Series: Quantum Mechanics
November 13, 2024
Quantum Field Theory
Glossary
- Particles arise because their corresponding fields become "excited," - the quantum field raise its energy from its lowest (vacuum state) to a higher level (excited state). This leveling up of enegy 'excites' the field and yields a particle.
e.g. When the electromagnetic field raised its energy level, it reached 'excited' state and produced an electromagnetic particle, the photon...or light. - Gravity is Quantized - this means that the gravitational field yielded the graviton particle and can now be described by quantum mechanics at the smallest scales - whereas before, only General Relativity could describe Gravity. This implies that the Graviton Particle was discovered and now, Gravity can be described like all the other 3 forces in the Quantum Field Theory.
e.g. Gravity is now quantized with the discovery of the Graviton Particle. - Mediating - in Quantum Field Theory, this means "a particle carrying the force".
e.g. Graviton (the particle) is mediating Gravity (the force/energy) - Quantum (singular, plural is quanta) - the smallest discrete unit of a physical property, such as a particle. All particles are essentially quanta, but not all quanta are particles. But to simplify and avoid confusion, think of quantum as particles.
e.g. Photon is the quantum (particle) of electromagnetic radiation (quantum field), and a graviton (particle) is the hypothesized quantum of the gravitational field (quantum field). - Discrete - in Physics, it means "pixelated", made up of finite indivisible units with nothing in between. It’s the opposite of continuous, which describes something uninterrupted that can be divided infinitely. Discrete quantities are important because numbers are mathematically manageable and prevent infinities like singularities in a black hole. Also, a discrete system makes General Relativity compatible with Quantum Field Theory.
e.g. Waves are discreet packets of energy in Quantum Wave Theory.
TERMS / Specs:
- Planck length - 1.6 X 10-35 meters (1.6 is the multiplier that gives a precise numerical value to the scale, 10-35. It's like saying the distance from here to there is around 100 km, but the precise distance is actually 116 km)
- Planck energy - 1.22 X 1019 GeV
- Planck time - 5.4 X 10-44 seconds
Podcast
As I was watching a podcast between Sir Roger Penrose and Federico Faggin about Quantum Physics and consciousness, a few words were bounced around - quantum field, wave function collapse, Special Relativity and quantum gravity. I have a vague sense of what they are, but to pin them down? I had to ask AI and embark on a new learning curve about the quantum realm.
understanding the Double Slit Experiment is to understand Quantum Mechanics
Quantum Field Theory (Quantum Field Theory)
Quantum Field Theory is a theoretical framework combining Quantum Mechanics (reality at the sub-atomic level) with Special Relativity (electromagnetism, strong and weak nuclear force - gravity is not included). Quantum Field Theory successfully predicts the behavior of the fundamental forces (electromagnetism, strong/weak nuclear force) through its interaction with the Field - this is the cornerstone of the Standard Model of Particle Physics. In contrast, the Classical Field Theory (Classical Field Theory (Einstein)) describes forces, but does not produce particles, e.g. electromagnetic field when excited does not produce an electromagnetic particle. In Quantum Field Theory, particles arise because the Fields get excited. The Math holds up when dealing with electromagnetism and strong/weak nuclear force. But when gravity is introduced into Quantum Field Theory, anomalies and inconsistencies happen.
When gravity is treated under the Quantum Field Theory principle (as a force that produces a Graviton particle when the gravity field gets excited), the results produce an infinite number of infinities - the Math simply doesn't hold up - thus, to make the Standard Model work, gravity has to be excluded.
Special relativity
Special relativity is General Relativity without gravity (Special Relativity = General Relativity - gravity). Gravity is omitted because without gravity, the Standard Model is precise, predictable, and reliable. Once you throw gravity into the fray, the whole thing implodes. General Relativity (which includes gravity) was formulated by Einstein describing the behavior of space/time especially as they move at high speeds approximating the speed of light. Space and time are not separate but a singularity composed of 3 dimensions for space and 1 for time. Special Relativity gave rise to Time Dilation and E=MC2.
