The physics of shadows

Daniel and Kelly shine a light on the mysterious every day physics of shadows, including whether they can move faster than light.

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Episode Transcript

Speaker 1 (00:00):
Hey everyone, it's Daniel. I have a new book out
now called Do Aliens Speak Physics? About whether or not
we have physics in common with aliens. I think it's
a lot of fun. But here's a totally unbiased review
from Phil Plate, author of Bad Astronomy, Quote whites and
makes us think about how we think about aliens and
how we think about the universe at a fundamental level,

(00:22):
and does it in a readable, understandable, and even funny way.
If we ever meet aliens, the first thing we should
do is give them this book. So go out and
pick up a copy of Do Aliens Speak Physics? I
think you'll enjoy it. When you see the universe through

(00:46):
the lens of physics, you start to see physics everywhere.
Why is glass transparent but stone isn't? Why or bicycle stable?
How do tornadoes start? The mysteries of physics aren't just
out there in deep space. They're right here in front
of us, raising questions and demanding answers every day. Today
we'll tackle the topic that I've wondered about since I

(01:07):
was a little baby physicist, looking at the world and
wondering how it worked. All you need for this inspiration
is a light bulb and your hands with which you
can make something out of nothing. Shadows aren't really anything.
They're a lack of something. They're negative objects, but our
minds see them as positive, as a thing in the

(01:27):
world rather than just the absence of light, and shadows
have been surprising and confusing people for thousands of years.
Today we'll dig into the physics of shadows and ask
whether they can break one of physics' most hallowed principles.
Welcome to Daniel and Kelly's Extraordinary Shadowy Universe.

Speaker 2 (02:00):
Hello, I'm Kelly Wadersmith. I study parasites and space and
one of my absolute favorite things is when it's a
clear night and it's a full moon and I'm out
on the farm and you can see the shadows of
the trees and your own shadow in the middle of
the night. It feels sort of like spooky but fantastic,
and I just absolutely love it. I like, shadows.

Speaker 1 (02:19):
Are those star shadows or moonshadows?

Speaker 2 (02:22):
No, it's just that there's so much sunlight reflecting off
the moon and making it down, you know, to Earth
that you can see, you know, the shadows of the trees. Wait,
what did you ask me? Are they moonshadows. Yeah, they're moonshadows.
I'll call them moonshadows.

Speaker 1 (02:35):
Yeah, moonshadows are awesome. Yeah, I love it cool.

Speaker 2 (02:39):
As I was explaining it, I was like, there's no
way Daniel doesn't understand where the light is coming from.
Why am I explaining it to him? I must have
missed the question.

Speaker 1 (02:50):
Hi, I'm Daniel. I'm a particle physicist, and I do
understand why the moon is bright at night.

Speaker 2 (02:56):
Go ahead, Daniel, why's the moon bright at night?

Speaker 1 (03:01):
Are you doubting me? Or you're putting me on the spot?
Good's College left No, obviously, because the moon is being
illuminated by the sun. Just because we can't see the
sun doesn't mean that some parts of the moon can't
see the sun.

Speaker 2 (03:13):
And I've never lived in an area where there was
so little light pollution that I could see the shadows
cast by the moon. Another reason why Virginia is amazing.
So my question for you today, Daniel. So I was
looking at the question asked by the listener, and I

(03:37):
realized that faster than light questions sometimes just like make
my brain go, oh, this is really not making sense
to me. What physics concept that when you think about
makes you think, I just my brain can't really. I
have to accept that this is true because the science
is good, but my brain is just having trouble wrapping

(03:57):
itself around this fact confuses you about physics thermodynamics.

Speaker 1 (04:03):
Yeah, I've never really been a fan of statistical physics
and thermodynamics because it verges on chemistry. It's like you
start from all these micro states and these little particles,
and then you zoom out and you draw these conclusions
about the macroscopic state, but there's so many particles involved,
and I don't know, it just feels like there's lots
of approximations and considerations and you never really feel like

(04:26):
you're on solid footing. And when I showed up at Berkeley,
they make you take this qualifying exam to see like
how good is your physics. And I remember my advisor
at the time. He was like, good students pass this
exam on the first try, and I was like gold yep.
So I spent that whole summer before grad school studying, studying, studying,
and I spent most of it studying thermodynamics because I

(04:47):
knew that was my weak spot. And this qualifying exam
is terrifying. It's two eight hour days, right, so it's
like a serious ordeal. It's like a marathon.

Speaker 2 (04:56):
This is right when you get there. This isn't like
two years in or something.

Speaker 1 (05:00):
Well, you can wait and take it after you've taken
the grad school classes. But my advisor was like, the
best students show up and pass it on the first try.
And I was like, that'scish. Yeah, but I lucked out
and that year no THERMO questions, just zero. I was like, yeah,
all right, I'm gonna skate on through.

Speaker 2 (05:19):
And did you did you pass it on the first time.

Speaker 1 (05:21):
I did pass it on the first try, And then
I had to take up through my dnemics class and
I skated just over the minimum threshold for that class.

Speaker 2 (05:29):
Let me tell you, nice, but you did it, and
now it's behind you.

Speaker 1 (05:32):
Congratulations, And I'm a certified physicist and I don't have
to do themo dynamics, you know.

Speaker 2 (05:39):
Speaking of chemistry, last night, I was giving a talk
to a women in chemistry group over Zoom, and halfway
through I realized that I was describing a chemistry thing
and I suddenly got really insecure because I was like,
what if this is wrong? Because I just pretend to
know chemistry.

Speaker 1 (05:53):
Everybody pretends to know chemistry, even the chemists.

Speaker 2 (05:57):
And I was like, well, what if any of them
listen to the podcast and they know what I've said
about chemistry. But you know, I think it went okay
in the end.

Speaker 1 (06:06):
I think it's important to admit our strengths and weaknesses,
you know, that's part of being a scientist. But that's
not the kind of stuff that just got me into physics.
I wasn't always fascinated with concepts, but temperature and pressure
and this kind of stuff. I remember as a kid
thinking about light, you know, wondering like if I block
the sun, if I put my hand in front of
the sun, how does light get to that tree over there,

(06:28):
And just thinking about like the way light moves. This
is like six year old Daniel, like doing little experiments
and like, obviously now it seems like a silly experiment.
The light can get to the tree even if my
hand is blocking the light from my face. But you
don't know until you do the experiment, right, And so anyways,
I've always been super fascinated by light and by shadows.

