Portal Dilemma - There is an entrance portal on the face of a moving piston that leads to an exit portal on the face of an inclined surface. As the piston moves fast downward, it moves toward a flat platform with a cube. You could imagine that as the piston moves downward with the entrance portal on its surface, the cube gets teleported out of the exit portal on the inclined surface. Given this setting, the question is if the cube comes out with zero velocity or with the velocity of the piston.

Imagine a world where portals exist. You could enter a portal from one location and come out of another portal in another location. Throw in a few science fiction elements to this imaginative setting, and you find yourself playing “Portal”, a simulated physics-based puzzle video game.

Portal, the video game, features a “portal gun”, which fires an entrance portal onto a surface on the first fire and an exit portal onto another surface on the second fire. The game requires the player to use this tool to navigate complex spatial platforming and problem-solving puzzles.

I have fond memories of playing this game as a teenager. Recently, I came across an interesting portal-based discussion. The setting of this discussion is as follows:

There is an entrance portal on the face of a moving piston that leads to an exit portal on the face of an inclined surface at, let us say, 60° to the floor. Now, as the piston moves fast downward, it moves toward a flat platform. On this platform, there is a cube (object).

You could imagine that as the piston moves downward with the entrance portal on its surface, the cube gets teleported out of the exit portal on the inclined surface. Given this setting, the question is if the cube comes out with zero velocity or with the velocity of the piston.

I found the entire discussion surrounding this topic very fascinating, which is why I thought I would write about it. To begin the discussion, let us make the case for the scenario where the cube “plops” out (with zero velocity) out of the exit portal.

The Absolute Frame of Reference

One way to look at this scenario is by arguing for the conservation of momentum. That is, one could argue that the momentum/energy of the cube before and after passing the entrance portal has to be the same.

There is an entrance portal on the face of a moving piston that leads to an exit portal on the face of an inclined surface. As the piston moves fast downward, it moves toward a flat platform with a cube. You could imagine that as the piston moves downward with the entrance portal on its surface, the cube gets teleported out of the exit portal on the inclined surface. Given this setting, the cube plops out of the exit portal with zero velocity.
The absolute frame of reference — Illustration created by the author

There are a few ways in which one could try to justify this argument using physics. But all of these ways would have two things in common:

1. An absolute frame of reference

2. A discontinuity in space-time coordinates

Let us consider the most intuitive approach where you consider the same coordinate system for all the elements you see in the image. With this consideration, note that there is a discontinuity that occurs at the portal interface.

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The cube would undergo a discontinuous coordinate transformation as it passes through the entrance portal and undergoes a shift in velocity as it “plops” out of the exit portal.

The Inertial Frames of Reference

In this approach, you simply start looking at the events using different frames of reference and coordinate systems. Think about it this way. As far as the cube is concerned, the entrance portal is approaching it with a certain velocity, say, 50 kilometres per hour. As far as the entrance portal is concerned, the cube is approaching it with that velocity.

There is an entrance portal on the face of a moving piston that leads to an exit portal on the face of an inclined surface. As the piston moves fast downward, it moves toward a flat platform with a cube. You could imagine that as the piston moves downward with the entrance portal on its surface, the cube gets teleported out of the exit portal on the inclined surface. The cube whoohes out of the exit portal with the velocity of the piston.
The inertial frames of reference — Illustration created by the author

In other words, what the entrance portal “sees” is a cube moving towards it at 50 kilometres per hour, as if someone threw the cube at it. Here, the discontinuity occurs not at the portal interface, but rather somewhere inside the portal dimension. That is the discontinuity occurs in between the entrance portal and the exit portal.

As a result of the law of conservation of momentum, the cube would shoot out of the exit portal at 50 kilometres per hour.

Now, having considered these two approaches, which is more plausible?

The Cake is a Lie

Long ago, scientists of the Newtonian era believed that absolute space and time existed. This belief would approve of the scenario with an absolute frame of reference with discontinuity at the portal interface. As a result, the cube would “plop” out of the exit portal with zero velocity.

However, Einstein & Co. came along and proved that absolute space and time cannot exist. This important step led us towards relativity, which has enabled us to progress in science until today.

Considering relativity, the first approach which leads to the cube “plopping” out seems implausible unless our understanding of physics is broken.

Portal Dilemma — There is an entrance portal on the face of a moving piston that leads to an exit portal on the face of an inclined surface. As the piston moves fast downward, it moves toward a flat platform with a cube. You could imagine that as the piston moves downward with the entrance portal on its surface, the cube gets teleported out of the exit portal on the inclined surface. Given this setting, the question is if the cube comes out with zero velocity or with the velocity of the piston.
The Portal dilemma — Illustration created by the author

On the other hand, the scenario with the inertial reference frames packs the discontinuity inside the portal dimension. As a result, the cube would shoot out of the exit portal at the piston velocity. Considering relativity, this scenario seems much more plausible.

The catch here is that one could argue that both these scenarios break our current understanding of physics. I get that; we are operating inside a fictitious setting after all. However, given the two options, the cube shooting out of the exit portal seems much more in line with our current understanding of physics as compared to the cube “plopping” out.

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Reference and credit: Original post discussing the portal dilemma.

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