Download "Something Strange Happens When You Trust Quantum Mechanics"
Download this video with UDL Client
install
- Video mp4 HD+ with sound
- Mp3 in the best quality
- Any size files
%3Aformat(webp)%2Fi.ytimg.com%252Fvi%252FqJZ1Ez28C-A%252Fmaxresdefault.jpg&w=1139&q=75)
Table of contents
Please wait
Video tags
Subtitles
Russian
00:00:00
As a 42 year old who's
spent most of my life studying physics,00:00:03
I must admit
that I had a big misconception.00:00:06
I believed that every object
has one single trajectory00:00:10
through space, one single path.00:00:12
But in this video, I will prove to you
that this is not the case.00:00:17
Everything is actually exploring
all possible paths all at once.00:00:22
So let's start with a simple thought
experiment.00:00:25
Say you're at a beach when all of a sudden00:00:27
you see your friend
struggling out in the water.00:00:31
You want to go help them
as quickly as possible.00:00:34
So which path
should you take to get there?00:00:38
The shortest path is a straight line,
so you could head directly towards him.00:00:43
But you can run faster than you can swim,
and this path requires more swimming.00:00:48
So alternatively,
you could run down the beach00:00:51
to minimize the
distance through the water.00:00:54
But now00:00:55
the total
distance is longer than it needs to be.00:00:58
So the optimal path,
it turns out, is somewhere in between.00:01:03
To be precise, it depends on the speeds
at which you can run and swim.00:01:08
Now, you might recognize this
mathematical relationship because it is00:01:12
the exact same law that governs light
passing from one medium into another.00:01:16
So light also takes the fastest
path from point A to point B.00:01:21
What's weird about this is that as humans,00:01:24
we can see where we want to go
and then figure out the fastest route.00:01:28
But light, I mean, how does light know00:01:31
how to travel
to minimize its journey time?00:01:34
Now here is where
my misconception comes in.00:01:37
I shine a laser beam.00:01:38
The light just goes in one direction.
I throw a ball.00:01:40
The ball just goes in one direction,
you know?00:01:42
I would have answered,
there is nothing strange about this.00:01:45
Light sets off from point A
in some direction.00:01:48
And then a little while later
it encounters a new medium.00:01:52
And due to local interactions
with that medium,00:01:55
it changes direction,
ending up at point B.00:01:58
If you later find that of all the possible
paths, light took the shortest time00:02:02
to get from A to B, I wouldn't
think it was optimizing for anything.00:02:07
I would just think that's what happens
when light obeys local rules.00:02:11
But now I will prove to you that light
doesn't set out in only one direction.00:02:16
Instead, it really does explore all possible paths.00:02:20
And the same is true for electrons
and protons.00:02:23
All quantum particles.00:02:25
So the fact that we see things on single,
well-defined trajectories00:02:29
is, in a way, the most convincing illusion
nature has ever devised.00:02:34
And the way it works all comes down to a
quantity known as the action.00:02:40
In a previous video, we showed
how an obscure scientist, Maupertuis,00:02:44
made an ad hoc proposal
that there should be a quantity00:02:47
called action, which he defined
as mass times velocity times distance.00:02:53
And he claimed that everything
always follows the path that minimizes00:02:57
the action.00:02:59
Hamilton later showed that this action
is equivalent to the integral00:03:03
over time of kinetic energy
minus potential energy.00:03:07
Action was useful and an alternative way
of solving physics problems,00:03:12
especially when Newton's laws
get too cumbersome.00:03:15
But then, around the turn of the 20th
century, action showed up at the heart00:03:19
of a scientific revolution:
the birth of quantum mechanics.00:03:25
It all started with electric
lighting in Germany.00:03:28
Think about what it's like in the 1890s,
right?00:03:30
Electricity being more widely available,
at least in urban sectors.00:03:34
And things like, you know, light bulbs.00:03:36
They were new.00:03:37
They were literally the hot new thing.00:03:39
Germany wanted to replace all their gas
street lights with electric light bulbs.00:03:44
So an important question was
how do you maximize00:03:47
the visible light
given off by a hot filament?00:03:50
Scientists at a German research
institute, the PTR, studied00:03:54
how much light different materials
emitted as a function of temperature.00:03:59
At low temperatures, each material
gave off its own characteristic spectrum,00:04:03
mostly in the infrared,
but above about 500°C00:04:08
all materials started to glow
in the same way,00:04:12
with an almost identical
distribution of light.00:04:15
The hotter the object,
the more energy was emitted00:04:18
at every wavelength, and the peak
of the distribution shifted to the left.00:04:25
But they still didn't understand
how it worked theoretically.00:04:28
So that was sort of the next step, right?00:04:30
If you can understand how it works
theoretically,00:04:33
then you can use that theory
to potentially design your products.00:04:36
They started by imagining
the simplest object possible,00:04:40
one that would absorb all light
that falls onto it00:04:43
and perfectly emit radiation
based on its temperature.00:04:47
They came up with a hole in a metal cube.00:04:52
This hole is a perfect blackbody
because any light that shines onto00:04:56
it will go straight in, bounce
around inside, and eventually be absorbed.00:05:00
But this also makes it a perfect emitter.00:05:02
Any radiation inside the cube can escape
through the hole unimpeded.00:05:08
Theorists reasoned that electrons
in the walls of the cube00:05:11
would wiggle around,
emitting electromagnetic waves.00:05:15
These waves
would then bounce off the other walls.00:05:19
When you have two waves
of the same frequency,00:05:21
where one travels to the right
and the other to the left,00:05:24
they can interfere in such a way00:05:26
that they create places
where there's no wave amplitude00:05:29
those are nodes, and places where there is
maximum wave amplitude,00:05:34
the anti nodes. Waves like this are called
standing waves00:05:38
because they don't really move left
or right00:05:41
and inside a cavity,
given enough time and reflections.00:05:45
It is only these standing waves
that survive.00:05:48
All the other ones just cancel out.00:05:51
So a sort of order emerges from the chaos.00:05:57
In two dimensions, standing waves
look something like this.00:06:00
For shorter wavelengths
or higher frequencies, you can fit more00:06:04
and more different vibrational modes.00:06:06
Inside this cube,00:06:08
so that in three
dimensions, the total number of modes00:06:11
is proportional to frequency cubed,
or one over lambda cubed.00:06:16
The expectation was
there would be more and more waves00:06:19
inside the cube,
the shorter the wavelength.00:06:22
This led directly to the Rayleigh-Jeans law.
