Does the mass of objects increase as they approach the speed of light?

The concept of “relativistic mass” has been around almost as long as the theory of relativity. But is it a reasonable way of thinking about things?

No matter who you are, where you are, or how fast you are moving, the laws of physics will look exactly the same to you as they do to every other observer in the universe. This concept, according to which the laws of physics do not change when moving from one place to another or from one moment to another, is known as the principle of relativity and goes back not to Einstein, but even further back: at least to the time of Galileo. If a force acts on an object, then it accelerates (i.e. changes its momentum), and the amount of acceleration directly depends on the force acting on the object divided by its mass. In the language of mathematics, this statement looks like Newton’s famous equation F = ma: force equals mass times acceleration.

But when particles moving at speeds close to the speed of light were discovered, a contradiction suddenly arose. If too much force is applied to a small mass, and the forces cause acceleration, then a massive object can be accelerated to the speed of light or even exceed it! This is, of course, impossible, and it was Einstein’s theory of relativity that allowed us to resolve this paradox. This is usually explained through the concept of the so-called “relativistic mass”, i.e. in that as it approaches the speed of light, the mass of an object increases, so the same force causes less acceleration, preventing it from reaching the speed of light. But is this interpretation of “relativistic mass” correct? Only partly. Here is the scientific answer to this question.

In the vacuum of space, all light, regardless of wavelength and energy, travels at the same speed - the speed of light in a vacuum. When we observe light from a distant star, we are observing light that has already traveled from the source to the observer. — In the vacuum of space, all light, regardless of wavelength and energy, travels at the same speed – the speed of light in a vacuum. When we observe light from a distant star, we are observing light that has already traveled from the source to the observer.

The first thing that is important to understand is that the principle of relativity, no matter how fast you move or where you are, remains true at all times: the laws of physics are indeed the same for everyone, no matter where you are or when you take measurements. Einstein knew (what neither Newton nor Galileo could know) the following: the speed of light in a vacuum must be exactly the same for everyone. This is a stunning realization that goes against our intuitive understanding of the world.

Imagine that you have a car that can move at a speed of 100 km/h. Imagine that there is a cannon attached to this car that can accelerate a cannonball from rest to exactly the same speed: 100 kilometers per hour. Now imagine that your car is moving and you are firing a cannon, and you can control which way the cannon is pointed.

If you point the cannon in the same direction as the car is moving, the cannonball will move at a speed of 200 km/h: the speed of the car plus the speed of the cannonball.
If the cannon is aimed forward and upward while the car is moving forward, the cannonball will move at a speed of 141 km/h: a combination of forward and upward motion at an angle of 45°.
And if you point the cannon in the opposite direction, firing the cannonball backwards while the car is moving forward, then the cannonball will move at a speed of 0 km/h: the two speeds exactly cancel each other.

As demonstrated in one of the episodes of the program

This is what we usually see and it matches our expectations. And this is also experimentally true, at least for the non-relativistic world. But if we replaced the gun with a flashlight, the story would be completely different. You can take a car, train, plane or rocket moving at any speed and shine a flashlight from it in any direction.

The flashlight will emit photons at the speed of light, or 299,792,458 m/s, and these photons will always travel at the same speed (in a vacuum).

You could fire photons in the same direction your car is moving and they would still move at 299,792,458 m/s.
You can shoot photons at an angle to the direction of travel, and although this may change the direction of the photons, they will still travel at the same speed: 299,792,458 m/s.
Or you can shoot photons directly opposite to the direction of motion, and they will still move at a speed of 299,792,458 m/s.

The speed at which photons move will be the same as always – the speed of light, not only from your point of view, but from the point of view of any observer. The only difference someone will see depending on how fast you (the emitter) and they (the observer) are moving is the wavelength of the light: redder (longer wavelength) if you move away from each other, and bluer (smaller wavelength) as you move closer to each other.

For an object moving close to the speed of light and emitting light, the light it emits will appear shifted depending on the location of the observer. The one on the left will see the source moving away from him, and therefore the light will be red; someone to the right of the source will see it turn blue, or shift to higher frequencies, as the source moves towards them.