Gravity: The Rogue Particle
In General Relativity, gravity is not a particle but a result of mass/energy bending space/time (not as a particle caused by the gravitational field getting excited as per Quantum Field Theory). Another incompatibility is that in Quantum Field Theory, interactions are probabilistic (you don't know exactly the position and momentum of the particle until the Field gets excited and manifests the particle) while in General Relativity, interactions are deterministic (outcomes are computational and predictable). Quantum Field Theory only works with Special Relativity (without gravity), not with General Relativity (includes gravity). This is a fundamental problem in Theoretical Physics known as Quantum Gravity. If gravity is put in the Quantum Field Theory equation, issues come up basically because Quantum Field Theory and General Relativity have fundamental differences (Quantum Field Theory is probabilistic vs General Relativity being precisely predictable):
Environments where General Relativity is incompatible with Quantum Field Theory:
- Higher energies - Quantum Field Theory deals with energies far higher than energies we interact with in daily life. Some examples of high energy are the Large Hadron Collider (Large Hadron Collider doesn't have enough energy to detect a Graviton. Energies close to the Planck Energy are needed to produce a Graviton), cosmic rays (high energy particles from outer space), nuclear fusion in the sun, and Planck Energy (the highest theoretical scale in physics). These high energies are enough to probe deep into fundamental particles. The Higgs Bozon was discovered using the high energy released by the Large Hadron Collider.
- Small scales - Quantum Field Theory deals with the very small world like Planck Scale.
General Relativity and Quantum Field Theory Incompatibilities
1. Renormalizability
A Planck Scale is high in energy and infinitiesimally small. Infinites in a mathematical equation are essentially errors. In Quantum Field Theory, infinities happen, but they can be renormalized by tweaking the charge and mass of the particle to come up with finite predictions. But with General Relativity at these small scales, the number of infinities are infinite making the whole equation non-sensible - thus, Quantum Field Theory is not a compatible framework with General Relativity to come up with anything meaningful. The infinities resulting from Gravity at the small scale is not renormalizable.
2. Extreme Warping of Space/Time
At Planck's scale (where energies are high at a very small scale), Gravity (the curvature of space/time) is amplified so much that space/time curves extremely that the smooth/continuous Field background of Quantum Field Theory no longer holds - so everything collapses.
3. Singularities and Black Holes
In high energies, energy can be concentrated on a small region creating a mini black hole with a singularity having infinite density and gravity that it warps space/time to nullify the smooth/continuous background of Quantum Field Theory. This produces mathematical inconsistencies (non-renormalization of gravity) and physical paradoxes (black hole losing information, time being a fixed background in Quantum Field Theory but an intrinsic part of space/time in General Relativity, black hole having an infinite density in General Relativity but it warps space/time that Quantum Field Theory no longer operates) that collapse the equation. This doesn't necessarily mean the theory is wrong but it is incomplete - thus the proposal of alternate "Theories of Everything" like String Theory, Loop Quantum Gravity (quantizing space/time to harmonize Quantum Field Theory with General Relativity), and the Holographic Universe Model.
Quantum Gravity Theory
Because of the incompatibility between Quantum Field Theory and General Relativity, scientists have been searching for a theory that can include General Relativity (at higher energies and small scale) into Quantum Mechanics without any mathematical anomaly. Solving this anomaly is a big step toward the "Theory of Everything" - putting all the forces of nature in an elegant mathematical equation. There are several propositions:
- String theory - this suggests that you can go infinitiesimally smaller than the particle until you see its building blocks - vibrational energies resembling strings. How these strings vibrate causes particles to manifest - including gravity. For this to work, you have to deal with 11 dimensions - not just 4. Also, this cannot be experimented on. Also, it's been 40 years since the proponents have been working on this with nothing to show for.
- Loop quantum gravity (Loop Quantum Gravity) - this approach quantizes space/time into irreducible 'pixels' at the Planck's Scale (General Relativity treats space/time as smooth continuous fabric of the universe [not just a background] that is deterministic - you can compute distance and volume at any scale). Therefore, space/time is no longer an infinite continuous fractal but 'pixilated' (quantized and no longer divisible, just probabilities) in Loop Quantum Gravity. In String Theory, space/time is still fluid and continuous, but an emergent from tiny strings at a much smaller scale. But for now, this is still a hypothesis and not fact. There is no instrumentation currently to probe at Planck's Distance (1.6 X 10-35 meters) and Plank Time (5.4 X 10-44) seconds, so we don't know.
This has serious ramifications. If space/time is quantized, then it's computational. If it's computational, then it's programable. If it's programable, then perhaps this reality including us is just a program - a simulation, giving rise to the Simulation Hypothesis. - Black holes - black holes have an intensified gravity not explained by classical physics. Studying the nature of black holes might give an insight on quantum gravity.
Quantum Wave (Wave function)
Quantum Wave describes individual particles. It predicts where a particle might be and how it is behaving - it doesn't tell you exactly where it is nor its momentum (thus Quantum Field Theory is probabilistic). Particles have 2 features - wave-like properties or mass-like properties. Particles behave like waves but when they are observed or measured (like in the double slit experiment), the wave 'collapses' to a specific position of the particle (meaning they turn into a mass from being a wave).