At longer wavelengths.00:06:27
It matched the experimental data
pretty well,00:06:30
but at shorter wavelengths
the theory diverged from experiment.00:06:35
In fact, it predicted
that at the shortest wavelengths,00:06:38
an infinite amount of energy
would be emitted.00:06:42
This, for obvious reasons, became known00:06:44
as the ultraviolet catastrophe.00:06:49
The person to solve
this problem was Max Planck,00:06:53
but Planck almost didn't
make it into studying physics,00:06:56
because when he was 16 years old,
he went up to his professor and asked him,00:07:01
well,
maybe I could do a career in physics.00:07:04
To which his professor responded
that he'd better find another field00:07:07
to do research in, because physics
was essentially a complete science.00:07:11
You know, there was just a few tiny
little problems that they had to clean up.00:07:15
But besides that, it was over.00:07:19
But Planck didn't listen.00:07:21
By 1897, he was a professor himself,
and for the next three years he struggled00:07:26
to find a theoretical explanation
for blackbody radiation.00:07:30
He tried approach after approach,
but no matter what, he tried.00:07:34
Nothing worked.00:07:35
He said I was ready to sacrifice
every one of my previous convictions00:07:40
about physical laws.00:07:44
Then, in a quote ‘act of desperation’,00:07:47
he did something
no one had thought to try.00:07:50
According to classical physics,
the energy of an electromagnetic wave00:07:53
depends only on its amplitude,
not its wavelength or frequency.00:07:58
And it could take any arbitrary value.00:08:01
So any atom could emit
any wavelength of light00:08:04
with an arbitrarily
small amount of energy.00:08:07
But Planck tried restricting the energy00:08:10
so that it could only come in multiples
of a smallest amount.00:08:14
A quantum.00:08:15
And he made the energy of00:08:17
one quantum
directly proportional to its frequency.00:08:21
E equals hf, where h is just a constant.00:08:27
Think about what this does00:08:28
to the radiation coming from the blackbody
at a given temperature.00:08:31
The atoms in the cavity
have a range of energies.00:08:34
Some have a little bit.00:08:36
A few have a lot, and most of their energy
somewhere in between.00:08:40
For long wavelength
low frequency radiation, the energy00:08:44
HF of one quantum is small,
so all of the atoms have enough energy00:08:49
to emit this wavelength,00:08:51
and the spectrum matches
the really gene's prediction very well.00:08:55
But at shorter
wavelengths, higher frequencies,00:08:58
the energy of a quantum increases.00:09:01
And now not all of the atoms have
enough energy to emit that wavelength.00:09:06
This is why experiment diverges
from the classical prediction.00:09:10
The spectrum peaks
and then starts to fall because fewer00:09:14
and fewer atoms have enough energy
to emit one quantum of that radiation.00:09:19
And there comes a point00:09:20
when none of the atoms have enough energy
to emit one quantum.00:09:24
So here the spectrum must drop to zero.00:09:28
With this approach, Planck got a new formula
for the radiation spectrum.00:09:33
Now all that was left for him to do
was to tune the parameter h.00:09:36
And when he did this just right,
he got his formula to match up00:09:39
perfectly with experiment.00:09:44
But he was sort of troubled00:09:47
by his own formula because to him
it was just a mathematical trick.00:09:50
He had no clue why it worked.00:09:52
It was purely formal.00:09:54
And most importantly,
he had no clue what this H represented.00:09:58
I mean, he had introduced a new
physical constant without any reason.00:10:03
He wrote a theoretical interpretation00:10:06
had to be found at any cost,
no matter how high.00:10:09
So from that moment
on, he dedicated himself to finding one.00:10:14
He later reflected that after some weeks
of the most strenuous work of my life,00:10:18
light came into the darkness
and a new undreamed of perspective00:10:23
opened up before me.00:10:27
He introduces
what we now call Planck's constant,00:10:31
and it has the units of action. Planck's
constant, h00:10:35
is a quantum of action.00:10:38
Planck later proposed that any time
any change happened in nature,00:10:42
it would be some whole multiple
of this quantum of action.00:10:46
