The letter “c”: it’s not just a certain  cookie-loving monster’s favorite letter.

It also represents one of the most  important concepts in astrophysics. c is often called the speed of light,  but that’s actually a bit of a misnomer. It’s more like a speed limit for light.

Because in a pure vacuum,  light does travel at exactly c, or roughly 300 million meters per second. But if it’s traveling through  something like air or water, it interacts with all those  atoms, and gets slowed down. Except it also…doesn’t.

From the light’s perspective,  it is always traveling at c. Which is super weird. But do you know what’s even weirder?

You. You are also traveling at c right now. And no matter what you do, you cannot  travel any slower or faster than c.

And…how is that possible? Well, that’s Relativity for you. And it all comes down to the fact that  we aren’t just moving through space.

We’re moving through spacetime. [♪ INTRO] How fast do you think you’re going right now? Nope, you’re wrong. No matter what your answer  is, you’re probably wrong.

Relatively wrong, at least. The problem is that your answer depends on  what physicists call your reference frame… the specific frame of reference from  which you make all your measurements. For example, right now you might be sitting on  the toilet watching this video on your smartphone.

So from your perspective,  hopefully your speed is zero. But from the perspective of a sunbather  on the Moon, you’re zipping around pretty quickly because the Earth is  rotating relative to their vantage point. If you were in our studio bathroom in Montana, you’d be going 318 meters per second!

Meanwhile, an alien neighbor  in the Andromeda Galaxy might be watching our solar system  with an ultra high-powered telescope. And if they could measure your velocity, their result would reflect the fact that,  yes, the Earth is spinning on its axis. But also, it would include the Earth moving  around the Sun at 30,000 meters per second, our solar system hurtling  around the core of the Milky Way at 230,000 meters per second, plus the  Milky Way’s slow march towards Andromeda.

So who’s right? You, the lunar sunbather, or the Andromedan? Or some secret fourth answer?

Well, one of the most  fundamental principles in physics is that none of these reference  frames is objectively correct. They’re all equally valid, and our  rules for physics must be consistent in every single one of them. So how do we reconcile the observation that  in my reference frame I’m standing still, but some alien out there would see me  moving at 230,000 meters per second?

This was one of the most headache-inducing  questions at the turn of the 20th century. And it took a tremendous amount of work, and no small amount of academic  drama, to compile a consistent theory. Albert Einstein gets a lot of credit for  formalizing the theory of special relativity, but there were many scientists  working on these ideas for decades before Einstein published his seminal 1905 paper.

We can see the origins of the Principle of  Relativity in Galileo’s early 1600s writings on moving reference frames. But things really hit the  ground in the late 1800s. Basically, physicists were unpacking  the laws of electromagnetism… how stuff like electrons and  electric and magnetic fields work.

And it seemed like the laws of physics did  vary, depending on how fast an electron or whatever was moving relative to the  so-called “absolute” reference frame that was the emptiness of space. But thankfully, a Dutchman named Hendrik  Lorentz saw that physics could at least be locally preserved by introducing  a new variable he called local time. And in 1900, the mathematician Henri Poincaré published a set of “Lorentz  transformations” that could translate between two different local  times, a.k.a. reference frames.

These equations seemed to mathematically  fix the broken laws of physics. But they led to a somewhat freaky side effect that every science fiction fan  has heard of: time dilation. Basically, if you’re standing still and observing  a moving object for a certain length of time… which would put you in the rest frame  and the object in the moving frame… you and that moving object wouldn’t  actually agree on how much time had passed.

More specifically, the object’s clock would  record time as having moved more slowly. And the faster it was moving  relative to your rest frame, the greater that time dilation effect would be. For our puny human minds,  that sounds like nonsense.

But these Lorentz transformations  did what they needed to. They could describe how  electromagnetism worked in a way that matched observations, even if  scientists couldn’t explain why. Einstein, however, was unsatisfied  with this mathematical bandaid, so he completely discarded the idea of an  “absolute” frame that is perfectly at rest.

Instead, he placed himself in the  reference frame of a beam of light. And from this beam’s point  of view, it wasn’t at rest. It was traveling through a  vacuum at a fixed speed, c.

For Einstein, it didn’t matter  how large or small c was. It only mattered that it was constant, and stayed constant no matter which  reference frame an outside observer was in. Everyone…from the person sitting on  the toilet, to the alien in Andromeda, to the beam of light itself…would always  agree that the light was traveling at c.

