exchemist
Valued Senior Member
An electron has an existence independent of any medium, as do the other fundamental particles.
Do you have a link illustrating electrons being a quasiparticle? I'd be intrigued.
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Do you have a link illustrating electrons being a quasiparticle? I'd be intrigued.
exchemist
Valued Senior Member
Again, can you provide a link to this concept of separating an electron from its charge?
My instinct is this will be just a piece of mathematical treatment, rather than anything with observable consequences, but I am will be to be proved wrong if you have a reference.
--https://www.sp.phy.cam.ac.uk/research/1d-transport/SCseparation
I'm not the only one, I would say, who is surprised by this finding. Electrons have, until now, been considered as fundamental, indivisible, symmetrical. The symmetry looks different when spin and charge separate; I guess the mass goes along with the spin: however these two can be separated too, so you get three distinct quasiparticles.
What, if any, consequences this might have for the rest of the Standard Model, I can't say, "really".
'sigh'. I kinda hate to say this, but that's all a bit misleading.
To operate on a state, you need something physical--an electric or magnetic field, a photon tuned to a particular frequency. You need to have the particle you want to manipulate, interact with a physical field. This is how qubit operations on IBMs quantum computer are realised--the photons are in the microwave region.
There is no intrinsic mass, charge, or spin in the equation $$ |\psi\rangle = \alpha|0\rangle + \beta|1\rangle $$. To see operators, you will need to know something about particle energies; you need Hamiltonians.
I have no idea how to recover mass, charge, or spin from a pair of complex numbers.
It's important to realise that the wavefunction is not physical, it says nothing at all about physical fields. Also, the above equation describes a real complex amplitude for "a particle", it doesn't need to say what kind of particle. Maybe that will help.
So, for the younger viewers, the probability amplitudes of particles can be manipulated, but, you have to manipulate a real, physical particle to achieve this.
Check out (google is your friend) how IBM manipulates complex probability amplitudes of real particles trapped in a cavity. The physics is what determines how the amplitudes change; it's as if the complex amplitudes follow the particles around!
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I suppose physics can be unapologetic about what it is. It is what it is.
I also suppose (actually I know) that it's hard to assign the behaviour of a real physical particle to complex numbers (an obvious question is, why are quantum probabilities complex-valued, who ordered that?). Schrodinger struggled with it too. He tried to recover "physicality" from his results, by assigning an electron's charge to the wavefunction.
Today we can understand why that doesn't fly; one reason is given above: a wavefunction can be written that applies to particles with zero electric charge . . .
I also suppose (actually I know) that it's hard to assign the behaviour of a real physical particle to complex numbers (an obvious question is, why are quantum probabilities complex-valued, who ordered that?). Schrodinger struggled with it too. He tried to recover "physicality" from his results, by assigning an electron's charge to the wavefunction.
Today we can understand why that doesn't fly; one reason is given above: a wavefunction can be written that applies to particles with zero electric charge . . .
exchemist
Valued Senior Member
They still are indivisible. This research does not call that into question. So its impact on the Standard Model is nil.
What they have done is make analogues of phonons, effectively: waves or vibrations within the "sea" of conduction electrons. It is these phonon- analogous quasi-particles for which charge and/or spin are no longer associated with mass in the way that they are for an electron. No electron has been decomposed.
But thanks - another piece of curious solid-state physics.
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exchemist
Valued Senior Member
You misunderstand. I am speaking about mathematical operators.
To get the energy of a state you operate on its wave function with the Hamiltonian operator: H ψ= Eψ, or <ψ l H lψ> = E, to get the momentum you operate using the momentum operator, h/i ∂/∂x, in the same way, and so forth.
In QM, for every observable associated with a state, there exists a corresponding mathematical operator. More here: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/qmoper.html
In Information Science, for every observable with a mathematical operator, there is a corresponding Hamiltonian.
Without Hamiltonians and the notion of a physical action, all you have is general probability states, and no way to gain any information about them.
Mathematically, the Hamiltonians rotate the state vector (in the Bloch sphere); physically you add something with energy to the system, and see a response. You need to apply physics, which brings its suitcase full of math along with.
Yes, the quasiparticles are something like an algebraic result--a visualisation of some symmetry of nature, probably SU(2) is in there because of the fermion gas thing.
Let's try a context-switch, of the kind that requires an observer to encode information differently.
A small enough observer, "on-chip" will observe (the details of how observations are made can be left out for now) what look like particles with mass and spin moving around, or perhaps oscillating in place, while charged massless particles occupy centres of "activity". As far as this "conceptual" observer is concerned, spinons and chargons are real particles interacting with each other.
