You’re watching this video on a screen that depicts a seemingly continuous picture. This
is however just an illusion. If you look closer at the screen you’ll
see it’s made of tiny individual pixels. But from a distance this collection of pixels
appears as a continuous picture. This is analogous to how our universe appears
classical and continuous, but is fundamentally quantum. It’s made of discrete chunks of
energy as Max Planck famously showed in 1900. Thanks to him we have the famous equation
Where E for example, is the energy of a photon, f is the frequency of the light wave and h
is the proportionality constant that relates these two properties. This equation might
look simple, but it tells us something profound about nature.
It shows how a particle, represented by the energy it carries, is really just a wave packet.
Planck’s constant, h, is like the resolution of this packet of energy. It represents the
smallest amount of energy that any given frequency of waves can carry.
But how can a particle be a wave. What does this mean? And what makes us so sure that
this is the case? That’s coming up right now...
Before we go further, I’d like to recommend a documentary on MagellanTV called “Let
There be Life” And here is the part you’ll love. To show
their appreciation for Arvin Ash viewers, MagellanTV is offering this documentary on
Freeview for the next 7 days. This means that even if you don’t currently have a MagellanTV
membership, you can still stream “Let there be life” absolutely free for the next 7
days starting today.
This documentary demonstrates how the weirdness of quantum mechanics that I talk about in
this video, like the uncertainty principle, impacts our natural world and many aspects
of biology. This link to this is in the description.
You’ll find this and thousands of other fascinating documentaries on MagellanTV. It’s
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as well. So be sure to take advantage of this. The links are in the description.
By the end of 1905, we had two big equations in physics. Planck’s, Energy equals Planck’s
constant times the frequency, and Einstein’s equation from special relativity, Energy equals
the mass times the speed of light squared. A young physicist by the name of Louis de Broglie
who happened to be working on his PhD thesis, and was searching for a thesis topic, looked
at these two equations and combined them: MC^2 = hf, since c and h are constants, if
you ignore them in the equation for a moment, it simplifies to M=f – mass is essentially
equal to frequency. A simple high school algebraic manipulation of the equation yielded something
quite profound, and eventually a Nobel prize for de Broglie.
But this is weird because mass and frequency are properties of two completely different kinds of things.
Mass is associated with discrete objects. Frequency, on the other hand, is associated
with a wave. An object is like a basketball. We know where
it is. We can bounce it around. If we don’t bounce it, it will still be there.
A wave on the other hand, like water waves and sound waves, can disappear. But the water
and air will still be there even if the wave is no longer there.
Quantum mechanics, on the other hand, seems to be indicating something different. It seems to be saying
that the particle is not only a particle but is also a wave. They are not separate.
What is doing the waving? It’s bizarre…because nothing is doing the waving. The wave is the
particle. the particle is the wave. If the wave disappears then we don’t have
what we call a particle anymore. It simply ceases to exist.
But how is this possible? How can particles be waves? How can we say that this is correct?
Just because our math seems to indicate that this is the case, it does not mean that it
is reality, does it? After all, whenever we observe anything, or
measure anything, it always shows up as a particle with discrete qualities like charge,
or spin, or mass etc. When we observe particles in a cloud chamber,
they seem show up as discrete particles too, not waves. So how can physicists say that
a particle is a wave? Surely, this can’t be true...or can it?
This is where the double slit experiment comes in.
The original experiment done by Thomas Young in the 1800s showed
the wave nature of light. When a light source with the same
optical wavelength, or monochromatic light, is projected through two slits onto a screen
in the back, it makes an interference pattern.
This is caused by constructive and destructive interference of the light waves. The bright
spots are due to two wave peaks adding to the brightness, and the dark spots are caused
by the peak of one wave canceling out the trough of the other.
So this is not unusual because it is what we would expect a wave to do. It indicates
that light is a wave. But from Planck and Einstein we learned that
light comes in discrete packets of energy called a photon. So is a photon a wave or
a particle? Scientists tried to figure this out by shooting
one photon at a time through the two slits. If it was a particle like a grain of sand,
we would expect it to go through one slit or the other, and make a spot on the screen
either behind the first slit or the second slit.
But this is not quite what happens. The photon seems to randomly make a spot somewhere on
the screen. And if we shoot many thousands of photons, one at a time, we see that as
a whole, the photons make an interference pattern just as in the original Young experiment.
The photons, even though, they were shot one at a time, so had no chance to interference
with each other, seem to make an interference pattern as if they interfered. Each photon
contributes one dot to the overall interference pattern. This is weird.
Could it be that each photon somehow splits into two and interferes with itself before
reaching the screen? To test whether that’s what’s happening,
we can put a detector near one of the slits to see if the photon goes through that slit
or not. And sure enough, the detector tells us that the photon went through only one of
the other of the slits. But wouldn’t you know it, when the detector tells us that,
the interference pattern disappears, and what we end up with is two patterns on the screen,
just like what we would expect from a non-quantum particle like a grain of sand.
What happens if we turn off the detector? Well then, the interference pattern returns.
Maybe photons are special. They're just weird things.
Surely, other objects like electrons, atoms, and molecules
don’t behave this way, right? Wrong. These and any other quantum objects behave exactly
the same way. What this experiment suggests is that photons and quantum objects
show characteristics of both particles and waves – the wave particle duality of matter.
