American Physicist, and Nobel Laureate, Richard Feynman once said, “if you think you understand
quantum mechanics, you don’t understand quantum mechanics.” Quantum mechanics is
famously difficult.
Perhaps it’s difficult because it is so weird. The behavior of objects at quantum
scales is not intuitive. Our observations at the macro scale have conditioned us to
believe that objects should look and behave in certain ways. And these ways are not at
all how things are at the quantum scale.
So for example, what we call particles like protons, electrons, photons, and even atoms
are not like little marbles, they are fuzzy and non-discrete. Their positions and other
properties can seemingly only be expressed in terms of probabilities. Their properties
are uncertain. Measurement appears to make a difference in how they behave.
Why don’t we see this weird behavior for large objects like tennis balls?
How does the fuzziness of quantum objects transform into the solid and predictable macro
objects that we can see with our eyes?
Well, this is controversial, and in fact there is no consensus agreement. There are various
interpretations of what actually happens in the transition from quantum to macro scale.
In a prior video, I explained how two popular interpretations of quantum mechanics, the
Copenhagen and Many Worlds work. In this video, I’m going to take a look
at some of the more uncommon, and maybe even crazy interpretations. But keep in mind that
just because they are not common or sound crazy, it doesn’t mean that they are no
good.
Quantum mechanics itself is so crazy, that maybe we need one of these crazy theories
to explain it. So what are some of these unconventional theories. And why am I wearing this cap?
That and more is coming up right now!
Before I get into some of the amazing interpretations of quantum mechanics, I’d like to thank
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Now back to our subject. In the standard or Copenhagen interpretation, which is what is
typically taught to undergraduate students, particles are in a superposition. This means
that they are fuzzy. Their properties including location exist in multiple states at the same
time. We can only know the probability of finding its location and other properties,
if we were to measure it.
You might ask, what does superposition really mean? In quantum mechanics, there is no equation
that states exactly what some properties of a particle are.
These properties are expressed in something called a wave function which is part of the
Schrodinger equation, given by the Greek symbol psi.
Psi is a mathematical expression which describes the shape of what looks like a wave. It can
contain various properties of the particle, such as its location, velocity, angular momentum
etc. And psi evolves with time.
It turns out that even the time-independent form of the Schrodinger equation has a psi
function, and thus, probabalistic behavior.
But this fuzziness doesn’t fit with our observations because when we measure the particle
with an instrument, we CAN find its properties such as its location, to a good approximation.
So in order to reconcile the mathematics with observed measurement, Bohr and Heisenberg
interpreted the mathematics of quantum mechanics to mean that particles really are waves, and
have multiple properties, such as location at the same time, until they are measured.
This state of multiple properties at once is called superposition. This is where the
metaphor of the cat being dead and alive at the same time in the Schrodinger’s cat
experiment comes from.
One more point is that psi on its own has no physical meaning, but psi squared does
– it is the probability of finding a particle in a certain state, such as its location,
when measured.
This is the standard or Copenhagen interpretation. And if you buy it, then quantum mechanics
is inherently nondeterministic because we can never know the location or other property
of a particle in advance of measuring it. This measurement is thought to collapse the
wave such that the particle becomes discrete and localized, for example its measured location
becomes known.
It is important to keep in mind, that in this interpretation, the wave is not a physical
wave. it is simply a mathematical way to figure out the probability of finding a particle
in a certain state.
This is in contrast to DeBroglie-Bohm or pilot wave theory, named after Louis de Broglie
and David Bohm. It is also referred to as Bohmian mechanics.
This theory describes the wave function as real physical waves that push read particles
around. In other words, the particle and the wave are both real and discrete physical entities,
unlike standard quantum mechanics, where particles and waves are considered to be the same entities,
that is wave–particle duality. That is not the case in pilot wave theory.
