The problem between what we percieve boils down to scale. and it also follows that a bucket of balls can be described mostly using probabliity. the geometry of the bucket mattersbut also the scale of the ball.
My introduction of the 3rd and 4th order pythagorean allows an exact description of the first act of creation as a twist in space creating a binary bounded particle in a 3d manifold and consequentially TIME.
That first action converts consciousness into an expanding universe which we observe, Each action is followed by multiple actions forming a sphere of creation. That is all sub light and reflection produces a virtual universe filled with galaxies.
If you got this far can you understand what I just said?
Reality emerges
Particles are nature’s smallest constituents, but that doesn’t mean they’re fundamental. So what is the Universe made of?
https://aeon.co/essays/why-reality-is-more-than-the-sum-of-its-particles?
What is the world made of? For centuries, people have believed that matter is constructed from tiny, indivisible parts. Some of the earliest known references come from the Greek philosopher Democritus, who taught that the Universe was composed of atoms the size of dust motes floating in sunlight. Theravada Buddhism developed the concept of kalapas, indivisible bundles of properties fleeting into and out of existence. Alchemy’s description of fundamental ‘corpuscles’, expounded by Isaac Newton and others, derived from translations of Aristotle by mediaeval Islamic scholars. And Hideki Yukawa, winner of the 1949 Nobel Prize in Physics for his work developing the modern theory of elementary particles, took inspiration from a passage in the Zhuangzi, a Daoist text written during China’s warring states period, in which fast-moving entities puncture holes within formless chaos. Yukawa saw a parallel to particle collisions.
The concept of a particle, as we now refer to these indivisible parts, has therefore been repeatedly re-introduced in contradictory ways. The modern view continues this tradition. In late-19th-century physics, particles were tiny indivisible objects with well-defined positions and momenta. The advent of quantum mechanics led these clear waters to become muddied. But the basic idea persists: we are taught from a young age that matter is made of atoms, built from particles such as electrons, and electrons are not built from anything else. For this reason, these particles are sometimes said to be fundamental. But are they? Is the Universe really made from the smallest constituents, as a beach is made from sand?
The answer to this question, I will contest, is perhaps a surprising one: yes, the Universe is built from fundamental units – but fundamental need not mean smallest. This view is generally adopted by those physicists, such as myself, who work in the largest discipline within the subject: quantum matter. This is the study of quantum behaviours that manifest on everyday scales: the attraction of iron to a magnet, the flow of electricity along a wire, or the passage of sound through a crystal. In these settings, too, we find particles. But these particles are not elementary, like the electron: they are emergent.
The distinction can be pictured as follows. Imagine a lightbulb, its rays of light travelling to your eyes. We can ask what those rays are made of. Quantum mechanics has an answer: a ray of light is a stream of individual particles called photons. In turn, we can ask what the photons are made of. The answer this time is that they are not made of anything else: they are elementary. Now imagine that this lightbulb is of a vintage sort, and gives off a gentle hum. It emits waves of sound that travel to your ears. We can again ask what those waves are made of. And, once again, quantum mechanics has an answer: a wave of sound can be described by individual particles called phonons. Now, if you are familiar with the Standard Model of particle physics, you will know that it contains photons but not phonons. The reason is that phonons are not elementary. If you ask what a phonon is made of, there is an answer: it is a pattern of vibrations of the atoms in the air. In the study of quantum matter, however, we say it is an emergent particle.
So what are emergent particles? Are they as real as elementary particles? And, perhaps most importantly, can they tell us anything new about the nature of reality?
To answer these questions, we first need to agree on the meanings of the terms emergent, fundamental, and particle. Naturally, this being a philosophical discussion, each term has been widely debated, with textbooks devoted to each. I will give a short and hopefully not too offensive summary.
A phenomenon is emergent if it is built from parts but cannot be reduced to them without losing some key aspect of the description. One of the pioneers of quantum matter, Philip Anderson, conceived of the subject with an update to Aristotle’s adage: the whole is not only more than the sum of its parts – it can also be fundamentally different from it. Take ice, for example. Ice has emergent properties not present in any of its constituent water molecules. It is cold, say. Cold is not a property an individual molecule can possess. Ice is also rigid: push one edge of an ice cube and the other edge moves. This is neither a property of individual molecules nor of their sum, since those same molecules can also form liquid water, which does not possess such rigidity. Ice is purely emergent.
