Quantum Mechanics for Lay Readers

 

  I was writing about particle physics and the work at the European Organization for Nuclear Research (CERN) where two Malaysians went in my last article here. For a long time whenever I write something abstract to share in my WhatsApp group, my brother-in-law, Ong Geok Soo, a senior structural engineer in Singapore always remarked that what I was writing was like trying to understand quantum mechanics to him. Sometimes he would say it was like dark matter and dark energy in the universe to him even though what I wrote has nothing to do with this subject.

Since whatever I was trying to explain was alien like quantum mechanics to him, I have decided to write on this subject here.

 Furthermore, I have never written anything about quantum mechanics before, or about dark matter or dark energy in the universe.

Since I have just written an article on particle physics at CERN, I might as well write an article on quantum mechanics similar to particle physics to satisfy my brother-in-law.

Let’s try to understand this subject using very simple language so that it is reachable for everybody.

Quantum mechanics is the branch of physics I already heard of when I was still in school and I knew it was a very tough area in physics to understand, one that deals with the behaviour of particles at the smallest scales—such as atoms and subatomic particles like electrons and photons. It’s a world that’s very different from our everyday experiences, and it often defies our intuitions. Let us explain this in simple or semi-technical language:

1. The Basics of Quantum Mechanics:

Wave-Particle Duality: Particles like electrons and photons (light particles) can behave both as particles and as waves. This means that sometimes they act like little solid balls, and other times like ripples on a pond. The famous double-slit experiment shows this: when particles pass through two slits, they create an interference pattern, like waves, unless you observe them closely, in which case they act like particles.

a)  Quantum Superposition: In quantum mechanics, particles can exist in multiple states at once. For example, an electron can be in multiple places or spin in different directions simultaneously. This idea is captured by Schrödinger’s cat thought experiment, where a cat in a box is both alive and dead until someone looks inside.

b)  Quantum Entanglement: When two particles become entangled, the state of one particle is instantly connected to the state of another, no matter how far apart they are. If you measure one particle's spin, you immediately know the spin of the other, even if it’s on the other side of the universe. This phenomenon led Einstein to refer to it as "spooky action at a distance."

2. Key Principles and Equations:

Heisenberg’s Uncertainty Principle: This principle states that you cannot simultaneously know the exact position and momentum (speed and direction) of a particle. The more accurately you know one, the less accurately you can know the other. Mathematically, it’s expressed as:

Δx⋅Δp≥h4πΔx⋅Δp≥4πh​

Where:

• ΔxΔx is the uncertainty in position.
• ΔpΔp is the uncertainty in momentum.
• hh is Planck’s constant (a very small number).

Schrodinger’s Equation: This is the fundamental equation of quantum mechanics, describing how the quantum state of a physical system changes over time. It’s often written as:

iℏ∂∂tΨ=H^Ψiℏ∂t∂​Ψ=H^Ψ

Where:

• ΨΨ is the wave function, which contains all the information about the system.
• ii is the imaginary unit.
• ℏℏ is the reduced Planck constant.
• H^H^ is the Hamiltonian operator, representing the total energy of the system.

The wave function ΨΨ gives the probabilities of finding a particle in a particular state or position when measured.

3. Applications of Quantum Mechanics are:

a)   Electronics and Semiconductors: Quantum mechanics is the foundation of how semiconductors work. Transistors, the building blocks of all modern electronics (like computers and smartphones), rely on quantum mechanics to function.

b)   Quantum Computing: Unlike classical computers that use bits (0s and 1s), quantum computers use quantum bits or qubits, which can exist in superpositions of states. This allows quantum computers to perform certain types of calculations much faster than classical computers.

c)   Medical Imaging: Techniques like MRI (Magnetic Resonance Imaging) rely on quantum mechanics to image the inside of the human body non-invasively.

d)   Cryptography: Quantum cryptography uses the principles of quantum mechanics to create theoretically unbreakable codes, securing communication.

e)   Quantum Teleportation: Although not teleportation in the sci-fi sense, quantum teleportation uses entanglement to transfer the state of a particle from one place to another without moving the particle itself.

4. The Weirdness of Quantum Mechanics:

Quantum mechanics challenges our understanding of reality. In this realm, particles don’t have definite properties until they are measured, and they can influence each other instantaneously across vast distances. This challenges classical notions of cause and effect and leads to deep philosophical questions about the nature of reality.

