Quantum Mechanics: A Breakthrough Beyond Classical Physics
Abstract — This article looks into the theories of Quantum Mechanics. When classical notions of space and time dissolve, Quantum Mechanics was born, marking the departure from Newtonian (Classical) Physics. Great minds of renowned scientist (Einstein, Bohr, Heisenberg, Planck, Hawking and many more) challenges the conventional understanding of reality. They attempt to model a new reality whilst facing the paradoxes inherent in Quantum Mechanics. As such, we are confronted with the following questions: What lies at the heart of Quantum reality? How do we reconcile the quantum and classical worlds?
I. Introduction
Welcome to the very first part of my Quantum Physics series. What began as a curiosity for Physics during my A level years transformed into a researching hobby following my viewing of the film Interstellar and Oppenheimer. I started to read more about the subject through various Youtube videos by WIRED and BIG THINK — Dr. Michio Kaku, Dr Brain Greene and Dr Brain Cox explained complex, mind-boggling concepts with such simplicity. After which, I read the book A Brief History of Time by Stephen Hawking where he linked all the concepts mentioned in this article all together. It definitely inspired me to write this article.
Scientists describe the universe in two partial theories — the general theory of relativity and quantum mechanics. The general theory of relativity describes the force of gravity and the large-scale structure of the universe while quantum mechanics deals on extremely small scales. Both theories are inconsistent with each other, and they both cannot be correct.
My article is made out of the following sections. These are:
1) Time and Relativity
2) The Uncertainty Principle and Wave Particle Duality
3) Particle Physics and Fundamental Forces
II. Time and relativity
Newtonian Physics believed in absolute time. For instance, one could measure the interval of time between two events and its value would be equal whoever measured it. Time was completely separate from and independent of space. This may work when dealing with classical mechanics in our everyday life, but it does not apply for objects moving near or at the speed of light. This does not apply to the theory of relativity.
When Maxwell unified the partial theories on electrical and magnetic forces, Maxwell’s equations predicted that there could be a wave-like disturbances in the combined electromagnetic field and these would travel a fixed speed. Therefore, Maxwell predicted that electromagnetic radiation (classified by wavelength) should travel at a certain fixed speed (299792458 m/s), also known as the speed of light. The fundamental postulate of the theory of relativity was that the laws of science should be the same for all freely moving observers, no matter what their speed was. This is true for Newton’s classical laws of motion, but the idea was extended to Maxwell’s theory and the speed of light. This gave birth the Einstein’s famous E = mc² equation where it states that nothing may travel faster than the speed of light. The energy which an object has due to its motion will add to its mass, making it harder to increase its speed (only significant for objects travelling close to the speed of light). As an object approaches the speed of light, its mass rises ever more quickly, so it takes more and more energy to speed it up further. It can never reach the speed of light as its mass would have become infinite which indicates that we need to have an infinite amount of energy. In the theory of relativity, we have the abandon our Newton’s idea on absolute time, rather time is dependent on an observer’s frame of reference. This is illustrated using the fundamental light clock experiment.
Light Clock Experiment: A Layman Explanation
Imagine you have a really special clock. Instead of hands or digits, it has a beam of light bouncing between two mirrors, like a ping-pong ball bouncing between two paddles. Each time the light hits one mirror, it marks one “tick” of time. Now, let’s say you’re holding this light clock, and you’re just standing still. From your perspective, the light bounces straight up and down, and each bounce takes the same amount of time. So, time seems to be ticking away at a regular pace. However, let’s imagine you’re moving really fast (i.e zooming through space in a spaceship close to the speed of light. When you look at the light clock from inside the spaceship, something strange happens. Because you’re moving so fast, the light has to travel a little bit of extra distance to reach the top mirror each time it bounces. It’s like trying to bounce that ping-pong ball between paddles while you’re moving forward; it takes a bit longer for the ball to make its journey.
Even though the light is still bouncing at the same speed, because it’s covering a longer distance each time, it seems like it’s taking more time for each bounce. So, from your perspective inside the fast-moving spaceship, time actually seems to be passing a bit slower compared to someone who’s standing still and watching you zoom by.
That’s the essence of the light clock experiment. It shows us that how we perceive time depends on our motion. It’s like time itself is a little flexible and can stretch or shrink depending on how we’re moving relative to each other.