So it's kind of spooky, this breakthrough
that starts the ball rolling toward00:10:51
quantum theory brings action in not energy00:10:56
and not force. Action. Gives you a hint.00:11:01
At first, the quantum of action
got little attention.00:11:05
That is, until a 26 year old patent clerk00:11:07
came on the scene.00:11:11
In 1905, Albert00:11:12
Einstein claimed that Planck's theory
wasn't just a mathematical trick.00:11:17
It was telling us
that light actually comes in discrete00:11:20
packets,
or photons, each with an energy HF.00:11:24
Einstein used this insight
to explain the photoelectric effect00:11:27
how light can eject electrons from metal,
but only when00:11:31
the frequency is high enough.00:11:33
If the frequency is too low,00:11:34
no electrons will be emitted
regardless of the intensity.00:11:40
The idea of quantization spread.00:11:44
Eight years later,
Niels Bohr was trying to understand00:11:46
how an atom is stable
if it has a positive charge in the center00:11:50
and negative electrons whizzing around it.00:11:53
Why don't they just spiral
into the nucleus, radiating their energy00:11:56
as they go?00:11:58
And what he wants to do is,
he says there's something fishy00:12:00
about something being discrete
that seems to be the new ambiguous weirdo00:12:05
lesson of the new quantum of action. Bohr
realizes that as the electron00:12:10
goes around the nucleus,
it has an angular momentum.00:12:13
Mass times velocity times radius.00:12:17
So angular momentum
has the same units as action.00:12:21
And so what he decides to do is discretize
the orbital angular momentum.00:12:25
For no good reason00:12:27
he says, let me slap that on and say,
and imagine the electron can only be in00:12:30
one unit, two units,
three units of the same quantity H.00:12:34
And because it's talking about motion
in a circle, the factors two pi come in.00:12:38
So is really nh over two pi,
what we now call an h bar.00:12:42
This comes out of nowhere.00:12:44
There seems like
absolutely no good reason why00:12:47
angular momentum should be quantized.00:12:50
But by doing it, Bohr finds the correct
energy levels of the hydrogen atom.00:12:54
When an electron jumps from a higher orbit
to a lower one, the energy difference00:12:59
is given off as a photon
of a particular color of light.00:13:03
Exactly reproducing the hydrogen spectrum.00:13:06
And that was a pretty startling thing
to have fall out.00:13:09
I think that really was compelling.00:13:11
Take some quantity with the unit of action
and apply some, again, kind of ad hoc,00:13:17
discretization or quantization to it.00:13:20
Now, although it worked
spectacularly well,00:13:23
no one can make sense of it.00:13:26
That is until 11 years later.00:13:29
For his PhD,00:13:31
Louis de Broglie was contemplating
the recent discoveries in physics.00:13:35
And his big insight was that if light
could be both a wave and a particle,00:13:39
then maybe matter00:13:40
particles could also be waves.00:13:44
He proposed that everything.00:13:46
Electrons, basketballs, people,
absolutely everything has a wavelength.00:13:52
And he defined this wavelength
analogously to light as Planck's00:13:56
constant,
divided by the particles momentum or00:13:59
mass times velocity.00:14:03
Now, if an electron is a wave,
the only way it could stay bound00:14:07
to a nucleus in an atom is
if it exists as a standing wave.00:14:12
That requires
that a whole number of wavelengths00:14:15
fit around the circumference of the orbit.00:14:18
You could have one wavelength
or two wavelengths or three, and so on.00:14:23
So the circumference two pi
r must be equal00:14:26
to some multiple n times the wavelength.00:14:29
We can sub in de Broglies expression
for the wavelength to get the two pi00:14:33
r equals NH over mv,00:14:36
but we can rearrange this to get the mvr.00:14:39
The angular momentum
is equal to NH over two pi.00:14:45
That is00:14:46
precisely Bohr's quantized
angular momentum condition.00:14:51
But now we have a good physical reason
why it's quantized.00:14:55
Because electrons are waves00:14:56
and they must exist as standing
waves to be bound in atoms00:15:00
because they want to have constructive
interference, have a stable orbit back.00:15:04
That's pretty good.00:15:05
You get a dissertation out of that.
