Parallel universe portals: an infinite hall of mirrors?

Question

Parallel-Universe Portals

A solid material has been discovered that, when shaped into a ring and activated (by lowering its temperature below some critical point, let's say), it forms a parallel universe on the other side. This isn't a gateway into an existing alternate universe, but rather a duplicate of the host universe, identical in every way at the time of activation. However, over time (on the order of minutes), the two universes will desync due to slight quantum-scale differences that the portal produces on each side. (It’s the same type of parallel universe generation described in this previous Worldbuilding SE question, but I’m interested in a special case)

As long as a portal is active, it must be in the same position in both universes. If you move the portal from one end, it moves in the other. This means that a portal can never be used to cross distance or time. When I say that it is in the same position, I also mean that it faces the same direction. So if you walk into a portal, moving north, you will exit in another universe, still moving north. Walk south again? Back in your universe, moving south. Walk around the portal and walk north through it again? Back in your universe, moving north this time. (Moving through the portals isn't really relevant to this question, but I just wanted to give some examples so that what I'm describing is a bit clearer.)

Notably, portals duplicate existing portals. To illustrate this, imagine that you have an active portal linking your universe, universe 0, to another universe, 1.

After a few minutes, when the universes are desynced, your copy in universe 1 decides to open another portal (since it’s after the desync, you're able to choose not to open another portal in your universe). The end result is shown below, with 2 copies (joined by a blue portal) of your previous 2-universe system (joined by a red portal):

The Question

What happens if your copy doesn’t wait for a desync before opening the second portal? Suppose once the red portal opens, she waits only 1 second before opening the blue portal. Since you're both still synced, you'll open a portal at that time as well. So there are 8 universes, right? I don’t think so.

I think what happens is a “hall of mirrors effect.” Consider the two copies of you at the ends of this 8-universe chain. Why do they only have a red portal open? Shouldn’t they have also opened blue portals, since that’s what you did and they’re synced to you? By induction, the chain of universes should be infinite.

The question is: does the “hall of mirrors effect” produce a truly infinite chain of universes, or does something break the chain?

My current answer: the chain is infinite.

Reasoning: There’s some incredibly slight amount of desync that happens in that 1 second between the portals opening. If a limit exists, it probably depends on that. Let’s assume that 1 second of waiting causes a desync of 1 nanosecond (that is, that 1 second of waiting between portals cause you and your copy to behave almost the same, but with one of you on a 1-nanosecond lag). So the second blue portal opens 1 ns after the first.

I initially thought that this would make the chain finite, since each layer further from the starting layer would add time, until eventually the desync would be so large that the copies on the ends would be in a completely different state of mind and the hall of mirrors would be broken. But no, between 0 and 1 ns apart, the multiverse would resemble the second diagram, with 00 and 01 about to open their blue portals at the same time at t = 1 ns. Any role the tiny desync plays in the chain is gone by the first iteration.

Am I right? I’m not as sure about my answer as I’d like to be, and it feels a little wrong to have an actual infinity come up in this problem. After all, these portals are remarkably well-behaved in every other scenario I could think of. You can move them through each other and intersect them like chain links, all without making the multiverse implode or anything. I’m interested to see if this case has some subtlety I’m missing.

Answers could involve:

• The desync between the portals
• The time that light takes to travel between the portals
• The absurdly small probability of a quantum fluctuation causing, say, the portal to stop working, on a human timescale

Answers should not involve:

• Handwavium / built-in stopping mechanisms (i.e. the portals are designed not to work if another portal was opened less than a second earlier)
• The portals causing the universe to collapse (for General Relativity reasons or otherwise)
• Any assertion that the chain of universes doesn't exist at all (or at least think about it a while and draw some diagrams before posting. This is very easy to misunderstand. After a lot of thought, I'm confident that the chain starts, just not that it ends.)

Answer 1

Let's pretend I have 2 doors. I am the first state(A)

I make a copy, then I have 1 door left in each of 2 universes. My second state (B) is linked by door #1

Then using my second door, I make a copy creating resulting in 2 universes with 1 available door, and 2 with none, My third state (C) is now connected to (A) by the second door

At about the same time, (B) is also opening his second door to make state (D).

(B) now makes both ends. Here is where the infinity thing happens. In the exact same quantum of time as they are made, they also copy themselves.

And

etc...

So, with this visualization we can see it is infinite because no matter how many times you "unfold it", the ends will always have a copy of the 2nd state (B) with an unopened door. For this to be an eventually terminating pattern, your outside copies would need to be 3rd, then 4th, then 5th generation copies, but you will never generate more than a second generation copy that still has a door to open.

EDIT: You can also see from the visualizations that the duplication process never causes an overlapping of portals as I originally hypothesized. This means that you will not get an infinite energy buildup; so, the mirror effect should not destroy the lab causing a forced termination from a run-away interaction between the dimensions.