General relativity also explores the concept of time dilation. Remember that scene in Interstellar when the astronauts landed on Miller’s planet, situated near a black hole? Every hour spent there equated to seven years passing on Earth.
This phenomenon is explained by the concept of time dilation. General relativity states that time should appear to run slower near a massive body like the earth. This is because there is a relation between the energy of light and its frequency. As light travels upward in the earth’s gravitational field, it loses energy and its frequency decreases. This is best explained by the Twin Paradox experiment.
Twin Paradox: A Layman Explanation
Imagine you have two identical twins, Alice and Bob. Now, Alice decides to stay on Earth while Bob embarks on a journey through space in a spaceship travelling close to the speed of light.
According to the theory of special relativity, when Bob travels close to the speed of light, time for him will pass slower compared to Alice’s time back on Earth. This effect is called time dilation. So, from Bob’s perspective, time on his spaceship seems to be passing normally, but when he returns to Earth, he finds that much more time has passed for Alice.
Now, here’s where the paradox comes in: if time is passing slower for Bob, shouldn’t he be younger than Alice when he returns? Shouldn’t he have experienced less time? The paradox arises because from Bob’s perspective, he could consider himself stationary and see Alice moving away from him and then back again. So, according to his view, shouldn’t Alice be the one aging less? The resolution to this paradox lies in the fact that Bob accelerates and changes direction during his journey, while Alice remains stationary on Earth. Acceleration breaks the symmetry between their frames of reference, and it’s this acceleration that ultimately resolves the paradox. When Bob accelerates and changes direction, he experiences a different reference frame, which means he’s not strictly in the same inertial frame for the entire journey. Therefore, it’s Bob who ages less when he returns to Earth, not Alice.
In the theory of relativity, there is no unique absolute time, but instead each individual has his own personal measure of time that depends on where he is and how he is moving. We must accept that time is not completely separate from and independent of space but is combined with it to form an object called space-time. Space and time are now dynamic quantities where it affects the way in which bodies move and forces act.
III. The Uncertainty Principle and Wave Particle Duality
Newton’s theory of gravity led us to believe that the universe was deterministic where a set of scientific laws enable us to predict everything that would happen in the universe if we knew the complete state of the universe at one time (i.e their position and their speeds). If that is the case, a hot object will give off electromagnetic waves equally at all frequencies and since the number of waves is unlimited, this would mean that the total energy radiated would be infinite. This is obviously impossible. Therefore, Max Planck came about to suggest that electromagnetic waves could not be emitted at an arbitrary rate, but only in certain packets that is known as quanta. Each quantum had a certain amount of energy that was greater the higher the frequency of the waves, so at high enough frequency the emission of a single quantum would require more energy than was available. Thus, the radiation at high frequencies would be reduced and so the rate at which the body losses energy would be finite.
It’s implication for determinism is finalized by Werner Heisenberg and his uncertainty principle. It basically states that in order to predict the future position and velocity of a particle, one has to be able to measure its present position and velocity accurately. There is a limit to how precisely we can know the certain pairs of physical properties of a particle, simultaneously.
The Uncertainty Principle: A Layman Explanation
Imagine you’re trying to measure the position and velocity of a moving car. You decide to measure the car’s position by shining a flashlight on it. However, when you do this, the light from the flashlight changes the car’s velocity because it bounces off the car and gives it a tiny push. So, the act of measuring the car’s position affects its velocity. Now, let’s say you want to measure the car’s velocity more accurately. You decide to use a radar gun to measure its speed. However, the radar gun uses electromagnetic waves, which also interact with the car and affect its position. So, in trying to measure the car’s velocity more precisely, you end up affecting its position.
This scenario illustrates the essence of Heisenberg’s Uncertainty Principle: the act of measuring one property of a particle (like position or momentum) disturbs the other property. In other words, the more accurately we measure one property, the less accurately we can measure the other. This isn’t due to limitations in our measurement tools but is an inherent feature of the quantum world.
So, in the quantum realm, we can never simultaneously know both the exact position and exact momentum of a particle. There’s always a trade-off between the precision of our measurements. Particles no longer have separate, well-defined positions and velocities that could not be observed. Quantum Mechanics tells us that an observation does not produce a single definite result. Instead, they have a quantum state which is a combination of position and velocity.
