How do we measure the speed of light?

Daniel and Jorge talk about the history of how we measured this fastest of all velocities!

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Episode Transcript

Speaker 1 (00:01):
Hey, it Jorhan Daniel here, and we want to tell
you about our new book. It's called Frequently Asked Questions
about the Universe because you have questions about the universe,
and so we decided to write a book all about them.
We talk about your questions, we give some answers, we
make a bunch of silly jokes as usual, and we
tackle all kinds of questions, including what happens if I
fall into a black hole? Or is there another version

(00:22):
of you out there that's right? Like usual, we tackle
the deepest, darkest, biggest, craziest questions about this incredible cosmos.
If you want to support the podcast, please get the
book and get a copy not just for yourself, but
you know, for your nieces and nephews, cousins, friends, parents, dogs, hamsters,
and for the aliens. So get your copy of Frequently
Asked Questions about the Universe is available for pre order now,

(00:46):
coming out November two. You can find more details at
the book's website, Universe f a Q dot com. Thanks
for your support, and if you have a hamster that
can read, please let us know. We'd love to have
them on the podcast. Hey Daniel, I have a question

(01:11):
about the physics of the Internet. Oh, that sounds like fun.
Like what is the speed of email? You know, how
fast does it travel? If I write you an email?
When does it get to you? You know, I think
email might actually violate the laws of physics. What do
you mean they go faster than the speed of light?
Or do you mean like if it falls into a
black hole it's actually my inbox? Yeah, exactly like that.

(01:33):
I can tell you a story about one time I
had email violate causality No way. What happened? Well in college,
one time I sent a draft of an essay to
my TA for comments. She wrote back, Hey, looks great,
no comments. Then I realized I'd never attached it to
the email. It sounds actually violated the laws of her
responsibilities as a t A, not the laws of physics.

(01:56):
That's one interpretation. Is there a non physical interpretation? The
grad student union won't allow me to talk about that.
It breaks their laws. Hi. I'm Orge, my cartoonist and

(02:21):
the creator of PhD comics. Hi, I'm Daniel. I'm a
particle physicist and a professor UC Irvine, and I'm recording
this podcast on the same microphone Michael Jackson used to
record thriller. What what do you mean, like the same
microphone or the same brand, the same brand. I just
discovered yesterday that apparently I'm using a very well known,

(02:42):
famous microphone, which in the industry is known as the thriller.
Mike no way, Wow, is it extra? Kind of like
it has ex extra pops and extras to go a
little bit higher in your falsetto voice. It does make
me do a little dance every time you make a
really funny joke. So, yeah, you do the moonwalk when
we talk about the moon. I don't want you to
think about that too much in your head, but yeah,

(03:04):
let's say that's what happens. Yeah, But welcome to our podcast.
Daniel and Jorge explain the Universe, a production of I
Heart Radio, which is sort of like Thriller, and that
we take you on a thrill ride around the universe.
We don't raise the dead and dance them around, but
we do talk about everything in this universe that happens,
everything that gets extinguished, everything that flies around and amazes

(03:25):
us with everything that can do, and all the laws
of physics that seem to work together in harmony to
make this universe so crazy, so bonkers, so amazing and
yet so discoverable. Yeah, because it is a pretty thrilling universe.
And we like to take you on the moonwalk every
episode so we can think about the universe and possibly

(03:45):
even beat it. What is the moonwalk analogy? There? It
looks like you're moving forward, you're actually sliding backwards. Does
that mean like we're doing physics? We think we're understanding,
but really we understand less and less every year. You know,
basically we're faking the whole thing. We're actually moving the
progress of science backwards. We're walking backwards on evolution here,
but it looks like we're moving forward. I like to

(04:07):
think that our podcast helps science move forward in a
real way because it excites people and engages them in
this Species Why project, they're trying to uncover the mysteries
of the universe. Yeah. And also we're wearing red leather
jackets right now with a lot of zippers in it.
That's right. I only have one sparkly glove on. Does
that make me Michael Jackson? I have the other one.
It's like we're handshaking glittering gloves across the internet. That's right.

(04:31):
And we're trying to merge all the Jackson siblings into
one theory of Jackson, the unified theory of entertainment. Yeah,
of soul and R and P. But it is a
pretty thrilling universe, as we said. And this is an
interesting question about how fast do emails travel? Like, if
I read you an email and I hit send, does
it go to you at the speed of light? Right?

(04:53):
Because sort of, right, because electricity and signals over telephone lines,
they sort of go basically as fast this light. Right,
that's right. That information does travel at the speed of light.
You take like a wire, you send a pulse down it,
It does travel very very fast, essentially at the speed
of light. But we all know, of course, that email
doesn't arrive that quickly when you send it, because it's
got to go through all sorts of like computers who

(05:15):
do algorithms and weight on it and analyze it. And
so for example, my email here at you see I
sometimes it takes ten minutes to get one. Yeah, and
that's not even the emails you send me, which takes
me hours to even read. But yeah, the speed of
light is pretty fast. It seems to be basically the
speed limit of the universe. Right, Nothing in the universe
can go faster than the speed of light. That's right,
it seems to be this hard and fast limit. It's

(05:37):
just like a feature of our universe that there's a
maximum speed of information, which is really super cool philosophically
to think about, like why is that and how could
the universe have been different? And what does it mean?
But it's also really fun to think about, like how
did we figure that out? You know, something we know now,
it's something we definitely understand, but like obviously early humans

(06:00):
know that, and so I think it's always fun to
return to the moments that we cracked at these problems
that we like gained a new understanding of how the
universe worked. Yeah, because it's crazy to think that at
some point we didn't know what the speed of light was,
or even that it sort of had a speed I imagine, right,
Like I imagine early man probably thought light was instantaneous,
like you light a stick on fire and immediately the

