Mass misconception: Why we can’t outpace light speed

Einstein’s theory of relativity is one of the most mind-bending theories ever devised. In it, moving clocks tick more slowly than stationary ones, and rulers shrink. Perhaps the most shocking consequence of all is that nothing can travel faster than light.

This last one is very disappointing to space enthusiasts, as it dooms their hopes of ever speedily exploring the cosmos. Space is vast, with the closest star located four light years away. Even a simple radio signal, which travels at the fastest speed possible, will take eight years to make a round trip.

The idea that there is a maximum speed is pretty counterintuitive; after all, in everyday experience, you can make a car go faster simply by stepping harder on the gas or upgrading to a sports car. In rocketry, you can just let the rocket fire longer. So why is it that we can’t move faster than the speed of light?

The cosmic speed limit

If you read anything about Einstein’s theory of special relativity, you’ll probably read that the mass of an object increases as its speed increases. And this is kind of a satisfying and intuitive answer. It’s harder to push more massive objects and, therefore, if the mass of an object gets heavier, you have to work harder to go faster. And, if the mass of an object becomes infinite near the speed of light, then it would take an infinite amount of energy to push it even faster. Voila! Problem answered.

While this answer is satisfying and intuitive, it’s also wrong—at least in detail.

Now before anyone decides to quote me as saying that Einstein’s theory of relativity is wrong, don’t. Relativity does indeed state that an object with non-zero mass cannot go at the speed of light, and even massless objects cannot go faster than light. So, this mass misstatement is no help to those erstwhile interstellar explorers.

No, the issue is not that the claim of a maximum speed is wrong; the issue is that the explanation is wrong. So how does it arise?

Mass vs. inertia

The issue arises because we conflate two ideas: mass and inertia. Inertia is really the property that resists changes in motion. It’s just that at low speeds inertia and mass are the same thing. But this isn’t true at high speeds.

This is easiest to see with equations, so I’ll sketch them here, but if you’re not a math person, I’ll only use them sparingly. Everyone has seen Einstein’s most famous equation, E = mc², where E is energy, m is mass, and c is the speed of light. Taken literally, it says that energy equals mass times a constant. However, this equation is actually a special case. The fully correct equation is E = γmc², where γ is a factor that arises in essentially all of the equations of relativity. The factor γ is related to velocity, increasing as velocity increases. At zero velocity, γ equals one, while as velocity gets close to the speed of light, γ approaches infinity. This parameter γ changes, not the mass. Mass is constant.

Because relativity is so difficult for students to understand, physics teachers invented a pedagogical concept called “relativistic mass.” Relativistic mass is simply γ times mass. You can then put relativistic mass into Einstein’s famous equation, and it looks like the familiar form. And it’s possible to use relativistic mass for many other equations that are taught in introductory physics class. In essence, replacing mass with relativistic mass both makes it easier for students to learn the theory and also gives a nice and intuitive picture of what is going on, which has the nice consequence that it is easier for students to accept all of the relativistic weirdness. Relativistic mass is a student-friendly idea, not a real one.

Mind you, to point this out isn’t to criticize physics teachers. I’ve taught this slightly incorrect idea myself. Just as a doctor may prescribe a medicine that has a side effect, but the help is greater than the harm, physics teachers must balance the value of getting students to embrace relativity, with the consequences of this misconception being relatively small. Only students going on in physics will need to better understand the deeper and correct explanation.

So, what are the consequences of this misconception? Essentially, mass, relativistic mass, what does it matter? It matters because mass is not only a quantity that resists motion—it’s also a quantity that generates gravity. Therefore, many students think that the gravitational field around a fast-moving object increases. This would make sense if mass were indeed increasing. But it’s not.

This mass misconception illustrates a real problem with trying to explain a deep science concept using compromises; a motivated thinker will take the compromise as truth and push forward, often drawing a perfectly reasonable, but wrong, conclusion. The reasonable conclusion follows from what the person was taught, but it is wrong because the compromise wasn’t completely accurate. Sadly, there’s no substitute for a deep dive.

So, if you are one of those motivated thinkers who thought that a fast-moving object has a greater mass and greater gravitational force, on behalf of physics teachers everywhere, I would like to apologize. Mass does not increase with speed. Inertia does. The good thing is that many of the important consequences of relativity—most importantly the conclusion that nothing can travel faster than light—remain true.

The key message — beyond the one that while inertia does increase with speed, mass remains the same — is that it is easy for intelligent people to be misled by simplified explanations for complex problems. Thus, if you think you’ve found something that the professional scientific community has overlooked, perhaps it is because you began with one of these partial truths.