- 2904 - PARTICLE MASS - how can math describe this? The atomic particles: electrons, photons, quarks and other “fundamental” particles supposedly lack substructure or physical extent. We basically think of a particle as a point-like object Yet particles have distinct traits, such as charge and mass. How can a dimensionless point have weight?
------------------------ 2904 - PARTICLE MASS - how can math describe this?
- Everything in the universe reduces to particles that have mass, a question presents itself: What are particles and what is mass? Think about it, everything!
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- With any other object, the object’s properties depend on its physical makeup, its constituent particles. But those particles’ properties derive not from constituents of their own but from mathematical patterns. As points of contact between mathematics and reality, particles straddle both worlds.
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- A Particle Is a ‘Collapsed Wave Function’. So what’s that?
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- The quest to understand nature’s fundamental building functions began with the ancient Greek philosopher Democritus’s assertion that such things exist.
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- Two thousands years later, Isaac Newton and Christiaan Huygens debated whether light is made of particles or waves. The discovery of quantum mechanics some 250 years after that proved both luminaries right. Light comes in individual packets of energy known as photons, which behave as both particles and waves.
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- “Wave-particle duality” turned out to be a symptom of a deep strangeness. “Quantum mechanics” revealed to its discoverers in the 1920s that photons and other quantum objects are best described not as particles or waves but by abstract “wave functions” evolving mathematical functions that indicate a particle’s ‘probability” of having various properties.
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- The wave function representing an electron is spatially spread out, so that the electron has possible locations rather than a definite one. But somehow, strangely, when you stick a detector in the scene and measure the electron’s location, its wave function suddenly “collapses” to a point, and the particle clicks at that position in the detector.
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- A “particle” is thus a “collapsed wave function“. Why does observation cause a distended mathematical function to collapse and a concrete particle to appear? And what decides the measurement’s outcome? 100 years later and physicists have no idea.
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- Ok, a particle is a ‘Quantum Excitation of a Field’. In the 1930s, physicists realized that the wave functions of many individual photons collectively behave like a single wave propagating through conjoined electric and magnetic fields, exactly like the classical picture of light discovered in the 19th century by James Clerk Maxwell.
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- These researchers found that they could “quantize” classical field theory, restricting fields so that they could only oscillate in discrete amounts known as the “quanta” of the fields. In addition to photons, the quanta of light. Paul Dirac discovered that the idea could be extrapolated to electrons and everything else: According to quantum field theory, particles are excitations of quantum fields that fill all of space.
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- In positing the existence of these more fundamental fields, “quantum field theory” stripped particles of status, characterizing them as mere bits of energy that were excited fields. Quantum field theory allows researchers to calculate with extreme precision what happens when particles interact.
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- As physicists discovered more of nature’s particles and their associated fields, a parallel perspective developed. The properties of these particles and fields appeared to follow numerical patterns. By extending these patterns, physicists were able to predict the existence of more particles.
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- Once you encode the patterns you observe into the mathematics, the mathematics is predictive; it tells you more things you might observe. The patterns also suggested a more abstract and potentially deeper perspective on what particles actually are.
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- Particles are “representations” of “symmetry groups,” which are sets of transformations that can be done to objects.
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- Take an equilateral triangle. Rotating it by 120 or 240 degrees, or reflecting it across the line from each corner to the midpoint of the opposite side, or doing nothing, all leave the triangle looking the same as before. These six symmetries form a “group“.
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- The group can be expressed as a set of mathematical matrices, arrays of numbers that, when multiplied by coordinates of an equilateral triangle, return the same coordinates. Such a set of matrices is a “representation” of the “symmetry group“.
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- Electrons, photons and other fundamental particles are objects that essentially stay the same when acted on by a certain group. Namely, particles are representations of the “Poincaré group“, which is group of 10 ways of moving around in the space-time continuum.
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- Objects can shift in three spatial directions or shift in time; they can also rotate in three directions or receive a boost in any of those directions. In 1939, the mathematical physicist Eugene Wigner identified “particles” as the simplest possible objects that can be shifted, rotated and boosted.
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- For an object to transform nicely under these “10 Poincaré transformations“, it must have a certain minimal set of properties, and particles have these properties. One is energy.
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----------------- Energy is simply the property that stays the same when the object shifts in time.
