## The second trailer for Avengers: Endgame released last week giving Marvel fans their first glimpse of Carol Danvers — Captain Marvel — back on Earth. The question is, how can she look so young when 24 years have passed since the end of the Captain Marvel movie? Turns out Einstein has the answer.

The end of Marvel’s latest movie — Captain Marvel — sees the eponymous hero blast into space on a potentially long mission. We know from the Avengers: Endgame trailer that the Carol Danvers — played by Oscar winner Brie Larson — will return in that film looking relatively unchanged. The problem with this that there is a span of at least 24 between the stories in the two movies — Captain Marvel is set in 1995 and Avengers: Endgame is, presumably, set in 2019.

The answer to the question of why Carol has aged very little could be an in-Universe one — she is, at least partially, a member of an alien race that ages differently than humans. She is also powered by the Tesseract — an uber-powerful Marvel McGuffin — maybe this holds the key to her maintaining her youth.

But science does offer an explanation as to how Captain Marvel may have aged less than those she left behind on Earth — and it fits nicely in with how we last see her in 1995. As she races into space at high speed — Carol becomes subject to the strange and somewhat counter-intuitive rules that govern objects moving near-light speed.

Einstein’s theory of Special relativity could explain why Captain Marvel has held on her youthful appearance.

#### Time dilation — Moving clocks run slow.

One of the most interesting consequences that emerged from special relativity is the idea that spacetime is not a passive stage on which the events of the Universe play out— matter can change both the shape of space itself and also cause time to move slower.

Time is not an absolute quantity but a relative one. This emerges as a consequence of the Lorentz transformations that allow us to convert coordinates in one reference frame to another. Einstein was clear that the laws of physics should remain unchanged in all inertial frames, but that doesn’t mean that the coordinates of events governed by those laws are unchanged. In fact, it is quite possible for there to exist two frames in which two events occur in different orders.

To see why Carol has not aged despite time passing on Earth let’s pick up from the end of Captain Marvel. Carol hands a Nick a pager, with which he can summon her back to Earth. Let’s assume that Carol has an identical pager. Both have in-built atomic clocks and are syncronised before Carol leaves Earth.

Nick Fury’s Captain Marvel-upgraded pager as it appears in Avengers: Infinity War (Disney)To Nick, it appears that Carol is racing away from Earth at near light-speed and that her clock is running slow, but to Carol, it appears that Earth is racing away from her. She sees Nick’s clock as running equally slowly. Clearly, this doesn’t explain where the difference in the passage of time arises. Who is correct; is Nick’s clock running slowly or is Carol’s?

The key to answering this dilemma is to realise that, to escape Earth’s gravitational pull, and eventually, to escape the galaxy, Carol must accelerate. She must also accelerate to change direction and return to Earth.

During this acceleration, Carol’s frame is no-longer inertial. Whilst a traveller moving at a steady speed cannot tell if they are moving or their surroundings are moving past them — famously explained by Einstein as a passenger on train unable to tell if her train is moving away from the platform, or if it is the train she observes from the window pulling away from her train and its platform. This is not true of an observer in acceleration — which can most certainly be felt.

This means that no single inertial frame can be used to describe Carol’s journey, whilst Nick can be considered an approximately inertial observer — described by a single inertial frame.

We need to use three frames to describe the situation. We’ll call Nick’s frame on Earth S — and we’ll consider it fixed. When Carol is moving away from Earth in a straight -line at a constant velocity V close to the speed of light c. We’ll call this frame S’ — pronounced S prime. We’ll also select another frame for Carol, her return home at constant velocity — frame R’ — R prime.

We will call Carol’s departure from Earth in 1995 event 0, her instantaneous change in direction to return home event 1 and her arrival back on Earth as event 2.

Let’s lay these out on a space-time diagram.

A standard spacetime diagram given from the perspective of Nick’s fixed frame. The x-axis gives position, the y-axis gives time. You’ll see the y-axis is marked ‘ct’ rather than just ‘t’. This is because the time element (s) is multiplied by the speed of light (3.0 x10⁸ m/s) to ensure that time and space are given in the same units (m).We can see that the time between event 0 and event 2 for Fury on Earth is T=24 years, what we need to do now is calculate what the period is for Carol, which we will label Tc.

Tc will be comprised of two parts — the time between event 0 and event 1, which we will label Tc1. And the difference between event 1 and event 2 — Tc2.

After some maths, we get Tc1= T/2γ and Tc2 = T/2γ. So the total period Tc=Tc1 + Tc2 =T/γ. The symbol γ — the Greek letter Gamma — represents the Lorentz Factor, an extremely important quantity in relativity that holds the key to transforming coordinates from one inertial frame to another.

So now, what we need to do is calculate how fast Carol needs to have been travelling to return and appear mostly unaged. Let’s say that the average human can go roughly 5 years will out showing too many outward signs of ageing. So, we need to find the right Lorentz factor to get Tc =5 when T=24.

After a little bit of maths and fiddling around I managed to work out that the correct Lorentz factor to get us to Tc/T = 5/24 is γ= 4.8. So, what speed would Carol need to be travelling at to age only 5 years when Nick, and the rest of the planet, ages twenty-four?

How fast must Carol have been travelling through space to have aged only five years in the 24 years between Captain Marvel and Avengers: Endgame? (Disney)Turns out it’s 0.978c. That’s 0.978 of the speed of light and about 2.9 x 3.0⁸ m/s. So in order to have barely aged Carol would need to be able to fly through the vacuum of space at pretty close to the speed of light.

At this average speed, when Carol returns to Earth and compares the reading on her atomic clock to Nick’s she will find that 5 years have elapsed on her clock compared to 24 years on Nick’s.

Of course, it may be possible that she’ll be too busy fighting Thanos to check.

Captain Marvel is currently showing in cinemas. Avengers: Endgame opens on April 26th.