And based on this assumption, Einstein  derived the Lorentz transformations again, including the time dilation side effect. His 1905 paper—which, by the way, did not cite any other published papers  on the topic of relativity— finally united our physical intuition  of physics being the same for everybody, with the strange mathematical conclusions  of Lorentz, Poincaré, and others. Then in 1908, Hermann Minkowski  took things a step further by introducing his idea of a unified spacetime.

Instead of time being a separate dimension  that we treat totally different from space, spacetime lumps them all together. Or to put it in Minkowski’s own words, “Henceforth space by itself, and time  by itself, are doomed to fade away into mere shadows, and only a union of the  two will preserve an independent reality.” Which is a totally metal quote and proves we  should start training scientists in poetry again. But anyways, Einstein wasn’t quite satisfied yet, and went on to publish his work  on general relativity in 1915.

General relativity incorporated Minkowski’s  language of a unified spacetime, with the important distinction that gravity  itself shapes the spacetime continuum, which in turn dictates the  calculations of special relativity. Thanks to Brilliant for  supporting this SciShow video! Brilliant is an online learning platform with thousands of lessons in  computer science, math, and science.

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That link also gives you 20% off an  annual premium Brilliant subscription. So after all that, we finally had both  a brand new 4D perspective of reality, and the equations to translate  between reference frames. Which allows us to get back  to my original question: how fast are you going right now?

Just like Einstein, we must shed our  Earthbound concepts of time and space to enter Minkowski’s 4D spacetime. To measure a distance in 3D, let’s  call it ds, you can use this formula: ds squared equals dx squared  plus dy squared plus dz squared. dx, dy, and dz are the difference in  position along the x, y, and z directions. Minkowski’s proposal introduces  time as the fourth dimension, an equally important axis of motion.

So to solve for a four-dimensional  ds, we need to include a dt term. But there’s a catch! First, you’ll notice that the units of  distance are not the same as the units of time.

Meters are not equivalent to seconds. So the dt term usually gets  multiplied by a distance over time, also known as a velocity. Also known as c.

And to preserve the rules of physics, such as the speed of light being  constant in all reference frames, dt squared also needs to have the opposite  sign of the space variables, like this. But I’m definitely giving some of you out there  a headache, so let me simplify the equation. Physicists refer to ds as the invariant interval, because it’s always the same no  matter what reference frame you're in.

In other words, if two observers  are observing the same object, they may disagree on how much it moves through  space, or how long it takes it to do so. But if they plug in their values for  dx, dy, dz, and dt, and solve it, they will always agree on ds squared. In the laws of relativity, the  invariant interval is not relative.

And now, we can finally show how everything  in the universe, including light… including you…is always traveling at  exactly c, no matter how you look at it. Let’s take a look at your invariant interval. From your point of view, you’re sitting still.

It’s the world that’s moving around you. So all these terms are reduced to zero. Meanwhile, you still  experience the passage of time.

You’re moving through spacetime,  but just along the time axis. And how fast are you moving through spacetime? Well, it’s written right there! c!

But what about that outside observer who sees you traveling through space with a non-zero velocity? Doesn’t that change the calculation?? Can relativity explain that?

Well, think back to the invariant interval. That has to be the same for both of you. So if they measure a larger amount  of movement through space than you, how can ds stay the same?

That’s right. The amount of time they measure has to be lower. It’s our good old friend time dilation.

And that’s that. The invariant interval must be the  same in every single reference frame. And because you can always define a  reference frame where your velocity is zero, your speed through four-dimensional  spacetime will always be a constant: c.

You can swap this example for any  reference frame and any object, proving that everything in the whole  universe is traveling through spacetime at c. And if someone ever measures you traveling  slower than that…including yourself… well it just means they’re probably only  measuring your movement through space. Those silly billies.

It is difficult to stop thinking  of living in just a 3D space. And in our defense, we have done for  it our entire existence as a species. If not longer.

But we need to think beyond that if  we’re going to understand how weird and awesome reality is: we are  embedded in a 4D spacetime, traveling alongside the rest of the Universe  at a constant speed that happens to be c. Which is probably much faster than you expected. And in light of all this, maybe we should  rename c the “speed of everything”. [♪ OUTRO]