Speaker 2 (06:46):
Well let's not leave our listeners in the shadows. Let's
jump into today's topic. See, I did.

Speaker 1 (06:54):
Very nice. I was trying to get us there. Today's
episode is inspired by a question from a listener who
asked we could do a whole episode on shadows, and specifically,
they were wondering about three scenarios. One where you're standing
in the shadow of something like a tree, but you
can still see things around you. Why is it the
photons are reaching his eyes even if the sun is obstructed.

(07:15):
Number Two, he was wondering about what are shadows like
on the Moon? Are they sharper or darker than on Earth?
And then finally, of course, can shadows move faster than light?

Speaker 3 (07:26):
Oh?

Speaker 2 (07:28):
That sounds like it could be a trick question. I
think we should pass that on to our listeners.

Speaker 1 (07:33):
That's a great idea. So let's play a trick question
on our listeners. And so I went out there and
I asked them if they thought shadows could travel faster
than light. Here's what our listeners had to say on
this brilliant question. The obligatory answers, nothing can move faster
than the speed of light, but a sense that there
are multiple levels to this question. No, however, I would

(07:55):
say that they can appear to travel faster than light,
as they tend to loom larger than the object that's
being illuminated. But no, they can't travel fast and light.

Speaker 2 (08:03):
According to Einstein, No, they can't because they are the
absence of light, so they are related to light speed.

Speaker 3 (08:10):
If I had a spherical projector's screen at the orbit
of Pluto, and I had a bright light in front
of me, and then all of a sudden, I put
my hand in front of the bright light, it would
appear that a giant swath of shadow would go across
the screen all at once to me. But I think
to Pluto they would see it different, like it would
take this speed of light to go from one place
to another.

Speaker 2 (08:29):
Since you asked, it means that there's probably some exception,
so let's find out.

Speaker 3 (08:34):
I would say, No, shadows are the absence of light,
and light can only travel at the speed of light.

Speaker 1 (08:41):
That's a fascinating one. I'm gonna say, No, shadows aren't
a thing. There are absence of a thing. But the
answer Boyans would be doll I can't. Yes, but it
cannot be used for communication. Yes, shadows can move faster
than light, with caveat that only their appearance can move faster.

(09:02):
Than light. No, actual photon is moving faster than light.
I think so, because nothing's actually moving. It's just a
change in the pattern of light. But you're really breaking
my brain here. I think shadows are dependent upon the light.
It's kind of like the absence of light, and so

(09:23):
I think no. I think there's something like this about
the way the point where two blades of a scissors cross.
If the scissors are closed extremely quickly, I'll start see
how shadows could travel false with than the spate of light.
So I'm gonna say I travel at the same spade.

Speaker 2 (09:41):
So I think our listeners know us pretty well. A
couple of them are like, uh, this feels like a
trick question.

Speaker 1 (09:50):
I love hearing them use their physics knowledge and try
to work it out. Yes, some people got halfway there.
You know that nothing is actually moving. Other people are like, no,
this is an absolute principle and physics nothing can move
faster than the speed of light. But as usual, language
is the culprit here, because the principles of physics are
very clear mathematically, but things get fuzzy when you express

(10:11):
them in language, and so we're gonna end up splitting
the hairs between nothing and no thing, So.

Speaker 2 (10:18):
Thanks for playing along, even though we set you up
for failure over and over and over again. We appreciate you.

Speaker 1 (10:24):
We really do, We really do, And thanks to listeners
like Eric who write in with their questions and inspire
these episodes. We really want to hear what you are
curious about, because we want to scratch your itch about physics,
not just ours.

Speaker 2 (10:36):
Yes, we want to shine light on the darkness in
your lives. And if you want to contact us, you
can write us at questions at Danielankelly dot org. And
that's both to send us questions and to get on
the list of people that we send these trick questions to.

Speaker 1 (10:49):
Or just to tell us about your day and send
us cute pictures of your cat.

Speaker 2 (10:53):
Yeah, that'd be great.

Speaker 1 (10:54):
It works for everything, yep, I would love that.

Speaker 2 (10:57):
All right, Daniel, let's start with the basics. Shadows sound
like something where you're like, oh, yeah, I know what
a shadow is, But physics always makes simple concepts much
more complicated. So, Daniel, how would you define a shadow?

Speaker 1 (11:11):
A shadow is just the absence of light, And in
the simplest sense, this is fairly straightforward. If you have
a single source of light and you have things with
very crisp edges. Then you can use the concepts of
geometric optics where light travels and straight lines, and some
regions of your experiment will be illuminated and some regions
will not, and those are the shadows. And so places

(11:33):
that are obstructed from direct line with the light source
will be in shadow, and places that are not will
not be in shadow. So that's sort of the simplest,
clearest setup where the shadows are very straightforward.

Speaker 2 (11:45):
Okay, now give us some more complicated information, because I
know that's where you're going.

Speaker 1 (11:50):
Yeah, because we don't live in that kind of situation.
We never have a single source of light. Like number one,
Our light sources are not points. They're extended, right, They're
a little bit wide. And in physics we treat a
wide light source, you know, like a filament that's the
centimeter across, as a bunch of different sources of light.
You can treat it as like a set of pinpoint sources. Right,

(12:10):
So what happens if you have multiple sources of light, Well,
imagine two sources of light. You're in a room and
there's two light bulbs. Well, you can be in total
shadow if you are blocked from both sources of light, right,
And you can be in total illumination if you can
see both sources of light. But there's also a middle ground.
What if you're blocked from one source of light and

(12:31):
not the other, then you're in like half shadow, right,
And so now this is the fuzzy region. This is
actually called the penumber, places where you are blocked partially
from the full illumination but not completely. And so any
room that you're in, your shadows are going to have
these fuzzy edges because of their per numbers. Like I'm
in a room right now, and I have like four

(12:53):
banks of fluorescent lights, each of which is like a
meter across. So if I hold on my hand above
my desk, my shadows are very fuzzy. In fact, there's
like four of them and they partially overlap, and so
I don't have crisp shadows anywhere in my office.

Speaker 2 (13:06):
Oh, how sad.

Speaker 1 (13:08):
It's good good because otherwise the shadows would be very
very stark. Right, But this cost is really interesting effects
that are sometimes hard to understand.

