Does mass increase when nearing the speed of light? – Big Think

No matter who you are, where you are, or how quickly youre moving, the laws of physics will appear exactly the same to you as they will to any other observer in the Universe. This concept that the laws of physics dont change as you move from one location to another or one moment to the next is known as the principle of relativity, and it goes all the way back not to Einstein, but even farther: to at least the time of Galileo. If you exert a force on an object, it will accelerate (i.e., change its momentum), and the amount of its acceleration is directly related to the force on the object divided by its mass. In terms of an equation, this is Newtons famous F = ma: force equals mass times acceleration.

But when we discovered particles that moved close to the speed of light, suddenly a contradiction emerged. If you exert too large of a force on a small mass, and forces cause acceleration, then it should be possible to accelerate a massive object to reach or even exceed the speed of light! This isnt possible, of course, and it was Einsteins relativity that gave us a way out. It was commonly explained by what we call relativistic mass, or the notion that as you got closer to the speed of light, the mass of an object increased, so the same force would cause a smaller acceleration, preventing you from ever reaching the speed of light. But is this relativistic mass interpretation correct? Only kind of. Heres the science of why.

Schematic animation of a continuous beam of light being dispersed by a prism. If you had ultraviolet and infrared eyes, youd be able to see that ultraviolet light bends even more than the violet/blue light, while the infrared light would remain less bent than the red light does. The speed of light is constant in a vacuum, but different wavelengths of light travel at different speeds through a medium.

The first thing its vital to understand is that the principle of relativity, no matter how quickly youre moving or where youre located, is still always true: the laws of physics really are the same for everyone, regardless of where youre located or when youre making that measurement. The thing that Einstein knew (that both Newton and Galileo had no way of knowing) was this: the speed of light in a vacuum must be exactly the same for everyone. This is a tremendous realization that runs counter to our intuition about the world.

Imagine youve got a car that can travel at 100 kilometers per hour (62 mph). Imagine, attached to that car, youve got a cannon that can accelerate a cannonball from rest to that exact same speed: 100 kilometers per hour (62 miles per hour). Now, imagine your car is moving and you fire that cannonball, but you can control which way the cannon is pointed.

As shown in an episode of Mythbusters, a projectile fired backward from a forward-moving vehicle at the exact same speed will appear to fall directly down at rest; the velocity of the truck and the exit velocity from the cannon exactly cancel each other out in this take.

This is what we commonly experience and also lines up with what we expect. And this is also experimentally true, at least, for the non-relativistic world. But if we replaced that cannon with a flashlight instead, the story would be very different. You can take a car, a train, a plane, or a rocket, traveling at whatever speed you like, and shine a flashlight from it in any direction you like.

That flashlight will emit photons at the speed of light, or 299,792,458 m/s, and those photons will always travel at that same exact speed.

That speed that the photons travel at will be the same as ever, the speed of light, not only from your perspective, but from the perspective of anyone looking on. The only difference that anyone will see, dependent on how fast both you (the emitter) and they (the observer) are moving, is in the wavelength of that light: redder (longer-wavelength) if youre mutually moving away from each other, bluer (shorter-wavelength) if youre moving mutually toward each other.

An object moving close to the speed of light that emits light will have the light that it emits appear shifted dependent on the location of an observer. Someone on the left will see the source moving away from it, and hence the light will be redshifted; someone to the right of the source will see it blueshifted, or shifted to higher frequencies, as the source moves toward it.

This was the key realization that Einstein had when he was devising his original theory of Special Relativity. He tried to imagine what light which he knew to be an electromagnetic wave would look like to someone who was following that wave at speeds that were close to the speed of light.

Although we dont often think of it in these terms, the fact that light is an electromagnetic wave means:

This was cemented in the 1860s and 1870s, in the aftermath of the work of James Clerk Maxwell, whose equations are still sufficient to govern the entirety of classical electromagnetism. You use this technology daily: every time an antenna picks up a signal, that signal arises from the charged particles in that antenna moving in response to those electromagnetic waves.

Light is nothing more than an electromagnetic wave, with in-phase oscillating electric and magnetic fields perpendicular to the direction of lights propagation. The shorter the wavelength, the more energetic the photon, but the more susceptible it is to changes in the speed of light through a medium.

Einstein tried to think of what it would be like to follow this wave from behind, with an observer watching electric and magnetic fields oscillate in front of them. But, of course, this never occurs. No matter who you are, where you are, when you are, or how quickly youre moving, you and everyone else always sees light move at exactly the same speed: the speed of light.

But not everything about light is the same for all observers. The fact that the observed wavelength of light changes dependent on how the source and the observer are moving relative to one another means that a few other things about light must change as well.

This last part is critical for our understanding, because momentum is the key link between our old school, classical, Galilean-and-Newtonian way of thinking and our new, relativistically invariant way of thinking that came along with Einstein.

The size, wavelength, and temperature/energy scales that correspond to various parts of the electromagnetic spectrum. You have to go to higher energies, and shorter wavelengths, to probe the smallest scales. Ultraviolet light is sufficient to ionize atoms, but as the Universe expands, light gets systematically shifted to lower temperatures and longer wavelengths.

Light, remember, ranges in energy tremendously, from gamma ray photons at the highest energies down through X-rays, ultraviolet light, visible light (from violet to blue to green to yellow to orange to red), infrared light, microwave light, and finally radio light at the lowest energies. The higher your energy-per-photon, the shorter your wavelength, the higher your frequency, and the greater the amount of momentum that you carry; the lower your energy-per-photon, the longer your wavelength, the lower your frequency, and the smaller your momentum is.

