Portals

[Blue]

Yes I know the portals from Valve's Portal video games are impossible. But it was a thought that occurred to me last night, and I wanted to know:

In the video games, if you place a portal directly above and below, you can fall "forever".

You fall faster and faster, until you reach terminal velocity, and don't fall any faster.

Why?

Technically, shouldn't the air also have gravity imparting acceleration on it? Shouldn't the air you're falling "in" also fall with you, and accelerate the same way? I know why they would have a speed limit for falling in the video game, but it occurred to me that the air should be able to fall through the portal just the same any other object would fall through it.

Then I got to thinking as to how the physics of that would work, because:

Say we had a cylindrical chamber, with Portal A at the top, the exact diameter of the cylinder, and likewise shaped Portal B at the bottom. The volume of air inside the chamber would gain kinetic energy from falling through the cylinder just as the object falling through the cylinder would, and the only friction would be that of the walls of the cylinder. If the object, and the air, could just continuously accelerate forever (or however long it would take to reach the speed of light constantly accelerating towards the earth at 1g but never getting any closer), would not the earth itself accelerate in the opposite direction of the cylinder and object? A reactionless drive of sorts, as it changes its orbit.

Am I flawed in my gedankenexperiment?

[Seret]

Shouldn't the air you're falling "in" also fall with you, and accelerate the same way?

Why should it? Say you open a portal on the floor and ceiling, what would happen? Well, the air at ceiling height is likely to be slightly warmer (and therefore more buoyant), if anything you'd be likely to a get a slight movement of air up through the ceiling portal, which would flow up out of the floor portal ie: the air would flow upwards, rather than "falling" through the hole.

Overall though, you're probably not talking about a huge amount of air, certainly not significant compared to terminal velocity.

[Blue]

Why should it? Say you open a portal on the floor and ceiling, what would happen? Well, the air at ceiling height is likely to be slightly warmer (and therefore more buoyant), if anything you'd be likely to a get a slight movement of air up through the ceiling portal, which would flow up out of the floor portal ie: the air would flow upwards, rather than "falling" through the hole.

Thermal updraft would be insignificant compared to how much wash and drag your body would cause, pushing air and a current downwards, in the same way a spoon stirs tea in a mug.

[K^2]

There is a pressure differential between floor and ceiling equal to the weight of the air per unit area. So yeah, there will be an air flow between the portals. It will have a finite speed however. And, naturally, energy for this has to come from somewhere. Presumably, from whatever is powering the portals.

[Seret]

Thermal updraft would be insignificant compared to how much wash and drag your body would cause, pushing air and a current downwards, in the same way a spoon stirs tea in a mug.

Yes, but the tea also causes drag on the spoon. Air, like water has viscosity. This is the force that limits you to terminal velocity.

[Idobox]

As noted, falling would cause a downward air current, but not a nice cylindrical one.

When you move, you create a pressure wave in front of you and turbulence behind. The pressure wave would hit the sides of the portal, causing all sorts of weird effects, resulting in drag.

Turbulence means the moving will mix with rest of the room, once again creating drag.

For a fun experiment, take a vacuum cleaner and a shoe box. Cut two holes the size of the vacuum cleaner's, and suck the air. The engine will work a little harder and the box will make some noise and vibrate. That's obviously not the same as the portal thing, but pretty close. If you manage a window in your box, you ca use a smoke source (like incense for example) to visualize air streams.

[Blue]

Yes, but the tea also causes drag on the spoon. Air, like water has viscosity. This is the force that limits you to terminal velocity.

I didn't think about the viscosity of air.

As noted, falling would cause a downward air current, but not a nice cylindrical one.

Unless you were in a cylindrical space, which I proposed.

For the thought experiment, let's suppose the object is perfectly spherical and moving along the axis of the cylinder.

Eventually, the only friction would be the sides of the inside of the cylinder, and all the air would be moving at the same velocity as the object: terminal velocity. If the object is falling in a medium that is also traveling at the same velocity, would it not behave as one larger object, and thereby continue to accelerate faster than terminal velocity?

[ZetaX]

It would, but it would still be limited (i.e. there is a new terminal velocity) by friction between the air and the cylinder (and possibly the portals, however their physics works).

[Blue]

It would, but it would still be limited (i.e. there is a new terminal velocity) by friction between the air and the cylinder (and possibly the portals, however their physics works).

That makes sense. It would probably be approaching the speed of sound or something like that.

Thanks all. This has been a fun thought experiment.

[Idobox]

I should read better :/

If you assume no turbulence, which is not completely stupid in a steady state, the only limiting factor will laminar friction, which is extremely small with air. You would end up with pressure higher below the object and decreasing as you go down until you reach the top of the ball.

I have only done very basic fluid dynamics very long ago, so I won't try to do math, but I think it would be possible to go faster than sound this way, since the system would be quasi-static.

That being said, you could have some pretty hectic behavior while accelerating.

[minerman30]

What if it was in a vacuum?

[ZetaX]

Then I see no reason for this not to work. But to be in accordance with established physics like conservation of energy and (at least locally) of momentum, those portals should apply a force to whatever they are mounted on and they would use up (or in some cases recharge) some energy stored e.g. in them, or some other mechanism of this kind. Therefore: you entering a portal should probably apply a force in the same direction to the floor portal, and an opposing force to the ceiling one when getting out; if getting sufficiently high speeds, the resulting forces should rip apart every cylinder you can make.

Relativity might also be relevant, depending on how exactly they work (the game just talks about quantum stuff). Especially if you put a portal in spaaaaaaaaaaaaaaaaaaaaaaaaace...

[Dunbaratu]

The problem is that the air won't fall in a nice neat little cylindrical slice because the edges of that cylindrical slice are in contact with the non-falling air outside the cylinder. You'd get a lot of messy swirling currents both in and out of the cylinder from that contact.

[spudman2]

What if you shot one into the ocean?

[Winter Man]

I'd have thought that the portals would actually have to impart energy on you, what with moving you to a higher point in a gravity well. Either that or you have to force your own way through the portal with the same equivalent energy as physically raising yourself to the ceiling.

[K^2]

Or distort the gravitational field around them until they are equipotential. But yeah, one of these, definitely.

[CalculusWarrior]

What if it was in a vacuum?

I imagine that as long as there was nothing in your way, you could accelerate all the way up to just under light speed. That is of course, assuming that you have a constant acceleration of 1g and enough time to get up to that truly ludicrous speed. I think Scott Manley did a video on how long it would take to accelerate up to light speed; I forget the exact time period, but it was very long.