Speaker 2 (13:17):
So could you still like if you had one light
in a room and it was like a broad light,
like a foot wide or something, could you still have
like a shadowy shadow? Hey, a fuzzy shadow is what
I meant. If the light is like reflecting off of
the walls a lot and coming back underneath your hand.

Speaker 1 (13:36):
Absolutely yes. And so that's another contribution is that the
things in your room do not perfectly absorb light. If
everything in your room was a black body object where
it just absorbed light and didn't reflect any then you
would have crisper shadows. But if you have a white wall,
it's white because it's reflecting light. And so even in
this scenario where you have one source of light where

(13:58):
you expect crisp shadow, if your walls are white, they're
reflecting light, and so some of that light is going
to reduce the shadow. So yeah, there's lots of ways
that shadows get fuzzier because things are reflective and because
there are multiple sources of light.

Speaker 2 (14:12):
Can I tell you the story about the one time
I came across the word penumbra while doing research.

Speaker 1 (14:17):
Is it gonna make me spit out my coffee or
throw up?

Speaker 2 (14:20):
No, it's not gross. It's a little silly, but it's
not gross.

Speaker 1 (14:24):
So let's do it.

Speaker 2 (14:25):
We were reading about space settlement proposals, and there was
someone who was proposing that Mercury would be a great
place to set up a space settlement. Really really, yeah.

Speaker 1 (14:35):
Because the wonderful outdoor temperatures.

Speaker 2 (14:37):
Yes, right, So Mercury being the closest planet to the
Sun and with no atmosphere, it gets very hot on
one side and very cold on the.

Speaker 1 (14:46):
Other because it's tidally locked.

Speaker 2 (14:47):
Yes, right, but at the penumbra the temperature is pretty nice.

Speaker 1 (14:55):
How wide is that? It's like centimeters or meters.

Speaker 2 (14:58):
It's whe enough that they thought you could like put
a moving habitat that would have to constantly move to
stay with the p number, and if you fall behind
or get too far ahead, you die, you know, different ways,
depending on if you're going too fast or too slowly.

Speaker 1 (15:13):
I like that. If my house breaks down, I die
very quickly. Yeah, that's very relaxing. I could definitely take
a nap in that.

Speaker 2 (15:18):
Yeah. Yeah, I think I'll pass on this plan. The
other plan was to bury yourself underground at the poles,
where the temperature was also not so lethal. But anyway,
I'm happy where I am. Daniel. I've heard this phrase
shadow blister, and I have no idea what it means
what is a shadow blister?

Speaker 1 (15:35):
Shadow blister is a really cool effect whereas two shadows
get closer together, they seem to kind of merge, and
even more than that, it seems like they leap out
towards each other. They grow towards each other. So if
you like stand next to a telephone pole, you have
a shadow. Telephone pole has a shadow. As you inch
towards a telephone pole, you'll see your shadows merge, but

(15:56):
they don't just like overlap geometrically. When you get close
to the telephone pole, the two shadows grow out to
meet each other. It looks really weird. You're like, what
is going on in my shadows? Like hugging? Do they
know about each other? Are they conscious? Is this am
I living in some weird science fiction novel? No physics
can't explain.

Speaker 2 (16:15):
This well, So is it called a shadow blister because
you're not supposed to pop them when they get together,
because then they might get infected? Is why are they
called shadow?

Speaker 1 (16:22):
Way? To make it grow scalty way? To make it crisal?

Speaker 2 (16:24):
I had to get it.

Speaker 1 (16:25):
They called shadow blisters because they sort of grow out
beyond the edge of the existing shadow, So you can
create a blister on the light pole shadow because of
your shadow. Well, what's happening here is that you don't
notice that the telephone pole shadow has many layers. There's
the sort of major shadow, but then there's sort of
minor shadows. There's the panenumbers, right, and as your numbers

(16:46):
overlap with the numbers of the shadow, then you start
to notice these things. And Minute Physics, which is a
great channel on YouTube which is amazing explainers about lots
of stuff, has a great video on this. You really
got to see this video to understand it, so check
got that video. But the key concept there is the number,
the fact that shadows are almost never crisp because you
don't have single sources of light.

Speaker 2 (17:07):
That's awesome. I didn't know that at all. Yeah, exactly, Daniel,
I understand my world better.

Speaker 1 (17:11):
Now, And so obviously in our lives, most of the
shadows come from the sun, right or from interior lights,
but like Kelly told us, you can also get shadows
from any source of light, including the moon, which of
course originally comes from the sun. But it's still kind
of cool to be walking around at night and see

(17:32):
your shadow, and if the moon is dark and it's
an exceptionally clear night and you're out very very far
from light pollution. You can see something really awesome, which
is a star shadow. What you can see your shadow
from the stars.

Speaker 2 (17:46):
Yeah, how could you be sure that it was from
the stars? I get if you can't see the moon,
then it's definitely not the moon that's causing it. This
is crazy. I can't wrap my head around this.

Speaker 1 (17:54):
It's hard to identify because the stars come from all directions,
but in principle, right, it's there. And it's kind of
amazing poetic that those photons have crossed like billions and
billions of kilometers of space only to be like blocked
from hitting the Earth by your hand.

Speaker 2 (18:09):
Or whatever, by your dumb face.

Speaker 1 (18:17):
And it just reminds me of how frustrating it is
that all these photons come from all over the universe
splash on the Earth and mostly they're just ignored. Like
those photons carry so much information about what happened inside
that star, what was going on. You know, it's future,
it's history, it's hopes and dreams, and they just like
get absorbed by some plant or whatever, and that's just lost.

(18:41):
We are tapping into, like the tiniest bit of this
huge river of information that's coming at us from the
universe anyway, and sometimes it makes cool shadows for you
to go ooh nice.

Speaker 2 (18:53):
So Daniel clearly is suffering from a massive case of
fomo yes, missing out on what those photons could tell.
Let's take a break and hopefully Daniel doesn't descend into despair,
and when we get back, we'll talk about some more
complicated features of shadows.

Speaker 1 (19:28):
All Right, we're back and we're talking about light and shadows.
And Kelly's comment reminds me that I actually have a
solution to my existential angst about missing all those photons.

Speaker 2 (19:37):
How are you going to collect all the photons? Daniel?

