What is the Mach Number of the Speed of Light?

Added: 2026-05-26

[00:00:00]Now, I want you to really try to wrap your brain around this. Photons of light travel at an absurd speed of 299,792,458 m per second. That is so fast that light, a single photon of light, can circle the entire planet Earth seven times in one single second. But, I thought it would be fun to ask an interesting question. What would the Mach number of the speed of light be?

[00:00:32]It's kind of a silly question, but basically, if the speed of sound is Mach 1 in our atmosphere, and a bullet flies at around Mach 2 to Mach 4, depending on the bullet, what would the Mach number of a photon of light actually be?

[00:00:48]>> [music] [music] >> Now, let's start with something more familiar. Your car on the highway. It's cruising at everyday cruising speeds, maybe 30 m per second. That would be a typical speed. That's about 108 km per hour, or if you like, you know, English units, 67 mph. Now, that same speed on the Mach scale is about Mach 0.09.

[00:01:26]0.09, that's barely a whisper in terms of Mach scale. So, let's back up for a second and ask, what exactly is this Mach number thing anyway? It's just how many times faster than the speed of sound you're going. So, Mach 1 means you're traveling at the speed of sound, and you might remember that it took engineers and scientists a long time to even build an airplane to go through the sound barrier. Mach 2 would be two times the speed of sound in air. Now, it all depends on temperature and density and such, but the genius of the system is that it's relative. It automatically accounts for the fact that sound travels at different speeds, depending on the temperature and the air pressure. Now, you might have seen a Slinky, a coiled spring, right? So, if you extend it out in front, of course, you could wiggle it up and down. That's not really what a sound wave is. It's a compression wave.

[00:02:18]If you take that Slinky and you compress it from one end, you can see a disturbance ripple through the elastic nature of that spring. Now, you can think of the molecules in the air behaving the same way. They're colliding with each other. There's some attractive forces, there's some repulsive forces, right? And if you have trillions and trillions of these molecules, if I move my hand literally rapidly and then stop, I'm going to compress the air. I'm going to make it higher density right near my hand, cuz I'm ramming it. But, then what's going to happen is it's going to want to spread out, and then the propagation is going to continue, and this high pressure region that I form with my hand is going to then flow through the bulk air around. So, the speed of sound is basically how fast that pressure disturbance is moving through the air. That's what sound is.

[00:03:03]It's not the individual velocity of the molecules, because they're traveling actually really, really fast and slamming into each other in random directions. The speed of sound is not the individual velocity. It's the velocity of the disturbance as an outside force causes a high pressure region, how fast does that disturbance move through the air? Now, the actual speed of a sound wave in meters per second is going to depend on lots of things. It'll depend on the density of the material. That's basically how close together and how many atoms there are available to for this pressure wave to go through. Also, the temperature, how fast are these molecules moving and bumping into each other? All of that plays into it. But, Mach 1 will always be the speed of sound locally at that temperature and density and pressure in that medium. So, at sea level in typical conditions, sound propagates at about 343 m per second. So, that's fast enough to cross three football fields in one single second. Now, when Chuck Yeager actually broke the sound barrier in 1947, he wasn't just going fast, he was doing something many scientists thought was actually totally impossible at the time. Now, it was a tough problem, because as you approach Mach 1, air starts to behave completely differently.

[00:04:21]It basically compresses in front of you, and on an airplane, that would be the leading edges of the wings, you know, where we're rounded over here, the leading edge of the actual aircraft itself and things like this, the tail as well. And what happens is you get a massive pressure wave building up in front of the aircraft, and the aircraft begins to violently buffet and uh drag, the drag on the airframe spikes dramatically. Pilots report the controls getting mushy. When you move the stick, it doesn't really affect the aircraft in the way that it does at lower speeds.