(06:23):
light hits your eyeballs. Yeah. The Greeks had a lot
of totally uninformed debates on the topic, you know, speculating
endlessly about what light was, did it emanate from objects,
did it reflect from things? Did it travel instantaneously? Was
it a thing or not a thing? What does it
mean to be a thing? Man? Like the Greeks went
on and on and on with no information. It's amazing

(06:43):
to me, for thousands of years you could have uninformed
debates because of our discussions these days are informed. Well,
we have data, we can do experiments, we can learn things,
we can make progress, you know, without just like smoking
more of Bannan appeals and thinking about how the universe works. Man, Well,
it is pretty interesting thing to think about the speed
of light. And I think what's also interesting is that
it's not infinite, like it's a number, you know, like

(07:05):
the craziest you can go into the universe is a
specific number and nothing can go faster than that number.
That's right, Yeah, And it's interesting, right every time you
see a number in the theory of physics, you wonder
why that number? Did it have to be that? Could
it have been something else? If it could have been anything,
then why is it this value? Or if it could

(07:26):
only be one thing, then what are the rules that
make it have to be that one thing? And what
does that mean? So it's like a huge screaming clue
to me. Every time we see a number in physics,
what is it? Screaming and screaming, there's a secret here,
there's something else to be understood that in a hundred
years somebody else is going to win a Nobel Prize
for an explanation. And you have all the information you
need to arrive at that idea. You just don't see

(07:48):
it right. Yeah, And isn't it weird to think about that?
All other speeds that are greater than the speed of
light are basically impossible, like one per second faster than
the speed of light, impact any number from that number
to infinity is basically impossible in the universe. Yeah, the
universe says no, and it doesn't negotiate. There's no whidle

(08:10):
room there. You can't charm the universe into letting you
do something a little bit past the speed of light.
It's a firm no, it's a hard pass from the universe.
And what exactly is the speed of light? Daniel? How
how many digits do you know it? Too? Well? It's
funny you should ask, because in particle physics we say
the speed of light is one, like we use units
where the speed of light is just one, because we
can't be bothered to write it down all the time

(08:32):
because it's everywhere. So we have equations with like speed
of light square speed of light to the four speed
of light to the eighth, and so it just sort
of gets annoying. So we just say, let's just set
see equal to one, and then we can ignore it. Mostly,
let's ignore reality for our convenience. Let's have another lens
in which we look at reality in which it makes
more sense than we can boil it down to its

(08:52):
true fundamental essence and not get tangled up in little numbers. Right,
so you can take more naps, right, you can take
more naps. So a particle physicist is the wrong person
to ask about the actual value of the speed of
light insensible units. But we do define it as two
hundred nine million, seven hundred thousand, four hundred and fifty
eight meters per second. So that's the exact value of

(09:15):
the speed of light. The most people when they do
calculations just say three times tended them per second, right,
or like three hundred million meters per second. But it
is a very specific number, right, it's like eight and
like four or five. Nine is too fast. You can't
go that fast. That's right. It's a no on four
or five, nine and a half, no, five point one. No,

(09:37):
there's no flexibility, there's no negotiation. This is in Hollywood.
We're like, hey, we can find a deal. Right. It's
kind of weird, right that the universe would just pick
the number and nothing can go faster. Yeah, it's a
huge clue. That's telling you something really deep about the
nature of space and time itself, right, Like if the
loop quantum gravity is true and space really is a
big quantized foam bubble, then maybe this tells us about

(09:58):
how those foam bubbles talk to e other and you
can't get information from one phone bubble to the other
faster than that because they just aren't closely enough connected
or something. So I think it really does tell you
something deep about the nature of the universe. Yeah, and
it's a very specific number, and so I guess the
big question is like, how do you know it's that number?
To what accuracy do we know that's the right number,
that it's a maximum speed limit of the universe, and

(10:20):
how did we figure it out? So to be on
the podcast, we'll be asking the question, how do we
actually know what the speed of light is? That we
actually measured it, or are we guessing? You're right, you
figured out we always been guessing this whole time, and
you have revealed this like a Scooby Doo episode. You've

(10:41):
pulled off the mask. Well, a few minutes ago you
just said one, right, So I don't know what's true
anymore than you. They're all true. It just depends on
the units. Well, I guess I'm wondering, like, has anyone
actually tested, right, because nobody has actually tried to go
faster than the speed of light technically right, Like you haven't,
I haven't. I have totally tried apps. I've tried so
many times as a kid. I mean I didn't get

(11:02):
anywhere near the speed of light. But that doesn't mean
I didn't try to try. I mean like a credible try,
not like a far off by by ten decimal places.
That's true. But you know I did grow up to
work at a particle accelerator, which makes a pretty credible
attempt to get particles to go faster than the speed
of light. We take protons and we accelerate them. We

(11:25):
give them so much energy, and they go faster and
faster and faster, And what we see is that as
you add energy, the particles just don't get going much faster.
It's sort of a mind bend there, Like you can
add energy, there's more kinetic energy in these particles, but
they're not moving much faster. Right, it approaches a speed
of light. But I guess a big question is how
do you know what the actual speed of light is?