Speaker 1 (19:40):
Well, look, I figure if Dyson can come up with
its concept of Dyson spheres, which are basically just solar
panels that's around the Sun, I'm just going to make
a white sn sphere, which is basically space telescopes that's
around the Earth.

Speaker 2 (19:53):
Ah.

Speaker 1 (19:54):
Like, let's just give up our vision of the night
sky and replace it with like a solid bank of
telescope that gobble all that information. Imagine what we could learn.
I mean, every time we develop a space telescope that
appears at one little corner of the sky. We have
our minds blown by what we see out there, and
so think about what we could learn if we had
like a thousand, a billion times more capacity. It's never

(20:17):
gonna happen. But we're also never going to build the
Dyson Sphere, so I can put the White Sin sphere
into the same category of fantastical concepts.

Speaker 2 (20:24):
Yeah, if only we could collect all the photons and
deprive the plants of them, I'm sure that would be
great for all of us. I don't know who's who's
less realistic, you or Dyson, but it's a fun idea
to think about.

Speaker 1 (20:36):
All right, maybe just half the Earth then you know
when the Earth is in shadow?

Speaker 2 (20:40):
Which, oh, when it's in shadow? Okay, I was going
to ask which hemisphere you're going to condemn to.

Speaker 1 (20:45):
Let's have a vote. No, obviously at night. Yeah. So yeah,
this project gets more complicated and less realistic as we
think about it, but it was never gonna happen anyway.

Speaker 2 (20:54):
So, I mean, people are upset enough about starlink satellites
going in orbit. I'm not sure anyway, let's move on.

Speaker 1 (21:01):
So so far we've been talking about shadows from a
sort of geometrical optics point of view. Shadows just travel
in straight lines and like at the edge of an object,
either the light is absorbed or it passes. But the
wave light interacts with objects is more complicated than that,
and it makes shadows fuzzier and weirdly surprising. So shadows
played a really important role in the debate about the
nature of light. Is it a particle or is it

(21:24):
a wave?

Speaker 2 (21:24):
Is this the two slit experiment.

Speaker 1 (21:26):
Yes, the two slit experiment was part of it, but
that actually didn't settle the question in most people's minds
about whether light was a particle or wave until they
did this crazy shadow experiment. So what's the connection between
shadows and the particle or wave nature of light. Well,
if light is a particle, then shadows should be very sharp, right,
either the particle of light passes the edge of the

(21:46):
object or it's absorbed. But if light is a wave,
then it's more complicated because you get things like diffraction
and interference. So in the early eighteen hundreds, people had
done this experiment, like the Young double slit experiment, to
show that light had this like behavior, that it was
interfering with itself and so light was very likely a wave,
and you can see the same thing not just in interference,

(22:08):
but in diffraction. Diffraction is like the big sister of interference.
The way it works is, imagine you have like a
circular object and you shine a light on it, and
you have a screen behind it. What do you expect, Well,
you expect a circular shadow, right. If light is a particle,
that shadow should be perfect and crisp if you have
a single light source, because there's like an edge where

(22:30):
the particles just barely make it around the object, and
a tiny bit further in, for example, they don't, so
you get a very crisp shadow. With me still, yep,
I'm with you, all right, But if light is a wave,
that's not how light interacts with matter. What you need
to do instead is imagine a bunch of sources of
light all around the object, the same way as in
the interference experiment where you have two slits. The way

(22:51):
you think about that mathematically is each slit is now
a source of light. The light makes it through the slit.
You imagine that as a point source, and then those
two point sources interfere. Diffraction is like that, but now
you have lots and lots and lots of sources of
light all around the edge of this object. Everywhere the
light is making it around is a point source of light,
and those are all going to interfere. And so if

(23:13):
you look very carefully at the edge of shadows, you
can see this diffraction effect. There is no perfectly crisp shadow.
Even in a room filled with black bodies and a
single source of pinpoint light, you will still get these
fringes at the edge of shadows. You'll have like a
dark black center, and then you'll have a white band,
and then a black ring and then a white band.

(23:35):
You get this zebra shadow effect from the diffraction edges.

Speaker 2 (23:38):
So I've got a bright light and I'm putting my
hand under it and I'm not seeing the like. So
in our outline you have this great picture with ripples
that of course our audience can't see. But imagine like
you drop a rock in a lake and there's ripples.
There's a black spot where the rock got dropped, and
then there's ripples coming out from there. But that's not
what I feel like I'm seeing when I put my
hand under the light. And what was different about the

(24:01):
lab conditions that find these ripples obviously relative to my office.

Speaker 1 (24:05):
Yeah, well, you have to have a single source of light,
because otherwise you have all these panumbers which are overlapping,
and it's hard to isolate this effect. And you have
to have a room with no other reflections because this
is a subtle effect. It's not easy to see. But
it was not so subtle that two hundred years ago
they couldn't do it. And so the interference experiment and

(24:26):
this shadow diffraction experiment were very strong indicators that light
was a wave, not a particle. And at the time
people really believed, like Newton's idea that light was little corpuscules, right,
there was this little bits of stuff. So these were
hard to absorb, and there were lots of people who
like really dug in and they were like, this is absurd.
Light cannot be a wave. And one famous physicist Poisson

(24:49):
of Poisson statistics and all sorts of stuff. He studied
the theory in detail and he was trying to prove
it wrong.

Speaker 2 (24:55):
I have a feeling I would have been on team Poissan.
Light cannot be a wave. It doesn't.

Speaker 1 (25:00):
That's just because Poisson means fish, and you're always on
team fish.

Speaker 2 (25:03):
Kelly, I am always on team Fish. It's true. The
number of jokes that Fish people make about Poissan's statistics
is maybe nauseating.

Speaker 1 (25:12):
Off the hook, off the hock.

Speaker 2 (25:18):
Oh, thank you, Daniel, Okay, moving on, I had to.

Speaker 1 (25:21):
Dive into that one anyway. This is a great example
of something that happens in physics all the time that
people look for a ridiculous prediction from a theory as
a way to prove it wrong, but then it turns
out to actually prove it right. So Poissan did the
calculations and he discovered a weird prediction from the wave theory.
He discovered that at the center of that shadow, the

(25:42):
wave theory predicted a bright spot. Oh so you know,
the particle theory was the shadow should be perfectly circular,
and the wave theory predicted all these fringes, the zebra
lines at the edge, but also at the very center,
all of the waves add up and constructively interfere because
they are all equidistant from the edge, and so all

(26:02):
those photons should be in phase. And so Poissan was like, Aha,
this is a ridiculous prediction. You're telling me there should
be a bright spot at the center of the shadow
absurd and so this obviously disproves the wave nature of light, right.

