- This video was sponsored by KiwiCo. More about KiwiCo at the end of the show. I know what you're thinking. - Clickbait! - No one has measured the speed
of light, that's ridiculous. The speed of light is exactly
299,792,458 meters per second. We are so sure of it that since 1983, we've actually used the speed of light to define how long a meter is. It's just the distance
light travels in a vacuum in 1/299,792,458ths of a second. That definition ensures
that the speed of light is exactly this number, no decimals. But hear me out, in this video, I will prove to you that light may never
actually travel at this speed and I can say that because no
one has actually measured it. We can't measure the speed of light the same way we measure
the speed of anything else. Destin: I think we're recording everywhere. What are we doing? - This is a video about
measuring the speed of stuff. Destin: OK Tell me about how you measured
the speed of the baseball fired out of your cannon. - Well, to get the speed of the baseball, you need to know two things. You need to know the
distance between two points and you need to know
the time that it takes the baseball to travel
between those points. So basically we took
distance divided by time, and that's the speed of the baseball. And in our case, we were shooting
with a high-speed camera, so you basically just count the frames and then your clock is internal. Oh, you're going relativity. You're gonna do something
weird, aren't you? - You saw it coming. I can't believe it. Destin: Oh man! The thing I want to ask you
about is the speed of light. Destin: OK Could you measure the
speed of light like this? Imagine you have a laser
that can fire a beam through a perfect vacuum
for one kilometer. Start a timer the instant
you fire the laser beam and then exactly when it
hits the end, stop the clock. Except how do you know when
light reaches one kilometer if you and the clock are
at the starting point? Okay, so you need two
clocks, one at the laser and one at the end,
which stops automatically when it detects the laser light. But now, how do you make sure your two clocks are synchronized? Well, you could connect them via a wire and send a pulse from one to the other, but that pulse will travel
at the speed of light, so it will arrive with a time delay. You might think you can just
subtract that time delay but it is equal to the time it takes for light to travel one kilometer. That's what we don't know
and are trying to measure. Okay, new plan, start
with the clocks together and sync them up first and then send one of the
clocks down to the end. Now, what could possibly go wrong? Well, I'll tell you. The clock at the finish line was moving with respect to the one at the start and special relativity tells
us moving clocks ticks slow relative to stationary observers. So by the time the clock
reaches one kilometer, it will no longer be in sync
with the clock at the start. Can I tell you the only
solution to this problem? Ditch the second clock. Put a mirror at the end
to reflect the light back and use a single clock at the start to time the full two kilometer round trip. - Wasn't this actually done before? He was on a mountain and
there's a wagon wheel with a lantern and there's
something like a mirror on the other side of the mountain? I've always wanted to do this. - So, that sounds a little like how the speed of light was first experimentally measured by Hippolyte Fizeau in 1849. He shone a beam of light between the teeth of a rapidly spinning gear to a mirror up on a hill eight kilometers away. And then by increasing
the speed of the gear, he reached a point where
the reflected light passed through the next gap on the gear and so it was observed. So he measured the speed of light to be 313,000 kilometers per second, which is within 5% of the
presently accepted value. So someone has measured the
speed of light? or have they? What has been measured is the round trip or two-way speed of light, but no one has measured
the one-way speed of light. One thing I'm gonna throw at you. And I'm just gonna come out and tell you. It's like what if the speed
of light in this direction is different from the speed
of light in this direction? - Then that sounds like
a Veritasium video. (both laughing) - The question is could you figure it out? The kind of crux of this problem is that the only way people have managed to measure the speed of
light is for a round trip. No one's ever managed to measure the speed of
light in just one direction. It's possible that the speed of light is half of 'c' in one direction, and then instantaneous
on the return journey. Destin: What?! That's possible. Destin: Are you serious? - Think about communicating
with an astronaut stranded on Mars. Let's call him... Mark. We send out a signal and get
a response 20 minutes later. So we imagine our signal
takes 10 minutes to get there and the reply takes 10
minutes to come back, but it's possible that our
message took all 20 minutes to get there and the reply
came back instantaneously. There's no way we could
tell the difference between these two scenarios. But why would the speed
of light be different? Well, it's possible that there is some preferred direction
through spacetime. I mean, our universe
has a lot of symmetries, but there is also some asymmetry. For example, why is there so much matter relative to anti-matter? And physicists have worked out internally consistent theories of physics in which the speed of light is different forwards and in reverse. The speed of light could
vary by just a few percent up to at the extreme, going
'c' over two in one direction and infinitely fast in