Light can also, as Einstein himself demonstrated with his 1905 research into the photoelectric effect, transfer energy and momentum into matter: massive particles. If the only law we had was Newtons law the way were used to seeing it as force equals mass times acceleration (F= ma) light would be in trouble. With no mass inherent to photons, this equation wouldnt make any sense. But Newton himself didnt write F= ma like we often suppose, but rather that force is the time rate of change of momentum, or that applying a force causes a change in momentum over time.

The inside of the LHC, where protons pass each other at 299,792,455 m/s, just 3 m/s shy of the speed of light. Particle accelerators like the LHC consist of sections of accelerating cavities, where electric fields are applied to speed up the particles inside, as well as ring-bending portions, where magnetic fields are applied to direct the fast-moving particles toward either the next accelerating cavity or a collision point.

So, what does that mean momentum is? Although many physicists have their own definition, the one Ive always liked is, Its a measure of the quantity of your motion. If you imagine a dockyard, you can imagine running a number of things into that dock.

A large superyacht, MotorYacht GO, crashed into the Saint Maartens Yacht Club dock. The large amount of momentum in the yacht caused it to crash through wood, concrete, and even reinforced steel as it destroyed the dock. Momentum, for very large masses moving even at slow speeds, can be disastrous.

The problem is, going all the way back to Newton, that the force you exert on something is equal to a change in momentum over time. If you exert a force on an object for a certain duration, its going to change that objects momentum by a specific amount. This change doesnt depend on how fast an object is moving alone, but only by the quantity of motion it possesses: its momentum.

So what is it, then, that happens to an objects momentum when it gets close to the speed of light? Thats really what were trying to understand when we talk about force, momentum, acceleration, and velocity when we near the speed of light. If an object is moving at 50% the speed of light and it has a cannon thats capable of firing a projectile at 50% the speed of light, what will happen when both speeds point in the same direction?

You know you cant reach the speed of light for a massive object, so the naive thought that 50% the speed of light + 50% the speed of light = 100% the speed of light has to be wrong. But the force on that cannonball is going to change its momentum by exactly the same amount when fired from a relativistically-moving frame-of-reference as it will when fired from rest. If firing the cannonball from rest changes its momentum by a certain amount, leaving it with a speed thats 50% the speed of light, then firing it from a perspective where its already moving at 50% the speed of light must change its momentum by that same amount. Why, then, wouldnt its speed be 100% the speed of light?

A simulated relativistic journey toward the constellation of Orion at various speeds. As you move closer to the speed of light, not only does space appear distorted, but your distance to the stars appears contracted, and less time passes for you as you travel. StarStrider, a relativistic 3D planetarium program by FMJ-Software, was used to produce the Orion illustrations. You dont have to break the speed of light to travel 1,000+ light-years in less than 1,000 years, but thats only from your point of view.

Understanding the answer is the key to understanding relativity: its because the classical formula for momentum that momentum equals mass multiplied by velocity is only a non-relativistic approximation. In reality, you have to use the formula for relativistic momentum, which is a little bit different, and involves a factor that physicists call gamma (): the Lorentz factor, which increases the closer you move to the speed of light. For a fast-moving particle, momentum isnt just mass multiplied by velocity, but mass multiplied by velocity multiplied by gamma.

Travel the Universe with astrophysicist Ethan Siegel. Subscribers will get the newsletter every Saturday. All aboard!

Applying the same force that you applied to an object at rest to an object in motion, even in relativistic motion, will still change its momentum by the same amount, but all of that momentum wont go into increasing its velocity; some of it will go into increasing the value of gamma, the Lorentz factor. For the earlier example, a rocket moving at 50% the speed of light that fires a cannonball at 50% the speed of light will result in a cannonball traveling at 80% the speed of light, with a Lorentz factor of 1.6667 along for the ride. The idea of relativistic mass is very old and was popularized by Arthur Eddington, the astronomer whose 1919 solar eclipse expedition validated Einsteins theory of General Relativity, but it takes a certain liberty: it assumes that the Lorentz factor () and the rest mass (m) get multiplied together, an assumption that no physical measurement or observation can test for.

Time dilation (left) and length contraction (right) show how time appears to run slower and distances appear to get smaller the closer you move to the speed of light. As you approach the speed of light, clocks dilate toward time not passing at all, while distances contract down to infinitesimal amounts.

The whole point of going through all of this is to understand that when you moveclose to the speed of light, there are many important quantities that no longer obey our classical equations. You cant just add velocities togetherthe way Galileo or Newton did;you have to add them relativistically.

You cant just treat distances as fixed and absolute; you have to understand thatthey contract along the direction of motion. And you cant even treat time as though it passes the same for you as it does for someone else; the passage of time is relative, anddilates for observers moving at different relative velocities.

A light-clock, formed by a photon bouncing between two mirrors, will define time for any observer. Although the two observers may not agree with one another on how much time is passing, they will agree on the laws of physics and on the constants of the Universe, such as the speed of light. A stationary observer will see time pass normally, but an observer moving rapidly through space will have their clock run slower relative to the stationary observer.

Its tempting, but ultimately incorrect, to blame the mismatch between the classical world and the relativistic world on the idea of relativistic mass. For massive particles that move close to the speed of light, that concept can be correctly applied to understand why objects can approach, but not reach, the speed of light, but it falls apart as soon as you incorporate massless particles, like photons.

Its far better to understand the laws of relativity as they actually are than to try and shoehorn them into a more intuitive box whose applications are fundamentally limited and restrictive. Just as is the case with quantum physics, until youve spent enough time in the world of relativity to gain an intuition for how things work, an overly simplistic analogy will only get you so far. When you reach its limits, youll wish you had learned it correctly and comprehensively the first time, all along.

Go here to read the rest:

Does mass increase when nearing the speed of light? - Big Think