Speaker 2 (26:16):
That would be fishy.

Speaker 1 (26:19):
You're just waiting with that jail.

Speaker 2 (26:21):
You can see it in my face.

Speaker 1 (26:24):
And so this was a very strong argument to reject
the wave theory. But then a guy went out and
actually did it, a guy called Arago. He went out
and did this experiment and there is a bright spot
at the center of the shadow. Do you google this image,
you can see there is a tiny white dot. This
is now called the Arago dot. And it was very conclusive,

(26:44):
and people were like, okay, well, you know, we said
that wave theory makes this absurd, nonsensical prediction, so therefore
it can't be true. But then if the universe actually
does it that way, that's a pretty clear indicator that
the wave theory is correct. So while the youngs double
slit experiment and these diffraction experiments were very strong evidence
already of the wave nature of light, it wasn't until

(27:06):
this shadow experiment, seeing a light at the center of
the shadow that people were like, okay, fine, light is
a wave?

Speaker 2 (27:13):
What was poissan a good sport? And was he like,
oh you got me now I'm hooked on the wave theory.
I know I took your joke. But was Poissan convinced
after this or was he long gone by then?

Speaker 1 (27:26):
Well, the historical summary I read suggests that it wasn't
especially gracious about it. You know, he didn't like on
the spot admit the wave theory. He was skeptical for
a while, but you know, he went on to have
a perfectly fine reputation, so he definitely survived scientifically.

Speaker 2 (27:41):
Yeah, but you know, I still I like my scientists
to be gracious when they're wrong. But anyway, what are
you going to do? So first of all, you have
blown my mind because when I first looked at this picture,
I didn't see the little white dot in the center.
I thought that it was a speck on my screen.
And so while you were explaining it, I was moving
the outline up and down, and I was like, that
dot is actually on the image. Yeah, that's awesome.

Speaker 1 (28:01):
So shadows taught us something about the nature of light, right.
The patterns of shadows are much more complex than you
might imagine, and the wave nature of light really is
revealed by the patterns of the shadows.

Speaker 2 (28:11):
Yeah, so this is all a little hard to believe,
but I'm with you. But like, what next? Are you're
going to tell me that shadows have colors?

Speaker 1 (28:18):
Shadows do have colors? Yes?

Speaker 2 (28:19):
Oh?

Speaker 1 (28:20):
Absolutely yes. So far we've only been thinking about single
sources of white light and complete shadows. Right, but remember
we talked about panumbers, right, you can have multiple sources
of light, and so you can have intermediate shadows. Well,
now take those multiple sources of light, so you have
three of them, and you make those colors. You have
a filter for each one, so you have like a

(28:41):
red source, a green source, and a blue source. Anywhere
where you can see all three sources, you'll be seeing
white light. And anywhere all three sources are blocked, you'll
be in shadow. But what happens if you're in a
place where you're only blocking the red light, then you
have green and blue light, which make a cyan shadow.
Or if you block the blue light, the red and

(29:02):
green merge, making a yellow shadow, or if you block
the green, the red and blue combined to form a
magenta shadow.

Speaker 2 (29:10):
Daniel, Right, so I don't feel a good Yes, but
this is totally going against my into a shadows are black? Daniel?
Is there is there a good video online?

Speaker 1 (29:19):
Yeah? I'm sure you can find a good video. But
this sort of bends the definition of shadow. I think
is the issue because in these regions, is it really
a magenta shadow? Well, you're shining a red and blue
light on it, so people would say it's magenta because
you're shining magenta light on it, not because you've blocked
the green light. Right, And so it really depends on

(29:40):
how you define the things that are not fully illuminated
or the things that are not fully blocked. Are they
parts of the shadow? Are they the colored panumbers? Or
are they partially illuminated.

Speaker 2 (29:49):
This is a physicist trick.

Speaker 1 (29:53):
I'm retreating to philosophy to avoid being proven wrong.

Speaker 2 (29:59):
All right, well, maybe I'll try this with my kids
one day. Okay, so I have a son who loves swimming.
Constantly he's swimming. Is there anything interesting or different about
how shadows are cast underwater? Are their p numbers bigger something?
Because of how water defrects, deflex Oh? What is the
word defracts, bends, refracts, refracts. Thank you.

Speaker 1 (30:27):
Shadows and water are fascinating because it's a little bit counterintuitive,
but water casts a shadow, like if you pour water
into a glass and you shine a light on it.
And then have a screen on the other side. You
will see the shadow of the water. And at first
you're like, wait a second, why would water have a shadow?
Water is transparent, right, It's like glass. Light passes through it.

(30:48):
Why is it making a shadow? What's going on? Did
I find a glitch in the matrix? You have not
found a glitch in the matrix. Water is transparent, but
light does not pass through it without bending. And so
it's happening here is that the light is acting like
a lens and it's refracting a lot of that light away.
And so the shadow there doesn't come from the object
being completely opaque, but from it being darker behind the

(31:10):
column of water because some of that light has been
refracted away.

Speaker 2 (31:14):
Ah. So if you were to measure the light on
the sides of the water, it would be brighter after
you put the cup there.

Speaker 1 (31:20):
It might be a tiny bit, but it gets refracted
in many, many directions, so most of it are even
hit the screen. Yeah.

Speaker 2 (31:26):
So when you are standing in the ocean, which I
guess you get to do as a California and probably
pretty often. All right, that is pretty solid. So you're
standing in the ocean and it's a bright sunny day
and you can see shadows cast on the sand by

(31:47):
the water. Is that just because like the way the
waves build up, it's changing the patterns of how the
light is bent.

