So you may know of the "many-worlds hypothesis," a concept in quantum physics which in essence says that every time some "decision making" event happens in the Universe -- like an electron having to "decide" which way to jump next in its random path around the atomic nucleus -- then the Universe splits in two, one for each possible outcome. The result of this splitting is called many worlds, which is one hell of an understatement. Consider that the typical electron makes several million such jumps every second, and multiply that by the number of electrons in this galaxy alone, and you're immediately speaking of an uncountable number of spinoffs -- as in trillions to the trillionth power -- in the first few seconds out of the gate. And remember that every single one of those will immediately start splitting off into more Universes (not "new" Universes, mind you, because every single one is the same Universe, just with a different spin), and that if the measures of modern science are correct, this has been going on in relation to the Universe we know for about thirteen and a half billion years (and, face facts, even just a billion years is a longer time than you can comprehend).

I will now logically demonstrate (I think) that this theory is quite probably untrue: if there are trillions to the trillionth trillionth trillionth power alternate universes (and the number increasing by that much, exponentially, every minute) then there should be some where humankind sprouted earlier and developed technology far in advance of what we now have. And remember, if there is even one such Universe, than in another second there will be trillions of trillions of splitouts from it. Now, if there are in fact such advanced stages of technological achievement, there must be some in which man (or some superadvanced kind of future-man) has conquered the distance between the alternative Universes themselves, and can travel from one to another at a whim. And since the number of such Universes almost instantly climbs near infinity, there must be some Universe from which (as a matter of alternative history) future humans have visited our Universe. Now, I realize that there are a number of objections that you might raise. First, you could justly argue that all of these alternate Universes exist, but there is no way for events in one to affect another. This proposes a limitation on the power of science to act, and more importantly suggests that it is impossible for us to ever know if indeed there are any alternate Universes out there, because as the Heisenberg uncertainty principle relates, there is no way to observe something without altering it in some way. Or you may say that these alternate Universe types have simply not found our particular Universe, or have not chosen to visit it -- except that as soon as there's a choice to be made, infinite alternates would split off from which the other choice was made, i.e. to turn the alternate Universe visiting device in our direction, and thence to visit our particular corner of it.

You may also object, "surely visitors from alternative Universes must obey some code of conduct to prevent mucking about in the history of their neighbors," meaning in short that such visitors wouldn't make themselves known to be visitors. This is, after all, a satisfactory answer to the question, Where are all the time travelers? And where time travel exists in but a single Universe it might fall within realistic regulation in that Universe. But with nearly infinite multiple Universes, there must be at least one variation from that model (and therefore an uncountable number of variations of that model) in which the visitors have no such code (or it is unenforceable, or at any rate unenforced). So, rules aside, we should be absolutely flooded with visitors from alternative universes in garish Uranian t-shirts, loudly proclaiming themselves as such and lording about all sorts of impossible technology.

And here is an even more chilling consideration. Some alternative-Universe-crossers are bound to be warlike, and in fact alternative-Universe-conquerers, and some will have empires of equally uncountable numbers of Universes under thrall. Now, I mentioned before that in some Universe, the technology for alternative-Universe jumping must be known, and so it is that in another Universe, the technology must exist by which alternative Universes can be destroyed!! And, if there are bound to be warrior-Universes out there, there must be at least one Universe willing to defend itself from potential incursion by preemptively destroying all the others. So by all rights, our Universe should have been eliminated billions of years ago!! And yet, here we are, and so apparently we are alone not only in the Universe, but among all of them that ever could be....

This is an interesting question and even more interesting premise, but let's think about this a little bit. I think the possibility of being invaded is rather unlikely but certainly not impossible.

Infinite alternate universes does not mean an infinite number of chances to travel to ours. Unless, of course, ours is the only Universe beings in any other universe can get to. Then the chance we're being visited is 100%.

Now, if there was some warrior universe out there, the probability of other universe being invaded is somewhere around zero because they are one in an infinite number. Somebody must be getting invaded in such a scenario, but the chances of doing so is next to nil. Remember than infinity is a big number even when compared to infinity.

Another problem I have with the warrior invasion universe idea is that in an infinite number of universes the chance of being able to return to your own is also slim unless you either know your own way back, have some sort of homing beacon, or are able to keep a constant gateway open. I'd hate to be any early explorers...

Yet another problem is that if these invaders are anything like us, then they experience the dimensions in a rather limited three-for-space one-for-time sort of way and the Universe is Huge. Even with instantaneous teleportation technology (being invaders from outside the Universe they could probably pop in anywhere they wanted) it would take forever to find never mind conquer all the galaxies in the Universe. Entire races, planets, stars, and even galaxies would pass without anybody in them realizing they were at war. I' not sure it would be even worth conquering a universe. Time and Effort vs. resources. If you have access to your own entire universe it seems it would make sense to plunder that one forever and just move on once you're done.

And then there are the logistics for invading other universes. How many soldiers would it take? How smart would the generals have to be? Would they need a single universe that is just made out of computers linked together formulating strategy?

And what about Entropic universes? Places where there isn't enough order left for things to work. Dimensional jump into one of those and the only functioning energy would be that which you brought with you, and it would run out almost instantly.

In an infinite number of universes there probably is someone out there trying to take over others, but the probability of them succeeding or being able to maintain an invasion is so low due to the above problems I think we can rest easy.

At least tonight.

I feel a story coming on. Mmm. What an inspiring idea...

If I may interject as somebody who has actually put considerable study into simply the practical aspects of this problem, in response to the first writeup in this node:

Supposing there are 'infinite' universes (a universe for every possible movement of every possible quantum in every possible location in time and space), that would mean that not only are there inevitably bound to be universes containing entities who have the technology to travel to other universes, but there are inevitably bound to be very very many universes that are virtually identical to each other.
This means that any given universe-traveller would not have to visit every single 'version' of one universe in order to have studied or exploited it.

