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Until about 1900, all we had was classical mechanics. This is the mechanics of Isaac Newton
and James Clerk Maxwell. But after 1900, Max Planck ushered in an era of quantum mechanics.
And it explained the various anomalies in classical mechanics, such as why electrons
do not radiate energy and fall into the nucleus, as they should according to Maxwell’s equations.
Since that time, Quantum mechanics has become one the most proven and successful theories in
all of science. But, while equations such as the Schrodinger equation are
superb at making predictions and explaining behavior at quantum scales, when you start
asking the question. "what is actually going on," this is where the controversy starts.
Caltech physicist Sean Carroll says quantum physicists are like people with iPhones.
They know how to use it, and can do some great things with it, but if you ask them what
goes on inside their iPhones, they have no idea. Similarly, he says, physicists know
how to use the equations of quantum mechanics to predict all kinds of things, but ask them
how quantum mechanics actually works, and if they are honest, they will say they really don’t know.
But this hasn’t stopped physicists from speculating what the mechanism is.
These various speculations are known as interpretations of quantum mechanics.
The standard interpretation is called the Copenhagen interpretation because
if was devised in Copenhagen, Denmark by mainly Niels Bohr
and Werner Heisenberg in the 1920s. This is the interpretation taught to most students in college.
But even a majority of physicists do not agree that this is the correct interpretation. In fact,
there is no single interpretation that has a consensus agreement.
So what is the Copenhagen interpretation? What are
the best alternatives interpretations? Why do we even need an interpretation to begin with?
Those are some great questions, which I will attempt to answer…coming up right now.
The primary challenge of understanding quantum mechanics is that according to the equations,
all particles exist in a state of superposition. That is to say, that the properties of any quantum
particle such as its position, momentum, spin etc. is not only unknown, but is unknowable
until it is measured. In fact, before it is measured, the particle is said to be
in many states at once. It is not here OR there, it is here AND there at the same
time. It is not spin up OR spin down, it is spin up AND spin down at the same time.
This sounds crazy from our classical mechanics perspective
because we never experience large objects being in super position. When you hold a tennis ball,
you know exactly where it is and how fast it’s moving. So, the quantum
mechanical behavior predicted by quantum mechanics does not seem to fit with our world view.
One of the biggest challenges of quantum mechanics is trying to explain this transition from what
is thought to be the behavior of objects at quantum scales – superposition of multiple states
vs. their classical behavior upon measurement.
The various interpretations of quantum mechanics
can be thought of as attempts to explain this transition.
Most interpretations of quantum mechanics focus on the Schrodinger equation and the wavefunction
to explain quantum behavior. This equation was developed by Irish-Austrian physicist
Erwin Schrodinger in 1926. It contains a wave function, represented by the Greek letter psi.
German physicist Max Born formulated the interpretation of psi,
which is that the square of the absolute value of psi represents
the probability of finding a particle in any one particular state if we were to measure it.
The concept of measurement was introduced to
explain what we actually see when we make an observation.
The fact is that even if it were possible for us to directly observe quantum particles,
we would never see them being in superposition, we would only observe them being in one state or
another. We would only see the spin as up or down, not up and down.
Presumably, our observation acts like a measurement that destroys the super position.
To give you an intuitive feel, let’s look at some of the interpretations
in terms of the famous Schrodinger’s cat experiment.
This is a thought experiment proposed by Erwin Schrodinger to illustrate,
ironically, what he felt was the absurdity of assigning probabilities using his own equation.
In this thought experiment, we have a box. There are 4 things in the box. There is a cat,
a radioactive source – the emission of radiation is completely random according
to most theories of quantum mechanics, so this is the source of quantum mechanical randomness.
There is a radiation detector attached to a hammer, and a vial of poison gas like cyanide.
If the detector detects radiation, the hammer comes down and will smash the vial of gas and
the cat will die. If it doesn’t detect radiation, no gas is released and the cat will stay alive.
If we look at this from the quantum mechanical point of view, there are two possibilities for the
wave function of this system. If we presume that the quantum system consists of the just the cat,
prior to measurement, the wavefunction of the cat will look something like this:
Where the wave function describes the superposition of the cat being alive and dead.
We have one over the square root of two because there are two probabilities and the square of each
probability will be one half, and thus added together the total probabilities will be one.
The wave function always shows that the sum of all probabilities will equal one.
In the standard, or Copenhagen interpretation, as soon as you open the box and make an observation,
one of the probabilities comes true, and the other probability disappears.
So let’s say you observe the cat being alive,
that probability is now 100%. And the other probability of the cat being dead becomes zero,
so that probability goes away. This is called wave function collapse,
meaning the wave function has collapsed to one state – based on the 50/50 probability.
The wave function collapses as the result of a measurement
by an observer or apparatus external to the quantum system. A measurement is simply
an interaction of the quantum system with a classical system. In this case
it is you the observer opening the box and measuring whether the cat is alive or dead.
