What do luminous space cows have to do with Einstein’s most famous equation and accelerating objects gaining mass?

Is it true that an accelerating object gains mass?

This is something you may have heard from someone who has watched a few too many YouTube videos trying to explain all of physics in under two minutes. Let’s start with the basics. What do we mean by “accelerating” and “mass”?

Mass is how much stuff is in an object. Acceleration is any time an object changes its velocity – that includes speeding up and slowing down. How does this relate to a change in mass?

The cosmic speed limit

Like so many things in physics, the answer can be found in the work of Albert Einstein on relativity.

Einstein provided us with two theories of relativity: special relativity and general relativity. And, maybe a little counterintuitively, the more complicated theory is general relativity. Special relativity is special because it looks at special cases – involving massive amounts of energy, ultra-fast speeds and huge distances – all of them without gravity.

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Special relativity tells us about the relationship between speed and mass, space and time. Maybe you can see where we’re going with this. Einstein was compelled to think about these things because of the cosmic speed limit set by the speed of light – nearly 300,000 kilometres a second!

It’s commonly known that nothing can go faster than the speed of light. But why? With no speed cameras in space, what is policing this law of nature? And what happens when we try to exceed this speed?

We need to begin with the theory of relativity itself.

Relatively speaking, it is special

Say you’re sitting on a train, facing forward. The train is travelling at 60 kilometres an hour. You’re holding a tennis ball. Now let’s say you throw the tennis ball at 20 kilometres an hour in the same direction the train is going.

Ignoring air resistance – which would slow the ball down – from your perspective, the ball is travelling 20 kilometres an hour. But from the perspective of someone standing on a railway station as the train passes, the tennis ball is travelling at the combined speed of the train and your throw – 80 kilometres an hour.

Now imagine the train is moving at half the speed of light. Instead of throwing a tennis ball in the direction the train is headed, you shine a laser. Let’s get our friend on the railway platform to shine a laser in the same direction at exactly the same time.

From the tennis ball example, you might deduce that the light shone on the train is travelling at the combined speed of the train and the speed of light – or one-and-a-half times the speed of light. Therefore, a third observer thousands of kilometres down the track would see the light from the train arrive first… you would think. But this can’t happen, according to Einstein.

Einstein theorised that the speed of light is constant, so the light in the train would arrive at the third observer at the same time as the light from the platform. What changes here is not the speed of light, but time and space itself. Einstein suggested that we have to think differently about the meaning of words like “simultaneous”.

Space and time behave differently for different observers depending on their state of motion – or their “inertial frame of reference” as Einstein called it.

So, Einstein suggested that as objects approach the speed of light, time dilates (gets slower) and space contracts (gets shorter) according to an outside observer. The train travelling at half the speed of light appears shorter to an outside observer, and more time has passed for those not on the train which would look like a squished and blurred version of its former self. Only then can you explain why the light shone from the train and the platform are seen by the third observer at the same time.

It was thought experiments like these that led Einstein to his theory. Einstein noticed that there’s a relationship between relativity and energy.

Enter the luminous space cow

Imagine a luminous cow in space completely stationary. According to Newtonian mechanics, the cow has no kinetic energy – energy derived from movement. But the light coming from the cow carries energy, so the luminous cow is losing energy.

Now, if you were to zoom past the radiating cow in a spaceship, from your frame of reference, the cow moooo-ves past you. It therefore has a kinetic energy while still losing energy in the form of light.

Think of an ambulance driving past you with its siren on. As the ambulance moves further away, the pitch of the siren changes because the sound waves have further to travel.

Light acts in much the same way. As you zoom past the luminous space cow, light waves from the cow change colour and the energy given off by the cow according to you in your frame of reference is different!

But the total energy must be the same in both cases: whether you’re zooming past or not. You haven’t done anything to the glowing space cow.

Some simple algebra led Einstein to the most famous equation in the world: E = mc². Einstein worked out that energy (E) and mass (m) are equivalent down to a constant – the speed of light squared.

One way of thinking about mass is how hard it is to move an object. A more massive, or heavier, object is more difficult to move than a lighter one. The heavier object has more inertia.

Putting those facts into E=mc², given the speed of light is constant, the greater the energy, the greater the mass.

Stubbornness, mass and inertia

This gained inertia only becomes significant at very fast speeds. The gain increases as the object approaches lightspeed. At lightspeed, you would need an infinite amount of energy to overcome the object’s growing inertia.

All of this is based on Einstein’s assumption – that the speed of light is constant. In line with Einstein’s equations, though, particles of light ­– photons – have no mass meaning they have no inertia to overcome. This is why they can travel at lightspeed. It also opens up the possibility that when you travel close to the speed of light, the fact that time dilates – slows for you – means you could journey into the future. As long as you can get in the ballpark of 300,000 kilometres per second.

While you’re not going to notice an increased mass when you go for a run or even in a train or aeroplane, the physics behind the question is beautiful as it is befuddling. The universe is a very strange place indeed.