Theoretical Framework: Infinite Earths and Variations

Yes, if the universe is infinite and the set of elements finite, it stands to reason that an infinite number of Earth-like worlds could exist. Our cosmos might be a continually repeating pattern, where sameness and variety coexist. While repetition is the most probable scenario, it is not about exact replicas; tiny details can vary, leading to a diverse set of systems.

Mathematically, this can be seen as X Y, where X represents the infinity of sameness, and Y represents the infinity of variety. This synthesis leads us to believe that our universe might indeed repeat itself infinitely, albeit slightly differently each time. Each iteration would be a variation upon a theme, with our familiar patterns reappearing in countless different ways.

Quantum Causality and Cosmic Iterations

Beyond theoretical constructs, quantum causality provides a framework for understanding these cosmic iterations. According to this principle, within any consistently evolving causal system, regardless of whether it is finite or infinite, there will be repeated systems that closely and diversely mirror one another. Over extraordinarily long periods, systems are destined to repeat exactly.

As we dive deeper into the quantum realm, we find that as matter nears the speed of light, fusion of light elements occurs and fission of heavy elements takes place. This process does not entail infinite mass, as mass is distributed as energy and forces release. Recent findings suggest that the majority of mass resides in the interconnections of subatomic particles, not the particles themselves.

Manipulation of Mass and Its Properties

This new understanding of mass opens up a plethora of possibilities. If the non-localized influences on subatomic particle interactions can be identified, the potential to manipulate the properties of mass in matter emerges. One such property under study is the Higgs Boson, which is essentially one object with properties that make the appearance of dimensional space possible. Given that mass is now seen as a variant rather than an invariant, we might be standing on the brink of a new era where mass can be manipulated in ways previously unimaginable.

SLAC experiments hold the key to future discoveries. By isolating specific properties of mass such as the rate of radioactive decay, the conditions for decay or fusion, and non-Newtonian properties like angular momentum and inertia, we may unlock unprecedented technologies. Potential applications include cold fusion, quantum energy storage, and wireless power transfer.

Quantum Time Capsules and Future History

If the universe does indeed repeat, we might look for time capsules from our past lives. These could be direct messages left for ourselves, information requests to better document present conditions for future history, or a form of time travel itself. Although these concepts are part of science fiction, the potential for such phenomena in a universe where repetition is a certainty cannot be ignored.

As we continue to explore the cosmos and understand the quantum realm, the infinite repetition of Earth-like worlds becomes a more plausible scenario. By embracing the principles of quantum causality and the malleability of mass, we move closer to comprehending the complex and beautiful patterns that govern our universe.