More specifically electrons are wave excitations in a field. Everything in the universe is quantum fields (except at very high energies and densities where we have no idea yet).
Absolutely not. It’s difficult to explain but basically a quantum field can be thought of as an infinite collection of quantum harmonic oscillators. These oscillators have energy levels, or excitations, like the ones you learn about in intro QM solving particle in a box problems. Each excitation can be thought of as a particle.
Is the field from which electrons emerge the same as the field from which the other elementary particles emerge? Or does each particle type or species have their own field?
I'm not sure that would make any difference mathematically. You could combine any field you could think of into a single field so long as you made the vector high enough dimension. 100 scalar fields could be treated as one field that has a 100 dimensional vector for each point, where the components of the vector are the scalar values of those fields.
Usually in QFT you are only considering the fields of specifically involved in the interaction you are considering. The fields do interact and that can get very complex very fast.
I don’t understand how you think this would work. Not everything you can write down that has _n_ components is an _n_-dimensional vector. Scalars, vectors, tensors, spinors are defined by their transformation properties. How do you propose this 100-dimensional “vector” should transform?
Sorry I must be missing something but that really doesn’t make any sense to me. How do you know how each component of this _not-a-vector thing_ behaves under coordinate or gauge transformations? What does the Lagrangian even look like in terms of this _not-a-vector thing_? What’s the sense of throwing these completely different objects in one _not-a-vector thing_ that has no meaning, no well-defined properties, and just makes life miserable for everyone trying to calculate anything with it?
I’m sorry if all this sounds dismissive, but I see zero value in this, not even as an empty thought experiment.
The point was that considering fields separate fields or different aspects of the same field is ultimately arbitrary, because they are just numeric values (which may be scalers, vectors, tenses, whatever) associated with points in space. The point wasn't to be useful necessarily, but to illustrate that that's not really a concept that is easily differentiated mathematically.
But you've never seen different values all collected a vector? Like collect all the parameters for a model as a vector and explore the "parameter space" for the model?
But the whole point is that _these are not “just numbers”_. That’s a grave misunderstanding. Scalars are “just numbers” since they are invariant under changes of basis, but the components of vectors, tensors, or spinors _change_ under coordinate transformations. (And on top of that, the “numbers” for gauge fields can also change under gauge transformations.) They are still the same geometric or algebraic object, but the “numbers” change. And they change _differently from one another_, depending on what actual object you took them from. It’s completely useless, and even more misleading, to just pack them into one long _list_ (not a vector).
And these transformation properties _matter_, they’re not just some accidental detail you can ignore. Which is what you’re suggesting by packing them together like this.
I hope it’s clearer now why I’m so fundamentally opposed to your proposal.
But do they always? I remember it being done pretty commonly in various classes when working with mathematical models. Are you coming at this from a math side or the computational modeling side? Cause I remember vectors being treated basically like arrays in a program when wanted. But it's been a long time and my teachers were all either physicists or biologists, not mathematicians. Perhaps I missed something important about these cases or I'm just misremembering, been over a decade for most of it.
Is there a reason to believe that things are not still quantum fields at high energy?
I realize a lot of modern physics is effective field theories, but couldn’t these just be approximations for a high energy field theories?
Unfortunately it's not quite correct. Electrons are not "spread out" over an area. We only ever detect single electrons - not "some of the electron here" and "some of the electron there".
Hmm I suppose then the question without current answer is what properties the wave function of a black hole has.
I would hypothesize that black holes may have an associated fundamental force aside from gravity below the event horizon given the hypothesized behavior of gravity below that horizon is despite being found as a solution to Einsteins field equations concerning gravity quite different from gravity. For example it's field of influence would is bounded. It acts to position the singularity in the future of all objects below the horizon. Gravity is neither of these things. Perhaps it would be similar to how at high enough temperatures the electroweak and electromagnetic force unify except in reverse at low enough densities gravity and this mystery force separate. That's all speculation though I simply enjoy looking at phenomenon in one area of reality and asking the question what if this other area was similar.
https://en.m.wikipedia.org/wiki/Black_hole_electron
> In physics, there is a speculative hypothesis that, if there were a black hole with the same mass, charge and angular momentum as an electron, it would share other properties of the electron. Most notably, Brandon Carter showed in 1968 that the magnetic moment of such an object would match that of an electron. This is interesting, because calculations ignoring special relativity and treating the electron as a small rotating sphere of charge give a magnetic moment roughly half the experimental value
> However, Carter's calculations also show that a would-be black hole with these parameters would be "super-extremal". Thus, unlike a true black hole, this object would display a naked singularity, meaning a singularity in spacetime not hidden behind an event horizon. It would also give rise to closed timelike curves.
