"The
more I think of the physical part of the Schrödinger theory, the more detestable I find
it. What Schrödinger writes about visualization makes scarcely any sense, in other words
I think it is sh...... The greatest result of his theory is the calculation of matrix
elements."
Werner Heisenberg (8 June 1926)
At the mid 1920’s, there was an almost unknown
young physicist, an Austrian named Erwin Schrödinger who was trying to develop a general wave
mechanics theory to describe observation on the quantum level.
As it turned out now, this wave
mechanics was nothing but Heisenberg’s matrix mechanics other side of the coin.( Paul
Dirac unified the two mechanics into quantum mechanics.)
Schrödinger
developed what is known as Schrödinger equation. This equation states that there is a
wave associated with any particle (like the electron), and it is called the wavefunction
and it is spread out to fill the whole universe. The wave function is
stronger in one region, which corresponds to the position of the particle
and gets weaker farther away from this region but still exists even far away from the
“position” of the particle. Schrödinger equation is very good at predicting
how particles like electrons behave under different circumstances.
But there is a catch
… and a weird… very weird one, and that is when we make a measurement. When we
look at an electron, or measure it with a particle detector, the wave function is said to
“collapse”. At that instant, the position of the electron is known to within the
accuracy allowed by the fundamental laws. But as soon as we stop looking, the wave
function spreads out again and interferes with the wave functions of other electrons- and,
under the right circumstances with itself. (See
the two-slit experiment with electrons)
All of this is precisely quantifiable
mathematically and makes it possible to calculate how electrons fly into atoms, how atoms
combine to make molecules, and much more besides.
What does all of that mean in plain English?
It means:
There is a fortune
teller lady called Schrödinger equation who can predict and describe precisely and
deterministically the quantum state of the particle.
However, if you doubt in her ability and
decide to check on her by making a “measurement”, somehow she knows that you
want to check on her. She gets really mad and wild even before you or her knows the
outcome of the “measurement”. At that time
lady
Schrödinger equation transforms herself into a
“probabilistic fortune teller”, and all what she can tell you are probabilities
of various outcomes of your “measurements”.
When you “know” the result of your
“measurements”, the weird lady Schrödinger equation gets really crazy and
“collapses” or “jumps”. But does she collapse and disappear or jump to
a very far place? No, she jumps to the new quantum state which was revealed by your
“measurement”, as she is very keen to stay with you so you can ask her again to
predict the quantum state until you make the next “measurement”, and so on.
So actually collapse of
the wave function is equivalent to saying that we can know where things are, only when we
are actually looking at them. Blink and they are gone!
Lady “ Schrödinger equation” tells us too that particles are like
shy people. Their behavior depends on whether or not we are looking at them.
Born's Probability Interpretation
Max Born, the famous German
physicist took Schrödinger's work a step further. While studying how quantum mechanics
describes collisions between particles, he realized that the intensity of the-Schrödinger
wave was a measure of the probability of finding the particle at each point in space. In
other words, a measurement would always find a whole particle, rather than a fraction of
one, but in regions where the wave intensity was low, the particle would rarely be found,
whereas in regions of high intensity, the particle would often be found.