This key realization occurred to Einstein as he developed his original theory of special relativity. He tried to imagine what light, which he knew was an electromagnetic wave, would look like to a person moving behind that wave at close to the speed of light.

Although we don’t often think of it in these terms, the fact that light is an electromagnetic wave means:

that this light wave carries energy,
that when distributed in space it creates electric and magnetic fields,
these fields oscillate, in phase and at an angle of 90° to each other,
and when they pass other charged particles, such as electrons, they can cause them to move periodically, since charged particles experience forces (and therefore accelerations) when they are subjected to electric and/or magnetic fields.

This was established in the 1860s and 1870s, as a result of the work of James Clerk Maxwell, whose equations are still sufficient to describe classical electromagnetism. You use this technology every day: every time an antenna “picks up” a signal, that signal is generated by charged particles in the antenna moving in response to electromagnetic waves.

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

And no matter who you are, where you are, when you are and how fast you are moving, you – and everyone else – always see light moving at the same speed: the speed of light.

But not all properties of light are the same for all observers. The fact that the observed wavelength of light changes depending on how the source and observer move relative to each other means that some other characteristics of light must also change.

The frequency of light must change because frequency times wavelength is always equal to the speed of light, which is a constant.
The energy of each quantum of light must change because the energy of each photon is equal to Planck’s constant (which is a constant) multiplied by the frequency.
And the momentum of each quantum of light must also change, since momentum (for light) is equal to energy divided by the speed of light.

Scales of size, wavelength and temperature/energy corresponding to different parts of the electromagnetic spectrum. To study the smallest scales, it is necessary to move to higher energies and shorter wavelengths. Ultraviolet light is sufficient to ionize atoms, but as the Universe expands, the light systematically shifts to lower temperatures and longer wavelengths.

Light, recall, can have a huge energy range: from the highest energy gamma rays to x-rays, ultraviolet light, visible light (from violet to blue, green, yellow, orange and red), infrared light, microwave light and, finally, radio emissions with the lowest energies. The higher the energy per photon, the shorter the wavelength, higher the frequency, and greater the momentum; the lower the energy per photon, the longer the wavelength, lower the frequency, and lower the momentum.

Light can also, as Einstein himself showed in 1905 when studying the photoelectric effect, transfer energy and momentum to matter – that is, to massive particles. If the only law were Newton’s law as we are accustomed to seeing it – where force equals mass times acceleration (F = ma) – light would be in a quandary. Without the inherent mass of photons, this equation would make no sense. But Newton himself did not write the equation “F = ma,” as we often assume, but the statement that “force is the rate of change of momentum with time,” or that the application of force causes a “change in momentum” with time.

Inside the LHC, protons fly past each other at a speed of 299,792,455 m/s, which is only 3 m/s less than the speed of light. Particle accelerators like the LHC consist of sections of accelerating cavities, which contain electric fields that accelerate the particles in them, and ring-shaped bending sections, which contain magnetic fields that direct fast-moving particles either to the next accelerating cavity or to a collision point.

So what does this mean – momentum? Although many physicists have their own definition, I’ve always liked this: “It’s a measure of the amount of motion you have.” If you imagine a pier, you can imagine what the collisions of various objects with this pier will look like.

The boat can move both relatively slowly and quickly, but due to its low mass its momentum will remain small. The force it exerts on the dock in a collision will be limited, and only the weakest docks will suffer any structural damage when struck by a small boat.
In a dockside shooting situation, things will be different. Even though projectiles—bullets, cannonballs, or something more destructive like artillery shells—may have little mass, they will travel at very high (but still non-relativistic) speeds. With a mass equal to 0.01% but a speed equal to 10,000% of the speed of the boat, their impulses may be similar, but the force will act on a much smaller area. Structural damage will be significant, but only in isolated areas.
Or a slow-moving but massive object, such as a cruise ship, superyacht or battleship, could be pushed into a dock at extremely low speed. With a mass millions of times greater than the mass of the boat – they can weigh tens of thousands of tons – even an insignificant speed can lead to the complete destruction of the dock. The momentum of objects with large masses is no joke.

The large superyacht MotorYacht GO crashed into the dock of a yacht club in Saint Martin. Due to the large impulse, the yacht, destroying the dock, pierced wood, concrete and even reinforced steel. For very large masses moving even at low speeds, the impulse can be catastrophic.

