Thanks for your answer.
Absolutely. I should have placed the “any physical system characterized by ‘chaotic’ behaviour” on separate line to distinguish it from systems of random behaviour.
The simplest is just an infinite universe. If the universe truly is infinite (as it may well be), then somewhere, very far away, there’s a patch of it that looks almost just like this one, except for a few trivial changes (but there’s no way you’d ever be able to find it). Without FTL travel (which is probably impossible), it’d be flat-out impossible to reach such a region, and even with it, it’d be lost in the sea of all of the vast number of regions that are very different.
Slightly more complicated is the eternal-inflation one. The “multiple universes” are still located within space, but with the complication that the space in between is fundamentally very different than the sort of space we live in.
Then there are braneworld models, which (in their early forms) were the inspiration for terms such as “parallel universes”, or “planes”. Here, the idea is that another world might be very close to ours indeed, but in a direction that isn’t one of the familiar spatial dimensions we know of. What’s interesting here is that communication between the worlds might even be possible, by (perhaps) gravitational phenomena.
Finally, you have the “Many Worlds” interpretation of quantum mechanics. In a very real sense, this one isn’t as “real” as the others: The other worlds are hypothetical, the model doesn’t work at all if there’s any possibility of interactions between them, and there are other interpretations of quantum mechanics that work exactly as well without positing other worlds.
I’m surprised to see you post this! People have tried to make this point here several times and have always been easily shot down due to their misunderstanding of the different cardinalities of infinity. The power set of a set is always larger than the set.
Yes, and? The number of distinguishable universe-regions is countable (and, in fact, finite). It’s very large, of course, but in an infinite Universe, there must still be regions so similar as to be indistinguishable.
Um, cite?
Perhaps “distinguishable” in finite time? Or more like computable?
What determines the ultimate physical properties of these regions? What (theoretically) implies that there are many regions with, say, similar cosmic background radiation properties? (And is there any observational evidence for this type of cosmology?)
How similar two regions of space could be and still be distinguishable would depend on the quality of your measurement apparatus, but for any given set of apparatus, there would be some limit.
IIRC, “Many Worlds” has gained acceptance since it was first proposed by Hugh Everett back in the 50s, I believe. Nature did a cover story on it a couple of years ago. Today David Deutsch is probably one of its most prominent proponents. He’s famous for having originally proposed quantum computers, not for their ostensible utility, but because he believes they provide the best evidence of Many Worlds. In Fabric of Reality, he puts it like this:
To those who still cling to a single-universe world-view, I issue this challenge: explain how Shor’s algorithm works. I do not merely mean predict that it will work, which is merely a matter of solving a few uncontroversial equations. I mean provide an explanation. When Shor’s algorithm has factorized a number, using 10[sup]500[/sup] or so times the computational resources than can be seen to be present, where was the number factorized? There are only about 10[sup]80[/sup] atoms in the entire visible universe, an utterly minuscule number compared with 10[sup]500[/sup]. So if the visible universe were the extent of physical reality, physical reality would not even remotely contain the resources required to factorize such a large number. Who did factorize it, then? How, and where, was the computation performed?
I tend to think that this argument can be answered just by saying that, if such a quantum computer existed, its power comes from the intrinsic superpositional properties of entangled quantum particles, for which there are hypothetical explanations that need not invoke Many Worlds. Nevertheless, Deutsch’s explanation is certainly a fascinating one.
Sure, but given some limit, what’s the reasoning that some regions will conform to those parameters? Why would I be able to find multiple regions where galaxies have formed, for instance?
The “worlds” Everett was talking about are not places where you could hypothetically go; it’s just a (IMO sillily named) way of pointing out that quantum-mechanical states can be superposed; e.g., a quantum bit need not be either “0” or “1” - it could be, say, 3i/5 times “0” plus 4/5 times “1”.
That seems to be a matter of interpretation. What Deutsch is saying in the above quote seems consistent with a literal parallel-universes interpretation. Indeed, according to the commentary piece in Nature (Vol 448, 5 July 2007), the subhead to the title Many Lives in Many Worlds is “Accepting quantum physics to be universally true, argues Max Tegmark, means that you should also believe in parallel universes.”
