Why No One Has Measured The Speed Of Light

• 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.

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