An observer "off-chip" can see attachments from the chip to the rest of reality, so has to explain things differently. Are quasiparticles real? It depends on the context.
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exchemist
Valued Senior Member
So no impact on the Standard Model, then.
I'll leave the jury to deliberate on that.
Ha. I just realised I've been skipping over something of, well, interest.
exchemist is underlining the mathematics: operators in a vector space (with two complex dimensions !?), where the mathematics (as if it cares) describes what humans call "probability amplitudes".
So, without doing any physical experiments or manipulating any systems of particles, on paper I can describe with uncanny accuracy, what to expect if I do go and manipulate real physical particles with real physical fields (however I decide to set these up; I have to decide what I'm going to use to control the physics). That's the beauty of it; it works and no-one really knows why it does.
But you can do this kind of analysis of a physical system, one you haven't built yet, with complex vector spaces, using the complex frequency domain, Fourier and Laplace transforms, transfer functions that define a complex impedance to a frequency input and the system response. The basis of modern electronics. You can use this classical (because it's only one complex dimension !?) approach up to optical frequencies and communication at the speed of light.
Mathematics is useful like that. We get to understand something about physical systems, without doing measurements--we set aside real observables and manipulate their mathematical equivalents.
Why we can do this, and why complex vector spaces? I don't know that I can really say, and I studied electronics back when.
exchemist is underlining the mathematics: operators in a vector space (with two complex dimensions !?), where the mathematics (as if it cares) describes what humans call "probability amplitudes".
So, without doing any physical experiments or manipulating any systems of particles, on paper I can describe with uncanny accuracy, what to expect if I do go and manipulate real physical particles with real physical fields (however I decide to set these up; I have to decide what I'm going to use to control the physics). That's the beauty of it; it works and no-one really knows why it does.
But you can do this kind of analysis of a physical system, one you haven't built yet, with complex vector spaces, using the complex frequency domain, Fourier and Laplace transforms, transfer functions that define a complex impedance to a frequency input and the system response. The basis of modern electronics. You can use this classical (because it's only one complex dimension !?) approach up to optical frequencies and communication at the speed of light.
Mathematics is useful like that. We get to understand something about physical systems, without doing measurements--we set aside real observables and manipulate their mathematical equivalents.
Why we can do this, and why complex vector spaces? I don't know that I can really say, and I studied electronics back when.
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Ah yes, mathematics. Differential equations and all that.
Unfortunately if you want to pass that solid-state physics exam, you need to know what deBroglie waves are and how to use them mathematically, in a calculus of, well, wave-packets, I guess.
You learn a bit about the consequences of Heisenberg's uncertainty principle, but also about "wave-uncertainty"; i.e. observing a wave and wanting to know about its wavelength, or its frequency involves classical uncertainty.
Then you learn about deBroglie's thesis, and how you can use the above calculus to derive . . . Schrodinger's equation in one dimension.
Ok, well, it's a start. But after one, there are two, then three dimensions to solve for. You learn about these deBroglie waves in more than one dimension, ergo. You move on to quantum harmonic oscillators, how to plug in things like momentum and define energies (potential wells), you are on your way to . . . somewhere.
Otherwise, from the informational context, you need two qubits to transmit two classical bits; you can do this transmision of two bits so that nobody but the receiver can decode them, but it requires twice as many complex dimensions: i.e. the 2 x 2 in the Bell product.
This is the bumper sticker version of "quantum" information transfer; by entangling the probabilities (of measurement outcomes) and classically transmitting partial information, we get absolutely secure communication. That's us, not the universe . . .
Unfortunately if you want to pass that solid-state physics exam, you need to know what deBroglie waves are and how to use them mathematically, in a calculus of, well, wave-packets, I guess.
You learn a bit about the consequences of Heisenberg's uncertainty principle, but also about "wave-uncertainty"; i.e. observing a wave and wanting to know about its wavelength, or its frequency involves classical uncertainty.
Then you learn about deBroglie's thesis, and how you can use the above calculus to derive . . . Schrodinger's equation in one dimension.
Ok, well, it's a start. But after one, there are two, then three dimensions to solve for. You learn about these deBroglie waves in more than one dimension, ergo. You move on to quantum harmonic oscillators, how to plug in things like momentum and define energies (potential wells), you are on your way to . . . somewhere.