Speaker 1 (31:54):
Yeah, exactly, because the surface is not flat. If you
stood in a perfectly still body of water, you would
see no shadows from the water on the bottom of
the pool, for example. But as soon as you make
a ripple on the surface, then you're gonna see shadows
of those ripples. For the same reason that now when
the light is hitting the surface of the water, it's
not going straight down to the bottom anymore. It's getting

(32:16):
bent away. And so when you have a pool that's
just like sitting there and it's like gently fluctuating, you
get these amazing patterns on the bottom of the pool, right,
brighter spots where the light is being concentrated, in darker
spots shadows essentially where the light is being bent away.
And so again this is a case not a full obstruction,
but of like a rearrangement of where the light is going,

(32:38):
creating these patterns of light and shadow. Really beautiful. One
of my favorite things about water is that you're essentially
seeing the surface right You're seeing the shadows of the surface.

Speaker 2 (32:48):
I like that it keeps me from dying.

Speaker 1 (32:52):
Water is good. Yes, we are definitely pro water on
this podcast.

Speaker 2 (32:57):
Another place where I like looking at shadows is on
a foggy day. So like we on our farm, every
once in a while, the fog will like come up
from the bottom fields. And one, I like looking at
my shadow in it. But two, I like imagining that
a zombie movie is going to be filmed in my
fields because it's kind of creepy. But so is there
anything interesting about shadows in fog?

Speaker 1 (33:18):
Yeah, fog is wonderful for studying shadows because it shows
you where the light is. Right, It's like having a
bunch of lasers and throwing up dust particles in front
of them. You can see where the lasers are. And
so fog is just like a bunch of particles of
water suspended in the air, and they tell you where
the light is. And you can have a shadow on
the fog. And so there's a well known effect called

(33:39):
the brocked in specter effect where you can have a
shadow on a cloud. Right, And so, for example, if
you stand in front of a car with bright headlights
in the fog, you'll see your shadow on the fog
and it can be this like huge looming shape. Right.
But also if you stand in front of your headlights,
you could see your shadow on a cloud in the
sky if you do it right. Yeah. Cool, And that's

(34:01):
the incredible thing about shadows is that you know, there's
this projection effect where your shadow can be so much
bigger than you are, right, and so you can like
wave your arms and then like the huge sky version
of you is also waving its arms.

Speaker 2 (34:17):
So I want to imagine that the Brocken spec effect
is an effect from you know, somebody who was like
studying ghosts and got confused about what was happening with
the fog. But how did this actually get its name
because specter always sounds sort of ghostbustery to me.

Speaker 1 (34:34):
I don't know the exact history of it, but it
shows up in like Lewis Carroll and Samuel Taylor Coleridge poems,
so it's definitely a thing that's been around for quite
a while.

Speaker 2 (34:42):
Okay, awesome.

Speaker 1 (34:44):
It's sometimes called the Mountain Spector or Specter of the Brocken.

Speaker 2 (34:48):
Oh, oh, that sounds even cooler. Specter of the Brocken.
That sounds like it should be in like a Viking tale.

Speaker 1 (34:53):
It comes from this mountain in Germany, the Brocken. It
was first observed and described by Johann Schilberslog in seventeen eighty.
We saw his shadow on the Brocken.

Speaker 2 (35:03):
Ah cool, all right, learn something new every day, all right.
So every once in a while you'll hear about like
pressure fronts coming through and is that like air that
is more or less dense? And could that change how
shadows are made? I guess I'm trying to figure out
if your NeXT's going to tell me that air can
also impact shadows.

Speaker 1 (35:23):
Yes, air can have shadows for the same reason that
water can, right, because air is not a fluid of
constant density. When it is, light just passes through it.
But if some pockets of air have higher density or
lower density, then the light bends in exactly the same
way as it does when it hits the surface of
the water. And you can already see this effect like
when you look at heat rising above the road on

(35:45):
a hot day. Right, what you're seeing there are pressure
waves in the air, and that's changing how light goes through.
That's why you're able to see it, right, And the
similar consequences for how light moves through the air. This
is why, for example, stars twinkle right. Stars don't twinkle
in space, They only twinkle through the atmosphere because their
light is getting bent away from you in a sort

(36:07):
of a chaotic, turbulent manner. This is why telescopes on
the ground can't see as clearly as telescopes in the sky,
because light has passed through this complicated atmosphere. And they
have these amazing adaptive optics to counteract for this to
like in real time, bend the path of the light
back to regather all that light into a crisper image.

(36:28):
But effectively it's like a shadow. I mean, if you
looked at the ground as life passes through it, you
would see regions that are darker and regions that are
lighter because of these density fluctuations in the air.

Speaker 2 (36:39):
That's amazing. And you know, one of my favorite things
about this time of year is that so like, I
don't stay up late because I'm a total wimp, but
in the winter and in the fall, you get when
I go out to do the animal chores, it's already dark,
and so on clear days I can see the stars
twinkling and the other day, I was late to wake
up my kids because the stars were twinkling, and I
was like totally enamored of it and forgot about what

(37:02):
time it was and fell behind on my schedule.

Speaker 1 (37:06):
Well, this start twinkling effect is very cool, and it's
you know, the kind of physics you can enjoy any evening,
But the same physics gives you a really weird effect
during a lunar eclipse.

Speaker 2 (37:17):
What I am dying to hear about that. So let's
take a break to increase the suspense, and when we
get back, you'll tell us all about it. Okay, you

(37:45):
were going to tell us about shadows and eclipses, Daniel.

Speaker 1 (37:48):
Yeah, so I'm lucky enough to have seen a total eclipse.
This was in twenty eighteen. Amazing experience, and I went
into it not preparing to be amazed. I was like,
I know the physics, Yeah, it's cool, it's going to
get dark or whatever. But there was something really moving
about being in the totality having the sun be so
completely blocked. Momentarily, it just everything felt so odd. And

(38:10):
you know, I'm not a religious person, but I almost
felt spiritual at that moment. I tried to imagine what
it might be like to not understand the physics at
all and go through that experience feel like, WHOA, something
is happening today.

Speaker 2 (38:22):
Yes, we are all gonna die. That's absolutely what I
would think.

Speaker 1 (38:26):
Have you seen totality?

Speaker 2 (38:27):
No, In Virginia a year or two ago we got
a partial eclipse, but even that was pretty amazing. But
you know, as a biologist, I was trying to listen
to see if the nighttime animals were waking up and
being like, oh, what's going on? And I think there
was a little bit of that. I bet there was
a lot more that where you were.

