The Quantum Era

“Era of the absurd physics ”

There were two of the smartest people at the end of classical age of physics, Jeans and Rayleigh, and there was a problem in physics that whenever physicist thought of the emission of radiation in black body the curve of emissions at the table of both the mind lead to infinity at higher frequency which lead to fork somewhere in UV region of frequency toward infinity in the mathematics of Rayleigh and Jeans. The observation by Weins was saying different things about the way those emissions and absorption of radiation in black body, which ipso facto was a catastrophe in theoretical understand of radiation phenomenon. The premises where both were wrong is when they both defined the process of absorption and emissions of radiation is a continuous one.

After few decades of them, there was a physicist whose constant is popular as the fundamental physical constant of Quantum Physics, Max Planck. He corrected the premise, by saying that the radiation aren't fluxed like a flow of fluid does, rather they come in a bunch or packets of energy called 'Quanta'. This led to the conclusion that the actual emission and absorption phenomenon in nature is a descrete and not continuos phenomenon. The idea of continuum of here doesn't make sense thats why the quantum was in sense the real picture of how the simplest phenomenon such as radiation work.

Planck's revolutionary idea of quanta challenged the established view of classical physics. It opened the door to a new era – the era of quantum physics. But the story doesn't end there. The next big twist came with the introduction of wave-particle duality. Several years after Planck, Albert Einstein applied the concept of quanta to light, proposing that light energy comes in packets called photons. This explained the photoelectric effect, where light can knock electrons out of a metal surface. However, light also exhibited wave-like behavior, such as diffraction and interference. This duality – light being both a particle and a wave – was a major challenge to the classical understanding.

The deBrogglie wave theory of particles is the fundamental most premise of Quantum Physics. This suggest that, entities that we call particles have wave nature. It correlates inversely such that,
λ = h /(mv) is true for any matter waves. For particles as tiny as electrons, m is very small thus, λ is significant, hence it have a matter wave that actually can show wave behavior. Let us assume a particle as massive as a Earth, it would be much insignificant, thus the matter wave for objects massive such as us, doesn't even cease to exist. Thats why laws of quantum mechanics doesn't make sense in larger scale at all.

Erwin Schrödinger, a couple of decades later, took things a step further. He proposed a mathematical function called the wave function, which described the probability of finding a particle like an electron at a specific location. The wave function didn’t depict a definite path or position of the particle, but rather the likelihood of finding it in a particular region. This probabilistic nature of the quantum world was a radical departure from the deterministic world of classical physics.

There are two major interpretation of how Quantum Mechanics works:

Realist: Quantum mechanics describes an objective reality.

• Wavefunction is reality: The wavefunction itself is the fundamental reality. (Hugh Everett - psi-ontic)
• Pilot wave: Wavefunctions are "pilot waves" that guide particles. (David Bohm)

Anti-realist: Quantum mechanics does not describe an objective reality.

• Wavefunction is knowledge: Wavefunctions describe our probabilistic knowledge about a deeper underlying reality. (Niels Bohr - psi-epistemic)
• Albert Einstein: Disagreed with quantum mechanics, believing it wasn’t the "real thing."

Non locality of Quantum Mechanics

Entanglement, for instance, challenges our understanding of locality. The EPR experiment, described by the entangled state (Ψ(A,B)), suggests that two particles can share a correlated state, where measuring one particle (A) instantaneously influences the state of the other (B), regardless of the separation distance. This correlation appears to violate Bell’s Inequality, a mathematical expression based on local realism. Bell’s Inequality (Σ Sᵢ (a, b) P(a, b) ≥ B) predicts a limit on correlations achievable through local hidden variables (a, b). However, experiments have consistently violated this limit, implying non-local connections or a more profound departure from classical ideas of locality.

Some major interpretations of Quantum Mechanics based upon non locality:

Copenhagen Interpretation

The quantum mechanical system is governed by probabilities described by the arbitrary function called wavefunction (Ψ). This wavefunction doesn’t represent a classical particle trajectory but provides information about it’s probability. The Born rule (|Ψ(x)|²) allows us to calculate the probability density of finding a particle at a specific location (x) based on the squared magnitude of the wavefunction at that point. Unlike classical mechanics with its well-defined position and momentum, quantum mechanics embraces uncertainty quantified by the Heisenberg Uncertainty Principle (Δx Δp ≥ ħ/2). This principle states that the product of the uncertainties in a particle’s position (Δx) and momentum (Δp) is always greater than or equal to a constant value (ħ, the reduced Planck constant). The act of measurement here plays a significant role. Before interacting with a measuring apparatus, the particle exists in a superposition of all possible states, described mathematically by the wavefunction. This superposition collapses into a single definite state upon measurement, a concept not directly described by the standard equations but a postulate of the Copenhagen interpretation.