Entities are fundamental if they are independent of one another and form a basis for understanding all other phenomena. The atoms in the periodic table were once thought to play this role: a basis for understanding molecules, then living beings, and so on. But we later discovered that atoms can themselves be described in terms of elementary particles such as electrons, protons and neutrons. (Hence, we jumped the gun on calling them atoms!) Realising this, there are two possible conclusions to draw. One is to say that elementary particles are fundamental, not atoms. The other approach is to say that things can be fundamental at one level of description, while acknowledging that other things might separately be fundamental at other levels. Atoms are fundamental for chemistry, but not for nuclear physics. The latter is the approach typically taken by scientists and philosophers. This makes sense, since we cannot ever be sure if we have reached the bottom of the pile. For instance, protons are made from quarks, and various hypotheses such as string theory attempt to comment on some lower level of description still. Importantly, science can never tell us if ours is the lowest possible level of description: it can only posit this as a hypothesis that could be falsified by further data. So if we restrict ‘fundamental’ to mean ‘most fundamental’, or ‘fundamental at every possible level’, the concept would fall outside the realm of science.
I am struck with an idea – Eureka! The hole is like a particle, and the circling water is like its field
A particle was originally a pretty straightforward concept: it was something with a well-defined position (requiring it to be incredibly small) and a well-defined momentum. All of Newtonian mechanics can be written in terms of those two quantities, position and momentum, so particles were excellent candidates for fundamental building blocks of nature. Unfortunately, this all fell apart with the advent of quantum mechanics. Here we discover that position and momentum cannot be simultaneously well defined: quantum particle is therefore a contradiction in terms.
As such, there are many inequivalent things we mean by ‘particle’ in modern physics. A definition most physicists would be happy with is that a particle is an excitation of a quantum field. This of course begs the question as to what we mean by a quantum field. Fields made intuitive sense prior to quantum mechanics. They were devised by Michael Faraday to give a mechanistic explanation of the behaviour of magnets: moving a magnet over here appears to influence a compass needle over there, which seems a little too much like magic. So, instead, Faraday suggested that each magnet is the source of an invisible magnetic field; moving a magnet affects its field, and the change in the field at the location of the compass causes the compass to move. Fields remove the need for action-at-a-distance. By extension, when one electron feels the effect of another at some distance, we can say this is because each electron is a source of electric field.
The advent of quantum field theory allowed us to ask what the field itself is made of. Here things get a little circular. The field is made of particles, which are excitations of the field. Within the framework of quantum field theory, fields and particles cannot be conceptually separated. To motivate this symbiosis, consider an analogy. Imagine that, lying in my warm and luxurious bath, my gaze is dramatically drawn away from my navel as I realise I have inadvertently pulled out the plug. A swirling vortex forms in the water, centred on a filament of hole that connects the surface to the plughole. I am struck with an idea – Eureka! The hole is like a particle, and the circling water is like its field. I imagine shrinking to the size of a tiny fish, swimming under the surface. I would never have noticed the water before, but now I feel it through the circular pull of the vortex. Closer to the vortex, the pull would be stronger, suggesting some source at its centre. But no matter how close I get, within the water, the hole is always smaller.
This bathtub analogy sheds light on a long-running debate within physics and philosophy about whether it is particles or fields that are fundamental. One side has it that since we detect only particles, not fields, then the former are fundamental and the latter merely a mathematical abstraction. (I disagree with this, by the way: we detect fields all the time, such as when we move a compass with a magnet, and many experiments that purport to detect particles do so by detecting their fields.) The other side counters that particles emerge from fields, so the latter must be more fundamental. I admit I never really understood the debate. Particles and fields are inseparable: in the bath, the whirlpool-like hole connecting the surface to the drain exists only by reference to the water, but the water can circulate only by virtue of the hole. Trying to establish which is more fundamental seems to make about as much sense as arguing over what defines a room, with one side arguing it is the walls, and the other arguing it is the space between them.