In short, quantum mechanics is a fundamental theory that has revolutionized our understanding of the universe at the smallest scales. Its principles might seem strange or counterintuitive, but they have been confirmed by countless experiments and have led to numerous technological advances. As you delve deeper into this field, you’ll find that it reshapes your understanding of the very fabric of reality.

What about its relationship with Einstein Theory of Relativity that I heard when I was still in school?

Quantum mechanics and Einstein's theory of relativity are two of the most important pillars of modern physics, but they describe different realms of the universe and, for a long time, seemed incompatible. Here's an outline of their relationship:

1. The Domains They Govern:

Quantum Mechanics: As we discussed, quantum mechanics deals with the behaviour of particles at the smallest scales—atoms, subatomic particles, and so on. It operates on the principles of probability and uncertainty, and it’s most effective at describing systems at microscopic scales (like electrons, photons, and atoms).

Einstein’s Theory of Relativity: There are two theories here—Special Relativity and General Relativity:

Special Relativity (1905) deals with objects moving at constant speeds, especially at speeds close to the speed of light. It introduced the famous equation E=mc2

E=mc2, showing that mass and energy are interchangeable.

General Relativity (1915) describes how gravity works, not as a force but as the curvature of space and time (spacetime) around massive objects. This theory is most effective at describing large-scale phenomena, such as planets, stars, black holes, and the universe itself.

2. The Conflict:

a)   Incompatibility at Extremes: The core issue arises when we try to apply both quantum mechanics and general relativity simultaneously, especially in extreme conditions, like inside black holes or during the Big Bang. Quantum mechanics works well at tiny scales, while general relativity works at cosmic scales. But when you try to combine them—such as when considering the quantum behaviour of spacetime itself—problems arise. The equations from quantum mechanics and general relativity don’t fit together neatly.

b)    Different Mathematical Frameworks: Quantum mechanics relies on probabilities and operates in a mathematical framework where time is absolute (like in classical mechanics). In contrast, general relativity treats time as part of the spacetime continuum, which can be warped by gravity. This difference makes it challenging to combine the two theories into a single coherent framework.

3. Attempts at Unification:

a)  Quantum Field Theory (QFT):

 QFT extends quantum mechanics to include special relativity. It describes particles as excitations in underlying fields and works well for three of the four fundamental forces: electromagnetism, and the weak and strong nuclear forces. But QFT doesn’t include gravity.

b)  Quantum Gravity and String Theory: 

Many physicists believe that a theory of quantum gravity would reconcile quantum mechanics with general relativity. One of the leading candidates for this is String Theory, which proposes that all particles are not point-like but rather tiny vibrating strings. String Theory suggests that gravity and quantum mechanics could be unified in a single framework. However, this theory is still very much under development, with many aspects unproven and highly speculative.

c)   Loop Quantum Gravity: 

Another approach to quantum gravity is Loop Quantum Gravity (LQG), which tries to quantize spacetime itself. Unlike string theory, LQG doesn’t require extra dimensions and focuses on the quantum properties of spacetime.

4. Experimental Evidence:

So far, general relativity has been tested and confirmed at large scales, like the bending of light around stars or the detection of gravitational waves. Quantum mechanics has been confirmed in countless experiments at microscopic scales. But testing them together, in situations where both would be important (like near a black hole’s singularity), is extremely difficult with current technology.

5. The Quest for a Unified Theory:

The holy grail of modern physics is to find a Theory of Everything (ToE) that unifies quantum mechanics and general relativity into a single, all-encompassing framework. This would provide a deeper understanding of the universe, from the smallest particles to the largest galaxies.

To summarize, while quantum mechanics and Einstein’s theory of relativity describe different aspects of the universe, physicists believe that they are part of a deeper, unified theory. The challenge lies in bridging the gap between the quantum world’s uncertainties and the smooth, continuous fabric of spacetime described by relativity. This ongoing effort is at the cutting edge of theoretical physics and solving it could revolutionize our understanding of the universe.

I may write about dark matter and dark energy in the Universe later, an area in astronomy that has been troubling my brother-in -law for years that is completely unrelated to whatever I wrote

I hope the above is simple enough not just for my brother-in-law to understand, but for everybody