the other direction. Destin: Okay, so let me figure this out. So yeah, I kind of don't believe you. I kinda don't believe you. I don't believe you that
light is a different speed in one direction, but in the other, but I know you well enough to
know that you wouldn't call me and put a camera on me unless
you knew you were right and that's what scares me about this conversation. That scares me. - Now, you might think it is just simpler that light should travel at the same speed in all directions, but the truth is: that is a convention rather than an
experimentally verified fact. Einstein himself pointed this
out in his famous 1905 paper, On the Electrodynamics of Moving Bodies. He spends the first couple
of pages on the problem of synchronizing clocks at
different locations A and B. And he says there is no way that we can meaningfully
compare the times they measure unless we established by definition that the time required by
light to travel from A to B equals the time it requires
to travel from B to A. He's essentially defining
that the speed of light in opposite directions is the same. And he puts by definition
in italics to remind us that this is only a convention. It's known as the Einstein
synchronization convention. So the idea that the speed of light is the
same in opposite directions as Einstein would later write is neither a supposition nor a hypothesis about the physical nature of light, but a stipulation that I can make of my own free will to arrive at a definition of simultaneity. That sounds a lot more subjective than how I think most people would imagine the speed of light is defined. Destin: Dude, this is hardcore. (laughs) I've never thought about this. - I didn't think about this before either. I always assumed that when we said the speed of light is c, we meant the one way speed of light. There's no way to define
the one-way speed of light, so the only thing we can really define is the two way speed of light. Just look at the way Einstein defined c. It's for the round trip
from A to B and back. I don't know if you saw
on your physics classes, but whenever there was a light clock it would always bounce the
light up and then back. You would never see a light
clock just bounce light one way. And this is why the only
thing we can be certain is constant for all inertial observers is the two-way speed of light. For over 100 years, scientists have tried to
find a way around this to measure the one way
speed of light by itself. Here is a paper published in the American Journal of Physics in 2009 that claims to measure the
one-way speed of light. And here is the paper
debunking this study, pointing out that these authors were actually measuring
the two way speed of light. But I'm imagining you
might have some ideas for how to measure the
one way speed of light, so let's go through some of them. I mean, can't we just
use a high-speed camera that shoots at a trillion frames a second so we can actually see light
passing through an object? The problem is you're not only seeing the light pass through the object, you're also seeing it
bounce back to the camera, measuring the two way speed, not one way. Destin: Here you go. Get a spool of fiber optic cable. I don't know, like 186,000 miles. And you could shine the light here and you have the other
end of the fiber here and you could shine here and
then wait and see the delay, see if it's one second later over here. - The thing is like that fiber is going around and around and around, so it could be that when
the light goes this way over the top of the loop, it goes slower and then when it goes on
the bottom, it goes faster. It all averages out in the fiber. And you're essentially
getting lots of round trips in that fiber, so you're
never getting a one-way. What if you center a synchronizing device between your two clocks and
send out simultaneous pulses? Well, if the speed of light is
the same in both directions, this perfectly synchronizes your clocks. But if the speed of light is
different in each direction, one of the clocks will
be ahead of the other. And it will be ahead by
just the right amount so that when you measure
the speed of light, you'll find the value to be C even though that was not the
speed the light was traveling. This is the same reason GPS
synchronized clocks won't work. The whole GPS system is
based on the assumption that the speed of light is
the same in all directions. If the speed of light is
different in different directions, the light pulses from satellites will travel at different speeds so the clocks won't be properly synced. By that, I mean they will always measure c for the one way speed of
light whether it is or isn't. How about starting with
synchronized clocks in the middle and moving them apart with
equal and opposite speeds? That way, the time dilation
for each clock will be the same and they'll still be synchronized when they reached the end points. But again, this only works if the speed of light in
each direction is the same. If the speed of light
depends on direction, then so does time dilation. You might think you could move the clocks really, really slowly so that
time dilation is negligible. But if the speed of light is different in different directions, you can't just use the standard formula to calculate what that
time dilation would be. I mean, it could be a
lot worse than you think. So, the reality is we're stuck. We need synchronized clocks to measure the one-way speed of light, but we need to know the
one-way speed of light in order to synchronize our clocks. Now, this might sound like
just an academic concern, so I want to go through an example to illustrate just how
differently the universe works if the speed of light is not