Speaker 1 (38:42):
Actually this was in Idaho, I believe it was for
the path of totality for that eclipse really amazing. Totally
encourage everyone to see totality if they can. And there's
a really cool effect which I didn't see at the time,
didn't even know about until preparing for this episode, but
there are these things called shadow bands that happen during
a total eclipse for the same reason as star twinkling.

(39:03):
What's happening is that you have the sun now narrowed
to a very very very narrow source of light, right
instead of being a huge blob in the sky, you
have like a very thin crescent. So now sunlight is
very columnated. All the rays are very very parallel, and
what happens is it creates these thin, wavy lines of
alternating dark and light that can be seen moving and

(39:25):
undulating in parallel just before and just after the total
solar eclipse. So there's these like shadow bands of the eclipse.
Just the same way that a solid object will have
these diffraction patterns around, these zebra patterns. The moon has
those patterns a shadow on the Earth, but not for
diffraction reasons. It's for the same reason it's the star twinkling,

(39:47):
because now you have this column of light which then
gets bent randomly by the varying density of the air,
but it all is moving in a column, so you
get these bands. Really incredible. I want to see this
in person.

Speaker 2 (39:59):
I want to see that also, and I also, for
the first time, want to see our podcast as a
video episode, because the extent to which your arms were
moving to try to explain that was really fantastic.

Speaker 1 (40:10):
That's the Italian in me coming out, you know.

Speaker 2 (40:15):
So the listener asked a question about what shadows would
be like on the moon, and the context for the
question was you know the Moon has a very tiny,
thin atmosphere and exosphere. How does atmosphere impact the way
shadows are made? And would it be different if you
were on the moon. So like, what did the Apollo
astronauts see when they looked at their shadows?

Speaker 1 (40:34):
All right, well, I'm going to give you a pop quiz.
I've taught to you now enough physics on this episode
to answer this question. What do you think, Kelly? Do
you think shadows are crisper on the Moon or less crisp?

Speaker 2 (40:44):
I think that it's probably about the same because you
still have light reflecting from lots of different surfaces, and
I bet the surface of the Moon in particular is
pretty reflective. I guess here when the atmosphere changes in density,
that bounces light around and makes it a little bit
less crisp. And so maybe with no atmosphere, I'm gonna

(41:04):
guess crisper crisper.

Speaker 1 (41:07):
Yes, exactly, it's crisper. And the issue is the atmosphere.
I mean, think about how if you're standing on the Earth,
you look up, the sky is blue, right, what's the
color of the sky and the moon.

Speaker 2 (41:18):
Black?

Speaker 1 (41:19):
It's black right, because there's no atmosphere there to reflect light,
and so the atmosphere here is blue. That means that
you're getting light from all directions. Right, Yes, it's mostly
from the sun, and you can see shadows. But the
answer to Eric's other question is the reason you can
see still light when you're standing behind a tree and
the sun is blocked is because it's light reflecting everywhere

(41:40):
on the Earth, from all over the sky. And yes,
and all the buildings and whatever. But the atmosphere itself
is like bouncing light everywhere, and on the Moon you
have no atmosphere, and so it's much more geometric. Yes,
you do have rocks that are reflecting light, and of
course during the nighttime we see the reflection of the moon.
But the atmosphere is a big contributor to making shadows fuzzy,

(42:01):
and of course fluctuations in the atmosphere make that fuzzy.
So yes, the reason you still see stuff when you're
standing in shadow is because it's light coming from many sources,
not just one, and on the moon, shadows are crisper.
But shadows are also important on the Moon for another
reason that you might find interesting, which is they provide
place for water ice to accumulate. Right, because shadows on

(42:22):
the Moon are very very cold, right, The moon surface
is crazy, it's super hot, it's super cold. It depends
on are you in the blinding path of the sunlight,
and if you're not, then the water ice can survive.
And isn't there a place like on the lunar pole
where light never reaches?

Speaker 2 (42:37):
Yes, that's right, on both poles and places like Shackleton Crater.

Speaker 1 (42:41):
It's like eternal shadow or something really dark.

Speaker 2 (42:44):
Oh, craters of eternal darkness exactly.

Speaker 1 (42:48):
And shadows there are really important because they preserve water
eyes and if we ever do live on the Moon,
that would be really valuable. Right, So shadows could save
our lives on the Moon.

Speaker 2 (42:57):
Yeah, although I'll note that there's not a lot of
water in those shadows, but there is some. It could
get us started. We'd have to be real careful about
recycling it.

Speaker 1 (43:07):
Shadows have also really helped us understand the nature of
our place and the cosmos. Famously, more than two thousand
years ago, the Greeks used shadows to measure the radius
of the Earth. Right, Greeks so clever, so geometrical. They
realize that the Earth is probably a sphere because as

(43:27):
you move around it you can see different kinds of stars, right,
Different constellations emerge as you move around the Earth. So
the Greeks much smarter than like, you know, certain rappers
and YouTube influencers who still deny that the Earth is
a sphere. But they went beyond just saying, oh, the
Earth is likely a sphere. They use the behavior of
shadows and a little bit of geometry to measure the

(43:49):
radius of the Earth and got it pretty accurate, like
more than two thousand years ago.

Speaker 2 (43:54):
Well okay, so can you give us more details about
how they did that.

Speaker 1 (43:57):
Yeah. So, imagine you're in a city where the sun
is directly it's like high noon, and so all the
shadows point straight down, right, there's basically no shadows. Then
you have another city that's like hundred kilometers away, and
that city is not going to be at high noon.
It's going to have some shadows, right, And you can
measure the length of those shadows, and now make a

(44:18):
triangle where you know the distance between the two cities,
and you can measure the length of the shadow. The
length of that shadow depends on the curvature of the Earth,
because if the Earth was very, very flat, that shadow
would be small. And as the Earth gets more and
more curvature, that shadow would grow longer and longer. So
by measuring the length of the shadow in Alexandria at

(44:39):
the time that the sun was directly overhead in another
city which I can't pronounce, a Greek dude named Erasthenes
was able to measure the circumference of the Earth just
using like a stick and some geometry and measuring a shadow.

Speaker 2 (44:54):
So like Eritosthenes, I'm not gonna say it right uh,
called his friend down in Syena, was like, we're both
taking the measurements right now, though, how did I guess that?
Did they also have really good clocks or they just
were like that is okay, yeah, exactly, that's amazing.