What happens if the Graviton Particle is discovered?
The Graviton Particle is the Holy grail. This has been predicted but never produced. It takes high energy close to the plank energy to detect it (orders of magnitude greater than the Large Hadron Collider), if it can be produced. So far, its existence is only in theory. But when discovered, it is a game changer. If the Graviton Particle is produced by a super powerful particle accelerator, then Quantum Field Theory is validated - that gravity is a field giving rise to a particle. Does it mean that General Relativity is wrong? Does it mean that gravity is not caused by the warping of space/time (as per General Relativity)? Well, not exactly. This means that the warping of space/time is still real, but it is now caused by countless gravitons interacting with each other at the quantum level. In short, the warping of space/time (a feature of General Relativity), is an emergent phenomenon with Quantum Field Theory as an underlying principle. This means that gravity can now be explained complementarily by General Relativity and Quantum Field Theory - there is no more any contradiction. This means that General Relativity and Quantum Field Theory fall under a much bigger framework - that again would be the "Theory of Everything".
Quantum Field (QF)
QF is more pervasive because we are talking about the entirety of space (unlike wave function that only describes one particle). While QF is pervasive across space, there is a Field for each Particle Type - a proton field when excited, gives rise to a proton particle. Each Field gives rise to its particular particle e.g. the proton field, when excited, manifests the proton particle. This proton particle is the building block of reality as we see it. The Field is an energy that permeates all of reality including empty space. QF can create and destroy particles (eg photons are created and destroyed when they interact with other charged particles). In Quantum Field Theory, the Field is primary and the basic element - not the particles. Particles are just the excited state of the field - quanta.
Quantum Field (QF) vs Hilbert Space
On the surface, they both seem synoninous. Particles reside in a quantum field and a particle emerges when that part of the quantum field gets excited. Quantum Field is a space. Hilbert Space is a mathematical space describing all possible states of all particles within that quantum field. So it doesn't sound like a space but a calculation of what all probabilities lie within - it's like calculating all the possible moves in a chess game. While the chess pieces and the chess board are all contained in the Quantum Field.
If the Graviton is detected, General Relativity merges with Quantum Field Theory. Does that solve the "Theory of Everything"?
NO. Discovery of the Graviton is a monumental breakthrough. It puts gravity in the Standard Model of Particle Physics, but there are still incompatibilities between General Relativity and Quantum Field Theory at high energies (black holes and big bang) and small scale (Planck Scale).
- Space/Time - this is a sticking point and needs to be redefined between the 2 theories - Quantum Field Theory treats space/time as a fixed background while General Relativity treats space/time as a smooth continuous fabric.
- Unification with other forces - the discovery of Graviton still requires a unifying theoretical framework for gravity, electromagnetism and strong/weak nuclear force as aspects of the same fundamental interaction. There is no such framework yet. String Theory hopes to achieve this by suggesting gravity is an emergent phenomenon of an underlying fundamental substrate - a band of energy shaped like a string.
- Non-renormalization - the discovery of Graviton does not resolve the non-renormalization of gravity - it still produces an infinite number of infinities when factored into Quantum Field Theory.
- Dark Matter and Dark Energy - the Standard Model accounts for elementary particles and fundamental forces, but it cannot explain 95% of the known universe which is Dark Matter (gravitational force keeping the galaxies from spinning away) and Dark Energy (force accelerating the expansion of the universe). Dark Matter and Dark Energy do not interact with anything we know of. We cannot detect it, we cannot measure it. We just know 'there's something out there that accounts for these anomalies'.
- Wave function collapse - the discovery of Graviton does not account for the collapse of the wave function (when the field collapses into a particle). Physicists simply accept that as a fact but were never able to explain why.
- Experimentable and Producing predictions - the mathematical equation should be consistent for all forces and particles (no infinities). They should be experimentable producing what it predicted. But String Theory is not experimentable and hasn't produced any of its predictions (11 dimensions, supersymmetry, microscopic black holes, multiverse).
Properties of a Particle
Quantum objects remain quantized until measured, then the wave function collapses and the object becomes localized. But what are the ways to measure a quantum object?
- Momentum - this is the speed of the particle measured by Mass X Velocity. Because of the Complementarity principle, you cannot measure momentum and location at the same time. Momentum and location define how particles exist and move in space.
