In the previous post I made a (hopefully) compelling argument that option B is the most physical. However, portals are weird and I think they really need to be analysed in more detail before we settle on a definitive answer. In particular, as mentioned last time, I wrote a short Python script that simulates portals using matplotlib to visualise the results. I tried out multiple scenarios to help me understand what's going on. In this post I am going to cover the key results and why they work (or don't).
What to expect
In the following simulations the "ball" is a single point, represented as a red dot. The "in" portal is orange and the "out" portal is blue. Each simulation result shows 4 perspectives.
- The "aether" perspective (this can not exist according to Einstein and in my videos it is usually just one of the other 3 perspectives, but rotated and displaced) - top left
- The orange portal's frame - top right
- The ball's frame - bottom left
- The blue portal's frame - bottom right
Whilst the ball and portals are present in each perspective, they should really be looked at as if the ball is in the orange frame until it passes through the portal and enters the blue frame. The ball may still be visible in the orange frame, but technically the ball has passed out of it and entered the blue frame.
All simulations were performed twice, once with the physics of Option B (portal velocities contribute) and once with Option A (portal velocities do not affect the ball).
Stage 0 - Sanity check - moving door
To kick off, let's consider a simple scenario where the portals overlap completely, operating as a "door". The ball remains stationary and then the "door" moves over it. In other words the portals operate as a simple door and should behave as if nothing is there, not affecting the ball at all.
The result of this scenario should be identical in Option A and B, and we see that they are.
Option A
.
Option B
Stage 1 - Displaced Portals
So the simulation is clearly working OK. Let's try separating the portals (in space) but keep all the velocities the same. What do we see then?
Option A
Option B
Observations
The results are still the same! The ball is maintaining the momentum it has in the orange frame into the blue frame in both.
Stage 2 - Displaced & Rotated Portals
Now let's tweak things a little and rotate the output portal. What happens now?
Option A
Option B
Observations
Things are getting funky now. In option A, we don't let the portal velocity, or orientation, affect the ball so it just passes through unaffected, albeit with a small displacement in x and y beyond the portal displacement. This is caused by the rotation (the point the ball enters the portal, and switches to the other, is in a slightly different location in x and y). BUT! This kind-of breaks physics. As discussed before regarding inertial frames, the momentum in the orange frame needs to be preserved in the blue frame, and here it does not! The blue frame is rotated, so whilst the situation looks OK in the "aether" frame, it actually breaks physics elsewhere. In option B, however, things look even weirder and the ball ends up being fired to the left and up! What's going on?
Well, in order for the momentum of the ball going into the orange portal to be preserved when it leaves the blue one, the ball must leave the blue portal travelling in the positive x direction with no y component of velocity, because that's precisely how it enters the orange portal. This is actually what we see in Option B, when we look at the orange and blue frames in succession. The combined effect produces the strange behaviour we see in the top left plot, but according to the frames of reference, everything is fine! It is, in fact, the frame where it looks 'weird' that is unphysical.
Stage 3 - Displaced & Rotated & Moving Portals - The Portal Paradox
Finally, let's change the relative motions of the portals, decoupling them entirely. This is the portal paradox in full now.
Option A - "plop"
Option B - "whoosh"
Observations
The result here should be somewhat unsurprising given previous revelations and experiments. If we consider the momentum of the ball in the orange frame and then the blue frame, Option B preserves the momentum and Option A does not. But, there's a few things to talk about here as well. In Option A in particular, what's going on? Well, the "plop" was always technically "impossible" because for an object to pass through a portal it would have to have velocity in some capacity. As seen here, once it is in the portal it is stuck forever because it has no velocity and the endpoint portal has no velocity so as soon as it is inside the portal, it stops. It looks like it is stuck to the edge because the centroid of the ball is inside the portal, but the visualised marker extends beyond the edge.
Conclusion - Option B "Whoosh"
Overall, if we look at the arguments and the simulations performed, I think there's a pretty solid case for Option B being "the" answer. Physically it makes the most sense since it breaks the fewest rules. In particular, the principle of inertial reference frames being indistinguishable is preserved, which is the number one thing that Option A breaks. Many people will point to conservation of momentum being "broken" by Option B as the counter to this, but that this is not the case in Option A; i.e. "Speedy thing goes in, speedy thing comes out". The problem here is that speed (and by extension, momentum) is measured relative to something: an inertial reference frame. Option A assumes that the two inertial reference frames overlap and exist within the same, common, superset frame and that momentum must be conserved in that frame, which sees a ball shift in position and then start moving at a certain velocity. However, the original two frames (portal 1 and portal 2) still exist in this scenario and momentum is not conserved between them if the ball just goes "plop" as proponents of A feel it should. So momentum is not conserved in option A. Thus, B breaks fewer laws.
Although, as before, there will never be a truly definitive answer because portals are fictional and can be defined to behave however you like making both Options viable or even a secret unknowable 3rd option.
Option B is still my pick for most realistic outcome.
Other Articles in this Series
This is the final article in a five-part series about the Portal Paradox. If you landed here before reading the earlier articles in the series you can find links to all the articles here:
- Introduction to the paradox
- Portals as a concept
- How portals might look
- The Portal Paradox - the theory
- The Portal Paradox - simulation results - You are here!