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----------------- Momentum is the property that stays the same as the object moves through space.
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---------------- A third property is needed to specify how particles change under combinations of spatial rotations and boosts (which, together, are rotations in space-time). This third property is “spin.”
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- Particles have spin, which is a kind of intrinsic angular momentum that determines many aspects of particle behavior, including whether they act like matter (as electrons do) or as a force (like photons).
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- Deep down, spin is just a label that particles have because the world has rotations.
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- Different representations of the Poincaré group are particles with different numbers of spin labels, or degrees of freedom that are affected by rotations. There are, for example, particles with three spin degrees of freedom. These particles rotate in the same way as familiar 3D objects.
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- All matter particles, meanwhile, have two spin degrees of freedom, nicknamed “spin-up” and “spin-down,” which rotate differently. If you rotate an electron by 360 degrees, its state will be inverted, just as an arrow, when moved around a “2D Möbius strip“, comes back around pointing the opposite way.
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- Elementary particles with one and five spin labels also appear in nature. Only a representation of the Poincaré group with four spin labels seems to be missing.
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- The correspondence between elementary particles and representations is so neat that some physicists equate them. Others see this as a “conflation“. The representation is not the particle; the representation is a way of describing certain properties of the particle.
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- Particles have many layers. Whether there’s a distinction or not, the relationship between “particle physics” and “group theory” grew more complicated over the course of the 20th century. The discoveries showed that elementary particles don’t just have the minimum set of labels needed to navigate space-time; they have extra, superfluous labels as well.
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- Particles with the same energy, momentum and spin behave identically under the 10 Poincaré transformations, but they can differ in other ways. For instance, they can carry different amounts of electric charge.
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- As this “ whole particle zoo” was discovered in the mid-20th century, additional distinctions between particles were revealed, necessitating new labels dubbed “color” and “flavor.”
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- Just as particles are representations of the Poincaré group, theorists came to understand that their extra properties reflect additional ways they can be transformed. But instead of shifting objects in space-time, these new transformations are more abstract; they change particles’ “internal” states.
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- Take the property known as “color“. In the 1960s, physicists ascertained that quarks, the elementary constituents of atomic nuclei, exist in a probabilistic combination of three possible states, which they nicknamed “red,” “green” and “blue.”
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- These states have nothing to do with actual color or any other perceivable property. It’s the number of labels that matters. Quarks, with their three labels, are representations of a group of transformations called SU(3) consisting of the infinitely many ways of mathematically mixing the three labels.
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- While particles with color are representations of the symmetry group SU(3), particles with the internal properties of flavor and electric charge are representations of the symmetry groups SU(2) and U(1), respectively.
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- The Standard Model of particle physics, the quantum field theory of all known elementary particles and their interactions, is often said to represent the symmetry group SU(3) × SU(2) × U(1), consisting of all combinations of the symmetry operations in the three subgroups.
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- The Standard Model reigns half a century after its development. Yet it’s an incomplete description of the universe. Crucially, it’s missing the force of gravity, which quantum field theory can’t fully handle.
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- Albert Einstein’s general theory of relativity separately describes gravity as curves in the space-time fabric. Moreover, the Standard Model’s three-part SU(3) × SU(2) × U(1) structure raises questions.
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- Particles ‘Might Be Vibrating Strings’. In the 1970s, physics tried fitting the SU(3), SU(2) and U(1) symmetries inside a single, larger group of transformations, the idea being that particles were representations of a single symmetry group at the beginning of the universe. As symmetries broke, complications set in.
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- Researchers placed even higher hopes in “string theory”. This is the idea that if you zoomed in enough on particles, you would see not points but one-dimensional vibrating strings. You would also see six extra spatial dimensions, which string theory says are curled up at every point in our familiar 4D space-time fabric.
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- The geometry of the small dimensions determines the properties of strings and thus the macroscopic world. “Internal” symmetries of particles, like the SU(3) operations that transform quarks’ color, obtain physical meaning.
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- These operations map, in the string picture, onto rotations in the small spatial dimensions, just as spin reflects rotations in the large dimensions. “Geometry gives you symmetry which gives you particles“.
