Do Objects Get More Massive When They Move Close To The Speed Of Light?

The notion of 'relativistic mass' has been considered since the inception of relativity. But is this concept valid?

Regardless of your identity or location, the principles of physics remain constant for all observers in the Universe. This idea — that the fundamental laws do not alter with your position or time — is referred to as the principle of relativity, dating back not just to Einstein, but to earlier thinkers like Galileo. When a force is applied to an object, it accelerates (i.e., alters its momentum), with acceleration being directly proportional to the force divided by the object's mass. This relationship is captured by Newton's renowned equation F = ma, where force equals mass multiplied by acceleration.

However, the discovery of particles that travel near the speed of light revealed a paradox. If a significant force is applied to a small mass, one might expect to accelerate a massive object to light speed or beyond. This, of course, is impossible, and Einstein's theory of relativity provided clarity. It is often explained through "relativistic mass," the concept that as an object's speed approaches that of light, its mass increases, resulting in reduced acceleration for the same force, thereby preventing it from reaching light speed. But is this interpretation of "relativistic mass" entirely accurate? To some extent, yes. Here's the underlying science.

The first crucial point is that the principle of relativity holds true, irrespective of your speed or location: the laws of physics are indeed the same for everyone, no matter where or when measurements are taken. Einstein's significant insight was that the speed of light in a vacuum is a universal constant, a realization that challenges our intuitive understanding of the physical world.

Consider a scenario where you have a car capable of traveling at 100 kilometers per hour (62 mph), equipped with a cannon that can launch a cannonball at the same speed. If the car is in motion while the cannon fires, the outcomes vary based on the cannon's direction:

• If aimed in the same direction as the car, the cannonball will travel at 200 kph (124 mph).
• If aimed upward while the car moves forward, the cannonball will travel at approximately 141 kph (88 mph), combining forward and upward motion.
• If aimed backward, the cannonball will come out at 0 kph (0 mph), as the speeds cancel each other out.

This is our everyday experience and aligns with our expectations, holding true in the non-relativistic realm. However, if we substitute the cannon with a flashlight, the scenario changes dramatically. Regardless of the vehicle's speed, shining a flashlight emits photons traveling at the speed of light, or 299,792,458 m/s, consistently.

• When aimed in the same direction as the vehicle's motion, photons still travel at 299,792,458 m/s.
• When aimed at an angle, while the direction changes, the speed remains at 299,792,458 m/s.
• Even when aimed directly opposite to the vehicle's motion, photons continue at 299,792,458 m/s.

The speed of light is invariant, perceived consistently by any observer, regardless of their relative motion. The only observed difference arises in the light's wavelength: redshifted (longer wavelength) if the source and observer are moving apart, and blueshifted (shorter wavelength) if they are approaching each other.

This realization was pivotal for Einstein while formulating his initial theory of Special Relativity. He envisioned how light—an electromagnetic wave—would appear to someone traveling close to light speed.

Although often overlooked, the nature of light as an electromagnetic wave entails:

• The wave carries energy.
• It generates electric and magnetic fields as it travels.
• These fields oscillate in tandem and at right angles to one another.
• They can induce motion in charged particles, like electrons, which respond to the electric and magnetic forces.

This understanding was solidified in the 1860s and 1870s through the work of James Clerk Maxwell, whose equations continue to govern classical electromagnetism today. For instance, when an antenna captures a signal, it results from charged particles within it responding to electromagnetic waves.

Einstein's thought experiment involved envisioning what it would be like to follow an electromagnetic wave, observing its oscillating fields. However, this scenario never materializes. Regardless of one's identity, location, or velocity, everyone consistently observes light traveling at the same speed: the speed of light.

Nevertheless, not all properties of light are uniform across observers. Variations in the observed wavelength due to the relative motion of the source and observer necessitate changes in other light attributes:

• The frequency of light must vary, as frequency multiplied by wavelength equals the constant speed of light.
• The energy of each light quantum must change, as the energy of a photon is calculated using Planck's constant (a constant) multiplied by frequency.
• The momentum of each light quantum must also fluctuate, as momentum (for light) is defined by energy divided by the speed of light.

