We’re back to talking about Time considerations in the Buffy episode “Anne” (s03e01), and this time, our exploration into the demon universe leads us into energy exchange, speed changes, and explosions. We’re going in fast, hot, and… energetic?… okay, let’s get into it. 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 energy required to accelerate things

The first post in this series concentrated on the magnificent subject of special relativity, and all the wonderful effects that stem from it. In this post, we’re moving on to think about what kind of speed changes an object (or a randomly unsuspecting teenager) goes through when being thrown in. Before we get into this, let’s have a quick reminder about what we’re actually dealing with here.

The phenomenon and problem

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. 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. There are three main concerns with this episode; you can expand the section below if you want a reminder. Expand to be reminded of the scientific concerns in the episode
There are three main issues we are tackling on this exploration of the episode:
  1. Relativity: We have two places where time runs differently, which is where relativistic effects come in. If you haven’t already, you should read about this in part one.
  2. 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? This is what we’ll be tackling in this post.
  3. Biology: What happens to the human body as it climbs in or out of that portal? What happens when it’s halfway through?
  In this post, we’re going to explore the energies that are required to shift things from slow-time to fast-time. We’re throwing stuff into super-fast universe — What does that do?? How much energy are we dealing with? Would the universe(s) survive!? … We’re going to tackle these head-on. I’m excited. You excited? I’m excited.
More excited than that…

Time, movement and speed

Movement — and speed — are time dependent. This sounds obvious, but it’s worth repeating and emphasizing as we examine what happens when an object is tossed into the fast demon dimension. In the last post, we established that our universe is moving (really really fast) compared to the other universe. We also established that the portal openings themselves are also moving relative to one another, but not relative to each dimension they’re stuck in. This means that when we toss unsuspecting teenagers in, their velocity (directional speed) changes. We can see that immediately by looking at the equation that calculates velocity: \(velocity=\frac{\text{distance}}{\text{time}}\) Velocity depends on time, and if we have a time differential, we also have a difference in speeds.

We’re not using relativistic speeds

In the previous post we’ve established that Relativity has a huge role to play here, and that our universe, by being the subject of “time dilation” also moves reeeeeeeally really fast compared to demon-universe. We’re moving at 0.99999999962 time the speed of light compared to demon-universe. That’s fast. Should we consider the change of speeds of a thrown object (or teenager) based on that? Maybe… but we won’t.

Why we’re not using relativistic speeds

There are a couple of reasons why in this specific examination of speed changes we are going to choose not to use relativistic speeds, and instead stick with the more straight-forward Newtonian mechanics, where the speed we will calculate is the one that stems strictly out of the time differential.

Reason #1: Because those speeds are stupidly unhelpfully large

Yeah, they’re insanely high numbers that make no practical sense
To get from almost-rest to 0.99999999962 times the speed of light takes a LOT of energy. If we assume that passing through that portal is relatively quick (we’re going to assume about a second passage) then the energies we’ll have will be insane. Don’t believe me? Let’s look at how much energy it would take to get an object from 1 meters per second to 0.99999999962c meters per second. Show the Math
Kinetic energy is defined as the amount of energy required to accelerate an object from rest to its current speed, which is exactly what we’re looking for. \(KE=\frac{1}{2}mv^2\) To accelerate an object to 0.99999999962c, we’d need (I’m assuming 1kg, for the sake of an example) \(KE = \frac{1}{2}*1*(0.99999999962c)^2\) \(=0.49999999962c^2=4.494 * 10^{16} \text{Joule}\)
The energy required is equivalent to about 10 megaton of TNT. For comparison, “Fat Man”, the nuclear device dropped on Nagasaki, was 20 kiloton of TNT. We’re talking 500 times that. That’s insane. I want to say that nothing like that exists, but I would be wrong. But there’s another reason why we aren’t going to deal with relativistic speeds, and this one is slightly more observation-based than just “we don’t wanna deal with big numbers”. This one is about making assumptions based on our observations.