Tegmark offers the following interpretation:
Everett’s theory is simple to state but has complex consequences, including parallel universes. The theory can be summed up by saying that the Schrödinger equation applies at all times; in other words, that the wavefunction of the Universe never collapses. That’s it — no mention of parallel universes or splitting worlds, which are implications of the theory rather than postulates. His brilliant insight was that this collapse-free quantum theory is, in fact, consistent with observation. Although it predicts that a wavefunction describing one classical reality gradually evolves into a wavefunction describing a superposition of many such realities — the many worlds — observers subjectively experience this splitting merely as a slight randomness (see ‘Not so random’, overleaf), with probabilities consistent with those calculated using the wavefunction-collapse recipe.
As Tegmark tells it, the “correct” interpretation really depends on whether one prefers the mathematical interpretation or the more mundane intuitive one. The mathematical one is where the quantum wavefunction never collapses, but evolves into a vast number of classical parallel storylines, or worlds. The more intuitive observational one is simply that the wavefunction collapses randomly.
Perhaps it is not a question of physics, just when I hear the words “literal parallel-universes interpretation” it sounds to me like one could imagine taking a train from one to another, though obviously Deutsch couldn’t mean that since it doesn’t physically make sense. What one considers an “intuitive” interpretation obviously varies, too, since to me it seems that if C = A + B then C should be intuitively seen as a genuine state and not merely A and B in “parallel”; similarly that quantum particles simply don’t take a definite classical path from one point to another, as can be demonstrated by various benchtop experiments.
Deutsch’s argument is ultimately incoherent: it assumes that the computational resources the best known classical algorithm consumes should also be consumed by quantum computation, but there’s simply no reason to believe that. I mean, there’s even the possibility that a classical algorithm could be discovered that equals the quantum algorithm’s performance (although that would be quite surprising, to put it mildly), so in that case, Deutsch’s reasoning would lead to a ‘classical’ many-worlds theory, but without any need—all that’s been discovered would be that the computational resources needed to solve the problem weren’t what we thought they were.
This interpretation explains why I am still alive despite a few close calls. Perhaps I am dead in 99% of the universes (storylines), but of course I’ll be conscious only of one of the universes where … I’m still conscious.
When I read about the enzymes which implement the genetic code or photosynthesis, my imagination is staggered that these things evolved. Sure, they could arise by chance if the odds are only a septillion-to-one against, but are the odds really that good? Or perhaps, just like Quantum Immortality, we should know that odds-against events did occur in the universe(s) where we are conscious.
Which also explains why you’ve never slept!
Strictly speaking, all we can actually prove is that duplicate regions would exist, and at least one region must have an infinite number of duplicates (a straightforward application of the Pigeonhole Principle). We can’t actually prove that there would be any duplicates of our own specific region. But it would be infinitely unlikely for there not to exist any duplicates of our region, absent what could only be called divine intervention.
But that says zip about all parameters being discrete. If if any of them are continuous, then the whole argument falls apart.
So many formulas work so well for a continuous domain. Keep in mind that it was how some continuous formulas did not work that lead to Planck proposing quantum energies. If other “quantum” effects worked on everything things would break down all over the place, e.g., the Heisenberg Uncertainty Principle, the Schrödinger equation, etc.
Take the monitor I am looking at. To recreate that exact same monitor is some far off corner of the Universe would require an amazing series of steps going back to the early days of the Universe including the creation of intelligent life with incredibly specific properties, furthermore, that other monitor would have to exist now, not 100 years ago or in the future if it’s to be part of a current duplicate of our corner of the Universe. And the same with all other objects (and people!).
Some parameters might be continuous, but they can’t be measured to be continuous, which is good enough.
The Bekenstein-Hawking bound, at least on the most straightforward interpretation, implies that any volume of spacetime contains a finite amount of information scaling with its surface area. Consequently, there’s only a finite number of possible configurations for each spacetime volume, and hence, in an infinite universe, we should (modulo problems of defining a suitable probability measure) expect each configuration to be repeated infinitely often.
But that is only looking back and forward in time in the usual way. Could your monitor (or any part of ‘the’ universe for that matter) not be always intermingling and exchanging itself with parts of other ‘nearby’ universes at every instant? Whether such intermingling is fundamentally unobservable is an important question. But whatever the answer, there seems to be no specific universe. And those we think as ‘specific’, like the one(s) we think we exist in, may well have probability of exactly 0.