Answer 2

Of course this is all theoretically suspect as it is impossible (according to the rules of quantum physics) to create an exact copy of an existing state. Thus it would be impossible for your mystery portal material to form an exact parallel universe.

But putting that argument aside, your portal appears to act like a mathematical operator with an inverse. To illustrate: if you construct a portal $A$ then going through it once takes you from your universe $x$ to a parallel (initially 'identical' but now divergent) universe $y$. Passing through it again does the inverse operation - taking you from universe $y$ back to universe $x$. That is fine as lots of operators are their own inverses (for example multiplication by -1).

So mathematically $y = Ax$ and $x = A^{-1}y$ . This is consistent as

$A^{-1} y = A^{-1}(Ax) = (A^{-1}A)x = Ix = x$

But now consider adding a second portal $B$. To simplify the argument imagine constructing both of them simultaneously in universe $x$, so now you have a choice of going through portal $A$ to universe $y$, or through portal $B$ to universe $z$. Note that as you constructed them simultaneously, both $y$ and $z$ will have 'copies' of $A$ and $B$.

Here is where it gets interesting. Going back and forth through portal $A$ just takes you back and forth between $x$ and $y$.

Similarly going back and forth through portal $B$ takes you back and forth between $x$ and $z$.

If you go through $A$, then through $B$, then back through $B$ and back through $A$, you will find yourself in $B^{-1}BA^{-1}Ax = (B^{-1}B)(A^{-1}A)x = IIx = x$, so you end up back home again.

But if instead you go through $A$, then through $B$ and then 'back' through $A$ and then 'back' through $B$ you will be in $B^{-1}A^{-1}BAx$ and if $A$ and $B$ are non-commutative operators then $x = B^{-1}BA^{-1}Ax$ $\ne$ $B^{-1}A^{-1}BAx = x'$

If you repeat the path again and again you will get from $x'$ to $x''$ to $x'''$ etc. so you will cascade through an infinite hall-of-mirrors of alternate universes.

If you want things to be that way then fine, but if you don't want this to be a problem, all you need to do is define that in your universe 'portal-operators' are commutative operators (via some mysterious property of the portal material itself), which would dismiss all recursive loops as then $x = B^{-1}BA^{-1}Ax$ $=$ $B^{-1}A^{-1}BAx = x$ by definition.

Answer 3

Let's assume you don't open the two portals at exactly the same time. You always have 2 universes that have only 1 portal. Opening a portal in one of them gets rid of a 1-portal universe, but doubles the other one.

The rate of the doublings depends on the desync rate and the difference in portal-opening times. In your example, the second pair open a portal 1 second apart. That means your two clones have 1 second to desync. In that 1 second, how much do their opening times/probabilities change?

Then, consider the product of the probabilities of opening at each step. This infinite product is the probability of your infinite hall of mirrors.

Answer 4

I'll add to this letter number festival:

We have the starter universe where you have two buttons, one on your left and one on your right. The one on your right is A and the one on your left is B. This looks like this:

(1) 1[-]

One universe with no portals inside. You create portal A which links to another universe that is perfectly identical to the starter universe:

(2) 1[A]<>1[A]'

Note the apestrophe at the second universe "boundry" as upon creation the universes are absolutely identical! This changes almost immediately with quantum rippling effects through the universe but at the exact time of creation they will be identical! Now you immediately open portal B with one nanosecond before the second one opens:

(3) 1[B]'<>1[B+A]<>2[A]

The first paralel universe is now a different one, so its changed from 1[A]' to 2[A]. But thats not as interesting as 1[B]', which contains two exactly identical portals inside it... which means that even before 2[A] creates its second portal you have to write (3) like this:

(4) 1[B+A]'<>1[B+A]<>2[A]

But wait... since all A portals in universes 1[ ]' and 1[ ] are PERFECT COPIES of each other upon creation they can only lead to the exact same point, universe 2[ ]!

Tangent: if you do not accept that the identical portals will reach in the same universe than portal A inside 1[B+A]' would lead to universe 1[B+A]'', which would lead to 1[B+A]''' etc in an infinite loop that would happen even if you desynced before opening simply for having 2 portals simultaneously. Tangent over.

Then we move 1 nanosecond further and portal C opens while the other univers desyncs:

(5) 3[B+A]<>1[B+A]<>2[A+C]<>2[A+C]'

Again we see that upon then moment of creation 2[A+C]' will have the exact same portals at the exact same positions open, meaning that the A portal in it will lead back to the original unless you use the tangental interpretation which causes an infinite loop no matter if you open them synced or not.

Edit: testing if you have infinite universes.

Activate portal A.

Press the button for portal B, an automatic system fires a gun that will pass through portal B to portal A and activates portal B just before the bullet reaches it. This means that a bullet is in flight at perfectly the same trajectory and speed as the one in the other universe.

Both bullets pass through portal B and end up in each others universe, making it seem like nothing happened at all from the side-view. They then both pass through portal A simultaneously...