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- If any strings or extra dimensions exist, they’re too small to be detected experimentally. In their absence, other ideas have blossomed. Over the past decade, two approaches in particular have attracted the brightest minds in contemporary fundamental physics.
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- A Particle Is a ‘Deformation of the Qubit Ocean’. “it-from-qubit,” expresses the hypothesis that everything in the universe; all particles, as well as the space-time fabric those particles stud like blueberries in a muffin, arises out of quantum bits of information, or qubits.
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- Qubits are “probabilistic combinations” of two states, labeled 0 and 1. Qubits can be stored in physical systems just as bits can be stored in transistors, but you can think of them more abstractly, as information itself.
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- When there are multiple qubits, their possible states can get tangled up, so that each one’s state depends on the states of all the others. Through these contingencies, a small number of entangled qubits can encode a huge amount of information.
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- In the it-from-qubit conception of the universe, if you want to understand what particles are, you first have to understand space-time. Entangled qubits might stitch together the space-time fabric.
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- Calculations, thought experiments, and toy examples going back decades suggest that space-time has “holographic” properties: It’s possible to encode all information about a region of space-time in degrees of freedom in one fewer dimension, often on the region’s surface.
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- What’s most surprising and fascinating to physicists about this holographic relationship is that space-time is bendy because it includes gravity. But the lower-dimensional system that encodes information about that bendy space-time is a purely quantum system that lacks any sense of curvature, gravity or even geometry. It can be thought of as a system of entangled qubits.
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- Under the it-from-qubit hypothesis, the properties of space-time essentially come from the way 0s and 1s are braided together. The long-standing quest for a quantum description of gravity becomes a matter of identifying the qubit entanglement pattern that encodes the particular kind of space-time fabric found in the actual universe.
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- Our universe is positively curved. But researchers have found, to their surprise, that anytime negatively curved space-time pops up like a hologram, particles come along for the ride.
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- Whenever a system of qubits holographically encodes a region of space-time, there are always qubit entanglement patterns that correspond to localized bits of energy floating in the higher-dimensional world.
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- Importantly, algebraic operations on the qubits, when translated in terms of space-time, behave just like rotations acting on the particles. This is a picture being encoded by the nongravitational quantum system.
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- The fact that holographic space-time always has these particle states is one of the most important things that distinguishes these holographic systems from other quantum systems.
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- It’s tempting to picture qubits having some sort of spatial arrangement that creates the holographic universe, just as familiar holograms project from spatial patterns. The qubits’ relationships and interdependencies might be far more abstract, with no real physical arrangement at all.
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- There’s clearly more to understand. But if the it-from-qubit picture is right, then particles are holograms, just like space-time. Their truest definition is in terms of qubits.
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- ‘Particles are what we measure in detectors’. Another camp of researchers who call themselves “amplitudeologists” seeks to return the spotlight to the particles themselves.
These researchers argue that quantum field theory tells far too convoluted a story.
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- Physicists use quantum field theory to calculate essential formulas called ‘scattering amplitudes“, some of the most basic calculable features of reality. When particles collide, amplitudes indicate how the particles might morph or scatter.
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- Particle interactions make the world, so the way physicists test their description of the world is to compare their scattering amplitude formulas to the outcomes of particle collisions in experiments such as Europe’s Large Hadron Collider.
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- Normally, to calculate amplitudes, physicists systematically account for all possible ways colliding ripples might reverberate through the quantum fields that pervade the universe before they produce stable particles that fly away from the crash site.
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- Calculations involving hundreds of pages of algebra often yield, in the end, a one-line formula Unbelievable! Amplitudeologists argue that the field picture is obscuring simpler mathematical patterns.
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- Scattering amplitudes involving “gravitons“, the putative carriers of gravity, turn out to be the square of amplitudes involving “gluons“, the particles that glue together quarks. We associate gravity with the fabric of space-time itself, while gluons move around in space-time. Yet gravitons and gluons seemingly spring from the same symmetries.
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- The “amplituhedron” is a geometric object that encodes particle scattering amplitudes in its volume. Gone is the picture of particles colliding in space-time and setting off chain reactions of cause and effect.
- What is a particle from a physicist’s point of view? It’s a quantum excitation of a field. We write particle physics in a math called quantum field theory. In that, there are a bunch of different fields; each field has different properties and excitations, and they are different depending on the properties, and those excitations we can think of as a particle.”