To return to quantum fields, textbook descriptions often begin with the following construction. Picture a long chain of atoms strung together with chemical bonds, like a stretchy necklace with pearls fixed to an elastic cord. If an atom tries to move to the left it will be pulled back to the right, and vice versa. It is as if each atom is tethered to the spot by a quantum spring. This is how we picture it. To get from vibrating atoms to a quantum field, the final step is to blur your eyes: smooth things out so that you can’t see individual atoms any more, only their coarse-grained behaviour. The result, a smoothed-out picture of a bunch of quantum springs, is what we mean by a quantum field.
Say you ‘excite’ one of the atoms by giving it a whack. What happens? That atom begins vibrating more vigorously, shaking its neighbouring atoms, which shake their neighbours, and so on. The vibrations pass along the chain. At the coarse-grained level, this excitation of the quantum field is what we mean by a particle. In the case of an actual chain of atoms, we call this particle a phonon. It carries sound in the form of vibrations. But similar excitations exist in any quantum field. The phonon is an emergent particle: it can be reduced to the vibrations of atoms, but only at the expense of losing key aspects of the description (the intuitive notion of sound, say).
It is reasonable to ask how the picture just described – a coarse-grained description of quantum vibrations along a chain of atoms – can hope to describe elementary particles such as electrons and photons. The answer is that we can drop the atoms and keep the quantum springs. This might seem surprising. After all, the atoms were the only bit that was physically there, and the springs were just an abstraction to describe the atoms’ interactions. If there are no atoms, what is it that is vibrating? But this is just an updated version of the old concern that if light is a wave, it must be a wave in something. Albert Einstein explained that this need not be the case: light can exist without a medium. When describing elementary particles, the quantum springs exist at all points in space and time. It is not that they live in the vacuum: they are the vacuum.
If all of this sounds far-fetched, it is worth remembering that the predictions of quantum field theory (specifically quantum electrodynamics, the theory of photons and electrons) have been confirmed to one part in a billion. It is, by a significant margin, the most precisely verified theory in history.
Once we get to our finished picture with atoms smoothed away, there is no essential difference between the mathematical descriptions of elementary and emergent particles. We just happen to know that the latter would also admit a description in terms of atoms, should we choose to make it.
Emergent things clearly exist. For example, owls exist. They are real. But they are also emergent
Despite this, it is often suggested that elementary particles are ‘real’ whereas emergent particles are not. Emergent particles are sometimes called ‘quasiparticles’ to emphasise this reduced status. The reasoning is that phonons, say, are just a simpler description of the real atomic motion.
I would raise several objections here. First, emergent things clearly exist. For example, owls exist. They are real. But they are also emergent, as they admit a description in terms of atoms. Second, as mentioned earlier, the mathematical description of emergent and elementary particles is identical. If the mathematics says they are the same, on what basis can we claim they are different? The answer cannot depend upon the atoms since they were already smoothed away to reach the field description. And third, our evidence of emergent particles is as direct as that of elementary particles. For instance, fire electrons through a thin film of aluminium (by replacing the screen of your old cathode ray television with aluminium foil, say, while somehow ingeniously maintaining the vacuum seal). You will find that the electrons have less energy after passing through the foil. Importantly, though, you will find that the missing energy is always an integer multiple of some smallest amount – one, two, three and so on, but not 1.2 or 1.37. Why? Because the electrons lose energy by creating new emergent particles (called plasmons) within the foil. Each plasmon costs the same amount of energy to create. You can’t have half a particle, so the number of plasmons created is one, two, three, and so on. Emergent particles are necessary to account for such effects.
A weaker claim could be that emergent particles are real but not fundamental. But that would be to invoke the meaning of fundamental in which only one set of things ever holds that status. As we established, that claim cannot be made scientifically. The scientific claim must be that emergent and elementary particles hold precisely the same ontological status. In other words, they are just as real as one another.
The view I am challenging, that elementary and emergent particles are essentially different, arose as a matter of history. The textbook introduction I gave earlier treated elementary particles as an abstraction from emergent particles. But that is not how we came to understand elementary particles historically, and nor is it how we actually conceive of them now. The theories of elementary and emergent particles developed from different starting points, and it is only relatively recently that we have come to conceive of them on equal footing.
