Why no one has truly measured the speed of light.

It might have surprised you when you saw the title , we all know that the speed of light has been measured and that its exact value is 299,792,458 m / s , but I would never be making this blog if there wasn’t a catch . To understand why the speed of light has not have been truly measured, we need to first look at how to measure the speed of any other object .

Let us say I want to measure the speed of a small ball fired at an incredible speed out of a cannon. To measure the speed of the object we would essentially need 2 values . The distance between two points and the time that the ball takes to travel from one point to another . Then we just divide the distance by time which will result in the speed of the ball.

That would be = (Distance/time) = (3.88 / 7.8) = 469 m / s .

But here lies the question, can we measure the speed of light in this way?

Let us say we have had a clock which automatically starts and we take a strong laser which can fire light through one kilometer of perfect vacuum, and we fire the laser and start the timer. Except how do you even know when light reaches one kilometer if we and the clock are at the starting point?

Alright , so we need two clocks one at the start of the tunnel and one at the end which automatically detects and stops when light passes through it . But now the biggest issue becomes apparent , how do we synchronize the two clocks. If they aren’t in sync it would be impossible for the 2nd clock to know the timer has started.

You might have thought to add a wire between the two clocks to synchronize them but this wouldn’t work because the pulse in the wire would travel at the speed of light, and therefore would render the 2nd clock to stop at 0. If we try to sync the clocks beforehand via wire pulse, then fire the beam the value would be off by an unknown percent because the pulse will arrive at 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 , lets start with the two clocks together. Which are already in sync and move the 2nd clock one kilometer away and fire the laser. This seems to be the perfect and undeniable solution to the problem , unfortunately the 2nd clock would be moving in respect to the stationary one at the start and special relativity tells us moving clocks ticks slower relative to stationary observers meaning by the time the 2nd clock reaches the one kilometer mark it will be out of sync in respect to the clock at the start.

There is only one solution to this problem, we take out the second clock off the equation and in its place install a plane mirror, by doing this we can measure the total time taken by light to reach the mirror, reflect off it and come back. Therefore measuring the two kilometer round trip. By doing this scientists got the exact value of light as 299,792,458 m / s or 3 X 108 m/s approximately .

So someone has measured the speed of light? or have they?

Yes , the speed of light has been measured but its the round trip or the 2 way speed of light . No one has ever measured the one-way speed of light. What if the speed of light from A to B direction is different from the speed of light from B to A direction? If this is true , physics as we know it will change drastically. The center of the 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.

But why would the speed of light be different? Well, there may be some preferred direction through spacetime. Our Universe does have many symmetries but at the same time has quiet a few asymmetries, a good example would be the comparison between matter and anti-matter. Physicists have worked on many theories in which the speed of light varies forwards and reverse. This variation could be a small precent in one direction up-to infinitely faster in the other direction.

Albert Einstein himself pointed this out in his famous 1905 paper, On the Electrodynamics of Moving Bodies.

Einstein begins by writing about the clock synchronizing obstacle , where it would be impossible to synchronize 2 clocks to measure the speed of light. Einstein then states that there is no way that it is possible to knowingly compare the times they measure unless we settled the fact that by definition that the time required for light to travel from point ‘A’ to ‘B’ is equal to the time light takes to travel from point ‘B’ to ‘A’ . Therefore he is defining the speed of light to be equal is all directions without it being a verified fact. This is known as the Einstein synchronization convention.

Einstein would later say that the idea of the speed of light being the same in opposite directions 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.”

You might feel this might be only concerning to a physicist , so lets look at an example –

lets say on a future mission to mars , Matt an astronaut is trying to sync his clock with earth time. Exactly at noon mission control sends out a message that says “This signal was sent at exactly 12 o’clock”. Matt knows that there is a 20min round trip delay , and therefore assumes that there is a 10min delay from earth to mars and accordingly sets his clock to 12:10pm . He then immediately sends a message back to mission control that says ” This reply message was sent at exactly 12:10pm” . Mission control receives the reply at 12:20pm . Now both parties can confirm that the synchronization was successful . Now lets consider the speed of light to be different in different directions.

let us take the speed of light to be half of ‘C’ or (1/2) times slower that the speed of light from earth to mars and is instantaneous from mars to earth . Everything starts as normal , Exactly at noon mission control sends out a message that says “This signal was sent at exactly 12 o’clock”. But now it takes 20min for the message to reach Matt , But Matt does not know this and assumes it to be a 10min delay and sets his clock as 12:10pm and sends a reply which is instantaneous. Mission control receives the reply at 12:20pm and assumes the synchronization was a success . But in reality their clocks were completely out of sync

The same messages were received with the same local time delays in both cases, but their clocks are out of sync by 10min . What they think is the same moment for the other observer actually isn’t and there is no way anyone can ever recognize or correct this error. Imagine if someone on mars sends a message “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 by 10min, it would arrive at 12:30 Mars time, so Mark would reply 10 minutes.

Einstein chose the convention where the one-way speed of light is always the same but from a scientific perspective any other convention will be just as valid even ‘c’ being instantaneously or infinitely faster than the opposite direction .

It is very fascinating and interesting to see that two obverses could be seeing different realities at a delay.

Personally, I find it fascinating that this is something about the universe that is hidden from us.

In conclusion , there is no way of knowing if the speed of light is different in opposite directions and in reality we are stuck. It was surprising to me that the speed of light was defined as the way it is and is entirely based on an assumption. We are all taught this number of light in school without ever knowing how it came to be .

I hope this blog , got you thinking and made you excited for the many more mysteries that are waiting to be discovered in the universe .