Speaker 1 (45:08):
So this is really cool. But the fascinating thing is
that flat Earthers have not let this point go and
they argue that this experiment doesn't actually prove that the
Earth is round, and they're kind of right, oh no,
because even if the Earth was flat, you would still
have a shadow in one place when the sun is
directly overhead in the other city. That's true. Essentially, it's

(45:30):
like measuring the earth to have an infinite radius, but
you would definitely get a shadow, because this whole method
assumes that the sun is really really far away and
that the light is parallel essentially, But in the flat
earth model, the sun is very very close, and so
you would still get a shadow in one place and
not a shadow in the other. But there's a way
around it. All you need to do is add a

(45:51):
couple more sticks, so instead of just having two points,
you have like three or four, and the two models
give different patterns of shadows. In the flat earth model
you get a linear relationship between the length of the shadows,
and in the spherical Earth you get a non linear
relationship as things move around the curve of the Earth.
So anyway, we're pretty sure that the Earth is not flat,

(46:13):
and you can actually prove it using shadow and rod experiments.
It's true the two point experiment doesn't refute the flat earth,
but anyway, shadows do show us that the Earth is round,
and you allow us to measure the roundness of the Earth,
which is kind of amazing.

Speaker 2 (46:28):
That is amazing way to go shadows. So the last
question the listener had was the trick question that we
shared with our extraordinaries, which is do shadows move faster
than light. Yeah, so all right, now we have all
of the background, we need to understand the nuance to
this question. Yes, so take it home, Daniel.

Speaker 1 (46:49):
The answer is, yes, shadows do move faster than light.
What But but the problem is that the rule says
no thing can move faster than the speed of light
relative to anything else. But shadows are not a thing,
that's the problem. They're the absence of a thing, and

(47:10):
as a shadow moves, it's not really the same object.
So let's imagine a concrete scenario.

Speaker 2 (47:16):
Right.

Speaker 1 (47:17):
Let's say you have a screen in the sky instead
of the sky. You're like, you know, Daniel has built
his telescopes that block the view of the world, and
so you have exactly right, and you can imagine a scenario.
We have a bright source of light and you can
do like shadow puppets on the sky, right, or imagine
clouds or whatever, and you can move your hand a

(47:38):
small amount and the shadow will move a very large amount, right,
because the screen is very very far away, and so
this projection is far away, and you get this multiplier effect.
And then you can ask, well, if I move my
hand really fast and the screen is really far away,
could those shadows move faster than light, And the answer
is yes, in the sense that like the image of
your hand could be in one place and then fast

(48:00):
and then light could go from that one image to
another image the image the shadow could appear somewhere else, Right,
does that make sense? Like imagine somebody in the sky
shooting a laser from one shadow to the other. The
second shadow would appear before the laser arrived. In that sense,
the shadow is moving faster than light, and you're wondering, like,
how does that make sense physically? What's really going on?

(48:23):
And the issue is that the second shadow is not
the same thing as the first shadow, right, both of
them are being created by the absence of light. Nothing
is moving faster than light in the scenario, and there's
no way to communicate between the shadow one and shadow two.
There's no information passing. It's just like if I shown
a laser in one direction and then I turned it
off and shown it in another direction, the laser spot

(48:46):
would appear to move faster than light, but it's not
the same spot. Right, It's like I made a spot
and then later I made another spot. I'm connecting them
in my mind because they both came from the same laser.
But it's not like anything moved from laser spot one
to laser spot two the same way nothing went from
the shadows initial location of the shadow's final location. You
have a wave of light that's obstructed and not obstructed

(49:08):
that's creating the shadow, and then a different wave of
light that's creating a different shadow somewhere else. And your
mind is like, shadows are a thing, and so it
was here and it was there, and if I do
distance divided by time, I get a number bigger than
the speed of light. Yeah, that's true, but shadows aren't
a thing. It's like comparing where one thing is and
later something else is and calculating the velocity between those two.

(49:30):
It doesn't really work.

Speaker 2 (49:31):
Is that like saying that the information that the photon
has been stopped travels faster than a photon would travel.

Speaker 1 (49:38):
No, the photon. The information that the photon has been
stopped isn't traveling from shadow one to shadow two. It's
traveling from the source to shadow one, and from the
source to shadow too. Like you could signal somebody up
there in the sky using shadows or not shadows, but
that information obviously travels at the speed of light because
you're either sending photons or you're stopping to send photons.
But all that information novels at the speed of light.

(50:00):
And you could do the same for person two. But
you can't get information from shadow one to shadow too,
or there's no way for you to do that. You
can send information. All the information is coming from the
source of light to the shadows or the non shadows,
not between them.

Speaker 2 (50:15):
Got it.

Speaker 1 (50:16):
So the appearance of shadows can move faster than light.
But shadows are not really a thing. They don't carry information,
and so in that sense, you know they're breaking the rules,
but they're not really limited by the rules because they're
not a thing. They don't have information.

Speaker 2 (50:30):
Well, thank you Daniel for illuminating all of our understanding
of this question. I learned a lot and had a
lot of fun talking about shadows because.

Speaker 1 (50:38):
They're neat Well, I'm hoping we can help bring shadows
out of the darkness. Shadows are a wonderful way to
think about light and to think about physics and just
to like, you know, wonder in an everyday sense how
everything works. They're fantastic mysteries of physics all around us.

Speaker 2 (50:51):
There are and please send us your questions about the
mysteries of you know, physics, I guess if that's what
keeps you up at night, but definitely the questions that
you have about biology, which is a fascinating topic.

Speaker 1 (51:04):
And if you're the descendant of the famous physicist Poisson
and you want to write into defend his legacy, please do.

Speaker 2 (51:10):
All right until next time, Extraordinaries Daniel and Kelly's Extraordinary
Universe is produced by iHeartRadio. We would love to hear
from you.

Speaker 1 (51:24):
We really would. We want to know what questions you
have about this extraordinary universe.

Speaker 2 (51:30):
We want to know your thoughts on recent shows, suggestions
for future shows. If you contact us, we will get
back to you.

Speaker 1 (51:37):
We really mean it. We answer every message. Email us
at questions at Danielankelly dot org, or.

Speaker 2 (51:44):
You can find us on social media. We have accounts
on x, Instagram, Blue Sky and on all of those platforms.
You can find us at d and kuniverse.

Speaker 1 (51:53):
Don't be shy write to us.