[00:04:53]And the shaking and the violent buffeting gets more and more and more, and so aircraft were having a tough time getting faster than the speed of sound, mostly because the airframe would be shaken and damaged by the pressure that it was encountering at Mach 1. Now, Chuck Yeager's Bell X-1 rocket-powered aircraft literally punched through an invisible wall of pressure, breaking the speed of sound in the sky. Now, let's step it up a little bit. A high-speed train is faster. It hits about 90 m per second, faster than your car on the freeway, on the on the uh highway, for instance. And that's still about Mach 0.26, nowhere near the sound barrier, but impressively fast for something rolling on fixed tracks. Let's talk about something faster still. Commercial airliners, you might fly in an airplane, they cruise at around 250 m per second at altitude. That's roughly Mach 0.85.

[00:05:50]Now, commercial airliners fly just below the sound barrier on purpose, with one exception I'll talk about in a minute, because crossing the sound barrier actually requires completely different aerodynamics and fuel burn at absurd rates. Basically, the shape of the wings, the shape of the airplane, everything has to change if you're going transonic and supersonic. Now, the Concorde was an exception to this, because it cruised at about Mach 2.

[00:06:15]That's 680 m per second, literally outrunning its own sound waves.

[00:06:21]Passengers inside could actually see the sunset, right? And then watch it rise again by flying west faster than the Earth's rotation. Think about that. That must have been amazing to see. Now, fighter jets, military aircraft, take it much further. An F-16 can hit Mach 2, but an SR-71 Blackbird, which is the fastest air-breathing manned aircraft ever built, actually reached Mach 3.3.

[00:06:48]That's over 1,100 m per second. And at that speed, the titanium skin of that very special and beautiful, in my opinion, aircraft would actually heat up to about 260° C just from friction with the air moving so fast through the atmosphere. The SR-71 would actually expand due to the heat here we're talking about from the friction, so much that the fuel would actually leak out of the tanks on the ground. The pilots had to actually take off, refuel in midair once the tanks sealed from the thermal expansion, once they're going fast enough, and only then could they actually start their mission.

[00:07:28]Now, military missiles push it even faster. Hypersonic missiles can exceed Mach 20. That's crazy fast. That's over 6,800 m per second. At hypersonic speeds above Mach 5, air molecules don't just compress, they actually break apart. And at those speeds, the chemistry around the vehicle totally changes. It's not just going fast through the atmosphere, it's flying through a plasma sheath, because the atmosphere actually breaks down into a plasma. Now, here's where it gets out of this world. When a spacecraft actually reenters the Earth's atmosphere, coming back from orbit, it's typically moving about 7,800 m per second. That's roughly Mach 23.

[00:08:14]When I would work on the space shuttle program, I was in mission control, and I would watch the space shuttle coming in.

[00:08:18]We're monitoring the velocity. It was crazy how it would start out close to Mach 25, bleeding off speed with every single second as it comes through the atmosphere. And when the space shuttle would come in, slamming into the atmosphere at these speeds, the friction that it would create, just rubbing against and compressing the atmosphere, would cause the temperatures to exceed 1,650° C.

[00:08:42]That's hot enough to melt steel. That's why the shuttle and all spacecraft need some kind of heat shield, protective tiles, or something else. They're not optional, they're the only thing between the crew and total incineration. What about meteorites coming in from space hitting the atmosphere? They're going even faster. A typical meteor enters our atmosphere anywhere between 11,000 to 72,000 m per second. Here, we get to incomprehensible speeds, in my opinion.

[00:09:11]That's about Mach 32 to Mach 210. Most of them totally vaporize from friction with the atmosphere before they hit the ground. And so, as meteors come screaming through the atmosphere, their kinetic energy transforms into light and heat so intense that they create what we call shooting stars that we can see from hundreds of kilometers away. And what you're seeing is the same thing. The intense heat is literally breaking apart, ripping the electrons off the the molecules in the atmosphere, and so that's causing the light show. That's a plasma trail. Now, let's leave the atmosphere completely. Let's talk about the Parker Solar Probe. That's actually humanity's fastest spacecraft ever built. It reached a speed of 192,000 m per second at its closest approach to the sun. Now, that would be Mach 560 if calculated in the Earth's atmosphere.

