side of the box.  If you had filled the box with water it would have spread out to fill the entire box.  Putting the partition in place wouldn’t have forced all the water into one side or the other right?  The same is true for the wave function.

Once you open the box and look to see where the electron is, that’s when the wave function collapses.  Now the electron will pop into existence, most likely in one of the high probability areas of the wave function.  Thus it will now be in one half or the other.  If you found it one one side of the box and then closed the box back up the electron would again become a wave function, but this time only filling half the box since it can’t flow into the other half as long as the partition remains in place.  Thus once observed in one side of the box or the other, it will always remain in that half unless the partition is removed.

I know it’s not easy, but when particles aren’t being observed you have to stop thinking of them as little “things” and instead start imagining them as waves flowing and filling their possibilities.  In case you hadn’t figured it out, Schrodinger’s wave equation describes how those quantum waves move.

What’s interesting however is that despite being quite well known in the quantum world, Schrodinger was not a fan of this idea of wave functions collapsing.  One of his most well known thought experiments, “Schrodinger’s Cat” was actually devised by Schrodinger in order to demonstrate just how ridiculous this notion was.  Yet we now know that this concept of superposition isn’t ridiculous at all.

So what is Schrodinger’s Cat all about?  Imagine the same scenario as above, except now we have a way after dividing the box to open only 1/2 of it.  Suppose we put that box into another much larger sealed box.  In that box we place an electron detector which is hooked up to a poison dispenser.  We also of course must place in this larger box a cat.

The idea behind this is simple.  We have an electron in the small box, which is actually just a wave function which fills the box.  We divide that box into 2 halves.  The wave function is now on each half of that box which represents a 50% chance on either side that when observed the electron will be in that side.  We now open one half of the box. (without observing since this is in a sealed box)  Now the portion of the probability wave that was contained in that half of the box will move out to fill the larger box with the electron detector and the cat.

Now technically there is one flaw in this thinking, and that is rather or not we consider the cat to be a consciousness.  If indeed the cat is a consciousness (and I myself certainly believe it would be) then the moment the small box was opened the wave would collapse and the electron would either be in that side or not, which in turn would either set off the detector or not, which in turn would kill the cat or not.  Rather or not the cat is a consciousness is a much deeper discussion that we won’t address here.  Instead for now we’ll just say that for the purposes of this experiment we’ll consider the cat to NOT be a consciousness, meaning it won’t collapse the wave function.

Here’s what this means.  When that half of the small box is opened there is no electron.  Since there is no actual electron, the electron detector can’t possibly trigger.  At this point we only have a quantum wave in both halves of the small box and now filling the large box (with the cat) as well.

If you open the door to this large box and “observe” the results then all of the wave functions collapse.  This means that in the instant you observe, the electron “pops” into existence.  If it popped into the still sealed portion of the small box, then the cat is still alive.  If it popped into the open side of the small box or somewhere in the room then the detector would have wen’t off, and therefore the cat will be dead.

It’s difficult for us to wrap our heads around this without thinking that the cat was already dead or alive before we opened the door.  I mean, even if it wasn’t dead, it had to be alive right?  Let’s assume we don’t open this large room for a year.  We open the door and the cat is dead, but it obviously didn’t JUST die, it has decomposed and is nothing but a skeleton, so it had to have been dead all along right?

Schrodinger's Cat

Not according to quantum mechanics.  Yes, I know, it’s hard to try to imagine this.  What happened here was that the cat was in a state of superposition.  Meaning it was BOTH alive and dead at the same time.  This idea or concept, that the cat was both alive and dead at the same time is exactly what Schrodinger was trying to prove was ridiculous.  That it just wasn’t possible.

But we now know that in the quantum world superposition is absolutely possible.  Not only that, but superposition is the exact thing that allows quantum computers to work.  It’s what makes them so powerful.  The power behind them is something called a qubit.  A qubit isn’t on or off, or a 1 or 0 in the classical sense.  Instead a qubit can be both on and off, or a 1 and a 0 at the same time.  Superposition is a fragile state.  As soon as it’s observed the superposition collapses.  So before collapse it can contain various probabilities about which state it will be in when it does collapse.

As difficult as this is to wrap your head around, there is one concept that tries to explain it.  That’s the concept of having multiple universes, or a multiverse.  That’s a discussion for another day, but in the mean time here’s the easy way to think of it.  When you do the experiment above and push the “Go” button, the first box is divided.  This creates a split in our universe.  In one universe the electron is trapped in the sealed off portion of the box.  In the other universe the electron is trapped in the section of the box that then gets opened.  The box is then opened in both of these split off universes.  In one of them the electron detector never goes off and the cat is alive.  In the other universe the poison kills the cat.  So technically speaking the cat isn’t both alive and dead at the same time, it’s just that now there are two cats, one alive and one dead, each living in their own separate distinct universes.

What the probability waves describe in this instance is which one of these “universes” you would “jump to” when you open the door and look in.  Because the moment you do, you’re not actually collapsing the wave function at all, you’re simply just jumping into one universe or the other.

This means that every non-deterministic event creates split universes, or that all of these universes already exist where every possibility has happened, which means you are just “riding the wave” so to speak, following the branches from one universe to another.  You still have choice, you still have free will since every possible outcome already exists.  Each decision and outcome that changes which branch you follow simply leads to a new set of branches to follow and so on and so on.

We’re quite far down the rabbit hole now.  I think Neils Bohr said it best:

Niels Bohr

Hopefully you yourself are starting to understand it now.  There’s no turning back now.  We have a lunch date with the Mad Hatter after all!

Now lets take a break from the quantum side of things and let some of the knowledge you’ve gained find rest.  We’ll get back to the physics soon, but for now we’re going to switch gears to the Buddhism side of things and learn how to sit Zazen.

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