the same in all directions. Let's say on Mars, Mark is trying to synchronize
his clock with the Earth. At noon, mission control
sends out a message that says this signal was
sent at exactly 12 o'clock. When Mark receives this message, he uses the Einstein
synchronization convention to set his clock. He knows the roundtrip
time delay is 20 minutes, so he assumes the signal
must have taken 10 minutes to reach him. He programs his clock to 12:10 PM and sends a return message. This reply sent at 12:10. The message is received
on Earth at 12:20 PM, so both parties know the
synchronization was successful. When the clock reads 12:20 on Earth, it simultaneously reads 12:20 on Mars. But now consider what
happens if the speed of light is not the same in both directions. Let's say it is 'c' over
two from Earth to Mars, and then instantaneous
from Mars back to Earth. No one knows this, of course, so they continue to use
the Einstein convention. The message is sent from Earth, but now it takes a full
20 minutes to reach Mars. But Mark doesn't know this. And as before he assumes the signal took 10 minutes to reach him, so he sets his clock to 12:10 PM even though on Earth, it is now 12:20. Mark then sends this
reply sent at 12:10 PM, which is instantaneously received on Earth at 12:20 Earth time. The experience for the two
communicators is the same. The same messages were received with the same local time delays, but their clocks are out
of sync by 10 minutes. What they think is the same moment for the other observer actually isn't and there is no way
they can ever recognize or correct this error. Imagine if someone on
Earth immediately responded how long did this message
take to reach you? It's now 12:20. Well, the message would take
20 minutes to reach Mars, but due to the clocks being out of sync, it would arrive at 12:30 Mars time, so Mark would reply 10 minutes, a message that would
instantaneously reach the Earth at 12:40 Earth time. The space-time diagram shows
how there is flexibility in what you consider to be the same moment at two different locations and in how you define the
one-way speed of light. Einstein chose the convention where the one-way speed of
light is always the same, but from an experimental perspective, any other convention is just as valid, up to and including one
where the speed of light is C over two one way and
instantaneous the other way. And in that case, it's
interesting to think about what each observer is seeing
when they look at the other. Mark would be seeing the Earth
as it was 20 minutes ago, but Earth is seeing Mars in real time exactly as it is right now. And this effect wouldn't
stop at Mars, look beyond it and you could see stars
hundreds of light years away, not as they looked centuries ago, but exactly as they
are right this instant. One of the things is you
only know about that light when it reaches you and you
don't know anything about what journey it took to get to you. You just see it and it's there,
so like it's instantaneous. So an instantaneous
interpretation of that light is just as good as one
where it takes 'c' to reach us. - This is breaking my brain. Yeah, I mean, it's kind
of unknowable, isn't it? - It is unknowable. That's the whole point of the video. Is to say, we've all agreed and this is based on something
Einstein wrote in 1905. We've all agreed to just say
it's 'c' in every direction, but the truth is the
physics works the same whether it's 'c' or 'c' over
two and instantaneous or anything in between. As long as the roundtrip
works out to be 'c', none of physics breaks and that's the crazy thing. - So if we can never measure
the one-way speed of light, and if it makes no difference to any of the laws of physics, then what's the point in
even talking about it? Well, that is certainly
one valid perspective in a debate that has
been ongoing since 1905. Some physicists appeal to Occam's razor. Isn't it just simpler if light
travels at the same speed in all directions? Most working physicists just accept the convention
and move on with their lives, but I think it's important to point out that it is just a convention, not an empirically verified fact. Personally, I find it fascinating that this is something about the universe that is hidden from us. Sure, the round trip speed of light is 'c', but does the one way speed
even have a well-defined value? And if it doesn't, what does that mean for the
concept of simultaneity? When is right now on Mars? Does it even make sense to talk about things happening at the same time if they're separated by distance? Y'know maybe this is an odd quirk of the universe and there's no good reason for it or maybe, when physics takes
the next paradigmatic leap, our inability to measure
the one way speed of light will be the obvious clue to
the way General Relativity, Quantum Mechanics, space
and time are all connected. And we'll wonder why we
didn't see it before. Hey, this video was sponsored by KiwiCo. They create awesome projects
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The point about observing Mars as it is "now" is interesting. If such an extreme case was true (inf in one direction but c/2 in the other) would we not expect to see large discrepancies in our long range vision of the observable universe? If we make the assumption the big bang happened at the same time everywhere, and/or that the universe expands at the same rate in every direction, we would expect to observe stars that are older in the direction in which the speed of light is infinite than in the direction it is not. This is surely a measurable fact. This probably just passes the buck to assumptions of homogeneity about the rate of expansion of the universe though.