Otherwise, from the informational context, you need two qubits to transmit two classical bits; you can do this transmision of two bits so that nobody but the receiver can decode them, but it requires twice as many complex dimensions: i.e. the 2 x 2 in the Bell product.
This is the bumper sticker version of "quantum" information transfer; by entangling the probabilities (of measurement outcomes) and classically transmitting partial information, we get absolutely secure communication. That's us, not the universe . . .
Some notes about why we have as many dimensions as we do.
It's fairly obviously connected to the amount of complexity you can be allowed, in less or more a number of dimensions than the four we assert.
That is, since any equation of motion you might be able to write down and solve, for some unknown, is going to need enough variables in it that a solution exists, that seems to be the why, why we need that many dimensions.
Although motion in two dimensions, or one, seems logical, you need three because observing motion in less than three is computationally outside the problem domain. That is, life is impossible too, with less than three dimensions and time (for aging).
So even when something like an electron is trapped in a cavity and has no 1-dimensional motion, it still 'commutes' with all three, plus time. That must be true or IBM's quantum computer wouldn't do anything, right?
Electrons don't age. They gain or lose energy. Detector screens do this aging thing, or at least, that's what we claim, a pattern of dots is a history, a photo shoot of a population whose members are now, erm, lost to this record you have, in places unknown.
And it seems this "not knowing" is somehow as important as the pattern itself. Information depends on it though. Maybe they should call the movie Once Were Quasiparticles.
It's fairly obviously connected to the amount of complexity you can be allowed, in less or more a number of dimensions than the four we assert.
That is, since any equation of motion you might be able to write down and solve, for some unknown, is going to need enough variables in it that a solution exists, that seems to be the why, why we need that many dimensions.
Although motion in two dimensions, or one, seems logical, you need three because observing motion in less than three is computationally outside the problem domain. That is, life is impossible too, with less than three dimensions and time (for aging).
So even when something like an electron is trapped in a cavity and has no 1-dimensional motion, it still 'commutes' with all three, plus time. That must be true or IBM's quantum computer wouldn't do anything, right?
Electrons don't age. They gain or lose energy. Detector screens do this aging thing, or at least, that's what we claim, a pattern of dots is a history, a photo shoot of a population whose members are now, erm, lost to this record you have, in places unknown.
And it seems this "not knowing" is somehow as important as the pattern itself. Information depends on it though. Maybe they should call the movie Once Were Quasiparticles.
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Maxwell's demon was mechanical; a small conceptual 'being' who could open and close a mechanical trapdoor.
But the idea of an internal demon--a ghost in the machine--isn't really all that crazy. In fact we do it all the time; we assign anthropomorphic behaviour to inanimate matter. It isn't really there, of course, but we still can't help doing it.
(I can't help myself; when I feel this way, I wanna be someone else . . .)
So why not go the full monty? Why not a gravity demon, who rearranges the inertia thing so all the mass appears to be concentrated at the centre, of a planet, or a spinning top? It's actually a fundamental concept in Newtonian physics, but we know the mass is distributed about the centre as well as knowing it's also "at" the Newtonian centre.
Inertia is a clever demon. If you take a ring-shaped or torus-shaped bit of matter, the demon arranges for all the inertia to be "distributed" so it looks like a line, a circle of mass. This guy is the go-to if you want to know what the contribution of this inertial moment (not the matter itself, just its mass) is if you could observe from the centre.
With a simple ring, it's a correspondingly simple solution (for the little devil).
I think this is actually what we all do, without realising or bothering to acknowledge it. It's how we cope with being chunks of matter with inertia.
(When I get this feeling, it gets in my system . . .)
But the idea of an internal demon--a ghost in the machine--isn't really all that crazy. In fact we do it all the time; we assign anthropomorphic behaviour to inanimate matter. It isn't really there, of course, but we still can't help doing it.
(I can't help myself; when I feel this way, I wanna be someone else . . .)
So why not go the full monty? Why not a gravity demon, who rearranges the inertia thing so all the mass appears to be concentrated at the centre, of a planet, or a spinning top? It's actually a fundamental concept in Newtonian physics, but we know the mass is distributed about the centre as well as knowing it's also "at" the Newtonian centre.
Inertia is a clever demon. If you take a ring-shaped or torus-shaped bit of matter, the demon arranges for all the inertia to be "distributed" so it looks like a line, a circle of mass. This guy is the go-to if you want to know what the contribution of this inertial moment (not the matter itself, just its mass) is if you could observe from the centre.
With a simple ring, it's a correspondingly simple solution (for the little devil).
