Many World Interpretation

## Background of Hugh Everett

Hugh Everett was a graduate student of John Wheeler, who took the same class in mathematical physics as Eugene Wigner, who believed that the human consciousness was the primary element of the collapse in wave function; to give a summary of what a wave function is, it is a mathematical variable that describes the wave characteristics of a particle, For example, take P wave; P and its functions will always be described by its wave function; in one dimension a wave will be represented by a wave function.

For example:***ψ(x, t) = A cos(k x − ω t + ϕ)***

*x=represents the position of the wave*

*t=represents time in which the wave is positioned in*

If one has a sound wave for example

represented as ψ(x, t)

Corresponding to the pressure perturbation associated with the wave at position ***x*** and time ***T***. This should give you the general idea of what a wave function is without diving too deep into such a notion as that will be saved for another video adequately explaining the Hilbert space.

Everett presented a paradox towards Eugene Wigner's views aka the observer-dependent wave function collapse, with examples of Wigner's friend which goes as follows; if an observer observes another observer to whom does the wave function collapse to? Everett considered ways to solve such a paradox one of which was the standard statistical interpretation of quantum mechanics, which went to be criticized by Einstein as a result of it being an incomplete description a position affirmed in the EPR paradox.

## Explanation

This led to the foundations of what Tegmark referred to as the level III multiverse also called the Many-Worlds Interpretation theory which was founded by Hugh Everett himself. Everett abandoned the position of the state function being a complete description of a system after Einstein's criticism and instead posited it to be not a description of a single system, but of an ensemble system which posits the probabilistic assertions to arise from that very incompleteness, that is to say, the descriptions provided by the state function stem from probability because it is designed as incomplete; Before we continue again I have to make sure readers are understanding what is being conveyed.

State functions are variables that define the state of a system within the universe, having a system means you also have to define the state of that system; a state function can include many elements of that system be it temperature, volume or even pressure. The number of parameters used to describe that system corresponds to the dimension of state spaces if the system is specified by 2 parameters it is a 2-dimensional system represented as (D=2) likewise if it is 3 parameters it would be (D=3).

Back to Everett's new alternative. This new alternative assumed the correct complete description, which presumably involved further hidden parameters beyond the state function alone, which leads to not a probabilistic but deterministic theory, which posits the probabilistic aspects arising as a result of our ignorance over those hidden parameters we do not know of similarly in our classical statistical mechanics. This negated Einstein's criticism and instead combined Einstein's views of ensemble and Bohm's views regarding our ignorance over the "complete" "hidden" variables.

## The universal wave function

The last alternative Everett presents which is central to the idea of Many-Worlds Intepretation is the theory of universal wave function, which disregards the observer-dependent wave function collapse. He assumed the universal validity of the quantum description, by disregarding the observer-dependent wave function collapse; in this view, the general validity of pure wave mechanics is without any statistical assertions; that is to say, our measurements of certain quantum systems are mostly disregarded instead pure wave mechanics and all of physics and all physical systems even the observers followed this one state function of a composite system.

If you've heard about the cat box theory you'd know that our observing the cat is what decides the definitive state of the cat without observation it will always be in two states it will always be superposed, in layman's terms it is induced to quantum superposition a state where property x such as a particle or in this case the cat is in two different states at the same time state x and b; dead or alive before observation after observation it is then it can be defined is either dead or alive but not both. In contrast, the universal wave function collapse is observer dependent the observers themselves are subjected to the quantum superposition independently of their measurements but as a predication of this composite system called the **universal wave function**.

As Everett states: ***It has logical simplicity and it is complete in the sense that it applies to the entire universe. All processes are considered equally (there are no “measurement processes” that play any preferred role), and the principle of psycho-physical parallelism is fully maintained. Since the universal validity of the state function description is asserted, one can regard the state functions themselves as fundamental entities, and one can even consider the state function of the whole universe. In this sense, this theory can be called the theory of the “universal wave function,“ since all of physics is presumed to follow from this function.***

This leads us to the core elements of Many-Worlds interpretation, starting with irreversibility in a measurement posited as follows; When an observer performs an observation the result is a superposition, each element of which describes an observer who has perceived a particular value. From this time forward there is no interaction between the separate elements of the superposition (which describes the observer as having perceived different results) since each element separately continues to obey the wave equation. Each observer described by a particular element of the superposition behaves in the future completely independently of any events in the remaining elements, and he can no longer obtain any information whatsoever concerning these other elements (they are completely unobservable to him).

The irreversibility of the measuring process is therefore, within our framework, simply a subjective manifestation reflecting the fact that in observation processes the state of the observer is transformed into a superposition of observer states, each element of which describes an observer who is irrevocably cut off from the remaining elements. While it is conceivable that some outside agency could reverse the total wave function, such a change cannot be brought about by any observer which is represented by a single element of a superposition, since he is entirely powerless to have any influence on any other elements. There are, therefore, fundamental restrictions to the knowledge that an observer can obtain about the state of the universe. No observer can discover the total state function of any physical system, since the process of observation itself leaves no independent state for the system or the observer, but only a composite system state in which the object-system states are inextricably bound up with the observer states.

## Summary of the standards

Quantum states correspond to vector spaces in quantum mechanics these vector spaces being Hilbert space which is more of a probabilistic and abstract space than it is real space so if someone destroyed Many-Worlds Interpretation for example it would only be around 2-A at best if we account for Hilbert space then it should count for some hax like probability manipulation and quantum manipulation on a high 1-B scale.

Many-Worlds Interpretation should also have the infinite-dimensional Hilbert space specifically by necessity because I see people saying Hilbert space is not infinite-dimensional by necessity which is true but not in the case of Many-Worlds Interpretation. After all, Many-Worlds Interpretation should at the very least contain infinite quantum states which we know would exist because the quantum superposition would happen for infinite states those states being the parallel worlds themselves in Many-Worlds Interpretation which would be instantiated by the infinite-dimensional Hilbert space this is the easiest way to demonstrate the existence of the infinite-dimensional Hilbert space in Many-Worlds Interpretation which is why specifically when you read in Tegmark's multiverse types and you see type 3 which is Many-Worlds Interpretation they posit not the existence of a finite-dimensional Hilbert space but an infinite dimensional one.

Many-Worlds Interpretation needs the infinite-dimensional space Hilbert to function and describe those quantum states now I'm pretty sure Many-Worlds Interpretation doesn't grant any feat past 2-A for the reasons:

* it's not real space its not physical it's abstract and it's probabilistic.

* Hilbert space is not infinite-dimensional by default.

The latter is a silly reason while the former is more reasonable but existing beyond the very notion of Many-Worlds Interpretation should qualify at least for either high 1-B or low 1-A because if we include the notion it'll include that infinite-dimensional Hilbert space.

Just destroying it would only grant 2-A and possibly high 1-B hax like quantum manipulation or probability manipulation on that scale.

The distinction is similar to manipulating a concept of space time for example and existing beyond that concept the former in the wiki is only hax the latter could suffice to act as an AP feat to be low 1-C or possibly higher or whatever.