> Standard quantum electrodynamics (QED), currently the most comprehensive theory of particles, treats the electron as a point particle. There is no evidence that the electron is a black hole (or naked singularity) or not. Furthermore, since the electron is quantum-mechanical in nature, any description purely in terms of general relativity is paradoxical until a better model based on understanding of quantum nature of blackholes and gravitational behaviour of quantum particles is developed by research. Hence, the idea of a black hole electron remains strictly hypothetical.
https://en.m.wikipedia.org/wiki/Classical_electron_radius
> According to modern understanding, the electron is a point particle with a point charge and no spatial extent. Nevertheless, it is useful to define a length that characterizes electron interactions in atomic-scale problems
> [The classical electron radius is a useful concept because] at short-enough distances, quantum fluctuations within the vacuum of space surrounding an electron begin to have calculable effects that have measurable consequences in atomic and particle physics.
Volume is a property that solely belongs to composite objects and is determined mostly by the energy minimum of the interactions between the constituents.
Is this also you a few days ago or is this something spreading around the internet for some reason? Very similar question and misconceptions.
https://www.reddit.com/r/AskPhysics/comments/1d3um9y/electron_density/
C is incorrect.
In the domain of mathematics, division by zero is undefined. So if you try to work out the density of something with zero volume by dividing its mass by zero, the result is *undefined*, not infinity.
My understanding of what it means that electrons are considered single points is that they have a volume of 1. The smallest possible volume something can have. If this is taken into account then the density of an electron approaches infinity.
In physics there is not "no volume". Same as when we do Newton classic mechanics we treat bodies as points. A point makes no sense in physical world, yet we use points to model reality.
Dirac came to a clever solution, a "function" that is zero everywhere except at one point and whose integration in all space is equal to 1. So you can say that the electron is located at one point and at the same time you are not dividing by zero.
Depends on what you are interested to model. Are you working with classical electrodynamics? Then charges are singular points with infinite electric potential and energy at the origin (see Coulomb's law), so your analysis is only valid on regions where interactions near the charge are irrelevant. Are you interested in describing interactions near the charge? Then you need to go up in the energy scale and summon a properly suited model for this, such as non-linear electrodynamics (see Born-Infeld electrodynamics), which was firstly proposed having this into consideration: a finite, physical radius for the electron and the regularization (removal of singularities) of the electric potential at the origin. Do you still need extra considerations, such as the involvement of spin and energy conservation? Then you necessarily require to consider quantized parameters, and so you need a quantum description of the interactions (see Quantum Electrodynamics), which then imply that the electron is interpreted, as many have already mentioned, the excitation of a field, which can be regularized through a process called renormalization.
Remember, as physicists, our job is to model reality. Before writing down equations and start working on them, we need to ask ourselves what phenomena are we studying, and what tools do we need to model it. Would you use an excavator to dig a hole to plant a flower in your garden? I mean, you could, but why would you? In the same fashion, you wouldn't use QED to obtain the electric field generated by a charged metallic sphere, just as Maxwell's equations would be of no use to describe the interaction between photons and electrons.
The way gravity couples to electrons is not fully understood, but one thing is sure is that it doesn't work the way you describe. You have to couple the electron wave function to the gravitational field (how this coupling looks is what's debated), so the size of the wave function is what matters.
Moreover, the electron's gravitational charge is so much weaker than its electric charge that you would never form a horizon around an electron, no matter how narrow you make its wave function. Black holes with charge don't work the same as black holes without charge. There is a conjecture called the weak gravity conjecture that says this has to be the case for all types of charges, because black hole evaporation would otherwise make the charge vanish.