The problem with this interpretation is that it sets two set of rules for how particles
behave – one for before measurement, and one after measurement. But it doesn’t explain
how this transition happens. This is often characterized as the measurement problem.
Why did the other probability go away. What is the mechanism that collapsed the wave function?
Bohr might have said, well, it just fits the data. The data is that we observe only one event,
so all the other events that we could have observed no longer exist. We are just interpreting
quantum mechanics based on the data that we can plainly see. Don’t ask me how or why this happens.
Or you can say what Richard Feynman said when asked the question, “Just shut up and calculate.”
This is just not very satisfying because we, and, I won’t speak for you, but at least I,
need to know what’s really going on.
A popular alternative, the many worlds interpretation of the same event would be
that no collapse occurs. The wave function is the only true nature of reality. It never goes away.
This interpretation was formulated by Hugh Everett in 1957 as a graduate student at
Princeton University. And the followers of this interpretation, sometimes referred to as
Everettians, say that this is the simplest and most basic interpretation of quantum mechanics
because it introduces no other assumptions or equations, other than the Schrodinger equation.
In our cat analogy, the distinction that the many worlds interpretation makes vs. the
Copenhagen interpretation is that it says, hey, you as the observer are also a quantum system,
and you are entangled with the cat. So the wave function includes
more than the cat. It also includes you, the observer. It would look more like this,
where one part of the wave function is that the cat is alive, and you observe it as such,
and the other part where the cat is dead and you observe it dead:
That is one wave function. When you opened the box, the reality that you observed,
where the cat is alive, is but one world. However,
there is another world in which you would have found the cat to be dead.
Both worlds where you found the cat alive and where you found the cat dead exist.
You just happen to find yourself in one of them. So the question is why do we find ourselves
in the one branch where the cat is alive, and not the other one?
Everettians argue that other versions of ourselves in the other worlds are asking the same question.
You just happen to be asking it in the world you find yourself in.
Every universe is equally ‘real’ to those living in it.
To embrace this interpretation, you have to accept that many,
perhaps infinite, worlds exist, all with different quantum outcomes.
The problem is that
this does not seem to fit with our experience, because
we have no inkling of the other versions of ourselves. Where are the other ones?
If we really are entangled with the cat,
then shouldn’t some part of me feel like I saw the cat alive as well as dead?
But this never happens. There is never a world where I see the cat both dead and alive,
where half of me saw the cat alive, and the other half saw the cat dead.
So how does the split of the worlds occur? Everettians say it is due to decoherence.
So what the heck is decoherence? Quantum decoherence is the physical process
that is used to describe how quantum states transition to the one state that we experience.
The Copenhagen interpretation treats wave function collapse as a fundamental process
without explaining the details of how it happens. Decoherence attempts to explain what appears to be
like wave function collapse, but in MWI-speak,
it is a splitting of worlds. No wave collapse actually occurs.
If the universe was composed of only you and the cat and nothing else, then you and the
cat would be in a coherent superposition. This would be represented by our original
equation here:
The key realization is that in reality, you have more than just you and the cat entangled.
Both you and the cat will also be entangled with your environment because THAT is also
a quantum system. So, for example, the cat will be entangled with what’s inside the box,
atoms of air, photons from black body radiation, etc.
All these objects will be entangled with the cat. And you will also be
entangled with your environment. The environment inside the box for a cat
that is alive will be different than the environment for a cat that is dead.
Why? Because a dead cat’s interaction with the air molecules and photons will be different,
not only because it’s position will likely be different, but also other factors such as
heat produced etc. So Psi now looks like this, where there is an added component of the cat
and you being entangled with environment 1 in one case, and environment 2 in the other case:
These two environments are completely different.
Because the entanglement with the environment now enters the picture,
the coherent superpositon between you and the cat is broken.
The Schrodinger equation says that the two parts of the wave function above are perpendicular to
each other, that have no connection to each other. This can be interpreted as two separate worlds.
It is as if the universe splits into two separate realities. This is decoherence.
Decoherence is another way of explaining how quantum superposition gets lost, by interaction
with the environment. You can also think of this as the quantum nature of the original 2 component
system leaking information into the environment due to it entanglement with the environment. I
made a video about information leak using tennis balls, if you want to check it out here.
The problem is that since there is no overlap between the branching wave functions,
no communication or connection between the worlds exists. So it is unclear whether we
could ever verify whether the other worlds exist. The only evidence is
the mathematics of the Schrodinger equation. An experimental verification may not be possible.
Now if the idea of quantum superposition and randomness makes you uncomfortable,
I want you to relax because there are completely deterministic interpretations as well.
One is the de Broglie-Bohm, or pilot wave theory, also known as Bohmian mechanics.
Another fascinating theory I like is an Objective collapse theory by Roger Penrose,
who combines principles from general relativity with quantum mechanics.
And these two, along with some other crazy interpretation will be the subject of my next
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