That's pretty good.00:15:07
It is this wave nature of quantum objects.00:15:10
That means they no longer
have a single path through space.00:15:13
Instead,
they must explore all possible paths.00:15:19
Now, I have thought about
and taught the double slit experiment00:15:22
hundreds of times
without fully realizing this implication.00:15:26
In the double slit experiment.00:15:27
I feel like the mental thing
that I'm doing in my head is like, okay,00:15:30
well, the beam is not perfectly straight,
and of course it's going to intersect00:15:34
both of those slits because they're really
close together. You know?00:15:38
But then
I heard this story about a professor00:15:40
teaching the double slit experiment,
and it makes everything so clear.00:15:45
So the professor starts by explaining
the setup.00:15:49
Electrons are fired one at a time00:15:51
through two slits
to be detected at a screen.00:15:55
Now, because you can't say for certain
which slit the particle went through,00:15:58
quantum mechanics tells us
it must go through both at the same time.00:16:02
So to get the probability of finding
a particle somewhere on the screen,00:16:05
you simply add up00:16:06
the amplitude of the wave
going through one slit, with the amplitude00:16:09
of the wave going through the other slit
and square it.00:16:15
But that's when a student raised his hand.00:16:18
What if you add a third slit?00:16:21
Well, you just add up the amplitudes
of the waves00:16:23
going through each of the three slits,
and you can work out the probability.00:16:28
The professor wanted to00:16:29
continue,
but then the student interjected again.00:16:33
What if you add a fourth slit and a fifth?00:16:37
The professor, who is now clearly losing
his patience, replies, I think it's clear00:16:41
to the whole class that you just add up
the amplitudes from all the slits.00:16:45
It's the same for six, seven, etc.00:16:50
but now the bold student
pressed his advantage.00:16:54
What if I make it infinite slits00:16:58
so that the screen disappears?00:17:01
And then I add a second screen
with infinite slits00:17:04
and a third and a fourth.00:17:08
The student's point was clear.00:17:12
Even when we're not doing
a double slit experiment,00:17:14
when it's just light or particles
traveling through empty space,00:17:18
they must be exploring all possible paths.00:17:22
Because this is exactly how the math00:17:24
would work if you had infinite screens,
each with infinite slits.00:17:28
You have to add up the amplitude
from each slit.00:17:31
That's just the way it works.00:17:34
According to the story,00:17:35
the student was Richard Feynman,
and while the story is made00:17:38
up, the logic is flawless.00:17:41
Because if you believe
in the double slit experiment00:17:44
that you can't tell which of the two slits
the particle went through,00:17:47
then you have to consider the possibility
that it goes through both.00:17:52
By that same logic, any time00:17:54
any particle goes from place
one to place two.00:17:57
You have to consider
all the possible paths00:18:00
it could take to get there, including ones
that go faster than the speed of light,00:18:03
including ones that go back in time,00:18:05
and including ones that go
to the other side of the moon and back.00:18:09
I feel like I can't go to the sun
and back.00:18:10
You have to restrict it
to be local, right?00:18:12
So the math doesn't do that.00:18:14
I mean, you could see that
just in the double slit experiment, right?00:18:18
And we'll do light because then there's
no funky business with the speed.00:18:21
If you're going to say like,
this path interferes with this00:18:24
path and these distances
are different, right.00:18:27
And so clearly
they can’t have the same speed.00:18:30
So you need to consider
paths that have different speeds.00:18:34
Feynman's way of doing quantum mechanics00:18:36
suggests that anything going from00:18:38
one place to another is connected
in every possible way.00:18:42
And the internet is kind of like that too00:18:43
connecting us to anything,
anywhere, at any time.00:18:47
At least in theory,
there are still artificial barriers00:18:51
like geo blocks and country restrictions
that block off parts of the internet.00:18:55
But fortunately, there's today's sponsor,
NordVPN, which can help knock down00:19:00
those barriers.00:19:01
Just connect to one of their thousands of
servers, for example, this one in the US.00:19:05
And it looks as if you're accessing
the internet from there.00:19:08
The team and I travel a lot to make these videos,
and using a VPN is a game changer.00:19:13
It allows us to access the news sites 00:19:15
and articles we need, no matter
where in the world we are.00:19:19
And personally, I also love that NordVPN
allows me to stay up00:19:21
to date with how the Canucks
are doing back in Canada.00:19:25
Not very well at the moment.00:19:28
Canucks have a real shot00:19:29
at the Cup this year.00:19:34
But to try NordVPN
for yourself,00:19:35
sign up at nordvpn.com/veritasium.00:19:39
Click that link in the description
or scan this QR code.00:19:42
And when you do,
you get a huge discount on a two year plan00:19:45
and an additional four bonus months
for free.00:19:48
It's the best deal and it also comes
with a 30 day money back guarantee.00:19:53
So head to nordvpn.com/veritasium
to try it out risk free.00:19:57
I want to thank NordVPN
for sponsoring this part of the video.00:19:59
And now let's get back to Feynman's crazy
way of doing quantum mechanics.00:20:05
So according to Feynman,
any time a particle, a photon, or even a00:20:09
macroscopic object moves from point 1 to point 2,00:20:12
it has some chance to take any path.00:20:15
And as preposterous as it might sound.00:20:17
He found that we need to include
all these paths in our calculation,00:20:21
where each path is weighted the same.00:20:25
So why00:20:26
then, do we not see all those crazy paths?00:20:29
Well, that's because we still need
to add up their amplitudes.00:20:33
For simplicity,
imagine we only have three paths.00:20:37
Then here's what we're going to do.00:20:39
First, let's take this one.00:20:40
When the particle wave starts
following it, we start a stopwatch.00:20:44
It goes around and around very fast,
and when it gets to the end point,00:20:48
we hit stop.00:20:50
We'll do the same for the other two paths.