Huh, so looking at the Mars example this is 'just' a diffeomorphism (t,x) -> (t+a x/c, x), right? This would map (t, c t) to (t+ a t, c t) and (t,-c t) to (t- a t, -c t), so the speed to the right would be c/(1+a) and the speed to the left would be c/(1-a).
That's not part of the Poincare group, because the metric is changed, but it doesn't seem unreasonable to call this a symmetry of flat space. I'm guessing that the corresponding charge would be M^0i, the same one as we have for Lorentz boosts, but I can't eyeball a proof.
EDIT: I think you can then conclude from this that the impossibility of directly measuring the one way speed of light is a direct consequence of General Relativity, so trying to find counterexamples to this is tantamount to trying to disprove GR. The fact that we always have to look at a closed loop to measure c like this makes me wonder if looking at this in terms of holonomies could be interesting.
Couldn't we determine the one way speed of light is equal in each direction via the relativistic doppler effect? If person A is travelling at velocity v to person B and shines a light beam at a predetermined frequency f, there is an expected frequency shift that is dependent on the speed of light, specifically the ratio between the travellers velocity and the speed of light.
https://en.wikipedia.org/wiki/Relativistic_Doppler_effect#Relativistic_longitudinal_Doppler_effect
If we set up an experiment where person A travels toward person B from different directions, wouldn't the frequency shift in the emitted light be different depending on the direction person A was travelling if the one way speed of light was different in different directions?
I feel like most comments are tackling the wrong message here. This video is not really about what-if the speed of light is different in different directions, but about the concept of simultaneity and the problem of synchronization between two different observers, which goes to the heart of special relativity. Everyone is coming up with clever ideas why surely the speed is the same in all directions, referring to the Michelson-Morley experiment, cosmological observations, Maxwell's equations and what not. And it probably is, it seems to be a reasonable assumption, but that's not really the point here.
Here's a thought. In Maxwell's equations, the speed of light can be derived as a combination of the electric permittivity and the magnetic permeability of the vacuum. (https://en.wikipedia.org/wiki/Speed_of_light#Electromagnetic_constants)
If the speed of light were different in opposite directions, wouldn't this necessitate that at least one of the electric permittivity and magnetic permeability through the vacuum must also be direction-dependent?
I could be wrong, but as I understand it both the permittivity and permeability can be measured by means not requiring synchronization of clocks — for example the permittivity can be measured using distance measurements plus the capacitance of a capacitor, and the permeability is dependent on the definition of the ampere, which is based on measuring the amount of electromagnetic force due to a certain amount of electric current.
So either the capacitance of a capacitor must somehow be direction-dependent, or the electromagnetic force imparted by a given current must be direction-dependent.
Why does noone measure a three-way speed of light? Using two mirrors instead of two, so the first mirror reflects the light perpendicular onto a second mirror, which then reflects the light back to the clock. I just calculated it for both the case of isotropic speed of light and a case, in which light traveled in two directions (up and left) instant, while for down and right speed of light was equal c/2. In the case of isotropic light it should need longer. I used nothing else then those assumptions and Pythagoras. For the sake of simplicity I let the light travel diagonally from mirror two to clock up and left, so it should travel this distance instantaneous. Right?
https://imgur.com/vl9piqH
I suppose this wouldn't work, but I can't quite grasp why.
This shows how a nice regular universe can emerge from a weird one with variable directional speeds of light. Our universe might secretly be disgustingly complicated and we have no way to measure it.
Probably late for the game, but using light's nature as electromagnetic waves would work. Consider a source emitting e.m. waves (light) at known frequency and wave length. Then a receiver in the same intertial frame measures the same after the light has travelled and this is done in several directions (most conveniently by just waiting a day on earth).
Since the number of oscillations is unaffected by the speed with which the wave propagates, a different speed of light would either change the frequency or the wave length (since there would be more or less oscillations between emitter and receiver depending whether c is slower or faster).
Frequency and wave length can both be measured and this method does not need any kind of temporal sychronization.
In the extreme case, where c would be infinite, this e.g. could result in an extremely large wave length, since the phase at emitter and receiver would be equal (so there is not "waving" in between), while the frequency is unaffected.