(11:45):
Like the actual number, Yes, so that you can measure
by actually looking at light and measuring it, but you
can also see the protons approach it. Right. We have
these limits in physics all the time where you can
see something is approaching a limit and as em topically
gets closer and closer and closer, and so you can
alculate what that limit would be if you went to
infinite energy. You can extrapolate mathematically to figure out like

(12:06):
what is the limiting case, either from looking at protons
to see what they are approaching, or just by directly
measuring the speed of actual beams of light itself. Well,
that's kind of what we're going to get into today
is kind of the history of how we've gone about
measuring light and also what are some of our best
current measurements of it and some really surprising twists about
what we do and don't know about the speed of light,

(12:29):
some light twists or some dark twists a little both. So,
as usually, we were wondering how many people out there
knew the answer to this question, how we measure the
speed of light? So Daniel went out there and ask
people on the internet if they knew how we measured
the speed of light. That's right, So thank you to
everybody who, during these strange pandemic times, have stepped up

(12:50):
to fill in the gap left by you see Irvine
students and answered questions online. If you'd like to participate
for a future episode of the podcast, please don't be
shy and right to us two questions at Daniel and
Jorge dot com. So think about it for a second.
What would you answer? Here's what people had to say. Well,
if we already had space travel by the time we
were trying to measure that, we could have sent a

(13:15):
radio transmission from the moon with time stamp and see
how long it took to get there. So I don't
know exactly how we measured the speed of light, but
I would guess by measuring the time required for light
to travel a certain distance, maybe by using the mirror experiment,
where the time required for light to travel to the

(13:38):
mirror and back from the mirror is recorded, and since
we know the distance and time, we can find the
speed of light. Oh, no idea. I mean it was
theoretical at first, and then they tested it. So then
a particle accelerator I think Galla Lao tried to measure

(14:01):
the speed of light using lanterns at set distances across fields.
I assumed that wasn't successful, though, and I assumed that
we've also tried to measure it by bouncing signals off
the moon in more recent times. I don't know, though,
what the first successful measurement of the speed of light was.
I guess maybe they worked out like the distance between

(14:22):
two objects in space, and then worked out how quickly
light traveled between them and did the maths. I don't know.
That's a really good question. So I've been racking my
brain trying to think of this, because I swear I've
learned this in high school or college physics. But I
couldn't tell you know how we measured the speed of light.

(14:43):
A guy climbed a mountain and shone a light at
a rotating mirror on another mountain and counted how long
in between for the late come back. So what do
you think of these engineering ideas for how to measure
this incredible speed. I think they're a little light on substance,

(15:03):
but they're pretty good attempts. A lot of people didn't
seem to have sort of an idea of how we've
done it. Maybe, you know, they could think about ways
that they could do it, but I guess not a
lot of people. You know what the latest and greatest
measurement is. Yeah, and the challenge, of course is that
it's super duper duper fast. Like we talked about the
speed of light being three million meters per second, that's

(15:24):
sort of hard to understand, you know, what does that
really mean? I think it's easier sometimes to think about
it in terms of how far light goes in a
very short amount of time, rather than in a full second. Actually,
think about light is traveling about one foot every nanosecond,
so like a light nanosecond. You know the concept of
a light year, how far light travels in a year.
A light nanosecond is about one ft or thirty centimeters.

(15:47):
For those of you on the metric system, I totally
reject that that way of looking at the first of all,
it's English units using feet instead of meters, and also
a nanosecond that doesn't have a lot of meaning to me.
I guess, well, I guess you don't get a lot
of things done in a nanosecond. But I'm pretty efficient,
you know, I can answer ten emails in a nanoseconds.
So you live in another reality, it seems no, no,

(16:11):
obviously not. But you know, when you're talking about like signals,
like how long is it going to take my information
to go down this cable? I have one piece of
equipment over here, another piece of equipment over there ten
feet away, so you know it's gonna take ten nanoseconds
to get from here or there. And sometimes if you're
building electronics, right, you need to know are these signals
gonna be coordinated with the gap going to be between them?
And so it's helpful sometimes to think about light in

(16:32):
terms of how long it takes to move across a
reasonable distance, because I don't really know what three hundred
million meters is, but how can we measure it in
terms of like in the blink of an eye, Like
let's say a blink of an eye, is I don't know,
a hundred milliseconds, how long can that light travel in
those hundred milliseconds. Well, you know, a hundred milliseconds is
only a tenth of a second, right, and so a

(16:55):
tenth of a second would be thirty million meters, So
it's still pretty are that light can go in the
tense of a second, right, thirty million meters, it's about
thirty tho kilometers, right, which is about yeah, that's right,
thirty millions is just under twenty thousand miles. So like,
if I blink, then light can travel basically once around

(17:15):
the world kind of almost maybe if you're at the
latitude of like North America, like could go around the
Earth in the blink of an eye. And that's really
the challenge of measuring the speed of light that it's
so darn fast that for all extents and purposes, for
the things we do, it's essentially infinite. And that makes
it really really challenging because you either need incredibly vast

(17:36):
distances so you can accumulate some like reasonable amount of
time between when you send a message and when it arrives,
or you need to be able to measure really really
short times. And so imagine you're like Aristotle five thousand
years ago, How could you possibly set up an experiment
to measure something over vast distances or very short times? Yeah,

(17:56):
because I guess you know, it's hard to measure something
that happens in the blink of an eye, right, especially
if you're in the thousand years BC or something that's right,
if all you have is like you know, a clay tablet,
a stick and a robe, then like what are you
gonna do? And these days, even for us, it's not
easy to see the impact of the speed of light.
You know, it impacts things like spaceflight communication. If you're

(18:17):
on Mars driving a rover, then sure, and there's an
impact of the speed of light not being infinite. But
here on Earth, you know, it doesn't really make a
difference in your life very much. If you're like the
designer of a computer, then you think about this, like
how long did it take the information and go across
my CPU? And can I optimize the design of it
to bring things closer to speed up my computer? But

(18:37):
unless you're driving rovers on Mars or designing CPUs, you
probably don't think about the speed of light very much. Yeah,
it's probably pretty instantaneous to you in an intuitive sense.
But I think if a big question is like, how
do we know it's this particular number, right or not? Yeah,
well that comes from the things we measure, and we
have no like theoretical preference for that number. It's not
like the kind of thing we could have derived where

(18:58):
we're like, well, it has to be this number, it
can only be this number. It's just a measurement, right.
Often in physics there are things where you know, there's
something we know happens in the universe, but we don't
know why it's this way and not the other way,
and so we just have to measure it. Things like
the mass of the Higgs boson, or the mass of
all the particles, or you know, the strength of gravity.
These are things we don't know why they are that