And then we add up00:20:57
the arrows, square the result.00:21:00
And that is
then proportional to the probability00:21:02
the particle took those paths
to get there.00:21:05
In this case
the arrow and square are pretty small, so00:21:08
the probability of the particle going from
1 to 2 using these paths is small.00:21:15
Compare that with these three paths.00:21:17
For example.00:21:20
Well now the arrow is much larger.00:21:23
And this is important.00:21:25
The larger the resulting arrow, the higher
the probability of that event happening.00:21:30
Now in these examples the stopwatch is not
actually measuring time.00:21:34
Instead it measures
something called the phase.00:21:38
Just as in the double slit experiment,
when a wave takes a different path00:21:41
from point 1 to 2, it will end up there
with a different phase.00:21:46
And this phase is what determines00:21:48
the amplitude of the wave at that point.00:21:52
Mathematically, we can write the amplitude
our stopwatch as e to the I phi,00:21:57
where phi is the phase.00:22:01
As the particle wave follows a path,
its phase increases.00:22:05
Winding the vector around.00:22:08
So now the big question is how much00:22:10
does the phase change for each path?00:22:13
Well, to answer that, imagine
we split up the path into many tiny00:22:16
sections, each one
so small that it's effectively straight.00:22:21
Then in each00:22:22
section, the particle wave goes
a distance delta x and a time delta t,00:22:27
and the increase in phase
is easy to compute.00:22:30
It just depends on the wavelength
and frequency of the wave.00:22:34
To find the total increase in phase
for the whole path,00:22:37
we just add up all the little phase
increases of all the individual sections.00:22:42
But we can sub in lambda equals
h over mv from de Broglie,00:22:46
and using e we can sub in for frequency.00:22:50
We can also simplify by writing h over two
pi as h bar.00:22:54
To get this expression.00:22:57
Then we can take delta t to the right.00:22:59
And if we make delta
t infinitesimally small,00:23:03
then we can replace this
sum with an integral.00:23:06
But now Dx by Dt is just velocity.00:23:09
So we can write this as m b squared.00:23:13
Now we know that in the simplest case
the total energy00:23:15
e is just kinetic plus potential energy.00:23:19
And subbing that in we're left
with the integral00:23:21
over time of kinetic energy
minus potential energy.00:23:26
But wait a second.00:23:27
That is just the classical action.00:23:31
So it's action that determines00:23:33
how fast the stopwatch turns.00:23:36
As the particle moves along a trajectory,00:23:38
its action increases,
and that is what increases the phase.00:23:43
And what's important to note is that h
bar is tiny.00:23:46
It's about ten to the -34 joule seconds,
which is way00:23:50
smaller than the action
of any everyday object.00:23:54
That means the phase of ordinary objects
on ordinary paths00:23:58
spins around zillions of times,
eventually pointing00:24:01
in some random direction.00:24:05
If you consider a slightly different path,00:24:07
the action may be slightly different
say 0.01 joule seconds different.00:24:13
That doesn't seem like much,
but divide it by h bar00:24:17
and the arrow will spin around
ten to the 32 more times.00:24:20
So again, it will just point
in some random direction.00:24:25
This is what00:24:26
happens
to almost all of the possible paths.00:24:29
So when you add up the phases,
they just cancel out.00:24:32
They destructively interfere.00:24:35
The only exception is for the paths
closest00:24:38
to the path of least action,
because these paths are at a minimum.00:24:42
So if you make tiny changes to the path
to first order,00:24:46
the action doesn't change.00:24:50
And so for other paths that are very close
to the path of least action,00:24:53
their arrows point
in basically the same direction.00:24:57
They constructively interfere.00:24:59
And that is why those are the paths
we see.00:25:03
This explains how light knows where to go.00:25:07
I mean, it doesn't.00:25:08
It just explores all possible paths,00:25:11
but the past we end up seeing are the ones
that interfere constructively.00:25:16
And those are the paths of least action.00:25:23
So really,00:25:24
this is how classical mechanics emerges
from quantum mechanics.00:25:28
It's why a ball follows the trajectory
it does, and how planets orbit the sun.00:25:33
They don't really have a precise
trajectory.00:25:36
Instead, everything explores
all possible paths.00:25:40
It's just that massive particles
have large actions compared to hbar,00:25:44
so that only paths extremely close
to the true path of least action survive.00:25:49
Which is why they're much more particle
like.00:25:51
If you go to much smaller particles
like electrons or photons,00:25:55
the actions are much smaller,
and so there's more of a spread00:25:58
in which trajectories
they actually end up taking.00:26:02
Now, you might say,
I still don't believe you,00:26:05
but Casper has this incredible demo00:26:08
that should convince you 100%
that this is really how the world works.00:26:15
To do it, I've taken a light,
a mirror and a camera.00:26:19
Now there are infinitely many paths
that the light could take.00:26:22
And according to Feynman,
we have to add the contributions of each them.00:26:25
Including paths that go like this.00:26:29
Now, you might say he's crazy.00:26:31
I'm not crazy. That's what happens.00:26:33
