This post specifically pertains to the butterfly effect at the classical and quantum level.
Butterfly effect is undoubtedly one of the most beautiful theories, but it also creates more chaos.
To start with, let us get on to an example to know butterfly effect at a greater notion.
The classic example is that a butterfly flapping its wings at the right time and the right place could cause a tornado on the other side of the world. It is not that a butterfly flapping its wings simply causes a tornado. An event like a butterfly flapping its wings is related to a chain of other events which ultimately cause a tornado.
For in shorters, check out this video:
Above example is not solely trustworthy, to make this more engaging we take another example.
Assume that you found Sci-Hole stories interesting and so you subscribed to Sci-Hole(just by refreshing this web page and providing your mail) and when you get the next story directly to your inbox you read it and find it interesting, and so you shared the post in all of the social media platforms. Assume that the post you shared caught the attention of a small startup(or something like that) and while seeing your profile on social media they found some post that you posted one year ago and found that useful for their startup and so they hired you to give some ideas for their startup. Now assume some decades later, your idea was used in a slightly different manner to have a major breakthrough in science and tech. By building on those ideas some centuries later humans are able to create tech that can travel at the speed of light and this advanced tech is used to harness (extract) energy from a black hole, or to meet aliens(if they exist). All this happened because you just subscribed to Sci-Hole(just by refreshing this page). This is just a possibility. Though the initial events are small, this can create a huge impact on future events that you may not be aware of.
BUTTERFLY EFFECT
Scientifically many believe that butterfly effect is caused because even a small action by you will ripple through space and time, which will cause a huge effect in the future. In the perspective of classical chaotic theory, damage or modification to a state will magnify exponentially.
But at the quantum level, things work differently. To understand that let's take an example,
The protocol: Alice prepares the central qubit with the gate P, and applies the scrambling unitary U^ . Bob measures the central qubit in any basis defined by the gate R, with S flipping the qubit to the corresponding post measurement state. Alice is still able to reconstruct the encoded information via a single decoding unitary U^†.Let there be two people named Alice and Bob. Alice wants to hide an original state of one of her qubit(named as a central qubit), which she achieves using a processor P that implements fast information scrambling during a reversible unitary evolution of many interacting qubits. To recover the central qubit from the scrambled one Alice uses a time-reversed protocol. Let Bob be an intruder who wants to get the original state of a central qubit, but as the qubit is scrambled, Alice is sure that Bob cannot get any information. But Bob, during his trails to get the state of central qubit destroys the destroys all the quantum correlations between central qubit and rest of the system. Now Alice is in trouble because she doesn't have any knowledge about other qubits that Bob used in the process of finding the original state. But after a unitary evolution during time t1, a projective measurement along a random axis is applied to the central spin, without collecting any data from the measurement outcome. Then, the system evolves backwards in time during t2, followed by a state tomography for the central spin. When t2= t1, the final measurements contain information that can be used to fully reconstruct the initial state of the central qubit.
By this, it can be proved that damage and modification to a state at the quantum level amplify linearly rather than exponentially like at the classical level. This means butterfly effect does not happen at the quantum level. This means that for time travellers, there is no need to worry about the butterfly effect at least at the quantum level. As the name of the title goes, reality will heal itself from damage caused by our actions at the quantum level.
At the quantum level, it is proved that the butterfly effect does not work but what happens at the classical level
But that's the idea for another Sci-Hole story.
Credit(photos and content):
References:
S. L. Braunstein and A. K. Pati, Quantum Information
Cannot Be Completely Hidden in Correlations: Implications
for the Black-Hole Information Paradox, Phys. Rev. Lett.
98, 080502 (2007).
J. Li, R. Fan, H. Wang, B. Ye, B. Zeng, H. Zhai, X. Peng,
and J. Du, Measuring Out-of-Time-Order Correlators on a
Nuclear Magnetic Resonance Quantum Simulator, Phys.
Rev. X 7, 031011 (2017).
F. Arute et al., Quantum supremacy using a programmable
superconducting processor, Nature (London) 574, 505
(2019).
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