Does physics claim that every possible world has or will exist?

At present, mainstream physics posits that the underlying level of all natural phenomena is quantum mechanical.

There exists the standard model of particle physics, a mathematical model, where it is posited that the elementary particles and their interactions build up matter as we know it, classical theories emerging smoothly from the underlying quantum mechanical framework.

Quantum mechanics is a probabilistic theory, the elegant mathematical formulations can only predict a probability for the location and time of an event, given by the solution of the quantum mechanical equations. For example, there are no orbits of electrons around atoms, but orbitals, probability loci.

For mainstream physics, a measurement is a specific instance manifested out of all the possible values that the probability distribution ( the complex conjugate square of the wavefunction) offers, misleadingly called "collapse of the wavefunction".

There exists the so called "many worlds interpretation"

The many-worlds interpretation is an interpretation of quantum mechanics that asserts the objective reality of the universal wavefunction and denies the actuality of wavefunction collapse. Many-worlds implies that all possible alternate histories and futures are real, each representing an actual "world" (or "universe"). In layman's terms, the hypothesis states there is a very large—perhaps infinite2—number of universes, and everything that could possibly have happened in our past, but did not, has occurred in the past of some other universe or universes.

It is not the mainstream view. It is interpreting mathematical functions and integrals as a version of reality, but there is no way that this can be checked by experiment.

It is the old conundrum: does mathematics define nature or nature is modeled by mathematics? Started at the time of Pythagoras and Plato, and this is its latest manifestation.

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In short: No.

Based on the Many-Worlds-Interpretation of QM, you can make statements of this kind, but as the name says, it is just an interpretation, whose ontological statements are highly controversial. There are other interpretations which provide the same physical results, which do not state the existence of multiple worlds, which at least shows that this is in no sense "proven".

Just because all things are possible, does not mean that all possibilities actually exist. And then, to say they simultaneously exist goes even further. They merely exist as "possibilities", or possible outcomes but last I checked, possibilities do not fit into the same category of physical realty. I never understood why something is assumed to automatically exist because it's existence is "possible". It's all very much of a stretch. It's kind of like treating the actual number 2 as a real thing when no such thing exists. You can have 2 oranges or apples but the number two itself is just a concept. That's what they are doing with QM.Because the concept of number two works so well and so often, they treat it like a real thing, when it is a concept.