Another possibility is I could come here00:26:36
and go.00:26:37
Or it could come here and go.00:26:39
Or it could come
where you'd like it to come and go.00:26:42
And it can go over here00:26:45
and go and so on and so on.00:26:47
And these are all possibilities.00:26:48
And every single one of these paths
has their own little arrow.00:26:51
So what we can do is we can look at all
those arrows and see where they line up.00:26:55
And so if I turn on this light,
that's exactly where you see it reflects00:27:00
that at the angle of incidence
is equal to the angle of reflection.00:27:04
But now what I'm going to do
is I'm going to cover up that spot00:27:07
so that we no longer
see the light reflect.00:27:09
And then I'm going to prove
that really Feynman is right.00:27:12
That really light
also goes like this.00:27:15
It's just that most of the time,
those effects are cancelled out.00:27:18
Now that sounds impossible, right?00:27:21
But let's zoom in to this tiny piece
right here.00:27:24
Then we see all these different paths
and all the arrows just go around00:27:28
and around in circles.00:27:29
So when you add them up,
they all just cancel out.00:27:33
But what if I cover up about half of them
like so.00:27:37
Well, now when I add up those arrows you
suddenly do see a large resulting arrow.00:27:42
And so if I can somehow cover up
this mirror in many, many tiny strips,00:27:46
then I should be able to get the light
to reflect like this.00:27:50
And I can do that with this piece of foil
right here on this piece of foil.00:27:55
There are about a thousand lines
per millimeter, and that should be enough00:27:59
to get this effect.00:28:00
So let me turn off the lights.00:28:03
So let's see
I'm going to turn it on in 321.00:28:08
We see it.00:28:13
That is so cool.00:28:14
It actually looks a lot weirder
than I was expecting it to.00:28:17
I was expecting more like, one spot,00:28:19
but there's many, many spots
where it's reflecting.00:28:22
Oh, okay. Okay.00:28:23
And just to show,
I haven't been cheating you, right00:28:26
underneath is my finger.00:28:29
And even with the light
on, you know, we see the light reflect.00:28:34
And if we remove the cover,00:28:37
then what do we see?00:28:40
Yeah, we see exactly the normal reflection00:28:44
where it's always supposed to go,
which is right there.00:28:47
And then we've got
now all these extra reflections,00:28:50
all these extra bits
where the pattern just lines up.00:28:54
So very, very cool.00:28:57
When I was talking about this
with a friend, actually,00:28:59
he said, yeah,
but you're using a diffraction grating.00:29:01
That's kind of like cheating.00:29:02
You get all these other reflections
right now00:29:05
and this light is just
going in all directions.00:29:08
And so there's one other thing.00:29:10
I've been super, super curious to try.00:29:13
I also want to do this with a laser
where I shine the laser right next to it.00:29:18
And then if light does take every possible
path, we should also see it00:29:22
come off here.00:29:23
It probably shouldn't work.00:29:25
I actually have a laser right over here00:29:28
and we can see when I shine it.00:29:32
It really does.00:29:33
Just go to one spot
and you can see where that spot is.00:29:36
It's right over there, which is about the
same place where we had our reflection.00:29:40
And you can also see right now if00:29:44
we look at this view that you cannot see
the laser light at all.00:29:47
Right.00:29:48
Like I could see the laser, but I have to
bring it out all the way over here.00:29:52
And then I'm able to sort of
see the light.00:29:55
But if I just put it up here,
you can see the reflection.00:30:00
Now, what I'm going to do next
is I'm going to put00:30:02
this foil, this magic foil,00:30:06
and I'm going to put it over here
and we can turn off this.00:30:10
And now let's see what happens
when I turn on the laser.00:30:17
Wait wait wait wait.00:30:19
No way,00:30:22
no way.00:30:23
It works.00:30:25
It works. Wait. What?00:30:27
Look where the laser is going.00:30:30
Oh, my God, it actually works.00:30:34
What? What?00:30:37
This is definitely the coolest demo
I've ever done.00:30:40
So what I was doing is I was holding
the laser, and I can show you right now.00:30:44
I was shining it down, like, this way off.00:30:47
And you could still see it reflect.00:30:50
But if I take this away, it disappears.00:30:53
And if I put this back, it appears00:30:57
so that it shows really that we cannot00:31:00
get rid of the area which gives zero
that it really is canceling out.00:31:05
And if we do clever things to it,00:31:07
we can demonstrate the reality of the
reflections from this part of the mirror.00:31:15
So light and by extension,00:31:16
everything really does
explore all possible paths.00:31:20
It's just that most of the time
the crazy paths destructively interfere.00:31:25
That's because the actions of nearby paths
change rapidly.00:31:28
Now, I've studied physics00:31:30
for most of my life,
and I feel like I never really appreciated00:31:33
how important action
and the principle of least action are.00:31:36
But now I think I finally get it.00:31:39
And I finally get why.00:31:40
If you ask theoretical physicists
what they're working00:31:42
on, they'll rarely talk about energy
or forces.00:31:45
Most of the time,
they'll talk about action.00:31:48
Nobody in particle physics approaches
particle physics00:31:52
from a viewpoint other than least action.00:31:55
But we teach physics historically,
