## Buffyverse Physics: It’s about Time (Pt 1: Relativity)

We are going to delve deep into this one. We have a demon dimension where time moves super-fast, and we have so much to talk about: Relativity, Energies, Biology… We’re talking “Anne” — season 3 episode 1 — an episode that deals with Time.

*Note: If you haven’t watched Season 3 Episode 1 of Buffy the Vampire Slayer, be aware that this post will contain spoilers. Even though it was released in 1998 (twenty years, y’all!) it’s a super fun watch, so go watch it first, and come back for some science.*

## The phenomenon

Buffy encounters a demon that unceremoniously throws teenagers into a portal to another dimension where they are forced into hard labor. When they’re too old, they’re tossed out into our universe again.

Except in demon-dimension, time passes super fast compared to ours; 100 years in demon-verse is only 1 day in our universe, so what was 70 or so years for the poor teenager doing hard labor, is less than a day for Buffy.

We learn that fighting demons is time consuming, which leads to an extremely important existential question: *If Buffy created a belt out of wrist watches, would it be a complete waist of time?*

… Okay okay, I’ll stop while I’m ahead. Let’s jump into the science of Time.

## The problem(s)

Here’s the thing. Time is important — nay, *fundamental* — to our understanding of the universe. The way our universe behaves is closely connected to how time moves and how we perceive it.

If we are throwing random mostly-unsuspecting teenagers into a portal where they rapidly move from regular-time to fast-time, we have some ‘splainin to do.

There are three main issues we are going to talk about in this series of posts, all of which touch on the effect of changing time references and how time (and speed) work:

**Relativity:**We have two places where time runs differently. There is a Physical theory that touches on the effects of that, and that is “Special Relativity”**Energy:**Time affects movement and speed, so if an object moves from slow-time to fast-time, it becomes faster… How much energy is required? What happens to this energy, where does it go?**Biology:**What happens to the human body as it climbs in or out of that portal? What happens when it’s halfway through?

As always, we’re using the (fictional) events in this episode to examine real science, while acknowledging the universal laws of physics inside *Buffy the Vampire Slayer*, which are, pretty clearly, different in some aspects than the real world.

That means we can examine what our known science tells us, and then examine how the universe of the show solves any inconsistencies. That’s right, there are ways to solve all the problems I’m raising, so bear with me through this exploration, and we’ll see how **Buffy not only wins over demons, but wins over physics, too.**

Strap in, scoobies, we’re going in fast!

## Time and space, and how they’re related

When we look at our universe and how it behaves, we describe it through a four-dimensional model: Three spacial dimensions (x, y and z) and a time dimension (t). That is, we look not only at where things are, but at where they are at any given time. This allows us to predict phenomena.

While in our current known universe we haven’t yet found any portals that lead to demon dimensions (I’m looking at you, CERN,) we do have examples where time does change and shift on us.

It is well established, proven, and demonstrated time and time again: Our perception of reality, and the mechanics of time,** depend on who’s looking, where they are, and how fast they go**.

Yup. Welcome to my favorite theory in all of Physics: Special Relativity.

## Introduction to Special Relativity

Special relativity is one of my most favorite physical theories. It’s well established, well accepted, and was demonstrated time and time again through… well… time.

The theory itself establishes two main (and revolutionary) claims:

- The laws of Physics are the same no matter how fast you’re going
- The speed of light is constant everywhere

These two statements sound pretty straight forward, but what they actually mean revolutionized the entire field of Physics and the way we examine our universe.

Here’s a breakdown of each of those statements:

- I experience physics the same no matter how fast I am.

If I am on a moving train and I throw a ball up in the air, it will fall down to my hand as if I was standing still. That means the ball gains my (and my train’s) speed along with me. If I throw that ball forward, it will have the speed I tossed it at**plus**the speed of the train. - Light travels at light-speed no matter what frame it is in.

Light, no matter what, never goes faster than \(2.99*10^8\) meters per second, ‘c’.

If I shine a flashlight forward on a moving train, the light will go at speed ‘c’ and not c+train-speed, because light speed never changes.

Unlike the ball I tossed in #1, light beam does not care it starts out already moving.