The particles are real and have a position the whole time. They are just being guided
by the wave function which evolves according to the Schrodinger equation. Because the particles
are real and have a real position, this theory unlike Copenhagen, is completely deterministic, in
principle. The wave provides a set of potential trajectories, but the particle takes only
one trajectory.
It eliminates the measurement problem because the particles have a definite position at
all times. So no collapse occurs because there is no superposition to begin with.
How the wave guides the particle is described by a new equation that is introduced to accompany
the standard Schrödinger equation.
This is called the “guiding equation.” This describes the actual configuration over
time of the particle even when its unobserved. In other words, it pilots the wave. Q collectively
describes the positions of all the particles in the quantum system. And this expression
describes the change in position, or velocities of the particles in terms of the wave function
Some scientists say this adds needless complexity and new physics. But the guiding equation
has the wave function in it, so it is not completely new.
In this scenario, the trajectory of a particle only appears random because we don’t know
its initial starting point. But if we did, we could potentially predict where the particle
would be at all times, and where it will end up. So the uncertainty in this scenario is
due to our inability to measure the particle’s initial state, not because the particle’s
position is inherently unknowable. This is a departure from the Standard Copenhagen interpretation,
where randomness is part of reality.
The position and velocity of the particle are hidden variables. And they are needed
for this theory to work.
Now, you might say, but I thought Bell’s inequality rules out hidden variables in quantum
mechanics. It rules out only local hidden variables. Pilot wave theory is a non-local
hidden variable theory. Ok, so what is a non-local hidden variable?
Let’s take the example of a tennis ball. If I wanted to measure its mass, position,
or velocity, I would need to measure it at the tennis ball. I could not measure the air
around it to find the mass or position of the tennis ball. So the hidden variables of
the tennis ball are located at the tennis ball. That is a local hidden variable.
Bohmian mechanics does not quite work that way. A particle’s properties are not entirely
located at the particle. It’s position and velocity depends on the configuration of the
system given by the wave function.
But the wave function extends to all of space. In other words, these variables are distributed
throughout the entire universe, not just at the particle. This may sound incredible, but
it allows Bell’s inequality to hold, and so pilot waves cannot be ruled out based Bell’s
inequality.
But this presents a problem because it means that the configuration of the wave function
in a distant parts of the universe can simultaneously affect each other. This instant communication
is in direct violation of special relativity which shows that no faster than light communication
can take place.
In addition, simultaneity doesn’t really exist in relativity, because it depends on
your choice of coordinates.
Because this theory violates special relativity and rejects the idea of superposition, it
is not compatible with the best current theory of physics – which is quantum field theory
or QFT. I made a video about QFT if you want to check it out. QFT requires all possible
paths (or superposition) to be equally real.
In pilot wave, the particle takes only one path. There is no superposition. This is one
of the biggest reasons many physicist don’t support pilot wave theory.
But this theory has several other problems. Another problem is that real waves are pushing
real particles around. But the particles don’t push back. The wave function has to evolve
autonomously.
This is in direct violation of Newton’s third law, which is that for every action
there is an equal and opposite reaction.
You might also think that this theory can’t explain the double slit experiment, which
shows that particles act like waves when not measured, but act like classical particles
when measured.
This was actually explained by Bohm and others. They said that the particles goes through
only one of the slits, but the wave function is defined at both slits. So the pilot waves
end up looking like this. The particle takes only one trajectory.
But when you place a measuring instrument, the instrument creates an interference of
the waves ruining their quantum behavior. And this causes the particles to just follow
classical trajectories. So the results are the same as in standard quantum mechanics.
Thomas Bohr, grandson of Niels Bohr makes a good point. He says, while this theory restores
one classical element – real particles being pushed by real waves, it creates a new mystery
- how or why a mathematical wave function that’s spread everywhere in space is bolted
in certain places to physical particles.
Now, why don’t we just make some measurements and figure out if this theory is correct?