(19:19):
number and not some other number. And the speed of
light is like that. It's just something we have to
go out and measure, like it could have been another number, right,
it could have been three, or we don't know, right,
it could be that it has to be this number
because there's some deeper theory of physics that constrains it
and makes it only work for this value. But we
don't have that theory of physics. According to our theory,

(19:41):
it could have been any other number. But of course
we don't expect that our theory of physics is the
final answer. And it's exactly the kind of place where
I see there are opportunities right where we say, well,
we don't have an explanation for this, so let's keep
looking for an explanation. To me, it's unsatisfying. People say, well,
it could have been anything. It was just random or
one element in the multi verse. So this is just
what it is. There is no explanation to me. It's

(20:03):
a clue that says that probably is an explanation. Keep digging, right, like,
maybe it tells you something specifically about why the universe
was the way it had to be. We just don't
see it yet. And it's also interesting to think that
it's not just the speed of light. It's like the
maximum speed that information can travel in the universe, like anything.
It's not just light that travels at the speed of light.

(20:25):
It's any particle without mass. Yeah, and it's sort of
a misnomer, right. We discovered light moves at this speed first,
and it is the speed of light in a vacuum.
But really it should be like the speed of space
time or the speed of information, because, as you say,
anything that doesn't have mass, and that means like a
graviton if they exist, or a gluon for example, anything

(20:46):
that doesn't have mass has to travel at the speed
of light, and only the speed of light, and nothing
else that does have mass can travel at that speed.
So it really is a special speed in the universe,
more than just the speed of photons. Right, maybe you
should have been called the speed of nothing. You like
that because light is technically nothing. It has no mass,

(21:06):
and nothing can go faster than it. No, because it
takes no time to do nothing, Right, like you didn't
do anything? How long? Did that take? No time at all?
So nothing is instantaneous. It's zero divided by zero. So,
if anything, I think that would have been more confusing.
All right, well, let's get into what we've done throughout
the thousands of years of human history to measure the

(21:27):
speed of light, and then let's get into our latest
measurements of that number. But first let's take a quick break.
All right, Daniel, we are measuring the speed of light

(21:47):
today on the episode Are you ready? I'm gonna clap
and then you tell me how long it took. All right,
that was exactly one clap per clap. There you go.
That's the joy of particle physics. Units. The answer is
always one or E or pie in particle physics. That's
why it's always one of the three. But yeah, like

(22:09):
you were saying earlier, it's pretty hard to measure the
speed of light because it's so fast, right, Like, you
can't just like turn on a flashlight, run over there
and see when the light arise. Like it moves faster
than anything can move. So it's hard to like you know,
beat it or coordinate the measurement of it. So, like,
how did the people in ancient times even approach this question?
I think in ancient times they had a different attitude, right,

(22:30):
They were not empirical. They were not of the mind
to go out and discover things in the universe by
doing experiments. They were much more internal. They thought that
they could understand the universe just by thinking about it.
You know. They had lots of crazy theories about the
way things work, theories that could be easily disproved in
like an afternoon of experimentation, you know. Aristatilian physics really

(22:51):
doesn't make any sense if you do any experiments. So
they really didn't even try to measure the speed of life.
They mostly just like talked about it and thought about it.
It wasn't all about five hundred years ago when this
concept of like, oh, let's go out and measure things
in the universe, let's try to see if our theories
actually work. This concept of empirical science came about that
people really started to actually try to measure things. And

(23:13):
the earliest recorded measurement I could find was from Galileo
about five years ago. Well do you think maybe people
didn't try before because they just had no means to
do it. You know, they didn't have accurate clocks or
ways to measure things. They certainly didn't have the means
to do it. If they had tried, they definitely would
have failed. But you know, I don't think they even
thought to try. Like I think, it's hard to take

(23:35):
your mind out of the current modern concept of science,
where we learned from the universe by doing experiments. That's
a fairly new idea. Aristotle, for example, had this idea
of how things fall, and he thought, for example, if
you're on a boat, that was moving and you dropped
a ball while you were on the boat, that the
ball would somehow get left behind, that it wouldn't just
like move with the boat. And like if you just

(23:56):
went out with a boat and a ball, you could
disprove this idea in an afternoon, right unless it's windy. Yeah,
and Galileo, like thousands of years later, proved that this
was false and literally overturned all of physics with a
boat and a ball in about ten minutes. So these
guys weren't limited by their physical capabilities, they just were

(24:17):
limited by the idea that you should go out and
actually measure stuff. What can you do with the boat
and a ball? Galileo used it all up right, like
early Nobel prizes. That's all the equipment you needed. I see,
the fruit was hanging lower before. Yes, exactly. Nobody even
tried to measure stuff back then, so he said, Galileo
tried to measure the speed of light. And then how
did he do it with lanterns? Yeah, he had lanterns

(24:38):
and he put them about a mile apart, and he
tried to time it the most accurate clocks you could
back then, and he tried to like you know, shine
a lantern and then measure how long it took to
get from one spot to the other with two coordinated clocks.
And you know, he failed to notice any difference. He
couldn't measure any time between when the lantern was revealed
and when the information arrived at the other side. Interesting

(25:01):
like he synchronized two clocks or two watches, and then
he had one watch, like go a mile away, and
then he said, Okay, I'm gonna turn on this lantern,
and when you see it turn on, you record the time.
And they came back and said it was the same
time exactly. They couldn't measure any difference, right, They couldn't
tell the difference between light being super duper fast but
finite speed and light actually being infinite speed. And the

(25:23):
reason is that the delay, like how long it takes
light to go a mile, is just eleven microseconds, and
so to measure that unique clocks that are more accurate
than eleven microseconds, and five years ago he definitely did
not have that. So did he conclude that speed was
infinitely fast or that he just didn't He couldn't measure it.
It was too fast to measure. It was too fast
to measure and these days, what you would conclude from