In an infinite portal universes the bullets simply hit whatever is behind portal A, a small target for example.

In a looped universe both bullets simultaneously try to exit portal A in the exact same position, speed and trajectory. A few things can happen:

The bullets coordinate systems function like a combined [3d+1]+[3d+1] coordinate system, the bullets simply collide with each other and fall to the ground.

The coordinate systems dont line up and each part of the bullet exiting will do so and occupy the exact same space as a perfect copy of itself. If string theory is right you might get lucky and the vibrations that make up the bullets information just double in size, transmuting the bullet to whatever its new vibration is.

Otherwise you now have not just fusion but actual particles down to the smallest gluon or whatever is smallest currently trying to force itself into the same position. This will likely mean it creates micro black holes that instantly evaporate as the bullet passes through (and the resulting explosion pushes back). Dont be there.

But perhaps the most interesting question... if you throw something through portal A in universe 2 it will have to exit in BOTH the other universes... What happens? Are they divided or copied?

Gag reel:

Schrödinger comes along and places a measuring device. Portal A is created, making both universes essentially a quantum-entangled entity. Portal B is opened and at the same time Schrödinger measures his own universe to be up or down.

Universe 3 flips upside down. In an infinite portals universe number 2 also flips.

In a looped universe, everything not yet desynced inuniverse 2 now has to be both up and down and cannot be up and down.

Answer 5

There isn't enough desync for one portal to open and not the other.... so you can still treat A and B as a single unit, so when AA and BB open, they are a mirror of A/B. Meaning AA and BB end up linking to each other leaving you with 4 universes, not 8 or infinity.

Answer 6

There's no definitive answer, following is a few possible explanations.

Trying to hold strictly to "syncing":

1. Open a portal from universe A to universe B, portal is called A0<->B0 (bit to designate portal location)
2. While synced, universes A and B each open a new portal. Since they are synced, these new portals are in the same location and go to the same universe, C. We now have A0<->B0, A1<->C1, B1<->C1. We have overlap at universe C's 1-location, with portals going to A1 and B1; we also have overlap at A0 and B0, since on C's 0-location must be identical to A's and B's 0-location.

You end up with 3 universes and the portals A0<->B0, A1<->C1, B1<->C1, A0<->C0, B0<->C0.

Without really holding to syncing (it generally breaks immediately):

1. You create the first portal, ending up with universes A and B, with a portal A0<->B0 (again using bits to denote which portal location we're looking at)
2. While synced you and your B-universe double create new portals. Presumably in the same place, since you're synced.

3. Couple possibilities here:

   • This new pair of portals could either be another portal between universes A and B, so you have A0<->B0 and A1<->B1 (which means we de-synced immediately, because our 1-location portals go to different places; or each portal opens to both itself and the other universe's 1-location)
   • Or, this new pair of portals both go to new universes, so you've got A0<->B0, A1<->C1, and B1<->D1. (This would also appear to de-sync A and B immediately, since they have different portals in their 1-locations; or each portal could open to itself, and to both new universes (A1<->A1, A1<->C1, A1<->D1, B1<->B1, B1<->C1, B1<->D1))

4. In the second case, universes A and B both have two portals, and we know where they both go. However, universes C and D each have a portal we haven't determined yet. And there again seems to be two options (there's more, but I'm ignoring the strict-syncing cases):

   • Portals C and D are literal copies of their parent-universe's portals: which means that in universe C, in the same place as universe A's A0<->B0 portal, universe C also has a portal to universe B. Same thing in universe D (based on universe B this time). So, we've got: A0<->B0, C0<->B0, A0<->D0, A1<->C1, B1<->D1. This is scary, because I don't know what happens when there are two portals to different universes in the exact same place (explosion? walking into a portal means you walk out of both other portals?).
   • The new portals go to new universes and we have A0<->B0, A1<->C1, B1<->D1, C0<->E0, D0<->F0. Now we have universes A, B, C, D with two portals each... but E and F with undetermined portals.

5. Repeat 4 infinitely many times, instantaneously. This happens since these are simply copies of portals that already exist.

So, you end up with 2, 4, or infinitely many portals. There may be other solutions, trying to be strict with syncing is complicated.

Answer 7

For the chain to be possible, there would have to be a some delay in the creation of a parallel universe. In the case that the other universe is instantly created, it would be more like holding a mirror up to the existing reality. If there was a ‘pulse’ from the ring that created the other universe, the creation of a new portal would occur every time the pulse reached where an existing portal was. This chain would be infinite, or practically infinite. If portals act as a way to create a mirror copy of current reality, no chain would form.

Clarification

Desync times would not have an effect in the case of a pulse as already existing portals are affected. Unless a ring was destroyed at any point in the chain during the formation(which would take an endless amount of time) the chain will be cut off at the mirror of that universe as each portal mirrors current connected reality.

I will post reference images later if you need clarification