The problem is that, as Newton knew, the force acting on something is equal to the change in angular momentum over time. If a force is applied to an object for a certain time, this will lead to a change in its momentum by a certain amount. This change does not depend on the speed of the object’s movement, but only on the “amount of motion” it has – its momentum.

So what happens to an object’s momentum as it approaches the speed of light? This is what we are trying to understand when we talk about force, momentum, acceleration and speed as we approach the speed of light. If an object is moving at 50% the speed of light and it has a cannon that can fire a projectile at 50% the speed of light, what will happen when both speeds are directed in the same direction?

You know that the speed of light is unattainable for a massive object, so the naive idea that “50% speed of light + 50% speed of light = 100% speed of light” must be wrong. But the force acting on a cannonball, when fired from a relativistically moving frame of reference, will change its momentum by exactly the same amount as when fired from a state of rest. If shooting a cannonball at rest changes its momentum by a certain amount, causing it to acquire a speed equal to 50% of the speed of light, then shooting at it from a position where it is already moving at 50% of the speed of light should change its momentum is the same amount. Why then will its speed not be equal to 100% of the speed of light?

Simulation of relativistic travel to the constellation Orion at various speeds. As we approach the speed of light, space not only becomes distorted, but the distance to the stars also decreases, and travel time becomes shorter. To create illustrations

Understanding the answer is key to understanding the theory of relativity: the whole point is that the “classical” formula for momentum – momentum equals mass times velocity – is only a non-relativistic approximation. In reality, it is necessary to use a formula for relativistic momentum, which is slightly different and includes a coefficient that physicists call denoted (γ) – Lorentz factor, which increases more the closer you get to the speed of light. For a fast moving particle, momentum is not simply mass times velocity, but mass times velocity times gamma.

When applying the same force as to a stationary object, to a moving object, even a relativistic one, its momentum will change by the same amount, but all this momentum will not go to increase its speed, and part of it will go to increase gamma – the Lorentz coefficient. In the previous example, a rocket traveling at 50% the speed of light and firing a cannonball at 50% the speed of light would result in the cannonball traveling at 80% the speed of light, and the Lorentz coefficient would be 1.6667. The idea of ”relativistic mass” is very old and was popularized by Arthur Eddington, the astronomer whose 1919 expedition to observe a solar eclipse confirmed Einstein’s theory of general relativity, but it takes some liberties: it assumes that the Lorentz coefficient (γ) and rest mass (m) increase together, and this assumption cannot be verified by any physical measurements or observations.

Time dilation (left) and length contraction (right) show that time moves slower and distances become smaller the closer we get to the speed of light. As we approach the speed of light, clocks slow down more and more, and distances are reduced to infinitesimal values.

The point of all this is to understand that when moving near the speed of light, there are many important quantities that no longer obey our classical equations. You can’t just add up the velocities like Galileo or Newton did; you have to add them up relativistically.

Distances cannot be considered fixed and absolute; it is necessary to understand that they contract along the direction of movement. And you can’t even assume that time passes for you in the same way as for someone who is watching you – it is relative and slows down for observers moving at different relative speeds.

The light clock, formed by a photon reflecting from two mirrors, tells the time for any observer. Although two observers may not agree on how much time passes, they will agree on the laws of physics and the constants of the universe, such as the speed of light. With the correct application of the theory of relativity, it will turn out that their measurements are equivalent to each other. The phenomenon of time dilation, first discovered by Lorentz in the 1890s, soon led Einstein to the discovery of special relativity.

It is tempting, but ultimately incorrect, to blame the discrepancy between the classical and relativistic worlds on the idea of relativistic changes in mass. For massive particles moving close to the speed of light, this concept can still be applied to understand why objects can approach the speed of light without reaching it, but it falls apart once you include massless particles such as photons.

It is much better to understand the laws of relativity as they really are than to try to squeeze them into a more intuitive framework, the application of which is fundamentally limited. As with quantum physics, until you’ve spent enough time in the world of relativity to get an intuitive understanding of how things work, an overly simplistic analogy will only get you so far. When you reach its limits, you will regret not studying it correctly and comprehensively the first time.