Although light is made out of waves, Planck’s quantum hypothesis tells us that in some ways it behaves as if it were composed of particles where it can be emitted or absorbed only in quanta packets. At the same time, the uncertainty principle implies that particles behave like waves where we do not have a. definite position but spread out with certain probability. For some purposes it is helpful to think as particles as waves and for other purposes, it is more helpful to think as waves as particles.
It has been proven to exhibit both particle-like and wave-like behavior through various experiments in the field of physics. One notable experiment demonstrating light’s particle nature is the photoelectric effects. In this experiment, light shining on a metal surface causes the ejection of electrons, similar to how particles collide and transfer momentum. This phenomenon can be explained by treating light as a stream of particles called photons.
Conversely, the wave nature of light is exemplified by the double-slit experiment. When a beam of light passes through two closely spaced slits, it creates an interference pattern on a screen behind the slits, indicating the characteristic behavior of waves. These experiments, along with others like the Compton effect and diffraction patterns, provide compelling evidence for the dual nature of light, which manifests as both particles (photons) and waves in different experimental contexts.
Wave Particle Duality: A Layman Explanation
Imagine you’re watching a basketball game. At times, you see the players dribbling the ball and passing it around like discrete, individual particles — they behave like basketballs. This is akin to the particle-like behavior of matter, where particles have definite positions and can interact with each other as distinct entities. However, at other moments, you notice ripples forming on the surface of a pond when a player takes a shot. These ripples spread out and interfere with each other, creating patterns like waves. This wave-like behavior is similar to how particles, such as electrons, exhibit interference patterns when they pass through a double-slit experiment.
So, just as a basketball player can exhibit both particle-like behavior when dribbling and wave-like behavior when shooting, particles in the quantum realm can display both particle-like and wave-like characteristics depending on the experimental setup.
By observing the interference between particles, we are able to better understand the structure of atoms. During my A-levels, I was taught that electrons orbit the nucleus just like how planets orbit around the sun where the attraction between their electrical charges prevent the electrons from spiraling inwards and colliding with the nucleus. Wrong! This assumes that the electrons do not lose energy. If it does, it would rapidly collapse to a state of high density (just like how a star collapse into a black hole). Niels Bohr suggested that electrons do not just orbit about the nucleus at any distance, but at a specified distance.
Moreover, electrons orbit around the nucleus as a wave where its wavelength depends on its velocity. Electrons are described by wave functions that represent the probability of finding the electron in a particular position around the nucleus. These wave functions have characteristic shapes, often resembling standing waves, which represent the allowed energy levels or orbitals in which the electron can exist. These orbitals represent regions of space where the probability of finding the electron is highest. The shapes and orientations of these orbitals are determined by the quantum numbers that describe the energy, angular momentum, and orientation of the electron within the atom. When an electron occupies an orbital, it behaves as a standing wave, with certain wavelengths and frequencies that are determined by the boundaries and shape of the orbital. The electron does not orbit the nucleus in a classical sense but rather exists in a superposition of states within its orbital, exhibiting both particle-like and wave-like behavior simultaneously.
Richard Feynman explains wave-particle duality using the following concept. The particle is not supposed to have a single path in space-time, instead, it is supposed to go by every possible path where each path is associated probability — it contains the size of the wave and position in the cycle. Its probabilities are the waves summed together. This can then be scaled up to more complicated atoms. Thus, quantum mechanics allows us in principle to predict everything we see around us, within the limits of the uncertainty principle.
IV: Particle Physics and Fundamental Forces
In high school, we learned that the protons and neutrons were our elementary particles. Wrong again! Experiments using the collision of protons and neutrons at high speeds indicate that these protons and neutrons are made out of even smaller particles. They are called quarks which are also classified as fermions, a type of particle with half-integer values of spin.
There are six types of quarks, known as flavors, which are named up, down, charm, strange, top, and bottom. Each quark has a corresponding antiparticle, known as an antiquark, with opposite electric charge and other quantum numbers. Quarks are never found in isolation due to a property called color confinement. This means that quarks are always bounded together in groups of two or three to form composite particles called hadrons. Protons and neutrons, for example, are made up of three quarks each. Thus, we can create particles made up of other quarks.