I think this is actually what we all do, without realising or bothering to acknowledge it. It's how we cope with being chunks of matter with inertia.
(When I get this feeling, it gets in my system . . .)
The reasoning is that Maxwell proposed this "idea" in order to resolve a "problem" with entropy in thermodynamics.
100+ years later, we have the fundamental limits of computation, and an exorcism of sorts. A gravity/inertia demon might motivate the same kind of result. (yeah . . .)
I need a good prediction demon here.
Ahem; the fact that a ring of ordinary matter has its inertia focused along a line says something about topology and the inertia tensor. A ball of ordinary matter has a real internal centre of mass, a torus doesn't. Difference is the fuel in the entropy engine--the demon can tell the difference between these two arrangements.
Maxwell's demon was supposed to 'sort' molecules based on their different velocities (but in the end, couldn't).
100+ years later, we have the fundamental limits of computation, and an exorcism of sorts. A gravity/inertia demon might motivate the same kind of result. (yeah . . .)
I need a good prediction demon here.
Ahem; the fact that a ring of ordinary matter has its inertia focused along a line says something about topology and the inertia tensor. A ball of ordinary matter has a real internal centre of mass, a torus doesn't. Difference is the fuel in the entropy engine--the demon can tell the difference between these two arrangements.
Maxwell's demon was supposed to 'sort' molecules based on their different velocities (but in the end, couldn't).
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Write4U
Valued Senior Member
If you consider that these "beings" are non-conscious mathematical entities, then the term quasi-intelligent mathematical mechanics is perfectly suitable to describe these values and functions.
Yep. For instance, I had to have a word with my guitar string demon this morning.
After which, the bloody strings still need tuning.
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So let's take our demon vehicle for a ride. On a layer of TaSe2. Local conditions are: expect strong magnetic fields and low temperatures. Better pack the rug and some blankets.
Who will be in the passenger seat? Are we going to be able to see electrons out the left side of the vehicle?
Who will be in the passenger seat? Are we going to be able to see electrons out the left side of the vehicle?
This might not be a great example, but I'm just playig with ideas.
When the Romans built a road, they weren't usually concerned about building a structure that needed vertical alignment. A road is built close to the ground, with a small or no vertical structure off the ground level.
So right there, Roman road builders figured out they didn't need to include information about the vertical. Which leaves the two along the horizontal, and the remaining problem of building a road in a straight line. One thing it illustrates is you only need two dimensions to map points on the surface to each other.
Although, the vertical does come back into it, in an approximate form. A straight line between two roadbuilding engineers was found, using a pair of vertically oriented sticks, one of them had an elaborate sighting mechanism. Today we know the vertical direction can be found by drawing two intersecting lines, deciding how long they are, their angle at the intersection, and calculating the normal vector.
So it's available without needing to "push" it into a third dimension; there it is with just two on a flat surface, roughly the Euclidean plane.
So put the road back in; two Roman engineers, if they wrote down all the measurements, know some information about how some mass is distributed. Plug their coordinate system back in, and you have a way to determine how this matter will behave if subjected to an external torque, or just a sudden impulse.
What the Romans did is what builders still do, if you need the vertical aligned accurately. It's called a plumb bob, and you don't want it to be a pendulum. At least, you don't when you want it to be vertically aligned.
When the Romans built a road, they weren't usually concerned about building a structure that needed vertical alignment. A road is built close to the ground, with a small or no vertical structure off the ground level.
So right there, Roman road builders figured out they didn't need to include information about the vertical. Which leaves the two along the horizontal, and the remaining problem of building a road in a straight line. One thing it illustrates is you only need two dimensions to map points on the surface to each other.
Although, the vertical does come back into it, in an approximate form. A straight line between two roadbuilding engineers was found, using a pair of vertically oriented sticks, one of them had an elaborate sighting mechanism. Today we know the vertical direction can be found by drawing two intersecting lines, deciding how long they are, their angle at the intersection, and calculating the normal vector.
So it's available without needing to "push" it into a third dimension; there it is with just two on a flat surface, roughly the Euclidean plane.
So put the road back in; two Roman engineers, if they wrote down all the measurements, know some information about how some mass is distributed. Plug their coordinate system back in, and you have a way to determine how this matter will behave if subjected to an external torque, or just a sudden impulse.
What the Romans did is what builders still do, if you need the vertical aligned accurately. It's called a plumb bob, and you don't want it to be a pendulum. At least, you don't when you want it to be vertically aligned.
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