Many World Interpretation (MWI)

The Many-Worlds Interpretation (MWI) offers a radical perspective on quantum mechanics. It proposes the universal wavefunction (Ψ) encompasses all potentialities, existing objectively. Unlike the wavefunction collapse of the Copenhagen Interpretation, MWI suggests no such collapse occurs. Instead, the Schrodinger equation (iħ dΨ/dt = HΨ) governs the entire universe’s evolution, with the Hamiltonian (H) representing the system’s total energy. This continuous evolution implies that every possible outcome of a quantum interaction leads to a branching of the wavefunction. In essence, the universe splits into a multitude of realities (each a 'world’)… one for every possibility … described by separate wavefunctions. The probabilities for these branches are determined by the Born rule, similar to the Copenhagen Interpretation. Decoherence, a process where a quantum system interacts with its environment, plays a crucial role in explaining the classical world’s emergence. Whilst the mathematics of quantum mechanics (Schrodinger equation, Born rule) is the same, MWI reinterprets them, proposing a vast multiverse containing all possible realities.

Pilot Wave Interpretation

The Pilot Wave Interpretation, also known as Bohmian mechanics, describes a deterministic course through the probabilistic nature of quantum mechanics. It introduces a hidden variable, the particle’s actual position (q), alongside the familiar wavefunction (Ψ). The wavefunction, no longer solely responsible for probabilities, evolves according to the ubiquitous Schrodinger equation (iħ dΨ/dt = HΨ), where iħ is the reduced Planck constant and H represents the system’s Hamiltonian (total energy). Crucially, a definite equation dictates the particle’s motion

(dq/dt = m∇S/ħ),

where m is the particle’s mass, ∇S is the gradient of the wavefunction’s phase (S), and ħ is again the reduced Planck constant. This guidance equation mathematically links the particle’s movement to the wavefunction’s properties. The Pilot Wave theory offers a realist perspective, suggesting particles have definite positions at all times, guided by the wavefunction, even when not observed.

Hidden Variables

The Hidden Variable Interpretation seeks to restore a deterministic undercurrent to the probabilistic world of quantum mechanics. It postulates the existence of additional variables (λ), beyond the standard wavefunction (Ψ), that govern a system’s state. These hidden variables are presumed to hold precise values for all measurable properties, even before measurement. The wavefunction (Ψ), in this interpretation, reflects an incomplete picture, representing an ensemble of possibilities weighted by a probability density function.

The Schrodinger equation (iħ dΨ/dt = HΨ) might be reinterpreted to incorporate the influence of these hidden variables, guiding the system’s evolution deterministically. However, a key challenge lies in formulating a hidden variable theory that reproduces all quantum mechanical predictions, including those that seemingly require non-locality (like violations of Bell’s Inequality). The search continues for a mathematically rigorous hidden variable theory that can figure out the underlying determinism, if any, within the quantum mechanical world.

What are odds?

Consider these,

- The effect are themselves in fundamental causation and they can only be described using correlation.

- The probability density function is the solution of a differential equation of arbitrary function corresponding to wave nature of a particle.

- The more probable outcomes are the one which are the most random one, where particles are supposed to exist.

- When, you observe the outcome, then the outcome become unprobable.

- Uncertainty leads to Probability.

This is not the statistical utopia. This is absurdity in very fundamental of Quantum Mechanics.

Summing up Quantum Mechanics

Over a century since Planck’s revolutionary postulate (E = nhν, 1900) shattered the edifice of classical physics, quantum mechanics (QM) has established itself as the unrivaled paradigm for describing the microscopic world. Heisenberg’s uncertainty principle (Δx Δp ≥ ħ/2), formulated in 1927, cast a profound light on the inherent limitations of knowledge in the quantum realm. It established that the more precisely we determine a particle’s position (Δx), the less precisely we can know its momentum (Δp), and vice versa. The success of QM is undeniable, with the Schrödinger equation (iħ∂Ψ/∂t = HΨ) accurately predicting the behavior of atomic and subatomic systems. However, the probabilistic nature of QM, given by the Born rule, and the wavefunction collapse postulate continue to challenge our classical intuition. Recent advancements in areas like entanglement, defying Bell’s inequality (Σ Sᵢ(a, b) P(a, b) ≥ B), suggest non-local correlations that violates classical explanations. Meanwhile, interpretations like the Many-Worlds Interpretation (MWI) offer alternate perspectives on the wavefunction’s role, raising profound questions about the nature of reality. As we come along further into the 21st century, QM stands poised to continue its remarkable journey, decoding the absurd nature of the fundamental of universe and potentially leading to a grand unification of the fundamental forces.

On the other hand, String theory, with its elegant mathematical framework (e.g., Klein-Gordon equation: ∂²Φ - m²Φ = 0), is a promising candidate for a TOE, aiming to unify the fundamental forces (electromagnetic, strong, weak, and gravity) under one roof. However, challenges remain, such as reconciling string theory with gravity and finding experimental verification. The pursuit of a TOE continues, driven by the desire to unveil the ultimate mathematical structure governing our universe.