(25:44):
an experiment like that is you would measure a minimum speed.
If you knew how accurate your clocks were, you could say, well,
light is at least as fast as some number. He
just said, well, I don't know. It's either infinite or
it's very very fast. Right. He didn't have the right clocks.
But then later the people had better clocks. People had
better clocks. But actually the first measurement of the speed

(26:05):
of light being not infinite didn't come from using a
very fast clock. It came from using really really long distances, right,
Because that's that's two ways to kind of slow speed down, right,
Either give it a long distance to go over, or
use a really accurate clock. Yeah. So a Danish astronomer
about a hundred years later he realized that light bouncing

(26:26):
off of Jupiter's moon Io could be used to measure
the speed of light. What. Yeah, because Io orbits Jupiter. Right,
it's a moon of Jupiter and it goes around It
takes like forty two and a half hours to go
around Jupiter. And when it comes around the back of Jupiter,
it emerges from the back of Jupiter, and you can
see it. So if you're watching Io from Earth, then

(26:48):
you see it emerged from behind Jupiter every forty two
and a half hours. And so that's sort of like
a clock for the universe, right, it should happen every
forty two and a half hours, because Io's orbit is
very regular. It's a little bit more complicated because either
it can be in Jupiter's shadow or can be physically
behind Jupiter. But let's put that aside for now. Oh,
I see, because you can actually see the moves of
Jupiter if you have a telescope from the sixteen hundreds, right, Like,

(27:11):
you can see the little dots and you can see
the little little dots kind of floating around it. Yeah,
and Galileo is the first person to see these, and
so with a pretty basic telescope five years ago, you
can see these dots and you can plot the trajectory
of them, and you can see, like, okay, Io is
coming out from behind Jupiter. And people watch these things
and look for patterns, and they noticed something really interesting.
They noticed that it is true that Io comes out

(27:33):
from behind Jupiter every forty two and a half hours,
but that during some parts of the year that time
is a little bit shorter, and other times of the
year that time is a little bit longer. So like
the time between Io emerging from behind Jupiter gets longer
during one season and shorter during other seasons. And somehow
that tells you the speed of light, and that tells
you the speed of light because the reason those times

(27:55):
gets shorter is because the Earth has now gotten closer
to Jupiter and Io than it was last time, and
so the light doesn't have is far to go to
get to Earth. And the reason the times between the
reappearances get longer is when the Earth is moving away
from Jupiter. So now the light has further to go
when it has to reach Earth to tell you that
Io has emerged. If speed of light was infinite, then

(28:17):
I would always appear every forty two and a half hours.
This wouldn't matter at all. But because the distance between
Earth and Io is growing or shrinking, then this period
grows or shrinks. And so this Danish astronomer realized, oh
my gosh, I can use this information to calculate the
speed of light. Whoa interesting right, because sometimes we're in
between measurements of when you see the moon the Earth

(28:40):
will have moved. Is that what you mean, like sometimes
it moves a lot in that time, and sometimes it
doesn't move a lot exactly. And so when we are
moving further away from Io during that part of the
year that we're like zooming away from it, than those
times between Io's appearances will get longer. And when we've
come around the other side of the Sun and we're
zooming towards Io, then we're shortening that instance that light

(29:00):
has to go. Like, if you were making these measurements
from the Sun where the distance between you and I
wasn't changing, then they would be perfectly regular. Or if
the speed of light was infinite, so that every time
Io came around the back of Jupiter you instantly saw it,
then the measurements would be regular. But since the distance
is changing and it takes a finite time for light
to cross that distance, then you can measure how fast

(29:23):
light moves across these incredible distances. I guess the distance
is changing, and it's changing in a kind of predictable way,
so you can measure the speed of light. And so
what did they find. They get pretty close to what
the actual speed of light is. He got to within
about twenty of the real speed of light. Which is
pretty incredible. That's like a B B minus. Yeah, well

(29:45):
it's much better than Galileo. Did you know Galileo got
an F So at least this guy is passing well technically,
I don't know, because Galileo thought it was pretty fast. Yeah.
But I love these stories where you like tricked the
universe or corner the universe into revealing some piece of formation.
This guy didn't build this experiment. He discovered this experiment.
He's like, wait a second, this random configuration of stuff

(30:08):
reveals this piece of information everybody wants to know, And
all I have to do is use my telescope and
calculate a few numbers and boom, now I have this number. Interesting,
but did he know like the relative positions of the
planet in order for him to know exactly like how
much more the Earth at moved? Like do we know
the orbits that will back then? We didn't know the

(30:28):
orbits that well back then. But actually, all you have
to know is the orbital distance of the Earth. You
just have to know the radius of the Earth's orbit,
because that's the difference between the path of light when
the Earth is furthest away and when it is closest away,
So you can look at the calculations online, but you
can do with some pretty basic information about the orbits. Wow,
I imagine you could do it today, right Like if
you just had a nice back yard telescope, you could

(30:50):
measure the speed of light to you could get a
b in your back yard. Absolutely you can. And I
was chatting with one of our listeners, Brian Fields, if
the theoretical particle physicists, and he said he did this
lab in college and he actually sent me his rite up,
And so it's the kind of thing you can now
assign to undergraduates in physics and they can totally extract

(31:11):
this basic constant of the universe using simple tools and
everyone gets a D in the class. Then what was it?
The next step in measuring the speed of light? So
the next step was improving on Galileo strategy rather than
doing astronomical measurements. There was a guy in the eighteen
hundreds named Fizzo who sent a beam of light further away,
so instead of one mile, he sent it five miles.