- Location - this is the location of a particle in space (in Quantum Field Theory, this is the location of the particle in its quantum field). A particle's location is not well defined until it is measured. Its location is probabilistic (it's like flipping a coin...you don't know if it's head or tails until it lands) and described by its wave function. Measuring the particle collapses the wave function and the particle's location can now be determined. Knowing a particle's location means you cannot know its momentum - the two properties are complementary. Momentum and location define how particles exist and move in space - but they cannot both be measured simultaneously.
Does it also mean that the particle exists in all its possible locations at the same time (superposition)? Existing in all possible location at the same time (until measured) - this has no classical analog. There is no comparative equivalent of this state in the classical physical world. A few popular interpretations are offered to explain this weird behavior of Quantum Mechanics: Copenhagen Interpretation (it simply says the location of a particle exists but it's not known where until it is measured. NOTE that Superposition explains location differently - that a particle's location exists in all possible places at one time until measured). Another interpretation is the Many Worlds Interpretation (this says the particles exist in all parallel universes at the same time). - Spin - this is the angular momentum of the particle. This has nothing to do with 'spin'. This has no counterpart in the real world. Spin is quantized and can take discreet values. e.g. Fermions (particles mediating mass) like electrons, protons and neutrons have a spin value of 1/2. However, bozon (particles carrying energy) like photons, have a spin of 1.
- Charge - this is the electric charge of a particle which determines how it interacts with electromagnetic fields. e.g. electrons have a negative charge, protons have a positive charge and neutrons have no charge. A particle's charge determines how it interacts with other particles and other fields.
Particle Location: Quantum Mechanics vs Quantum Field Theory
Although both disciplines are parallel and overlap, they still have minor differences. Where is a particle located? Both give nuanced answers.
- Quantum Mechanics - a particle exists in ordinary 3D space and its location is determined by its wave function. The wave function gives probabilities of where this particle is located in space - the particle exists at a specific point, but we don't know where. It is not known exactly where this particle is - just probabilities. When there is an observer or when it is measured, the wave function collapses and the exact location of the particle is determined because it materializes as a 3D object with mass, charge, spin and momentum.
- Quantum Field Theory - a particle is an excitation (increase of energy level from vacuum state to a higher level) of a quantum field. This quantum field spans all of 3D space. Quantum Mechanics does not consider the Quantum Field - particles materialize directly from 3D space. The location of the particle in the quantum field is superpositioned (existing in all possible locations within its quantum field). When measured, the quantum wave function collapses causing an excitation of an area in the quantum field where the particle appears. This excitation localizes the particle in 3D space/time. Note that only part of the field gets excited to produce a particle - it's not the entire field. This means that one field can have multiple particles within it, all in superposition.
e.g. when an electron field gets excited, the electron particle appears. When an electromagnetic field is excited, photon (light) is visible.
When the Wave Function Collapses, does it always manifest a particle?
It depends on what you are measuring. If you are measuring the location, then a particle appears. If you are measuring energy, then an energetic state appears. If you are measuring momentum, then a wave with a specific wave length apperears. If you are measuring spin, the wave function collapses into a spin orientation (spin up, spin down with values like -1/2 or +1/2)
Ending Thoughts
It took me 4 days to wrap my head around General Relativity, Quantum Field Theory, and Special Relativity. Whoa! I've asked AI more questions with every answer it gave me. I kept drilling down until I got a comfortable level of understanding. It was a deep rabbit hole and I was only at the opening. I could have gone deeper, but I have other things to do.
What's my takeaway? Well, it gave me insight on the deeper substrates of reality far beyond our human perception. Collapsing the wave function by the sheer presence of my mind gives me an idea how consciousness relates to reality. Or how reality could be architectured through consciousness. It made me wonder what lies beyond the limits of our human perception. Many things began to race in my mind. Once you ponder on them, you see reality beyond the daily grind. Reality has many layers to it. This makes me ponder on existence, purpose and life.
Devouring knowledge about anything that interests you is very rewarding - your curiosity is satiated, you find bearing, you might even find out what role you are playing in this cosmic stage, and Sperhaps you can even see a way to make it a 'call to action' for greater productivity. All this is now possible because of AI. Before AI, my questions were left unanswered or it would have taken days of research to gain that information. It was a huge stumbling block. Now, the world's knowledge base is accessible at your fingertips - there is no excuse anymore to remain ignorant. The more I learn, the more I appreciate the richness of this universe and the more I find meaning in my human existence.
--- Gigit (TheLoneRider)
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Sir Roger Penrose and Federico Faggin
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