[00:10:05]This probe, if you could do it, could travel from Tokyo to New York in less than 1 minute. Let's talk about the Earth. The Earth is orbiting the sun actually really fast, about 30,000 m per second. That would be Mach 87 all by itself. Of course, there's vacuum in space, so Mach number doesn't make sense, but on this scale it's interesting to talk about. Now, it's crazy to think about that the entire Earth is screaming through space at a velocity nearly 100 times the speed of sound, and we don't feel a thing because we're in free fall around the sun. And also because the Earth is moving and everything on the Earth is moving, nothing is moving relative to me. I don't notice this motion at all. Now, Mercury, the innermost planet, is screaming around the sun at about 47,000 m per second. Even Neptune, way far away from the sun at the outer edge, is still managing to go 5,400 m per second as it orbits around the sun. Now, these speeds are necessary because if you're going too slow in an orbit, then you're not going to go all the way around. You're just going to fall in to the sun, right? And if you go too fast, then you're going to be on an escape trajectory and leave. So, the orbit of the planets is a balancing act with just the right speed so that we can fall around the star or whatever it is you're orbiting uh at their exactly the right speed so that you close on your trajectory as you go around and around again. You're in a constant state of free fall. So, we've talked about slow things, from cars on the freeway to trains, talked about bullets and aircraft, and the speed of the planets going around the sun. Let's talk about what we set out to talk about, the speed of light. So, as I said before, light travels at a mind-boggling 299,792,458 m per second in vacuum. I mentioned before that it's so fast it could go around the Earth seven times in one single second. And scientists decided that this speed was so fundamental, so constant, so important that they literally redefined the meter, the length of the meter, based on the speed of light. The meter is actually now defined as the distance that light travels in the fraction 1 over 299,792,458 of a second. Now, Einstein showed us that the speed of light is special. It isn't just fast, it's the speed of causality, of cause and effect, itself.

[00:12:34]It's basically the speed at which the universe updates or can transmit information to other parts of the universe. For instance, if the sun actually exploded or just disappeared, I know it won't do that, okay? But if it did, we wouldn't actually know about it for about 8 minutes and 20 seconds. Not because the light is slow getting to us, but because that's how long it takes for information, including the gravitational influence of the sun, to cross 150 million kilometers, about 93 million miles, all the way to Earth. Now, nothing with mass, like nothing made of atoms, can actually reach light speed.

[00:13:14]We can accelerate it, and as you accelerate mass faster and faster, you gain what's called relativistic mass.

[00:13:20]That requires even more energy to go faster. To actually reach light speed would require literally infinite energy.

[00:13:28]In other words, the universe has a speed limit, and it's enforced by the fabric of space-time itself. I want you to think about it this way. What would be more difficult to accelerate? A baseball in your hand, just by throwing it, or a automobile or a train? Let's say you're behind a train. Or let's say you're floating in space behind a giant spacecraft and you're trying to push it.

[00:13:50]Which one of those two things would be more difficult to accelerate? Well, it's going to be pretty easy to throw the baseball, and it's going to be really hard to push a train or a spacecraft.

[00:13:59]Well, what's the difference? Well, one of them has more mass. The baseball has very little mass. The train or the spacecraft has a lot more mass. So, that's the property called inertia.

[00:14:08]That's what we call it when it's difficult to move things that have a lot of mass, like a refrigerator, a sofa, a spaceship, or whatever.

[00:14:16]Now, remember that famous equation, E = mc squared. Right, that really has a lot of information in it. What it basically says is that the energy content of something is equal to its mass, a massive object has mass in kilograms, times the speed of light squared. And the speed of light is a gigantic number, so when you square it, it's a gigantic number. C squared is gigantic. When you multiply by the mass of anything, like this little remote control, I don't know, it's a little fraction of a kilogram or something. But if you multiply by c squared, the energy content of this thing is enormous. Now, I'm a space nerd. I want to build a ship to go faster than light speed. So, what do I do? I'll put a big rocket engine on this thing, and I begin to accelerate it. But now it's moving. Now, what is movement? It's kinetic energy. So, if I give energy to this thing, it's going faster, right? But here's the problem.

