The Quantum Butterfly Effect
discover.lanl.gov
discover.lanl.gov
The infinity of universes in which you can exist is reduced to a lesser infinity by the reverse time travel, since you could only have travelled backwards from universal states in which those specific conditions still existed, ergo reality appears to the traveller to be self healing.
That’s one of the things about MWI that is irritating, even though it still seems the most likely to me. It covers the testing parameters so completely that it is impossible to test. You always end up in a lesser infinity, but an infinity nonetheless. What we need is a way to quantify randomness in such a way that we might detect a change in the dimensions of infinities or something, but that seems improbable at best.
I'm not 100% sure, but wave function collapse might involve some non-linearity somewhere, whichight also be detectable in some fashion.
On the other hand, Bohm's interpretation seems pretty ad hoc. And it also includes all of the other worlds that MWI has in it via the pilot waves that continue to exist and propagate forever. (The pilot waves never collapse.) It's just that only one of those many worlds ends up being "real".
Necessarily, this lesser infinity of universes would tend to be extremely similar, and would average out to some kind of consensual reality, with the variation noise only becoming evident if one looked very closely (superposition, casimir effect, uncertainty principle, etc)
So the act of observation would merely divide this lesser infinity into two lesser infinities which would be distinct unless they were reunited by a reverse-time coherence such as many quantum experiments have demonstrated.
I would suspect that statistically, such reverse-time coherences are pretty common inside of one's personal light cone, so in this respect, I would guess that the "universe bandwidth" is probably quite robust and requires a pretty significant (macroscopic scale) effect in order to divide permanently into distinct infinities for a given observer.
Of course this is all just metaphysical conjecture, but Id be interested if anyone is seriously thinking along similar lines.
The popular idea of the butterfly effect in weather has always seemed suspect to me, due to the fact that air is a naturally damped system; a butterfly’s influence on air drops over distance, and likely falls off fast enough that the probability it can affect something even a few miles away is below atomic or quantum thresholds. The analogy between weather and simple mathematical chaotic systems seems specious.
Looking around a little it seems like some physicists are starting to agree, and believe Lorenz’ observations based on his weather modeling has more to do with the modeling and limited numerics than reality: “the limited predictability within the Lorenz 1969 model is explained by scale interactions in one article[22] and by system ill-conditioning in another more recent study.[25]” https://en.wikipedia.org/wiki/Butterfly_effect#Recent_debate...
Aren't the Copenhagen interpretation and Heisenberg uncertainty principle an immediate indication that Quantum systems can only be chaotic?
Quantum systems are not chaotic but intrinsically indeterminate, insofar as the initial conditions of a system have no relation to the observed state. Chaotic systems are deterministic, and therefore classical. Quantum chaos tools attempt to bridge the gap.
As a layperson I found the first page to be more succinct and intuitive than the article.
> Let Alice have such a processor that implements fast information scrambling during a reversible unitary evolution of many interacting qubits. She applies this evolution to hide an original state of one of her qubits, which we call the central qubit. The other qubits are called the bath. To recover the initial central qubit state, Alice can apply a time-reversed protocol.
> Let Bob be an intruder who can measure the state of the central qubit in any basis unknown to Alice. If her processor has already scrambled the information, Alice is sure that Bob cannot get anything useful. However, Bob’s measurement changes the state of the central qubit and also destroys all quantum correlations between this qubit and the rest of the system.
> According to the no-hiding theorem, information of the central qubit is completely transferred to the bath during the scrambling process. However, Alice does not have knowledge of the bath state at any time. How can she recover the useful information in this case?
> In this Letter, we show that even after Bob’s measurement, Alice can recover her information by applying the time-reversed protocol and performing a quantum state tomography with a limited amount of effort. Moreover, reconstruction of the original qubit will not be influenced by Bob’s choice of the measurement axis and the initial state of the bath.
> This effect cannot be explained with semiclassical intuition. Indeed, classical chaotic evolution magnifies any state damage exponentially quickly, which is known as the butterfly effect. The quantum evolution, however, is linear. This explains why, in our case, the uncontrolled damage to the state is not magnified by the subsequent complex evolution.
f(cQbit)=> bath = decompose(cQbit)
Bath now has information about the central Qbit stored in the bath.
Any measurement of cQbit changes the state of cQbit and destroys any correlation with the bath.
Regardless of the state of cQbit: you can rebuild the cQbit with the information about cQbit stored in the bath.
f(bath)=> cQbit = compose(bath)
This effect seems trivial as I've explained it. So I assume I got something wrong.
Is it just the process of restoring from the bath into the cQbit that's complicated, or has a bunch of gotcha's? It seems like the state of the cQbit is inconsequential if you can just overwrite (:ah... the gotcha) it with the info from the bath.
If you can rebuild the cQbit from just the bath, then there's no information in cQbit, right?
I assume the factors that mitigate/negate the no-cloning theorem are that the bath is not a qBit, but a collection, that the state's are initially entangled. It could also be that the initial state of the cQbit is known, instead of unknown.
the no-broadcast-theorem is what covers mixed states instead of pure states. https://en.wikipedia.org/wiki/No-broadcasting_theorem
``` The theorem[1] also includes a converse: if two quantum states do commute, there is a method for broadcasting them: they must have a common basis of eigenstates diagonalizing them simultaneously, and the map that clones every state of this basis is a legitimate quantum operation, requiring only physical resources independent of the input state to implement—a completely positive map. A corollary is that there is a physical process capable of broadcasting every state in some set of quantum states if, and only if, every pair of states in the set commutes. This broadcasting map, which works in the commuting case, produces an overall state in which the two copies are perfectly correlated in their eigenbasis. ```
So it seems that there is some wiggle room, and specifically when you start working with collections instead of single qbits, things get weird.
But I'm a layman, and that was just a walk down wikipedia.