To illustrate this historical evolution of the idea of emergent particles, consider three classes of object that we have come to understand as an electron within matter. Each description is valid, but in a different scenario.
The simplest class, and the earliest understood, is that of an elementary electron flying into a crystal that is an electrical insulator (quartz, say). Upon entering the crystal, the electron continues to behave largely as it did outside. It has a mass and an electric charge. These properties, however, become modified. We can understand this with a classical analogy. Picture the elementary electron as a small, heavy marble. Say you want to measure its mass. To do so, you could shake it back and forth, precisely recording the force required to impart a given acceleration; the mass is the ratio of the two. Now imagine re-doing this experiment in the bath, with the marble underwater. You will need to impart more force to achieve the same acceleration. This is because you are no longer just moving the marble: you are also moving the water. The marble has seemingly gained mass through its interaction with the water. The story is similar when the electron enters the crystal. Its properties change because it interacts with the surrounding atoms. Attempting to move the electron requires an additional effort, as you are now pulling against the crystal as well.
It is again tempting to suggest that this new ‘emergent electron’ – the electron with the changed mass – is not real, or not fundamental. Is the real thing not just the elementary electron plus some interactions? But as well as falling foul of the earlier arguments, the claim that the only real thing is a non-interacting electron is problematic for a number of reasons. First, electrons, whether elementary or emergent, are always interacting. They interact via their charge with all other charged objects in the observable universe, and via their mass with all other massive objects. Second, any measurement of an electron, or any other particle, requires an interaction with the measuring device. Third, therefore, the existence of any hypothesised non-interacting particle could never be measured even in principle, and cannot be a scientific hypothesis.
The first marble drops to the cup’s bottom. As more marbles are added, the cup fills, and subsequent marbles must go on top of earlier ones
Historically, the next class of emergent electron to be understood was in metals. Here the story is more subtle than it might first appear. For example: what happens when you connect the terminals of a battery with metallic wire? Well, metals contain many electrons that are not bound to particular atoms. The voltage across the wire causes them to move, and thereby establishes a flow of electrical current. However, if we measure the number of electrons involved in this current, we find that it is minuscule compared with the number of unbound electrons. Why?
The reason can be understood by returning to the marble analogy. Forget the water for now. Instead, think of the wire full of electrons as like a cup full of marbles. To get there, take an empty cup and drop marbles in one by one. The first marble drops to the bottom of the cup. As more marbles are added, the cup fills, and subsequent marbles must go on top of earlier ones. Each marble would like to minimise its energy by sitting as low as possible, but later marbles are constrained to sit higher than earlier ones.
The same is true of the electrons in the metal. Imagine somehow removing all the electrons from the metal, then re-adding them one-by-one. The initial electrons occupy the lowest-energy states. Later additions find those states occupied and must instead occupy states of higher energy.
To picture the effect of the battery, imagine lightly shaking the cup in an attempt to get the marbles to move. The lower marbles are stuck in place. Only the marbles at the top are free to move. This is why only a tiny minority of electrons carry all the current in the wire.
Just as a marble added to the cup must sit on top of all others, an electron entering a metal cannot be understood without reference to all the pre-existing electrons. It interacts with them, but it also becomes quantum-mechanically entangled with them. From this perspective, it is remarkable that this second class of emergent electron – the elementary electron plus the interactions and entanglement with all others in a metal – resembles an elementary electron at all. In fact, it does, but this idea (called Fermi liquid theory) took many decades to understand.
As Anderson said, the whole is not just more than the sum of the parts: it is also different
The final class of electron in matter is the most recently understood, and the least widely discussed outside of quantum matter communities. I should add a caveat that the evidence so far is indirect. To return to the original analogy, consider the vortex within the bathwater. There is no marble in this picture, but the vortex itself has a number of particle-like properties: for example, you cannot have half a vortex, just as you cannot have half a particle; two or more vortices can interact at a distance via the bathwater; you could even ascribe a mass to a vortex by trying to impart on it an acceleration as before. The analogy between vortex and particle is not perfect, since vortices are not quantum. But, in certain crystals, quantum vortices do exist. They are members of the third class of emergent particle, excitations of what is called an ‘emergent gauge field’.