Reason #2: Because the portal-entrances behave like they’re local to their environment

Here’s the thing. We don’t have any real phenomenon to go and refer to in real life in order to figure out how to deal with Buffy’s multidimensional dilemma. What we do have, is what we see on our screens while we watch the show. What we see is an opaque doorway that has a very small (if at all) transition between the two universes, and that when things pass, their perceive internal speeds remain the same. Instead of thinking about it as the object trying to catch up with the moving universe, we’re going to consider it as the object catching up with the change of time.
It’s not wrong, Buffy, it’s just not quite right
Since we’re dealing with a doorway, this is reasonable. Also, all of our calculations will be (massively) low-balling what would have otherwise happen if we considered relativistic speeds, so when we conclude, we can account for that. Physics is all about orders of magnitude, anyways… mostly.

So how much energy would it take!?

Okay, now that we have accounted for relativity, let’s see what it would mean to toss a body through the portal if we consider straight-forward time-change as our focus. As we established above, the equation for velocity is time-dependent. If we have a time differential, it will affect our calculation. In slow-time, an object would move slowly, and fast-time, an object will (suddenly) move really really fast. Even though the object itself, from its own perspective, may have not changed speeds — there is still a transition being made from slow to fast. We’ll make a couple of quick assumptions here, for the sake of the calculation:
  • We’ll take into account a thin teenager mass; 50 kg (110 lb)
  • The time differential is 1 day on earth for 100 years in demon universe
  • Passing through the portal is not instantaneous (that’s a mess, physics’ly) so we will assume it takes about a second to pass through.
  • The teenager falls (or is pushed) into the portal at 1 meters per second
We quickly calculate the time differential: Show the Math
\(t_{\text{demon world}}=\delta_{\text{time differential}}*t_{\text{our world}}\) \(\delta_{\text{time differential}} = \frac{ t_{\text{demon world}} }{ t_{\text{our world}} }\) \(=\frac{ 365.25_{d/y}*100_{y} }{ 1_{d} }=\frac{36525_d}{1_d}\) \(=36525\)
Our universe is 36525 times faster than the demon universe. When the teenager is pushed in, they have a velocity of 1 meter per second, but the “per second” that we’re talking about is our world. In demon world, it would be per 36525 times faster.
Watch out slamming those breaks…
How much energy would it take to accelerate a teenager from 1 m/s to 36525 m/s ? Show the Math
We calculate the kinetic energy of an object at 36525 meters per second: \(KE=\frac{1}{2}mv^2=\frac{1}{2}*50kg*(36525*1m/s)^2\) \(=33,351,890,625 \text{Joule}\) \(=33.4 \text{Giga Joule}\)
33.4 Giga Joule of energy is required to whisk our poor teenager from 1 meter per second to the whopping 36525 meters per second of the demon universe, so that they can “keep up” with its fast-time. Giga joule. That’s about equivalent to a couple of tons of TNT.
An explosion from later in the series, but it should appear here, instead

Everything explodes

Yeah, boom. Big boom.
Granted, it’s not as big as when we took relativistic speeds into account, but it’s still pretty damn big, especially if this is what happens every time anyone passed through that portal. So… what happens to this energy? We are, after all, in uncharted dimension-switching territory here. It’s not like we can go to the nearest CERN and observe an actual dimension portal… all we have is what we see on the show, so we will let that inform our conclusions.

Conclusion: The portal absorbs a lot of energy

There is no explosion in the demon dimension whenever a teenager (or a Buffy) passes through it. Where does the energy go?? Probably, from everything we see in the episode and what we know about how the real version of physics (and conservation of energy) works — into the portal itself. Whatever we do with science fiction, it’s fairly clear that to open a portal to another dimension is costly. It takes energy (and sometimes a blood sacrifice, perhaps even that of your previous lover *cough*) and it is very likely that it takes energy to stay open. It’s pretty reasonable, then, to assume, that the portal absorbs the energy expelled by the bodies traveling through it, and that it uses that energy to keep itself open. Which means that if people and objects stop going through the portal (say, after Buffy prevails against the demons) it may as well lose energy and close on its own.
Willow, doing the math
Way to solve the problem long-term, Buffy! There we have it. The change in speeds requires energy, and the energy feeds the portal. Hoorah for science, and hoorah for Buffy! In the next post, we’ll examine what is happening to the physical bodies of the teenagers that are climbing out. What would happen to a human body when they’re halfway through that portal, part of their bodies in slow-time and part in fast-time? Does the Buffyverse have a solution for that? The answers are “ouch” and “yes” respectively. You’re going to have to stay tuned for part three to see how those manifest. Remember — 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!

References and resources