Quantum mechanics is one of the most successful theories in all of science.
Using its mathematical equations, scientists can accurately predict how tiny particles
like photons of light, and electrons in electrical currents behave.
It can be used to explain everything from the atomic structure of the elements,
to the shapes of molecules to the cosmic structure of the universe.
But amid all its useful equations and accurate predictions, a troubling question remains.
Although Quantum mechanics clearly works, what does it mean?
What is it telling us about the true nature of reality, the way the universe actually is?
The rules at the level of atoms and subatomic particles
seem to be different from the ones we’re used to in our everyday experience.
They seem weird. For example, particles appear to be fuzzy and spread out.
They seem to be in two places at once, or two different states at once,
or affect each other instantly over any distance.
But is that really what quantum mechanics says?
All these claims are no more than clumsy attempts to interpret the theory using everyday language.
But everyday language wasn’t designed for the quantum world.
It was designed for the macro world of classical physics, which is what we observe at human scales.
Here, objects can be seen and touched and watched as they follow
predictable paths in space, at precise speeds that we can measure.
Surprisingly for such a well established and accurate theory as quantum mechanics,
there is still no consensus on what it really means.
Physicists differ in what they think quantum theory tells us about the world.
Some think it’s every bit as concrete and definite as our classical world.
Some see a multiverse where all possibilities exist. For others,
quantum mechanics sets an ultimate limit on how much we can really know about reality.
If you hear an expert insist that they know what it means,
be cautious! In this video I’ll tell you why it’s so hard to be sure of the answer,
but also what we can say for sure about it. That’s coming up…right now.
Many things inspired me to make this video, but one documentary which really influenced
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If we want to understand quantum mechanics, we have to start with the math
because that’s where the heart of the theory lies.
But don’t worry, I’m not going to derive any equations, just describe them.
Arguably, the most important quantum equation was figured out in the mid-1920s
by Austrian physicist Erwin Schrödinger.
He was picking up on the suggestion of French scientist Louis de Broglie
that maybe quantum particles can behave like waves.
Schrodinger came up with an equation to describe this waviness, and it looked a
lot like the equations scientists had used to describe ordinary waves, like those in water.
This equation may look complicated, but at it’s heart it is just an equation
describing energy. kinetic energy plus potential energy equals total energy.
It includes a mathematical function called the wave function, which encapsulates all that can
be known about a quantum object like an electron or atom, or even a molecule.
The object’s wave function, usually written as the Greek symbol , has a particular value at
all points in space. And this value depends on the state that the quantum object is in.
For a single quantum particle for example in a square box,
the wave function of the lowest-energy state has a single peak in the middle.
If you know the wave function, Schrödinger’s equation lets you figure out, for example,
where you’ll find the particle in space, or how fast it is travelling, or how much energy it has.
But what is the wave function? That’s the key question we need to answer to
understand what quantum mechanics is telling us about the world. In some ways, pretty much
all the arguments that still rage about this question boils down to disagreements
about what a wave function really is. If we plot out a typical wave function
for a particle, it looks a bit like a wave. But a wave of what?
For example, a water wave is made of water molecules. But a wave function for a quantum
object isn’t really made of any substance other than information about the object.
The amplitude of a water wave is simply the height of the wave.
The amplitude of a wave function is simply its value at any point.
In addition, the amplitude of a quantum wave function is generally a complex number,
which means that it contains some term that is an imaginary number,
which is the squre root of a negative number. It’s not a whole number like 1, 2, 3 and so on.
What does imaginary number mean? Well, it’s not a physically meaningful quantity.
But they are useful in simplifying the mathematics of anything that oscillates.
But when we square an imaginary number we get a real number. So the square of the wave function,
the value of psi squared, becomes a real number. This has no imaginary
component, and so it can correspond to the value of some real, measurable quantity.
At first, Schrödinger himself thought that the value of psi squared
at any point in space tells us what the density of the quantum object,
like an electron, is at that point. In other words, maybe the particle really is smeared out,
almost like a cloud of gas, with different densities in different places. But he was wrong.
German physicist Max Born said that the square of the wave function isn’t
the density of the particle. Instead, it’s a probability.
It tells us the probability that we’ll find the particle at that point in space – if we look.
If we add up psi squared for EVERY point in space, it will equal 1 – meaning that,
if we look everywhere, we’re bound to find the particle some where.
Born’s rule is at the heart of why quantum mechanics is such a peculiar theory,
and why it’s so hard to say what it means. Compare it to what we find in classical physics.
The equivalent of Schrödinger’s equation is an
equation of motion – like the one that describes the path of a basketball.