Makes sense? It took a bit to convince the scientific community — but these are absolutely and undeniably proven. They’re true!

The best way to explain Special Relativity is through visual examples. I was going to delve deep, but to be honest, there’s a really cool video, by PBS, that does a bang-up job, and seeing these effects on the screen is a lot more effective than reading theoretical claims.

Take a few minutes and watch it. I’ll give a couple of examples below if you don’t have time to watch, but won’t get into the “how” or “why” of these too much. Watch the video, it’s worth the time, really:

The two *main* phenomena that Special Relativity describes are time dilation and length contraction. They both stem from the two fundamental claims above, and their effects are mind boggling and incredible to think about.

### Time dilation

**The faster you go, the slower time passes for you**, relative to an observe in a slower reference frame.

The “Twin Paradox” (that isn’t a paradox at all) explains this best. Think of a pair of twins. One goes on a spaceship for a trip around the solar system, and one stays on Earth.

The traveling twin experiences a trip that takes, say, a month to complete. She gets back to Earth, excited to share her experiences — only to meet her sibling, who’s waited for years. Maybe even decades.

Yeah — it’s that meaningful. Time slows down for the traveling twin, significantly. Are they even twins anymore? This isn’t the type of paradox that implodes the universe — it’s the type that makes you stare at your clocks in confusion. You may not have even believed it, had it not be so incredibly repeatedly proven to be true.

This is the first part of why Relativity is awesome.

### Length contraction

And here’s the second part: **The faster you go, the more space is contracting for you, relative to me, the slower observer.**

I look at Bob in his train, but what I see isn’t a regular Bob — I see a squished Bob in a squished train. The faster Bob goes relative to me, the more squished I’ll see him and his train.

The Physics Classroom has a really good article with some animations demonstrating these effect.

These effects happen in any speed. Even when you’re in a regular car, your time is dilated and your length is contracted compared to a bystander looking at you from the sidewalk, but the difference in these speeds is so minuscule, we never notice it.

When you travel really really fast, though, we do notice. And it has significant effect. So significant, that we have to account for time dilation and length contraction in instruments we send to space.

Physics is awesome, y’all. Seriously. I could go on forever, in any frame of reference.

## So what does this have to do with Buffy?

Right, right, we’re not just here to gush about the incredibly awesome effects of Special Relativity (good thing you stopped me, guys) we’re here to examine the specific science of demons throwing teenagers into demon dimensions.

So here it is: We have normal-time dimension (our world) and super-fast-time dimension (demon) so we have two frames of reference, and we have relativistic effects. Huzzah!

…. except the portal is opaque, which means we don’t see into it, which means we wouldn’t really see any length contraction or time dilation. Good on the writers for preventing themselves a visual effects nightmare.

But that doesn’t mean relativity isn’t in effect in this episode. In fact, it’s a major driver for the plot.

## What makes time move faster in the demon dimension?

See, this is a great question.

As we’ve seen from looking into Special Relativity, the perception of time (the actual passing of time) changes based on reference frames. We, in the regular universe, experience time a lot slower than the demons in the demon-universe.

**This would happen if we are travelling really really fast relative to the demon-dimension**; so fast, that the time dilation we experience is 36525 times slower than demon-dimension.

But, you ask (I know you do) — How fast are we going relative to the demon-dimension?

Another great question, and we can find this out through some calculations..

We are told in the episode that our universe experiences 1 day for every 100 years in demon universe — that’s how much we are “time dilated”. If we know this, we can figure out how fast our universe is going relative to the demon universe. You can expand the calculation below, or look directly at the result.

Show the Math

We use the time dilation calculation to see how fast we’re going. Since time passes slowly on our world, we assume the demon world is our observer, and we’re the ones who are moving.