Think of it in terms of Borges' "Library of Babel". In the short story, the library contains a vast number of books with the same number of letters on every page, and the same number of pages. The number of books is ridiculously vast, but it is not truly infinite, because there is only one of each precisely-oriented series of letters and pages. Even so, there could potentially be literally billions of books which are identical except for a single letter out of place. There could be hundreds of billions of books identical but for a single word different. If you had a billion copies of "A Wrinkle in Time", even if you changed one letter or one whole word, it would still read to you as the same story contained in any other copy of "A Wrinkle in Time".

Now apply this to any visitors with advanced, universe-travelling technologies. Suppose their mission is exploratory. They will already know that in a given 'sector' of every possible reality, there will be a vast number of nearly-identical universes. They only have to pick one to research to know the gist of all the rest which bear a strong similarity to it.

In other words, for all we know, we've already had visitors, or another version of this universe has already had visitors, and we simply weren't in the place and time to notice them being here/there. They may simply have gotten all their data from a nearly-identical universe.

In the case of exploitative missions, if you have virtually unlimited realities to exploit, the chance of finding any single, specific reality is effectively so low as to be probability-zero.

After some /msg discussion with Pandeism Fish, I decided it would be suitable to add these points to the writeup.
First Pandeism Fish suggested a Universe destroying Universes, to which I replied "If you destroy three hundred trillion universes, it still doesn't go anywhere near infinity."
Pandeism Fish suggested a Universe destroying ALL other Universes, and I replied "If such a way exists, then it would cease to work immediately, because the 'one' that remains in existence would, at Second 1 following the destruction of the last of the other universes, itself create infinitely more universes with the infinite minute variations in movement of quanta. It's a self-defeating proposition."
Pandeism Fish suggested a Universe perpetually destroying other Universes, and I replied: "if ANY universe had found a way to destroy ALL the others but itself... then you and I could not possibly be having this conversation."

The above write-up exhibits a lack of understanding about how quantum mechanics works, to the point where it dismisses the Many-Worlds Interpretation (MWI) of quantum mechanics (which is considered to be true by most physicists who study this sort of thing) with two paragraphs of conjecture and pseudoscience. The fact is that while Copenhagen is the prevailing theory in popular science, the majority of people doing work in the field of quantum mechanics ascribe to MWI, because at the base level they both make sense, but as one dives deeper into theory, more and more problems arise with Copenhagen while the number of problems with MWI remains generally consistent. Now onto why the position taken above is incorrect.

Consider the list of real numbers between 0 and 1. It should be intuitively obvious that this list is infinite. It should also be intuitively obvious that the number 2 is not in the list. Neither is 3. Or 4. This simple example shows that not only does an infinite list not contain everything, but that the list of things that are excluded from the infinite list can itself be infinite. The list is bound by certain parameters - only numbers between 0 and 1.

Just as there is an infinite list of numbers that aren't between 0 and 1, there are an infinite number of universes that cannot exist in MWI. Where waveform collapse would occur in other interpretations, universes decohere in MWI to account for all possible outcomes of the would-be waveform collapse. But, and here's the important point, all of these universes are bound by the same parameters. If the gravitational constant of the universe is 6.7428 x 10-11 N (m/kg)2 before the split, all of the worlds created after the split have the same gravitational constant. Impossible things, by definition, cannot occur. So while there may be universes where you are dead, or dating Scarlett Johansson, or working as a regional collections supervisor for a box company, there are no universes where electrons weigh more than protons, or where the weak force doesn't exist, or where causality can be violated. If it can't happen here, it can't happen there.

This leads to another factor that isn't considered above. The definition of MWI itself precludes communication between universes. This may sound convenient - after all, if no communication can occur between worlds, how can anyone ever prove or disprove the theory? The answer is beyond the scope of this writeup, but suffice it to say that universes do not interact with each other, but they do interfere, and given sufficient technology (which does not exist yet) this can be detected. The point is that MWI prohibits travel between universes. That means that if it's not possible here, it's not possible anywhere, and if it is possible here, MWI is wrong. The two are mutually exclusive.

Now, to clear up a few misconceptions in the above writeup:

"Consider that the typical electron makes several million such jumps every second, and multiply that by the number of electrons in this galaxy alone, and you're immediately speaking of an uncountable number of spinoffs -- as in trillions to the trillionth power -- in the first few seconds out of the gate."

MWI splits only happen when a thermodynamically irreversible event occurs. While events like these are common occurrences, the orbit of an electron around a nucleus does not constitute such an event.

"First, you could justly argue that all of these alternate Universes exist, but there is no way for events in one to affect another. This proposes a limitation on the power of science to act, and more importantly suggests that it is impossible for us to ever know if indeed there are any alternate Universes out there, because as the Heisenberg uncertainty principle relates, there is no way to observe something without altering it in some way."

First, there is always a limitation on the power of science to act. A very basic example: it's impossible to accelerate anything with mass to the speed of light. Period. End of story. There may be a way around this fact (for example, an Alcubierre Drive), but no science is going to override this. Second, the Heisenberg Uncertainty Principle does not state that there is no way to observe something without altering it in some way. This is Syfy Channel science. All Heisenberg says is that there are pairs of physical properties for microscopic objects that cannot be mutually determined to some arbitrary precision. The observer effect is what causes observation to alter that which is being observed, and it doesn't apply to macroscopic objects. Watching a dog run down the street doesn't alter the dog in any way, because it's not a quantum object.

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