Using wave-particle duality, light and gravity can be described in terms of particles and these particles have a property called spin. Spin refers to an intrinsic property of particles that is somewhat analogous to the spinning of a classical object like a top. However, it’s important to note that spin is a purely quantum mechanical property and doesn’t correspond to actual spinning motion in the classical sense. Furthermore, all these particles obey the Pauli’s Exclusion Principle. It states that no two identical fermions can occupy the same quantum state simultaneously within the limits given by the uncertainty principle. It explains to us why matter particles do not collapse to a state of very high density under the influence of the forces produced by particles with different spins. If the matter particles have very nearly the same positions, they must have different velocities.
The Pauli’s Exclusion Principle: A Layman Explanation
Imagine a room with seats for only two people. Pauli’s exclusion principle would mean that if two people are already sitting in those seats, another person cannot occupy the same seats at the same time. This principle applies to fundamental particles like electrons, which are fermions. Since electrons are identical particles, they cannot occupy the same energy level and spin state within an atom.
Pauli’s Exclusion Principle tells us the existence of an anti-particle and highlights the fundamental forces of our universe. When physicists were exploring the properties of particles and their interactions, they found that certain processes, such as electron-positron annihilation, violated conservation laws if only particles were involved. This led to the proposal of antiparticles as a way to conserve various properties, including electric charge and other quantum numbers. Antiparticles are particles that have the same mass as their corresponding particles but opposite electric charge and other quantum numbers.
For example, the antiparticle of the electron, called the positron, has the same mass as the electron but a positive electric charge. In terms of quantum numbers, the positron has opposite values compared to the electron. When an electron and a positron meet, they can annihilate each other, and their mass is converted into energy in accordance with Einstein’s E = mc² equation. In theory, there could be anti-worlds and anti-people made out of anti-particles.
Secondly, forces between matter particles are often described in terms of the exchange of force-carrying particles, which mediate the interaction between the matter particles. This framework is based on quantum field theory and helps explain how forces arise between particles.
For example, in the electromagnetic interaction between two charged particles, such as electrons, the force between them is mediated by the exchange of photons. When one electron emits a photon, it experiences a recoil due to conservation of momentum. This change in velocity of the emitting electron is akin to the emission of a force. The emitted photon then interacts with another charged particle, transferring momentum and potentially changing the velocity of that particle upon absorption. Similarly, in the strong nuclear force between quarks, the force is mediated by the exchange of gluons. When a quark emits a gluon, it experiences a recoil, and the exchanged gluon may interact with another quark, leading to a change in its velocity upon absorption. Thus. real particles can be emitted when matter particles interact with each other by exchanging virtual force-carrying particles.
Essentially, these force-carrying particles can be grouped into four fundamental forces of our universe according to the strength of the force they carry and the particles in which they interact with. They are the following:
- Gravity: As mentioned above, gravity is the force responsible for the attraction between massive objects. It operates on large scales, such as between planets and stars. Real gravitons produce a hypothetical particle called the graviton. Just as photons are the force-carrying particles of the electromagnetic force, and gluons are the force-carrying particles of the strong nuclear force, gravitons are proposed to be the force-carrying particles of gravity. Gravitons are predicted to mediate the interactions between massive objects and generate gravitational waves as they propagate through spacetime.
- Electromagnetism: Electromagnetism is the force responsible for the interaction between electrically charged particles. Real photons are the force-carrying particles of the electromagnetic force. When charged particles interact, they exchange photons, which mediate the electromagnetic interaction. Photons propagate through space and carry electromagnetic energy, enabling phenomena such as light, electricity, and magnetism.
- Strong Nuclear Force: The strong nuclear force is the force that binds quarks together inside protons and neutrons and holds atomic nuclei together. Real gluons are the force-carrying particles of the strong nuclear force. Gluons mediate the interactions between quarks, exchanging gluons between them. This exchange of gluons generates the strong force that binds quarks together, confining them within particles like protons and neutrons.
- Weak Nuclear Force: The weak nuclear force is responsible for certain types of radioactive decay and interactions involving neutrinos. Real W and Z bosons are the force-carrying particles of the weak nuclear force. These bosons mediate the interactions between particles involved in weak nuclear processes, such as beta decay. The exchange of W and Z bosons leads to the transformation of one type of particle into another, changing the identity and properties of the particles involved.
These four fundamental forces govern our universe. The goal of physicist is to unify these four forces together to find the “God” equation that can explain our universe.