and no least action00:31:59
is almost like the new kid on the block
for understanding physics.00:32:02
And so, yeah, we build up to it.00:32:04
But in reality,00:32:05
I think life's a lot easier once
you realize this underlying principle,00:32:09
because when you do,
then all you have to do is write down00:32:12
the correct Lagrangian
so you get the right action and out come00:32:16
the laws of physics.00:32:17
So you've got a separate Lagrangian
for classical mechanics,00:32:21
for special relativity,
for electrodynamics, and so on.00:32:25
It's a single mathematical framework
that, once you've learned it,00:32:29
then you can apply it in different places
in exactly the same way.00:32:34
The hunt
for the theory of everything, right.00:32:36
The thing that will encompass
all of physics00:32:38
in reality, what people are asking is
what is this Lagrangian00:32:41
that can spit out all of the laws
of physics in this universe?00:32:45
That's really what they're asking.00:32:47
The moment
we haven't really found that right.00:32:48
Because we can
we can sticky tape things together,00:32:52
but we don't know if that's the proper
mathematical structure.00:32:55
So that's what people are hunting for.00:33:01
This was our second
video on the principle of least action.00:33:04
And I know we've covered a lot,
but you might still have some questions.00:33:07
So we are hosting a Q&A
over on our Patreon.00:33:11
You can submit your questions there,
and we'll also post the Q&A there.00:33:15
And it's all for free.00:33:16
If you want to submit a question
or watch the Q&A.00:33:19
Head over to Patreon.com/Veritasium
and you can make a free account.00:33:23
Or you can support us a little bit as well
if you'd like.00:33:26
I'd also like to thank NordVPN
for sponsoring this video.00:33:29
Check them out by clicking the link in
the description or scanning this QR code.00:33:33
And finally,
I really want to thank you for watching.Description:
Does light take all possible paths at the same time? 🌏 Get exclusive NordVPN deal here ➵ https://NordVPN.com/veritasium It’s risk free with Nord’s 30 day money-back guarantee!✌ A massive thank you to Dr. Andrew Mitchell for all his help and expertise. If you want to delve further into this topic then we highly recommend his lecture on Classical physics derived from quantum mechanics: https://www.youtube.com/watch?v=2iuLwWDYC4U&t=1s We’re incredibly grateful to Prof. David Kaiser, Prof. Steven Strogatz, Prof. Geraint F. Lewis, Elba Alonso-Monsalve, Prof. Christopher S. Baird, Prof. Anthony Bloch, and Prof. Stephen Bartlett for their invaluable contributions to this video. A special thanks to Mahesh Shenoy from FloatHeadPhysics for his help with this video. Check out his excellent intuitive video on the UV Catastrophe here (Sep 2024): https://www.youtube.com/watch?v=ALEDjjAVZSY ▀▀▀ 0:00 What path does light travel? 2:40 Black Body Radiation 6:47 How did Planck solve the ultraviolet catastrophe? 9:42 The Quantum of Action 13:25 De Broglie’s Hypothesis 15:16 The Double Slit Experiment 20:00 How Feynman Did Quantum Mechanics 25:01 Proof That Light Takes Every Path 31:16 The Theory of Everything ▀▀▀ Sign up to our Patreon to watch the Q&A for free: https://www.patreon.com/c/veritasium Try Snatoms! A molecular modelling kit I invented where the atoms snap together. https://ve42.co/SnatomsV ▀▀▀ References: Armin Hermann (Nov 1974). The Genesis of Quantum Theory (1899-1913). - https://ve42.co/genquanttheor Richard P. Feynman (1985). QED The Strange Theory of Light and Matter. - https://ve42.co/qed A fantastic book on the history of the Principle of Least Action: Rojo, A. and Bloch, A. The Principle of Least Action: History and Physics. - https://ve42.co/Bloch2018 Coopersmith, J. (2017). The lazy universe: an introduction to the principle of least action. Oxford University Press. - https://ve42.co/LazyU PBS Space Time. (Nov 2021) - https://www.youtube.com/watch?v=Q_CQDSlmboA Sabine Hossenfelder. (May 2022) - https://www.youtube.com/watch?v=A0da8TEeaeE Max Planck (1901). On the Law of Distribution of Energy in the Normal Spectrum. Annalen der Physik - https://ve42.co/lawdistenergy Paul Ehrenfest (1911). Welche Züge der Lichtquantenhypothese spielen in der Theorie der Wärmestrahlung eine wesentliche Rolle?. Wiley Online Library - https://ve42.co/quantthermrad Nils-Erik Bomark and Reidun Renstrøm (Aug 2023). The Ultraviolet myth. Proceedings of Science - https://ve42.co/uvmyth Planck's law. In Wikipedia - https://ve42.co/planckslaw PBS Space Time. (Jul 2017). - https://www.youtube.com/watch?v=vSFRN-ymfgE&t=10s Einstein and The Photoelectric Effect. (Jan 2005) via APS News - https://ve42.co/einsteinphotoelec Louis de Broglie (1924). On the Theory of Quanta. - https://ve42.co/theoryquanta Larry Sorensen (2012). Path Integrals 1. University of Washington - https://ve42.co/pathintegrals Feynman’s Method of “A Particle Exploring All Possible Paths”. (Mar 2018) via Pure Dhamma - https://ve42.co/allposspaths A great intuitive video on the Feynman path integral approach - https://www.youtube.com/watch?v=Sp5SvdDh2u8&t=1253s Origins of Quantum Theory. via University of Pittsburgh - https://ve42.co/origquanttheor Images & Video: Nobistor Altona 1880 via NDR - https://ve42.co/streetlight Edison incandescent lights by William J. Hammer via Wikimedia Commons - https://ve42.co/edinclights The full expanded form of the Standard Model Lagrangian by Chen Ning Yang et al. via