(31:31):
So he was trying to measure a longer time distance.
He had this really clever trick for measuring really short
time periods. He put a beam of light that passed
very close to a gear that was rotating. So imagine
like gear like the one you have on your bicycle.
It's got a little teeth on it, and as it spins,
light can go through sometimes when it's not blocked, and

(31:51):
then when it hits the gear, when it hits the
tooth of the gear, then it's blocked. And if you
arrange things just right, then light flies through between the teeth,
HiT's a mirror, comes back, and then flies through the
next tooth. And so if you arrange things just right,
then the light can make it there and come back
and not be blocked. And if you're going at the

(32:11):
wrong speed, then it's going to hit one of the teeth,
either on the way out or the way there. And
so you can arrange things just right to get the
right speed in the right distance, so you can get
light to go there and back and not miss a tooth.
And this is the way to measure how long it
takes light to go there and back if you know
like the rotation speed of your gear. Well, this sounds
pretty tricky in advance, I guess the big question is

(32:34):
how did they get the light to go five miles
bounce off a mirror and come back and still be
sort of like you know, legible. Like they didn't have
lasers back then today. They only did not have lasers
back then. Five a lot, right, Like any beam of light,
if it's a little foggy or something, it will make
it five miles and back. That's true. But you know,
they did have optics, and they had powerful lenses. Even

(32:55):
Newton was studying lenses, and so they had ways to
concentrate beams of light. But yeah, that was definitely a
challenge back then making a powerful enough beam of light.
But you know, light can go pretty far, so you
need like a clear night, right, This would be an
experiment would be better to do in space because you say,
light will scatter off of the atmosphere, but you only
need a few photons. Also, I see, so they had
some sort of like focused beam of light, I guess,

(33:17):
but they didn't have electricity, so they must have used
like candles or fire. Yeah, that's a really good question.
You know. I read a few descriptions of this experiment
and they all just say the light source, So I
wasn't able to figure out what the actual source of
light is. So either some time traveling physicists lend them
a laser, or they like really focused beams of light
from the sun, or maybe like early electricity allowed them

(33:38):
to generate really bright bulbs or aliens. Possibility, the simplest
explanation first, that's also on an experiment that like people
can do in their backyards, right kind of Yeah, if
you have a rotating gear that's very precise and a
five mile long backyard, then yeah, go for it. That's right.
If you're a billionaire and live in a state, anything
is possible for that's right right to us. We'll send

(34:00):
a kid for one billion dollars from measuring the speed
of light. And then I imagine that we've gotten much
better at these kinds of measurements, and so let's get
into those and our current understanding of what the speed
of light is. But first let's take another quick break.

(34:26):
All right, we are measuring the speed of light, and
you can do it in your back yard if you're
a billionaire. Yeah, you can actually also do it in
your kitchen these days. Oh no kidding, Wow, I have
a five mile long kitchen. You don't need a five
mile long kitchen. Actually, all you need is say microwave
and a chocolate bar, and you can measure the speed
of light at home in about twenty seconds, no kidding,

(34:47):
How does that work? Well, Light, of course is a wave,
and so if you know the frequency of the wave
and you know the wavelength, you can combine those two
pieces of information to get the speed of the waves.
And so people do of these now in very high
end experiments using cavity residences. The most precise measurements of
the speed of light we have sort of inexperiments, come

(35:08):
from these cavity residence experiments where you measure the wavelength
of the light and you measure it's resident frequency. But
you can also do a simpler version of that at home.
You just take a chocolate bar and you put it
in the microwave. You microwave for about twenty seconds, not
enough so it's totally melted, but enough that it's just
started to melt. And take it out and you'll notice something.

(35:29):
You'll notice that it's more melted in some places than
in others. There's like hot spots m interesting, and that
is basically the shape of the wave of light of
the microwave light that's right. The distance between those hot
spots is one half of the wavelength of the microwaves,
because that's where they have like added up concretely to
give you like the most energy. And so what you're

(35:50):
seeing there is like the actual physical wavelength of the
photons passing through your chocolate bar, and it's like a
few centimeters. So it's something you can reasonably measure using
a chalk the bar in your microwave. And then all
you have to do is look up the frequency that
your microwave uses. Usually it's like two and a half
giga hurts or something. Combine those two numbers together and boom,

(36:11):
that's the speed of light. Interesting, but I guess you
know inside the microwave, isn't it bombarded by microwaves from
all directions? Is that the wave inside of my microwave
that like coherent, that untouched, that sort of neat? Yeah, unfortunately,
it is right, and that's why you have hot spots
and cold spots. We have a whole episode about how
microwave ovens work, and usually they have like one source

(36:31):
of the radiation and so it puts the stuff out
in this kind of pattern where you get this constructive
and destructive modes. It would be much better if it
was like incoherent and evenly distributing the energy, which is
why you usually have like a spinner to move your
food through this field of microwaves. So they use a
sort of a simpler radiator and it has these features
to it. I guess the tricky part though, is measuring

(36:52):
the frequency of the LightWave, right, because I mean that's
like gigaherts. You don't really have a clock that can
measure that. You'd have to trust the greave manufacturer. Yeah,
it's sort of cheating because they've done the hard part
for you of measuring the frequency. But it's also a
cool thing to like physically see the impact of light
being a wave, to like to see the distance between

(37:12):
the crests of the light wave in a physical thing
that you can do in your kitchen. That's sort of cool.
But you're right, when we make the actual measurements, like
when we actually want to figure this out ourselves, then
we use very precise cavities and we measure the residents
frequency and the wavelength of the most simultaneously, because you
can't just look that stuff up. And is it required
that you have to eat the chocolate afterwards, because then

(37:34):
you're cheating not just the universe, but you're diet a
little bit. No, that's the bonus of doing physics. Man,
Sometimes you make a delicious experiment that gets a little messy,
all right, So nowadays we use much more like constraint environments.
I guess a cavity and you have a wave of
light and you know exactly what the frequency is, and
you can sort of see the wavelength and that gives

(37:55):
you one measurement of the speed. Like nowadays, we don't
really like do these experiments meants where we send it
off to one place and then measure how light it
takes to come back. We use something like this. Yeah,
it's much more precise to use interference effects or residence
effects because they're very very sensitive to very small shifts
in one wave to the other. And so the way
the cavity residence experiment works is you measure both the

(38:18):
wavelength and the resident frequency. Are you build some precise
cavity and that determines the wavelengths of like standing modes
inside the cavity, or do you have like two mirrors essentially,
and you want light to go back and forth between
those mirrors in a way that it doesn't cancel itself out.
You need light to have a wavelength so that an
integer number of those wavelengths adds up to exactly the

(38:40):
width of the cavity. So there's only like certain modes
of the cavity where you can get this sort of effect.
And then you just measure the resident frequency, like at
what frequency of light? What color of light do you
get these residences? So you can measure the width of
your cavity and measure the frequency the color of light
that goes in there that achieves residents, and together you
can get a very accurate measurement of the speed of light.