[00:15:06]We already know that E = mc squared. So, if I give this thing energy, then that is the same thing as giving it some equivalent amount of mass. E = mc squared. If I accelerate this, I've given it energy, right? And if I accelerate it more, I've given it more energy. But more energy this thing has by E = mc squared, it means it must have gained some equivalent amount of mass.

[00:15:28]But you already know that things that have more mass are harder to accelerate.

[00:15:33]In other words, the more I accelerate a spacecraft, the faster it goes, the more energy it has, the more relativistic mass it gains because of mass-energy equivalent equivalence. But as it has more relativistic mass, it's harder and harder to accelerate it. So, the more energy I give anything with mass, the harder and harder and more difficult it begins to accelerate it even more. And as I get closer to the speed of light, it becomes impossible to accelerate it more because you would literally need infinite energy, all the energy of the universe, to accelerate this tiny remote control all the way to the speed of light. Because as anything travels faster, it's gaining energy. When it gains energy, that's the same as gaining mass, which makes it harder and harder to accelerate. So, I think we can build spacecraft to go really fast one day, but we're not going to be able to push something faster than the speed of light with a conventional type of pushing rocket engine of some kind. Notice I chose my words really carefully. We're not going to be able to do it by pushing mass. There's lots of other theories about bending space and time with exotic energy and shortening the distance from here to the nearest star and other kind of exotic things that we don't and we don't fully understand physics, either.

[00:16:44]So, there's always a possibility we will learn something that will help us, but we're not going to be able to do it by strapping a bigger rocket engine to a ship and trying to push it faster. Now, particles without mass, namely photons, the particles of light, light waves themselves, they must travel at the speed of light. They can't go faster and they can't go slower. From a photon's perspective, if if it could have a perspective, zero time passes during any journey that a photon takes, whether it's from the sun to my eye, from the flashlight to the wall, whatever. A photon from a star 10,000 light-years away experiences no time, literally zero time, in its own reference frame between its creation and the absorption in your eye. So, here's the moment we've all been waiting for, what we've all been building to. What is the Mach number of the speed of light if it could have one?

[00:17:35]Now, if we're talking about light moving through the atmosphere at sea level, um taking some liberties here because the speed of light actually is a little different when it's traveling through matter or not, but work with me here.

[00:17:46]The Mach number of the speed of light would be calculated to be Mach 874,030.

[00:17:54]Now, take a minute, here we have the punchline, to let that sink in. Not Mach 1, not Mach 2 or 3 like a bullet flies, you know, not Mach 100, orbital speed of a of a planet or something. Uh Mach 874,000 and some change, 874,030.

[00:18:13]So, when I say the speed of light is incomprehensible, I literally mean I cannot conceive of a speed that fast.

[00:18:19]The closest I can get is when I visualize the size of the Earth and a photon going seven times around the planet in 1 second. The problem with that is I can't actually visualize the size of the Earth because I've never traveled all the way around the Earth.

[00:18:31]Suffice it to say, the speed of light is really, really, really fast. So, just let it sink in while the fastest hypersonic missiles we can build, they barely scratch Mach 20. The Parker Solar Probe, the fastest thing we've ever built, goes Mach 560.

[00:18:50]Light, photons of light flowing from the sun to our eyes, is Mach 874,030.

[00:18:58]I'll be the first one to admit it's totally absurd. Mach number is a fundamental concept of atmospheres, right? It compares the speed of an object to the speed of sound propagating in an atmosphere or through some some some medium of some type that you're traveling through. And I'm comparing it to the speed of light in a vacuum. So, I'll admit it's a bit silly, but I think it's a fun thing to think about, and we can learn some things along the way. So, to wrap it all up, light speed in a vacuum, if converted to Mach number, is about 874,030.

[00:19:32]That's Mach 874,000 and some change. That's the answer, but the real story is that light doesn't play by the same rules as sound. It doesn't play by the same rules as fighter jets or even our fastest spacecraft. Light, by its very nature, is fundamentally different. It is the universe's ultimate speed limit. And as you ponder this, always remember to stay curious. Learn anything at mathandscience.com.