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- What we think of as elementary particles, instead they might be vibrating strings.
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- Particles are what we measure in detectors
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- Imagine a particle. What comes to mind? If you aren’t a theoretical particle physicist, chances are you picture a tiny ball, bobbing in space. Try to imagine that tiny ball as a particle with no mass.
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- Sometimes the word “mass” is used interchangeably with the word “weight.” That’s not entirely wrong. The mass of an object is measured by its resistance to a force. When you pick something up to test its weight, it is resisting the Earth’s gravity, so an everyday object’s weight on Earth is indeed one measurement of its mass.
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- But there’s more to mass than just a resistance to gravity, especially on the scale of the smallest pieces of matter. So physicists’ definition of mass gets a little more complicated.
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- Most fundamental matter particles, such as electrons, muons and quarks, get their mass from their resistance to a field that permeates the universe called the “Higgs field“. The more the Higgs field pulls on a particle, the more mass it has.
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- When it comes to composite particles like protons and neutrons, which are made up of quarks, most of their mass comes from the pull of the strong force that holds the quarks together.
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- Photons and gluons, two force-carrying particles, are fundamental, so they don’t host the internal tug-of-war of a composite particle. They are also unaffected by the Higgs field. They seem to be without mass.
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- “Massless particles” are purely energy. It’s sufficient for a particle to have energy to have a meaningful sense of existence.
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- These quanta of energy don’t have edges, and they don't have surfaces.
A better way to think of particles is as ripples on a quantum field. A quantum field has vibration modes like the harmonics on a guitar string. Pluck it with the right frequency and you get a particle.
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- The two particles physicists know to be (at least approximately) massless, photons and gluons, are both force-carrying particles, also known as “gauge bosons“. Photons are associated with the electromagnetic force, and gluons are associated with the strong force.
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- The graviton, a gauge boson associated with gravity, is also expected be massless, but its existence hasn’t been confirmed yet.
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- These massless particles have some unique properties. They are completely stable, so unlike some particles, they do not lose their energy decaying into pairs of less massive particles.
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- Because all their energy is kinetic, they always travel at the speed of light. And thanks to special relativity, things traveling at the speed of light don't actually age. So a photon is actually not aging relative to us. It’s timeless, in that sense.
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- To return to the topic of gravity: Gravity affects anything with energy, even a particle that has no mass at all. That’s why the gravitational attraction of objects like galaxies and clumps of dark matter curves the path of light passing by them in space.
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- It could be that the photon and the gluon are not the only massless particles in the universe. It could turn out that the lightest of the three types of neutrinos has zero mass.
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- There could be a lot of massless things out there that, either there’s no way to look for them, or rather we haven’t figured out how to look for them. It could be that there’s this whole other world out
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- But there’s more to mass than just a resistance to gravity, especially on the scale of the smallest pieces of matter. So physicists’ definition of mass gets a little more complicated.
Quanta of energy don’t have edges, and they don't have surfaces.
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- A better way to think of particles is as ripples on a quantum field. A quantum field has vibration modes like the harmonics on a guitar string. Pluck it with the right frequency and you get a particle.
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- The two particles physicists know to be massless, photons and gluons, are both force-carrying particles, also known as “gauge bosons“. Photons are associated with the electromagnetic force, and gluons are associated with the strong force. The graviton, a gauge boson associated with gravity, is also expected be massless, but its existence hasn’t been confirmed yet.
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- These massless particles have some unique properties. They are completely stable, so unlike some particles, they do not lose their energy decaying into pairs of less massive particles.
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- Because all their energy is kinetic, they always travel at the speed of light. And thanks to special relativity, “things traveling at the speed of light don't actually age. A photon is actually not aging relative to us. It’s timeless, in that sense.
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- To return to the topic of gravity: Gravity affects anything with energy, even a particle that has no mass at all. That’s why the gravitational attraction of objects like galaxies and clumps of dark matter curves the path of light passing by them in space.
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- It could be that the photon and the gluon are not the only massless particles in the universe. Scientists could one day find the graviton. Or it could turn out that the lightest of the three types of neutrinos has zero mass.
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- Or, something else that my grandson’s or granddaughter’s might discover?
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- November 16, 2020 2904
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