(39:01):
And that was like nine seventy five. The people really
perfected this and got like a super duper precise measurements
of the speed of light. But I guess, doesn't that
depend on how accurate your clock is to measure the
frequency of light and also how good you're you know,
ruler is to measure the size of your cavity, right, Like,
there are still I guess imagine limitations to how well

(39:22):
we know the speed of light. There were still limitations
for just those reasons, like people used crazy techniques to
measure the size of these cavities. Very very accurately, and
it's like a real tourtive force of experimental physics, the
clever strategies people came up with to measure these precisely.
These days, however, we have actually zero uncertainty on the
speed of light, zero uncertainty, like we know it to

(39:45):
an infinite number of digits. Yeah, so it's a bit
of a cob out answer, right, we don't know the
speed of light to an infinite precision if you set
an arbitrary length for the meter and an arbitrary length
for the second. Instead, we've decided we're going to use
the speed of light to define the length. We're going
to say we know this better than anything else, so
let's define everything else in terms of the speed of light.

(40:07):
So now the official definition of a meter is no
longer like here's a platinum rod in Paris. Instead, it's
how far light travels in a certain amount of time. Right,
Because I guess you're saying that if we picked a
valley for the meter in a valley for the second,
then that makes the speed of light that we measure
kind of dependent on what we pick for the meter
in the second. So instead it makes more sense maybe

(40:30):
from a global point of view. To define the meter
and the second by the speed of light. Yes, so
we define the meter by how far light travels in
a second, and we define the second by the oscillations
of some caesium atom. So now the meter is something
which depends on the speed of light and the oscillations
of the caesium atom. So now instead of asking like,

(40:51):
how well do we know the speed of light, it's like, well,
how well do you know the length of this platinum
rod in Paris? Oh? I see, So you're kind of
saying almost like we're coming up with the speed of light,
like we're inventing the speed of light, right, because we
just picked some numbers and then we call that the meter.
So therefore the speed of light is so and so
meters per second. Yeah, And it's just like in particle physics,
we could define the speed of light to be one

(41:13):
and everything is set relative to that. And so here
we're defining the meter so that the speed of light
is exactly two eight with no decimal places, like it's
exactly that number. And you know, I said, we know
it accurately. Really, we just define it to be that,
and everything is now relative to that. Number just kind

(41:34):
of blew my mind. It means we don't know what
the speed of light is, right, Like, technically, philosophically, you're
trying to say that we don't know what the speed
of light is. We just picked the number and said
that's it. We picked the number. We said, this is
what we call the speed of light. The speed of
light is a number, right, and we just assigned to
say it's this number, this length. And now the question
is what is length to mean? Length is relative to

(41:54):
the speed of light. It's just as good as saying
length is relative to this rot in Paris. But this
row in Paris has no real meeting or physical significance,
so it's sort of silly, whereas the speed of light
obviously does. And so it makes a lot more sense
to define things relative to the speed of light rather
than relative to an arbitrary chunk of metal. But yeah,
I think by using a number that doesn't have any
decimal places, right, you get that to be the meter,

(42:17):
and then you use that meter to measure the speed
of light. But then the number gives you was it's
a consequence of you picking that random number. Yeah, you
can't measure the speed of light anymore. You're exactly right.
It doesn't make any sense to define the meter in
terms of the speed of light and then trying to
measure the speed of light. Like, you can't measure the
speed of light in terms of the meter because the
meter is defined in terms of the speed of light.
It's circular. Instead, when you can do is define the

(42:39):
speed of light and then measure the length of a
rod in Paris in terms of that. Why anybody would
care the length of rod in Paris, I don't know,
But philosophically that's what you can do now. But I
feel like that's kind of like you're avoiding the question.
Like there is a speed of light, like there is
a certain amount of distance that light covers in in
one second in the universe, but it doesn't seem like
we know what that is to any sort of decimal place. Well,

(43:01):
we don't know what that is relative to that stick
in Paris. You're right, and we could spend a lot
of time and money measuring how fast light goes relative
to this arbitrary unit of distance we defined according to
this stick in Paris. But I think people decided that
doesn't mean anything anyway, Like what does it matter? How
many decimal places you get when your unit is arbitrary.