\(\Delta T_{\text{demon universe}} = \frac{ \Delta T_{\text{our universe}} }{ \sqrt{ 1- \frac{ v_{\text{our universe}}^2 }{ c^2 } } }\)

Let’s rearrange this equation to get the velocity:

\(v_{\text{our universe}} = c \sqrt{ 1- \frac{ \Delta t_{\text{our universe}}^2 }{ \Delta t_{\text{demon universe}}^2 } }\)

For every 100 years in demon world, we experience 1 day. 100 years is 36525 days. That gives us:

\(v_{\text{our universe}} = c \sqrt{ 1- \frac{ 1_{d}^2 }{ 36525_{d}^2 } }\)
\(=c\sqrt{ 1-\frac{1}{1334075625} }\)
\(=c\sqrt{0.99999999925}\)
\(=0.99999999962 c\)

We’re going at 0.99999999962 times the speed of light, compared to demon dimension.

Whoosh! Hold on to your beany, Willow! No wonder time’s so slow here compared to there. We’re flyyyyying!

## Another reason for the time difference: Gravity

Before we close this specific segment of the explanation (and move to the next) we should acknowledge another way for the time differential to exist.

General relativity.

Yeah.

You thought you were done, didn’t you? Ha, I say. Ha. It’s time to go over an alternative theory, and check if it’s valid.

General relativity describes the relation of spacetime as it touches gravity. The higher the gravitational pull, the slower time goes.

If you’ve seen the movie “Interstellar”, you might remember the planet near the black hole, where the water tides were pretty insane. Not only did the black hole wreck havoc on the tides, it also dilated time pretty significantly. That’s because it’s a massive piece of mass, right nearby, and it warps spacetime itself.

For this to be the reason of the time differential, though, we — in our real universe — would have to be the ones affected by the massive gravitational pull. Without going into too much of a magical stretch here, that seems completely implausible, even when we take into account Buffyverse magic stuff.

We don’t have, anywhere in the series or the real world, any acknowledgement or observation or any other sort of data suggesting that we’re near a big enough mass to produce the time difference. And since we have an alternative theory (that we’re moving really fast compared to demon-world) we can accept that, instead.

Hurrah for scientific inquiry!

Back to the actual point of this post.

## Conclusions

We’ve spent all this time examining special relativity, some aspects of general relativity, and figuring out how fast we are moving compared to demon-universe. What does that mean for Buffyverse physics?

### Conclusion #1: We’re super fast

Our universe is travelling at almost the speed of light, compared to demon-universe, which is why time moves so slow for us. We are inside a time-dilated universe compared to demon-world. HOW COOL IS THAT!

### Conclusion #2: The endpoints of the portal are moving

The portal serves as a doorway to the other frame of reference. We’re moving, the entry point of the portal moves with us, but its other side is moving at demon-dimension’s speed.

One side moves at one speed, the other at another, which means that anything that passes through will go through a (quick) change of velocities before they completely pass.

Where’s the energy to change speeds coming from? What changes the velocity? What happens to people who are climbing through when they’re halfway in and halfway out? Does it affect them? Their bodies? WHAT WILL HAPPEN!

… All of these are excellent questions, and I’m so glad you’re asking them because I thought about them too while watching the episode.

In the next posts, we’re going to continue exploring the science behind those multiple dimensions, and figure out how our not-so-merry band of teenage laborers deal with their predicament, the science way!

Check back for part two of this series, that will deal with the interesting concept of the energies required to change speeds quickly (and answer where that energy goes)

After all — we have Time!

Have something to say? Think I made a mistake, or found an error in the calculations? Speak up in the comments! You can also send me a direct message or say hi on Twitter!

## Dynamic relativity calculator!

If you’re wondering what would be the difference if the demon universe had a different time effect (or, maybe, if we find an alternative demon universe with a different time differential) you can check it out for yourselves, with my **dynamic relativity calculator**.

## References and resources

- Wikipedia, “Spacetime” https://en.wikipedia.org/wiki/Spacetime
- The Physics Classroom, “Mechanics: Work, Energy and Power”:

https://www.physicsclassroom.com/calcpad/energy - Wikipedia, “Annus Mirabilis papers”:

https://en.wikipedia.org/wiki/Annus_Mirabilis_papers#Special_relativity - Wikipedia, “Maxwell’s Laws of Electromagnetism”:

https://en.wikipedia.org/wiki/Maxwell%27s_equations - Wikipedia, “Hafele-Keating experiment”: https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment
- HyperPhysics, “Time dilation” http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/tdil.html