Well, this is another problem because the wave follows the Schrodinger equation. So
the results using pilot wave theory are identical to the results using the Copenhagen interpretation.
So no experimental consequences can be drawn from Bohmian mechanics that can’t also be
drawn the Copenhagen interpretation. In that sense, pilot wave theory does not add anything
to quantum mechanics other than reframing reality.
So it’s a matter of taste what you prefer. Are there any other better theories out there?
There is no perfect theory.
One intriguing theory is by 2020 Nobel laureate Roger Penrose, called induced collapse, where
he proposes a relationship between quantum mechanics and general relativity.
His logic is like this: since superposition requires particles to be in multiple positions
at the same time, and since particles have energy, this energy would create a bending
of space time according to general relativity. For example, if a relatively large mass particle
is in two locations at the same time, each one should create its own
gravitational field, yielding two superposed gravitational fields. According to Penrose,
it takes energy to sustain these dual fields. The higher the energy required to sustain
a system, the less stable it is. Higher mass objects would tend to revert to a lower energy
state of one particle with one gravitational field.
In other words, the superposition collapses when the space-time curvature reaches some
significant threshold. So what is this significant gravitational threshold? According to Penrose,
that is about one Planck mass or 2.1 x 10^-8 kg -- about 1% the mass of a mosquito. This
would explain why large objects are not in superposition, and we never see them as such
in our macro scale.
In this theory observers play no special role. The wave collapses depending on its energy,
regardless of observation, decoherence or anything else. The nice thing is that it can
be tested. If we can show a transition from quantum state to classical state at the Planck
mass scale, it would be strong evidence to support this theory.
Now here’s one of the craziest but most intriguing theories, in my opinion. It’s
called the transactional interpretation initially developed by John Cramer in 1986. It is non-local
and treats waves as being physically real.
It proposes that future events can have a retro-causal link explaining the correlation
between the particle properties and the measurements yet to be performed on them. This means that
later events can cause earlier events—that causation can operate backwards in time as
well as forwards in time.
Imagine a measuring device emitting a wave forward in time to an absorbing particle.
The absorber transmits a wave backward in time to the emitter. The backward traveling
wave can transmit information about measurements yet to be performed on a system. These two waves when
combined perform a transaction. This transaction looks like a spontaneous collapse of the wave
function. But because all this is retro causal, this theory argues that the wave function
never really existed in its pre collapsed state.
The retrocausal approach allows correlations between distant events like entanglement
to be explained without instantaneous action at a distance, since a combination of forward
causal links and retrocausal links can influence simultaneous distant events.
In fact, if you extrapolate this idea to the entire universe, and all of time, you can
argue that all backward travelling and forward travelling waves evolve to a single reality
that we experience in the present.
Unfortunately, this interpretation doesn’t generate any new predictions. It gives the
same results as the Copenhagen interpretation, so is not testable.
You might say all of these theories could be wrong, and you might be right, because
all appear to be incomplete.
But just because we do not have a perfect theory, it does not mean that quantum mechanics
is incorrect. That is absolutely not the case. Quantum mechanics is still arguably the most
successful and accurate theory of nature we have ever had. We just don’t really understand
how it works at a fundamental level.
And that’s ok…because scientists are energized by challenges, and future geniuses will figure
this out.
So let me first answer the question that is foremost on your mind. Why am I wearing this
cap? Well, remember that patch of hair on top of my head that so many of you were annoyed
by? Well, it’s actually a discoloration of the skin called Seborrheic Keratosis.
I didn’t know that it could be surgically removed until recently, so that’s what I
had done. I thought I would save you the eyesore of seeing a huge bandage on the top of my head.
But it has to be to be on there for the next one to two months, so you’ll be seeing this look for
the next few videos.
I’d like to thank my generous supporters on Patreon and Youtube. If you like my videos,
consider joining them. And if you have a question, post them in the comments below
And I will try to answer it.
I will see you in the next video my friend!