This understanding is crucial since momentum serves as a bridge between classical concepts and Einstein's relativistic framework.

Light spans a vast energy range, from high-energy gamma rays to X-rays, ultraviolet, visible light, infrared, microwaves, and finally radio waves at the lowest energies. Higher energy per photon corresponds to shorter wavelengths, higher frequencies, and greater momentum, while lower energy yields longer wavelengths and lower momentum.

Moreover, as demonstrated by Einstein in 1905 concerning the photoelectric effect, light can transfer energy and momentum to massive particles. If we relied solely on Newton's familiar law, force equals mass times acceleration (F = ma), light would face inconsistencies due to the absence of mass in photons. Newton framed it more accurately as "force is the time rate of change of momentum," meaning that applying force results in changes in momentum over time.

But what, then, is momentum? Although various interpretations exist, one appealing definition is "a measure of the quantity of your motion." Picture a dockyard with various vessels:

• A dinghy, regardless of its speed, maintains low momentum due to its minimal mass; it exerts little force when colliding with the dock.
• Conversely, a firearm's projectile, despite its lower mass, travels at high speeds, resulting in significant localized structural damage upon impact.
• Alternatively, a massive, slow-moving ship can inflict considerable damage due to its vast mass, even at low speeds.

Historically, from Newton's principles, the force exerted on an object translates to a change in momentum over time. The force applied to an object for a duration alters its momentum by a specific amount, dependent on its "quantity of motion" (momentum).

So what occurs to an object's momentum when it approaches light speed? This question encapsulates our exploration of force, momentum, acceleration, and velocity near light speed. If an object moves at 50% the speed of light and fires a projectile also at 50% light speed in the same direction, what will the outcome be?

Intuitively, one might think "50% light speed + 50% light speed = 100% light speed," yet this is incorrect. However, the force applied to the projectile affects its momentum similarly when fired from a relativistically moving frame or from rest. If firing from rest yields a speed of 50% light speed, then firing from a moving perspective must result in the same momentum change. Why, then, wouldn't its speed reach 100% light speed?

Understanding the answer is essential for grasping relativity: the classical momentum formula—momentum equals mass multiplied by velocity—serves merely as a non-relativistic approximation. The true relationship involves a different formula for relativistic momentum, incorporating a factor known as gamma (?), the Lorentz factor, which increases as one approaches light speed. For fast-moving particles, momentum is not just mass times velocity, but mass times velocity times gamma.

Applying the same force to an object in motion will alter its momentum equivalently, but not all of that momentum translates to increased velocity; some contributes to elevating the Lorentz factor. In the previous example, a rocket traveling at 50% light speed firing a projectile at the same speed results in the projectile traveling at 80% light speed, accompanied by a Lorentz factor of 1.6667. The notion of "relativistic mass," popularized by Arthur Eddington after validating Einstein's General Relativity in 1919, takes liberties by assuming that Lorentz factor (?) and rest mass (m) are multiplied, a hypothesis lacking empirical validation.

Ultimately, when approaching light speed, numerous vital quantities no longer conform to classical equations. Velocities cannot simply be added as in the classical framework; they require relativistic addition. Distances are not fixed and absolute; they contract in the direction of motion. Time cannot be treated uniformly; its passage is relative, dilating for observers moving at different velocities.

It may be tempting, but ultimately incorrect, to attribute the discrepancies between classical and relativistic worlds solely to relativistic mass. While this concept is valid for massive particles nearing light speed, it becomes inadequate when considering massless particles like photons.

Understanding the laws of relativity in their true form is far more beneficial than attempting to fit them into an intuitive, yet overly simplistic framework. Similar to quantum physics, gaining a genuine intuition for relativity requires time and effort. Simplistic analogies will only take you so far; once you reach their limits, you’ll wish you'd comprehended the subject thoroughly from the outset.

Starts With A Bang is authored by Ethan Siegel, Ph.D., writer of Beyond The Galaxy and Treknology: The Science of Star Trek from Tricorders to Warp Drive.