The Weinberg-Salam theory, attempts to unify electromagnetism and weak nuclear force. The key idea behind the Weinberg-Salam theory is the concept of gauge symmetry breaking, which describes how certain symmetries of the fundamental forces are hidden or “broken” at low energies, resulting in the appearance of distinct forces at different energy scales. In the case of the electroweak theory, electromagnetism and the weak nuclear force are unified at high energies, but at lower energies, they manifest as separate and distinct forces.
Weinberg-Salam Theory: A Layman Explanation
Stephen Hawking describes this using an analogy of roulette:
“At high energies (when the wheel is spun quicky) the ball behaves in essentially only one way — it rolls round and round. But as the wheel slows, the energy of the ball decreases and eventually the ball drops into one of the thirty-seven slots in the wheel. In other words, at low energies there are thirty-seven different states in which the ball can exist. If for some reason, we could only observe the ball at low energies, we would then think that there were thirty-seven different types of balls”
Specifically, the Weinberg-Salam theory introduces a new set of force-carrying particles called the W and Z bosons, which mediate the weak nuclear force. These bosons interact with particles involved in weak nuclear processes, such as beta decay. At high energies, the electromagnetic and weak forces are unified into a single “electroweak” force, described by a unified gauge symmetry.
Other theories also attempt to unify the fundamental forces. In the context of the strong nuclear force, Grand Unified Theories (GUTs) seek to unify it with the other forces of nature at high energies. The strong nuclear force is responsible for binding quarks together inside protons and neutrons, as well as holding atomic nuclei together. It is described by the theory of quantum chromodynamics, which involves the exchange of force-carrying particles called gluons between quarks.
GUTs propose that at extremely high energies — much higher than those accessible in current particle accelerators — the strong nuclear force, along with the weak nuclear force and electromagnetism, become indistinguishable from each other and are described by a single unified gauge symmetry. This unified force is thought to have existed in the early universe, shortly after the Big Bang, when temperatures and energies were much higher than they are today. The process by which the unified force separates into the distinct forces we observe today is called symmetry breaking. This symmetry breaking occurs as the universe expands and cools, leading to the distinct forces and interactions we observe at low energies.
In Particle Physics, we believe that the laws of physics each of three symmetries known as charge conjugation (C), parity (P), and time reversal (T). These symmetries play a fundamental role in our understanding of the behavior of particles and the interactions between them.
Charge conjugation involves flipping the electric charge of particles to their corresponding antiparticles, ensuring the conservation of certain quantum numbers such as electric charge. Parity symmetry reflects physical systems like mirror images, ensuring that processes look the same when left and right are interchanged. Time reversal symmetry reverses the direction of time, implying that physical processes should be reversible when played backward.
Why is this important? It is because these symmetries are linked to conservation laws, where charge conjugation symmetry implies the conservation of certain quantum numbers, such as electric charge, across particle-antiparticle interactions. Moreover, they offer insights into the fundamental forces and interactions between particles, explaining the rules governing particle behavior and the properties of the forces mediating these interactions. Furthermore, the observation of violations or confirmations of C, P, and T symmetries allows physicists to test the predictions of theoretical models, such as the Standard Model, and explore the presence of new physics beyond current frameworks.
Current experimental evidence supports the individual descriptions of the strong nuclear force, weak nuclear force, and electromagnetism provided by the Standard Model of particle physics. GUTs despite being an elegant theory, they have yet to be experimentally confirmed. GUTs also neglect the force of gravity as physicists believe that gravity is such a weak force when dealing with elementary particles. However, as gravity is always attractive no matter the range, its effects will add up. For a sufficiently large number of matter particles, it may dominate over all other forces. This will be explained through the quantum theory of gravity, notably in black holes.
V: Final Thoughts
In this article, I provided a theoretical introduction to quantum mechanics, contrasting its principles with those of classical Newtonian physics. Through this exploration, I had shed light on the fundamental differences between these two paradigms, highlighting concepts such as the uncertainty principle and wave-particle duality that challenge our traditional understanding of the physical world. These foundations intuitively lead to the concepts of particle physics, where physicists constructed models that capture the complexities of our universe. However, despite our best efforts, I hold the belief that our understanding remains limited. While models serve as invaluable tools for organizing and articulating our comprehension, they fall short of encapsulating reality and the origins of the universe. Thus, while we may strive to model and understand the universe, we are faced with the overwhelming number of assumptions and paradoxes which are limited by our human perception.
References
[1] A Brief History of Time — Stephen Hawking
