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You’ve probably heard the rule that you cannot travel faster than the speed of light (in a vacuum). And this is true.
You may also have heard that you cannot travel precisely AT the speed of light. But this is false…because you are, in fact, ALWAYS traveling at c. Good ol’ Relativity can explain why.
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Sources: https://docs.google.com/document/u/1/d/e/2PACX-1vTMGlt8e2TPezW44m9CBCuh-LjGWCJs-1-nxGphxUgPiAr-9xbgdIr6GzkCWmGnpzZBseESbGwch3FA/pub
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.
00:16: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.
01:31: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.
01:52:And it all comes down to the fact that we aren’t just moving through space. We’re moving through spacetime. 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.
01:11: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.
01:24: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!
02:41: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.
02:55: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?
02:13: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.
02:26: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,
03:42: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.
03:57: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…
03:11: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.
03:26: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
04:42: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.
04:57: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.
04:10: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.
04:26: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,
05:39: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.
05:55: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,
05:09: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
05:25: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
06:41: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
06:58: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.
06:16: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!
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07:58:You can give Brilliant a try for free for the first 30 days at Brilliant.org/SciShow, the QR code, or the link in the description. 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,
07:16: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.
08:33: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,
08:53: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.
08:09: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.
08:28: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,
09:45: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.
09:03: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.
09:19: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
10:36: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?
10:54: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,
10:10: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.
10:24: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.
11:38: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,
11:51: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”.
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