To understand this third class, this time consider a magnetic crystal. I will describe a particular type of magnetic crystal, called a quantum spin ice, although there are other examples showing similar effects. The magnetism originates from individual atoms, each of which has its own quantum magnetic field called a ‘spin’. (Strictly, the atoms are electrically charged ions, but this is not relevant to the story.) Starting from these spins, we can once again blur our eyes until we see only a quantum field. What form do the emergent particles take?
Three types emerge. The first is an emergent electron. This is deeply surprising, since this time there were no elementary electrons present. There were only ions with magnetic fields. As Anderson said, the whole is not just more than the sum of the parts: it is also different. The second emergent particle, the magnetic monopole, is stranger still. Whereas an electron has an electric charge, the monopole has a ‘magnetic charge’. It looks like the north pole of a magnet without the south. We learn in school that this is impossible: cutting a magnet in two gives two smaller magnets, each with a north and south pole, not separate north and south poles. But as emergent particles within quantum spin ices, magnetic monopoles can exist. The third type of particle is an emergent photon. Like the elementary photon, it sets the maximum speed at which signals can propagate within the crystal. It also mediates interactions between the emergent electrons and monopoles.
All three of these emergent particles are truly remarkable since they feature properties that are not present at the level from which they emerge. Emergent particles in other crystals are similarly able to take forms never seen among elementary particles. Magnetic monopoles are one example. Other emergent particles, such as phonons – particles of sound – cannot possibly exist as elementary particles (since sound cannot exist without a medium). There are crystals in which the charge and spin of an electron separate into particles (‘holons’ and ‘spinons’) that move independently, like the Cheshire cat separating from its smile. There are particles (‘anyons’) where passing one around the other causes both to turn into different particles. There are particles (‘bogoliubons’) whose charge can be in a quantum superposition of positive and negative. The general sense is that any particle you can dream up can probably be found within some crystal.
This remarkable fact raises a tantalising possibility: what if the elementary particles themselves are actually emergent? What if, underlying what we think of as reality, there is some set of atom-like things from which the proton, electron and so on emerge? A clear statement to this effect was made by Grigory Volovik in The Universe in a Helium Droplet (2003). To paraphrase his thesis: if we shrunk to the size of a few atoms and went for a swim in a cold quantum fluid, such as liquid helium, we would encounter a variety of emergent particles that would seem to us just as real and fundamental as the supposedly elementary particles do to us now. So what is to say that we do not already exist in such a fluid? As Volovik observes, some of the biggest unsolved problems in physics would be instantly and satisfactorily solved.
Others such as Xiao-Gang Wen and collaborators have introduced similar ideas, noting that such approaches seek a more fundamental description of reality than better-known ideas such as string theory. For example, string theory has to postulate the broad classes of particle such as ‘fermion’; but if reality is underpinned by a quantum fluid, these classes themselves can emerge naturally.
Neither Volovik nor Wen claim to have a final theory of elementary particles. Importantly, though, specific aspects of their ideas can be confirmed or falsified using existing technology and known materials. This allows us to make use of the resulting particles when confirmed. For example, anyons are taken seriously as a viable route to practical quantum computing.
So, are elementary particles emergent? Even if we can ever answer this, we will be faced with the same question of whatever we find. In the end, whether you like the idea comes down to personal taste and, perhaps, a degree of cultural upbringing. The more widely publicised attempts at a ‘theory of everything’ always struck me as suspiciously similar to themes in the Old Testament: the Universe was once describable by a single mathematical formula, but that one, true quantum field spontaneously broke in a cataclysmic event that resulted in the messy collection of particles we find before us. I find that the quantum matter perspective, on the other hand, resonates with me in a similar manner to the Daoist texts such as the Zhuangzi. From this new perspective, it is our current world that is beautiful. It grew from a swamp of possible theories, each ugly in its arbitrariness: it doesn’t matter which way we followed, as they all lead here.
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