(43:22):
We prefer to make a reasonable unit when that makes sense.
And the speed of light is the most important physical
constant in the universe, and so let's just define everything
relative to that, right, But then you're picking an arbitrary
number for that speed, Yes, absolutely, I don't know. I
guess it makes it more sense to me as a
lay person to pick an arbitrary length and then measure

(43:44):
the speed of light than to pick an arbitrary speed
of light and then define lights from that. Well, it's
philosophically their equivalent, you know. Check out our episode on
the basic constants of the universe, and you'll realize that
no number that has units on it ever has any meaning,
because it just depends on your definition of the units.
The old numbers that really have meeting are the ones
without any units, the ones that are pure numbers of

(44:05):
the universe. So the speed of light in that sense
is not actually that fundamental. It folds into the fine
structure constant, which is a unitless number and which does
determine sort of the structure and the nature of the
universe and electromagnetism. But I guess you know, like a
rod in Paris is something we can all go and
touch and see and like, hold right, and then we
can all agree that the speed of light goes so

(44:27):
and so fast. But I feel like this way of
doing things, like nobody can agree what the speed of
light is. Everybody can agree, we just choose a number.
Whereas a rod in Paris, it like grows and shrinks
when it gets hot in Paris. Does that change the
speed of light? Like, it's ridiculous to have the speed
of light depend on something so arbitrary as how big
this rod in the museum in Paris is like the

(44:47):
air conditioning breaks in Paris, and now we're all moving faster,
Like it doesn't make any sense. Yeah, why not? I
mean that's better than like making up a number for
the speed of light. Daniel, I can't handle this all right, Well,
come to Dawn and Rhee discussed philosophy. I'll give you that.
That's the way you're doing it, even though I don't
agree with them, all right, objection noted, Yeah, thank you.

(45:10):
I'm sure will cause waves in the physics community. So
that's kind of the way we're doing it. That means
that we kind of can measure the speed of light. Right,
once we've defined it, we can no longer measure things
in terms of it. Yes, So to answer the questions,
how do we measure the speed of light, we don't anymore.
We just picked the number. We just picked the number. Yeah,
and that number was based on almost nothing, right. Well,

(45:31):
that number, you know, defines a meter to be something
close to what it used to be, and so that's
pretty nice, but it could have been something else. We're
just to pick the number out of historical reasons, kind
of to approximate historical history. Yeah, we wanted the new
meter to be pretty close to the old meter so
that we didn't have to like change everything all that,
you know, make all new highway signs like oh, this

(45:51):
tunnel is now one meter high whereas it used to
be twenty meters high. That would be ridiculous. So once
again laziness. Yeah, consistency, manists knap consistency. It is very
important to physicists. And I'm getting the sense. But yes,
it seems like the answer is you can't measure the
speed of light anymore, right, because now we've defined the
meter as based on this number of the speed of lights,

(46:12):
it makes no sense to leasure the speed of light.
It's just what it is. Yeah, that's true. We can
no longer measure the speed of light relative to other
arbitrary units because it is now the arbitrary unit. Can
we measure it relative to some of these you know,
fundamental unitless constants that you measured, Like, you know, the
universe has these numbers that are immovable and fundamental to

(46:33):
the fabric of the universe. Can we use those to
get a real measurement of the speed of light? Now?
Because those numbers don't have units, and so they can't
determine numbers that do have units because those depend on
your choice of units, right, that's the problem with numbers
that have units. Anything that's like meters per second or
pounds per square inch or whatever is going to depend
on the units, which is why physics refers to talk

(46:54):
about numbers without units. But you know, I guess we
base time on some sort of fundamental physical thing, right,
like the oscillations of a crystal or whatever. Why can't
we do that with distance as well? We do, we do,
That's exactly what we do. And that's how a rod
in France. But like I don't know the width of
a proton or something like that. We'll think about it

(47:14):
as a certain number of light wavelengths at a certain frequency.
Because we defined the meter in terms of the speed
of light. Now light is our ruler. But then that
means we can't measure the speed of light. That's true. Yeah,
we've given that up because now it's our ruler, because
we've decided that that's exactly the most basic unit. Just
like you can no longer define how long it takes

(47:36):
caesium to do one oscillation because it's to find to
be one second, or is to find to be one
you know, six billions of a second or whatever. Because
we now define time in terms of that basic physical operation,
you can no longer measure how long that operation takes.
What can you say, like, let's measure the speed of
light by the frequency of caesium and also the width
of caeson Yeah, you could define distance using something else,

(47:59):
but you know it's not as fundamental is the speed
of light. The speed of light is really basic and
interesting to the universe. So I think that's why they
chose it. But you're right, these things are arbitrary, and
you could have said, you know, the meter is now
defined to be one third of the height of Jorge's room. Like,
you could have chosen anything. Some choices are better than others,
you know, and I think this is a pretty good one.
Let's just pick a number of It seems like a

(48:19):
crazy way to run thenation of the universe, Daniel, We're
doing our best. Do our best. I know it's not
your fault. You have limited power in the physics community.
All right, Well, I've mounted the chocolate bar in my mind.
I feel like I don't know what to trust anymore
in physics, Daniel, things are arbitrarily fast. Now. There is

(48:40):
no speed limit. There's just the speed limit that you're
telling me is the speed limit. That's right, Go out
there and break whatever speedimits you want. Jorhey, you're right, absolutely,
there are no rules when it comes to you. Well,
I think it's another kind of reminder. You know that
this is a tricky universe. You know, it's kind of
hard to measure things because everything is relative. Everything can change,
everything depends on kind of you know, how fast you're moving,

(49:01):
or how hot it is, or what you're measuring relative to.
So it's kind of hard to find footing in this universe.
It is but it also gives us a sense for
how the universe works. And I think it's awesome how
we as humans have figured out how to extract this
kind of information from the universe. I mean, until we
define it away is not interesting anymore. I think it's

(49:22):
fascinating to see, sort of like the historical sweep, how
long it takes, how the thousands and hundreds of years
it takes to figure out this one very basic thing
about something we literally see every day. And as the reminder,
please obey speed limits in your driving practice, because going
at the speed of light might get you a few
light tickets. But if you do manage to go at

(49:44):
the speed of light, please let us know. We'd like
to hear about it. But what if they interrupt your nap, Daniel,
It'll be worth it. They'll sit in your inbox for
ten seconds before you check all right. Well, we hope
you enjoyed that. Thanks for joining us, see you next time.

(50:05):
Thanks for listening, and remember that Daniel and Jorge Explain
the Universe is a production of I Heart Radio or
more podcast from my Heart Radio. Visit the I Heart
Radio Apple Apple Podcasts, or wherever you listen to your
favorite shows. Ye