We can use Newton’s laws of motion to write down a mathematical expression for its trajectory,
and use it to calculate exactly where the ball will be at each moment in time.
There are no probabilities, no ambiguity. We can say for sure
that if we look at one particular point in space at a particular time, we’ll find the ball there.
If we look elsewhere in space at that moment, we know that we won’t find the ball there.
But a wave function says that, for a quantum object, we might find the object
at many different places in space at any given instant, with various probabilities.
We can never be sure which of these it will be in.
And in fact if we can measure several different particles with the same wave
function in successive experiments, we’re likely to find it at different places each time.
The wave function itself can change over time – rising and falling like an ordinary wave, but
this simply changes the probabilities of finding the particle at different places for each instant.
As the physicist Roland Omnès has put it,
the wave function is “the fuel of a machine that manufactures probabilities.”
Now here’s what’s particularly perplexing. You might think that the wave function tells
us where the particle probably is at any point in time. But it doesn’t tell us that.
It tells us, as I said earlier, only the chance of finding it there if we look.
What if we don’t look? Well, then, all we have to go by is the wave function itself,
which says nothing about where the particle is. It only lets us figure out the probabilities of where
we’d find it, if we looked there, or made a measurement of some sort.
It’s often said the wave function implies that, until we look,
the particle is everywhere – or at least, is smeared out.
But that’s not really right, because Born’s rule doesn’t mean that.
Born’s rule is only about the probabilities
of the outcomes of measurements. This mathematical machinery
tells us not what the quantum world is like, but only what we’ll see of it if we measure it.
So the idea that before we measure it, the particle is everywhere,
is not quite correct. It doesn’t tell us what is, it only tells us what we might expect if we look.
But this also doesn’t mean that nothing exists until we look. A quantum world exists
whether we look or not. It’s just very hard to know exactly
what we can say about it before we look, beyond what its wave function is.
And that’s what is so peculiar about quantum mechanics, because unlike most other scientific
theories, it doesn’t give us a clue about what’s really happening but what we might experience when
we measure things. It says nothing obvious about what quantum reality itself is like.
All we can do is try to find the best story to tell about what’s really happening.
Now, one story from a famous experiment really does look as though
quantum particles can be smeared out. This is the famous double-slit experiment.
Richard Feynman called this the central mystery of quantum mechanics.
The set up of the experiment is something like this.
We fire photons or electrons or any quantum object, one at a time towards two closely
spaced slits, and then place a fluorescent screen on the other side. What we see is a
point-like single flash when an electron hits it after going through the slits.
This appear normal and nothing special. However, if we keep firing
multiple thousands of electrons, one at a time, we begin to see an interference pattern.
This may at first appear to be mysterious. How could single electrons fired one at
a time interfere when no two electrons had the opportunity to interact with each other.
But this really shouldn’t be such a surprise, because it is precisely what quantum mechanics predicts.
It predicts that we should see an interference pattern because
individual electrons are like waves.
It is very much like a water wave. If we sent a a water wave through the slits,
we would see an interference pattern on the other side.
Similarly, individual electrons would behave like a wave that passes through both slits too.
And this wave would split and emerge from each slit to interfere with each another.
You might say, ok then, why don’t we see a wave interference pattern on the fluorescent screen
when we send just one electron through the slits?
The reason is because the particle behaves like a wave as long as we don’t measure it.
But the fluorescent screen acts like a measuring device.
When we measure it at the screen, it takes a particle-like position.
So when electrons hit the screen, they are no longer in superposition.
They lose their quantumness. They take on a point-like appearance because they are
measured. The wave becomes localized to a fuzzy point.
The interference pattern is not visible when an individual electron is measured by the screen. But
if we measure thousands of individual electrons, one at a time, the interference pattern emerges.
This happens because more electrons show up on parts of the screen where
the probability amplitude is higher due to constructive interference of the wave,
and they don’t show up where the probability amplitude has destructive interference.
In other words, because the Schrödinger equation only gives us probabilities,
we have to make many repeated measurements of these individual electrons
to see if what we measure fits with those probabilities. And it always does!
So the double slit experiment should not be a mystery. It shows us exactly what quantum
mechanics predicts – that individual particles have wave-like behavior, which can be seen in
the collective pattern created by shooting lots of particles through the double slit and measured
on the screen. Had we not gotten this result, we would have to rethink quantum mechanics.
So again: what really is the wave function?
Is it just math that lets us predict what we’ll see in a quantum experiment?
Or is it a real, physical object – like an ocean wave – that tells
us about the underlying reality that causes those observations?
Some theories attempt to define the collapse as a real physical process.
To give you a fuller perspective, I invited fellow Youtuber and friend
Sabine Hossenfelder to tell you about these, as well as her favorite theory.
