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The Zero Delusion v0.99x

Zero signifies absence or an amount of no dimension and allegedly exemplifies one of humanity's most splendid insights. Nonetheless, it is a questionable number. Why did algebra embrace zero and dismiss infinity despite representing symmetric and complementary concepts? Why is zero exceptional in arithmetic? Is zero a "real" point? Has it a geometrical meaning? Is zero naturalistic? Is it universal? Digit 0 is unnecessary in positional notation (e.g., bijective numeration). The uniform distribution is unreachable, transmitting nill bits of information is impossible, and communication is never error-free. Zero is elusive in thermodynamics, quantum field theory, and cosmology. A minimal fundamental extent is plausible but hard to accept because of our acquaintance with zero. Mathematical zeroes are semantically void (e.g., empty set, empty sum, zero vector, zero function, unknot). Because "division by zero" and "identically zero" are uncomputable, we advocate for the nonzero algebraic numbers to build new physics that reflects nature's countable character. In a linear scale, we must handle zero as the smallest possible nonzero rational or the limit of an asymptotically vanishing sequence of rationals. Instead, zero is a logarithmic scale's pointer to a being's property via log(1)). The exponential function, which decodes the encoded data back to the linear scale, is crucial to understanding the Lie algebra-group correspondence, the Laplace transform, linear fractional transformations, and the notion of conformality. Ultimately, we define a "coding space" as a doubly conformal transformation realm of zero-fleeing hyperbolic geometry that keeps the structural and scaling relationships of the world.

Zero signifies absence or an amount of no dimension and allegedly exemplifies one of humanity's most splendid insights. Nonetheless, it is a questionable number. Why did algebra embrace zero and dismiss infinity despite representing symmetric and complementary concepts? Why is zero exceptional in arithmetic? Is zero a "real" point? Has it a geometrical meaning? Is zero naturalistic? Is it universal? Digit 0 is unnecessary in positional notation (e.g., bijective numeration). The uniform distribution is unreachable, transmitting nill bits of information is impossible, and communication is never error-free. Zero is elusive in thermodynamics, quantum field theory, and cosmology. A minimal fundamental extent is plausible but hard to accept because of our acquaintance with zero. Mathematical zeroes are semantically void (e.g., empty set, empty sum, zero vector, zero function, unknot). Because "division by zero" and "identically zero" are uncomputable, we advocate for the nonzero algebraic numbers to build new physics that reflects nature's countable character. In a linear scale, we must handle zero as the smallest possible nonzero rational or the limit of an asymptotically vanishing sequence of rationals. Instead, zero is a logarithmic scale's pointer to a being's property via log(1)). The exponential function, which decodes the encoded data back to the linear scale, is crucial to understanding the Lie algebra-group correspondence, the Laplace transform, linear fractional transformations, and the notion of conformality. Ultimately, we define a "coding space" as a doubly conformal transformation realm of zero-fleeing hyperbolic geometry that keeps the structural and scaling relationships of the world.

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ageable infinite quantity that resists an appropriate interpretation and impedes

deriving new results. True singularities are hypothetically possible but also the

primary source of criticism of GR. Specifically, the Penrose-Hawking singularity

theorems consider singularities inescapable, although they are invisible to us

outside of a black hole or even to an infalling observer [71,72,74]. If singularities

were genuine, they would perhaps reside within an elementary particle, as

virtual particles, a black hole, or any other elusive form [82], a possibility that

contrasts with their historical lack of evidence.

The surge of Quantum Field Theory (QFT) seemed to be able to overcome

the theoretical problem. Even though a field’s value can be zero everywhere classically,

our quantum universe cannot obliterate a field’s uncertainty. According

to QFT, which rules the Standard Model of Particle physics, quantum fields

are quantities of critical features of spacetime that at every point continually

fluctuate in their lowest energy state; the vacuum of a quantum field is unstable,

vibrating around a ground level represented by a positive minimum-energy

configuration. QFT can manage these fields separately by employing regularization

and renormalization techniques based on fitting parameters [77,112], usually

cutoff regulators, that attenuate singularities of observables and control

self-interaction loops to absorb divergences, giving rise to "effective theories".

For instance, adjustable infinitesimal distances allow calculating the particles’

specific mass and charge.

Nevertheless, this "quantum fuzziness" [193] is "not enough to deal with the

1/r 2 singularity in the gravitational force." In other words, an effective theory

of QG can be consistent but lacks predictive power because new infinities never

stop arising. To worsen things, the aggregation and integration of the so-called

vacuum’s zero-point energy density oscillations associated with every quantum

field contribute to the cosmological constant with a magnitude whose theoretical

value is ridiculously greater than the experimental data; the observed value of

the cosmological constant [137] beats zero slightly but significantly, begetting a

mild curvature of spacetime.

The experimental elusiveness of zero and the fundamental incongruency of a

singularity are enormous obstacles urging physicists to devise a theory of gravity

in conformity with GR and Quantum Theory [149,145,109]. Finitism is a must

because [177] "When Bohr tells us that quantum theory gives us the only objective

description of nature of which one can possibly conceive, is he not also

telling us that no description can make sense which is not founded upon the

finite? [...] Encounter with the quantum has taught us, however, that we acquire

our knowledge in bits; that the continuum is forever beyond our reach." This

reasoning suggests a route to arrive at a QG theory that combines the functional

definition of quantum action, the feasibility of countable discreteness, and

a constructive and practical concept of probability.

The unifying thread of this approach is Feynman’s Path Integral formulation

of the Principle of Stationary Action. The probability of an event is a mean of

the occurrence probabilities for the finitely countable possible ways, i.e., paths,

to fulfill the event, e.g., a trajectory between two points or a transformation

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