Quantum Mechanics is the theory about everything small.
How small? We'll get to that in a bit but the purpose of this post is to bring to light how strikingly different the constituents of the Quantum World are.
I think most of you have experience with the name electron. It is an elementary particle which was discovered at the start of the 20th century. Since then, there have been great experiments in particle physics which actually confirm the existence of something attached to an electron called the spin. Spin is a property inherent to an electron and only ever has two possible values in which it can be. Any attempt to attach an analogy with our normal world would kind of defeat the purpose; but still, you may think of it as gender. Spin is the gender, the electron is the person. Generally a person has one specific gender - male or female. Everyone does have one but never both. Although it is not an accurate picture (because the electron spin may juggle in between the two values) but it may suffice for an analogy, at the least. Let us bring in our spin and electrons then.
Let's proceed with our discussion further with something that we all are familiar with. A coin toss. The toss of a coin is a system - something which we can observe and predict the results of. It always shows us a head or a tail, regardless of the fact that how many times we throw it (the coin does not stand upright very often, so please no arguments here!). To see what the outcome for our unbiased coin was, we'll measure it once it falls on our hands or stops falling down.
One thing to note here is that the coin is always in one of the two possible states, heads or tails. Nothing else. Let's do something like that for our spin. We associate something called "degree of freedom" with the electron spin. It just means allowing or confining the spin to exist within certain possibilities.
For now, assume that those values are +1 and -1. These values are actually determined experimentally and what they represent can be thought of as the direction of the spin - whatever that is. (the experiment which does associate it with these orientations is reserved for another post!)
Before we go into the experiments let's understand something else too. We know that seeing or observing in our day to day lives is a trivial task. A car goes by us, the light bouncing off of that car falls into our eyes, forms an image on our retina, our brain processes it and we see the car.
All the above workings are taken for granted in the normal world as ,of course, the change produced by that light is infinitesimally small as compared to the size of the car which it is observing. We observe the car "as is". But what if we tried the same with the electron while measuring its spin? We will need an apparatus for that, something which can report to us if it detects the spin up or down. Think of it like our eyes, only much much more sensitive. For our purposes it is a black box and comes with a "this way up" sign for finding out its orientation. Let us bring in our apparatus.
Let us say we have our spin existing in some state. We keep our apparatus along "this way up" and measure it. Suppose we get the value +1. Alright. Let us again do a measurement without altering our apparatus' orientation. We again get +1. So far so good. This is like that first interaction prepares the state and the second one confirms it. Let us now flip our apparatus upside down and measure with it again. We get a -1. Okay. It seems like +1 is up and -1 is down. Fairly straightforward till now. It feels as if the spin is totally in either the "this way up" direction or opposite to it entirely.
Now imagine we rotate it by 90 degrees and see what happens.
+1. Seems strange. Let's do again. -1. Again , +1.-1.-1.+1.
Shouldn't we get 0 pertaining to our assumptions that +1 and -1 represented directions of spin pointing up or down? Because if something is pointing up or down, how can it also point right or left? It is kind of like saying that we place a glass upright and noted that it was upright with our head straight. Now if we tilt our head, the glass tilts with us too! That is indeed very mysterious. A stranger thing is that if we now rotate our apparatus in the z direction and measure it, it is not +1! It is random and comes out as +1 or -1.
Let us investigate further by repeating this experiment. We keep on doing these 3 steps -
Prepare the spin in +1 state by measuring it along z axis
Rotate the apparatus along the x axis
Measure the spin along x axis
Although we get a random series of +1s and -1s, something expected happens.
As the number of experiments goes on increasing, the average value of our experiment approaches 0 - the classical or the normal expectation. In other words the +1s and -1s add up to cancel each other out.
Now we see something familiar coming up in this strange world. Determinism broke down for one experiment but not on average. We still get the expected value as 0, just in a larger number of experiments, not individually. What this implies is that quantum world is as we expect it to be, on average.
But we are not confined to move the apparatus by 90 degrees or keep it initially in the upright z direction. For those of you who know a little bit about vectors, if we start with our apparatus pointing in any direction determined by unit vector n , prepare our spin and rotate it to point in the direction of unit vector m and then measure; the average value is actually equal to +/-n.m where . represents the dot product of the two vectors. The sign of the product is determined by the fact that whether we prepared our initial state as +1 or the -1. This is the general case for our experiments and has been indeed observed in real life.
So far then we have seen that the quantum spin is a strange little fella which does not behave as we expected it to behave but does not disappoint if we stick with it long enough! What we can derive from the above experiments is two things.
First is the fact that experiments are not gentle. An apparatus must interact with the system in order to record a result. Every experiment is invasive and quantum world makes a big deal out of it. Why? The below statement is the most accurate description of that :
"Any experiment strong enough to measure the state of a system is also strong enough to change it"
This is actually highlighted by the following experiment. Say you prepared your spin in the +1 state by measuring along z axis, rotated it 90 degrees and measured it along x axis. From above reasonings we can say that the x axis measurement is going to be random but what if you rotate the apparatus back to the z direction and measure the spin again? What you will notice is that the result is again random because the act of measuring spin in x direction leaves the spin in a totally random orientation along the z direction.
The second thing to note is that this world is probabilistic. What I mean to say is the outcomes of our experiments coincide with the normal expectations on average but not discretely or individually. This is also a reason why many people call it a probabilistic theory.
At this point of the article I think you also feel as confused, curious and excited as I was while first learning about this strange little world and I hope that you'll stick around for more of it to be revealed. Till then, keep on thinking...
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