Existence of Mathematically Possible but Physically Unattainable Entities

Can something exist that is mathematically but not physically possible? This question delves into the realms of mathematical abstraction and the physical world. While mathematics is an abstract system not bound by practical constraints, it can describe scenarios that are impossible to realize in our physical universe. Let's explore some examples and theoretical concepts to understand better.

Mathematical Abstractions Beyond Physical Constraints

If you mean something that is not possible in the sense of not being realistic in our real-world experience, then indeed, the realm of mathematics offers a wealth of abstract entities and concepts that transcend what is feasible in our physical reality.

For instance, consider an n-dimensional space where n is larger than 4. An n-dimensional hypercube, or even a 10-dimensional hypercube, exists purely as a mathematical construct. These higher-dimensional spaces have no physical existence; however, they are well-studied and understood in the field of mathematics. These constructs are useful in various scientific and engineering applications, especially in modern physics.

Dimensions and Mathematical Entities

Similarly, notions like infinity as a special class of numbers, a number occupying a zero-dimensional point for smoothness, or spatial dimensions less than 3 (which are invisible to us) are all mathematical concepts with no direct physical manifestation.

The zero-dimensional point can be conceptualized as a point in a sphere or a perfect sphere that perfectly represents the curvature and continuity of surfaces. This notion allows mathematicians to create smooth curves and surfaces without the need for any physical dimension.

Theoretical Constructs with Physical Implications

There are a multitude of mathematical constructs that, while theoretically possible, have no practical physical existence. For example, point masses and perfectly smooth surfaces are mathematical ideals that cannot be literally achieved in the physical world. Numbers, too, while incredibly useful, are abstract entities with no physical substance.

Yet, there is an intriguing intersection where mathematics intersects with the physical universe. In a recent development, a new discovery has revealed that a primordial wave system may have created the 'matter' of the hydrogen atom using a perfect mathematical system. This theory, which has been scheduled for publication in late 2023, suggests that certain mathematical principles govern the creation of physical entities. Although the practical realization of such systems in the physical world remains hypothetical, the theory underscores the profound connection between mathematics and physical reality.

The Limitation of Physical Realization

For something to be physically possible, it must be realizable through observable, measurable, and replicable means. Infinite speed, for instance, is possible mathematically but not physically. Similarly, while anti-matter is a concept that exists mathematically, it is challenging, if not impossible, to create and maintain in a physical setting.

The 20th-century theoretical physicists have pioneered the field of theoretical physics, where they have put vast emphasis on mathematical models to explain and predict physical phenomena. However, the applicability of these models in the real world is a different matter. Infinite speed and anti-matter, for example, cannot be achieved in our current physical and technological capabilities.

Conclusion: Mathematics and Physical Existence

In conclusion, while mathematics can describe a vast array of entities and scenarios, not all of these can be realized in a physical world. The limitations of physical existence mean that while something may be mathematically possible, it may not be physically achievable. The realm of pure mathematics is impressive and expansive, but its practical limitations are a testament to the wonder of both the mathematical and physical worlds.