And it also suggests that the act of measuring the object has a profound effect on the quantum
system. Why did it change when we measured it?
What caused this change to occur? This is the famous "measurement problem" in physics.
There is no definitive answer. Decoherence has been used to understand apparent
wave function collapse. I have video on this if you want to see it. But Decoherence does’t
generate actual wave-function collapse by itself. We know a big change happens upon measurement,
but not quite why it happens. I just mentioned the wave function. What does
this mean? To understand this, let’s compare quantum mechanics to Newtonian mechanics.
For Newtonian mechanics, the primary equation is F = MA – Force equals mass times acceleration.
But acceleration can also be written as the 2nd time derivative of position like this:
F = m * d2x/dt2 – this is the equation of motion in classical mechanics. If we solve
this for a particle’s position, we can find several things about it, such as its velocity,
kinetic energy, etc. So for example, if I know the initial position,
velocity, and all the forces acting on a basketball, I can tell you its exact position at a later
time. The equivalent primary equation for quantum
mechanics is the Schrodinger equation. In this equation, instead of solving for the
particle’s position, we need to solve it for something quite unique.
And that is psi – which is called the wave function. It’s called this because it has
similarities to waves that we find in classical mechanics.
The difference is there is nothing that’s doing the actual waving, the entire quantum
object can be described as wave-like. Although this equation looks complicated,
it is really just a statement of energy conservation. Total energy, represented on the left side,
equals the Kinetic energy plus potential energy on the right hand side.
Now what is psi – the wavefunction? It is a mathematical expression that represents
the state of a quantum system. It is related to the probability of finding the particle
in a particular location. Specifically, the square of the norm of the wave function gives
you the probability density of the particle. In other words, when you solve the Schrodinger
equation for a particle in a specific physical context like position, you don’t get a specific
value for position, like we would with Newtonian mechanics.
So I cannot tell you where the particle will be. I can only tell you the probability of
where you might find it if you measured it. So quantum objects are kind of smeared across
space. They are ambiguous. They are not like little balls that we can point to and say
– it’s there, and it’s moving this fast. You might ask, well, what else behaves like
this? The answer, truth be told, is that all matter behaves like this including things
like basketballs. And even your body is like this.
But if that is the case, then why don’t basketballs behave the way electrons do, or
atoms do – like waves smeared across space? Or let’s take something very small like
a grain of sand. Why don’t they behave like this?
The answer is because the wave behavior of objects that we can see with our eyes, like
sand grains or even dust particles is so small that we do not notice it.
You have to realize the scales that our macro objects occupy. An atom is on the scale of
one billionth of a meter. Even the tiniest grain of sand, that we can barely see would
be a hundred thousand times bigger than that. At this scale, we can’t see its wavelike
behavior. To understand why, let’s go back to de Broglie
whom I talked about at the start. He believed particles and waves have the same traits,
and he derived an equation that describes the wavelength of any particle.
This is called the de Broglie wavelength.
How did he come up with this? Using his original equality, mc^2 = hf. We can substitute v for
c - velocity for the speed of light. Then we get that f equals mv^2/h.
And then using the relationship v or velocity is equal
to wavelength times the frequency, we get that the wavelength, lambda is equal to h,
Planck’s constant, over mass times velocity, which is also momentum.
Using this relationship, we can find the wavelength of any particle. So for example, when we plug
in the numbers for an electron in a hydrogen atom, we find that its wavelength is 3.3 x
10^-10 meters. An atom has radius a of about 10^-10 m, so
its electron has de Broglie wavelength of about the size of the atom. This makes sense
because we know that the electron is somewhere in a cloud around the nucleus. And since the
orbit of the electron makes the size of the atom, this fits with our model. It’s quantumness
is apparent. But you’ll notice that since m, the mass
is in the denominator, for very massive objects, even small things that we can barely see with
our eyes, the wavelength becomes extremely small.
So for example, the wavelength of a small grain of sand that we can barely see with our eyes
moving 10 m/s would be about 10^-25 meters. And for larger things like a basketball,
the wavelength would be even smaller - 10^-34 meters.
This is extremely small – 24 orders of magnitude smaller than that of the electron.
To give you an idea of how small this is, the size of a proton is about 10^-15 meters.
So the wavelength of a grain of sand we can barely see would be billions of times smaller
than that. This is not measurable. Even one of our most sensitive instruments,
the LIGO detector that detects gravitational waves could not detect this.
A wavelength is about one quantum of action. The smaller the wavelength, the less quantum-like
the object is. If the wavelength becomes extremely small, any action of that object appears to
be continuous and smooth. This is why we don’t notice any weird behavior in macro scale objects.
The smaller the wavelength, the lower the wavy-ness or quantumness of the object becomes.
This is why particles with large wavelengths compared to their size like electrons, photons,
and other quantum objects exhibit wavelike and thus quantum-like behavior.
This calls into question, what exactly is a particle? For that matter, what is matter?
I'll have more on this in the next video but
for now, let me leave you with this teaser. There are no particles. Everything
is a wave…specifically a wave in a quantum field.
Electrons, and all other fundamental “particles”
are a wave or excitation in this field. The de Broglie wavelength of the particles is
the wavelength of these waves in the field. Don’t miss my next video. Until next time
my friend…