Wikipedia - https://ve42.co/stmodellang Muon Ray. (2011). https://www.youtube.com/watch?v=-QUj2ZRUa7c Muon Ray. (2011). https://www.youtube.com/watch?v=1C7abO7LtV0 Bohrs Atomic Model via EEEGUIDE.COM - https://ve42.co/bohrmodel ▀▀▀ Special thanks to our Patreon supporters: Adam Foreman, Albert Wenger, Alex Porter, Alexander Tamas, Anton Ragin, Autodidactic Studios, Balkrishna Heroor, Bertrand Serlet, Blake Byers, Bruce, Dave Kircher, David Johnston, David Tseng, Evgeny Skvortsov, Garrett Mueller, Gnare, gpoly, Greg Scopel, Juan Benet, Keith England, KeyWestr, Kyi, Lee Redden, Marinus Kuivenhoven, Matthias Wrobel, Meekay, meg noah, Michael Krugman, Orlando Bassotto, Paul Peijzel, qiaohui wei, Richard Sundvall, Sam Lutfi, Tj Steyn, TTST, Ubiquity Ventures, wolfee ▀▀▀ Directed by Casper Mebius Written by Casper Mebius and Derek Muller Edited by Trenton Oliver and Peter Nelson Animated by Fabio Albertelli, Mike Radjabov, Ivy Tello, Andrew Neet and Emma Wright Illustrations by Jakub Misiek, Tommy A. Steven and Cainejan Esperanza Filmed by Derek Muller and Casper Mebius Produced by Casper Mebius, Derek Muller, Rob Beasley Spence, Gabe Strong, Geeta Thakur, Emilia Gyles, Zoe Heron, Emily Zhang and Tori Brittain Thumbnail contributions by Ignat Berbeci, Ben Powell, Jakub Misiek, Ren Hurley, and Peter Sheppard Additional video/photos supplied by Getty Images and Storyblocks Music from Epidemic Sound
Mediafile available in formats
* — If the video is playing in a new tab, go to it, then right-click on the video and select "Save video as..."
** — Link intended for online playback in specialized players
Questions about downloading video
How can I download "Something Strange Happens When You Trust Quantum Mechanics" video?
http://uniloader.pro/ website is the best way to download a video or a separate audio track if you want to do without installing programs and extensions.
The UDL Helper extension is a convenient button that is seamlessly integrated into YouTube, Instagram and OK.ru sites for fast content download.
UDL Client program (for Windows) is the most powerful solution that supports more than 900 websites, social networks and video hosting sites, as well as any video quality that is available in the source.
UDL Lite is a really convenient way to access a website from your mobile device. With its help, you can easily download videos directly to your smartphone.
Which format of "Something Strange Happens When You Trust Quantum Mechanics" video should I choose?
The best quality formats are FullHD (1080p), 2K (1440p), 4K (2160p) and 8K (4320p). The higher the resolution of your screen, the higher the video quality should be. However, there are other factors to consider: download speed, amount of free space, and device performance during playback.
Why does my computer freeze when loading a "Something Strange Happens When You Trust Quantum Mechanics" video?
The browser/computer should not freeze completely! If this happens, please report it with a link to the video. Sometimes videos cannot be downloaded directly in a suitable format, so we have added the ability to convert the file to the desired format. In some cases, this process may actively use computer resources.
How can I download "Something Strange Happens When You Trust Quantum Mechanics" video to my phone?
You can download a video to your smartphone using the website or the PWA application UDL Lite. It is also possible to send a download link via QR code using the UDL Helper extension.
How can I download an audio track (music) to MP3 "Something Strange Happens When You Trust Quantum Mechanics"?
The most convenient way is to use the UDL Client program, which supports converting video to MP3 format. In some cases, MP3 can also be downloaded through the UDL Helper extension.
How can I save a frame from a video "Something Strange Happens When You Trust Quantum Mechanics"?
This feature is available in the UDL Helper extension. Make sure that "Show the video snapshot button" is checked in the settings. A camera icon should appear in the lower right corner of the player to the left of the "Settings" icon. When you click on it, the current frame from the video will be saved to your computer in JPEG format.
How do I play and download streaming video?
- in video formats, hover your mouse over "Streaming Video**";
- right-click on "Copy link";
- open VLC-player;
- select Media - Open Network Stream - Network in the menu;
- paste the copied link into the input field;
- click "Play".
- copy the video address (URL);
- select "Open Network Stream" in the "Media" item of VLC player and paste the link to the video into the input field;
- click on the arrow on the "Play" button and select "Convert" in the list;
- select "Video - H.264 + MP3 (MP4)" in the "Profile" line;
- click the "Browse" button to select a folder to save the converted video and click the "Start" button;
- conversion speed depends on the resolution and duration of the video.
For this purpose you need VLC-player, which can be downloaded for free from the official website https://www.videolan.org/vlc/.
How to play streaming video through VLC player:
To download streaming video via VLC player, you need to convert it:
Warning: this download method no longer works with most YouTube videos.
What's the price of all this stuff?
It costs nothing. Our services are absolutely free for all users. There are no PRO subscriptions, no restrictions on the number or maximum length of downloaded videos.