Hi Arvin, I have one thing to add. Quantum mechanics may seem weird to us because it’s
not actually the right theory. This is why some physicists have tried to improve quantum mechanics
by turning the collapse of the wave function into a physical process. This removes the ambiguity
about how to interpret the wave function. It’s a real thing and it really collapses.
There are three major approaches to this at the moment. The probably best known one is Penrose’s
gravitationally induced collapse. The idea is that a superposition of quantum particles
should also come with a superposition of quantum spacetimes. And those, Penrose says,
don’t exist long. So the wavefunction collapses. Another idea is called spontaneous collapse. And the
best known example is the GRW model. In this model, the wavefunction stochastically collapses
a little bit every now and then until it is entirely localized. And then, there is superdeterminism.
Superdeterministic models are also collapse models, but they are not stochastic. Instead,
the apparent randomness of quantum measurements is explained by hidden variables. It’s not much of a
secret that personally, I think Superdeterminism is correct. Thanks for letting me join.
Thank you Sabine. Be sure to check out her channel at the link in the description,
and while you’re there, subscribe for great physics content.
The problem is we can’t really see the wavefunction of a single particle because when
we observe the particle, like when the electron hits the screen in the double slit experiment, its
spread-out wave function seems to collapse to a single sharp spike where we find the particle.
Standard quantum theory, with its Schrödinger equation and smooth wave functions,
doesn’t actually provide any description of the measurement process.
We don’t really know why or how the collapse of the wave function happens.
We have to add in the collapse to the theory in a makeshift sort of way.
It’s even been suggested that our own conscious
awareness of the measurement result somehow alters the wave function.
There’s not really any good reason to think that’s true, though.
The collapse happens whether we are looking at it or not.
How it happens, and what causes it to happen is called “the measurement problem”
and it’s one of the biggest causes of arguments about what quantum mechanics means.
Some researchers say that we can’t deduce anything much about that “underlying reality”.
If all quantum mechanics gives us is probabilities about measurements,
we just have to accept that that’s all we can know.
And who really cares anyway about a question that seems more philosophical than physical,
as long as the theory correctly predicts the outcomes of experiments?
The extreme version of this view was summed up by physicist
David Mermin in the expression “Shut up and calculate.”
And it’s a view that some quantum physicists take today: they don’t want to bother about questions
that lie beyond what we can measure and observe, because that doesn’t seem like science.
They just use the theory to calculate what their molecules or devices will do.
Others go to the opposite extreme. They say that the most fundamental level,
reality really is a wave function.
This view is commonly shared by scientists and philosophers who
believe in the Many Worlds interpretation of quantum mechanics, often called the
Everettian view because it was first proposed by the physicist Hugh Everett in the 1950s.
In this view, the entire universe is a gigantic wave function. And we can probe little bits
of this wave function with our experiments. Because a quantum wave function encodes many
different possible outcomes – all those places in space, for example, that we might observe
a particle to be in, Everettians say that all of these are equally real.
We only observe one outcome, but the measurement also elicits all the other possible outcomes too,
in different worlds or universes. So while you might measure an electron to be in one location
in this world, there are other worlds where you meaure it in a different spot.
We experience just one, because the measurement itself
causes the universal wavefunction to split into separate universes,
where a copy of you measures something else. These worlds are isolated from each other.
Many Worlds is seen by many, who are growing in number,
as the conservative option: the one that adds the least to the bare math of quantum mechanics.
The fact that there are different interpretations of
what might really be happening is unusual for a scientific theory.
It is a frustration that there doesn’t appear to be a good way
to test which interpretation is correct.
Quantum mechanics seems to say that reality works in certain mathematically predictable ways,
but we can never see it working that way, because when be try to see it
by taking a measurement, it seems to work a different way.
And that’s what many scientists find so disturbing – that quantum mechanics doesn’t appear to
show that there is a set reality out there, independent of how we choose to look at it.
That seems to fly in the face of all that we’ve come to believe about science:
that it can tell us about how reality really is, regardless of what we believe.
But this doesn’t mean that an objective reality doesn’t exist. Quantum mechanics gives us a theory
that makes our measurements predictable, and it works the same for everyone, so it is repeatable.
Predictability and repeatability are the hallmarks of an objective reality.
But it appears we are not completely independent of this reality,
since we are also part of the universe that quantum theory describes.
Perhaps quantum mechanics is simply the kind theory we need
to understand a universe of that kind. And if you enjoyed this video, give us a
like and subscribe for a future follow up video on this topic. And if you have a question for me or
our viewers, put it in the comments section. I’ll see you in the next video my friend.