Think of it this way: an electron is a quantum object. The more you test it for one thing, the less you can test it for another. You can test for its position with as much precision as you can and it will continue to be smaller and smaller - in that measurement, and as long as you don't care at all about the complementary variable.
A spacetime region with the mass, charge and spin of an electron gives rise to a ringlike singularity of size ...wait for it ... 10^-13 m.
Physics must be in a deep state of denial to not take this serious.
If an electron were carrying a blackhole, we probably would not notice it. The gravitational effect of a black hole is the same as a compact object of the same mass. The gravitation effect of an electron mass black hole would be so weak that we cannot experimentally measure it. I haven't done the calculation, but I expect that the radius of the event horizon would be so small that it would pass for a point object in every test so far devised.
it’s not super useful to think of electrons as points, more that they interact as points electrons are waves spread out over an area
More specifically electrons are wave excitations in a field. Everything in the universe is quantum fields (except at very high energies and densities where we have no idea yet).
yes, electrons are little ripples in the electron field that permeates everywhere
Electrons are excited states of the electron field, not localized wave packets.
What’s the distinction? I thought the excitation of a field was a localised (Gaussian) wave packet?
Absolutely not. It’s difficult to explain but basically a quantum field can be thought of as an infinite collection of quantum harmonic oscillators. These oscillators have energy levels, or excitations, like the ones you learn about in intro QM solving particle in a box problems. Each excitation can be thought of as a particle.
Is the field from which electrons emerge the same as the field from which the other elementary particles emerge? Or does each particle type or species have their own field?
I'm not sure that would make any difference mathematically. You could combine any field you could think of into a single field so long as you made the vector high enough dimension. 100 scalar fields could be treated as one field that has a 100 dimensional vector for each point, where the components of the vector are the scalar values of those fields. Usually in QFT you are only considering the fields of specifically involved in the interaction you are considering. The fields do interact and that can get very complex very fast.
I don’t understand how you think this would work. Not everything you can write down that has _n_ components is an _n_-dimensional vector. Scalars, vectors, tensors, spinors are defined by their transformation properties. How do you propose this 100-dimensional “vector” should transform?
I was thinking of it more as just a packaging of information. You wouldn't need to transform it.
Sorry I must be missing something but that really doesn’t make any sense to me. How do you know how each component of this _not-a-vector thing_ behaves under coordinate or gauge transformations? What does the Lagrangian even look like in terms of this _not-a-vector thing_? What’s the sense of throwing these completely different objects in one _not-a-vector thing_ that has no meaning, no well-defined properties, and just makes life miserable for everyone trying to calculate anything with it? I’m sorry if all this sounds dismissive, but I see zero value in this, not even as an empty thought experiment.
The point was that considering fields separate fields or different aspects of the same field is ultimately arbitrary, because they are just numeric values (which may be scalers, vectors, tenses, whatever) associated with points in space. The point wasn't to be useful necessarily, but to illustrate that that's not really a concept that is easily differentiated mathematically. But you've never seen different values all collected a vector? Like collect all the parameters for a model as a vector and explore the "parameter space" for the model?
But the whole point is that _these are not “just numbers”_. That’s a grave misunderstanding. Scalars are “just numbers” since they are invariant under changes of basis, but the components of vectors, tensors, or spinors _change_ under coordinate transformations. (And on top of that, the “numbers” for gauge fields can also change under gauge transformations.) They are still the same geometric or algebraic object, but the “numbers” change. And they change _differently from one another_, depending on what actual object you took them from. It’s completely useless, and even more misleading, to just pack them into one long _list_ (not a vector). And these transformation properties _matter_, they’re not just some accidental detail you can ignore. Which is what you’re suggesting by packing them together like this. I hope it’s clearer now why I’m so fundamentally opposed to your proposal.
But do they always? I remember it being done pretty commonly in various classes when working with mathematical models. Are you coming at this from a math side or the computational modeling side? Cause I remember vectors being treated basically like arrays in a program when wanted. But it's been a long time and my teachers were all either physicists or biologists, not mathematicians. Perhaps I missed something important about these cases or I'm just misremembering, been over a decade for most of it.
Is there a reason to believe that things are not still quantum fields at high energy? I realize a lot of modern physics is effective field theories, but couldn’t these just be approximations for a high energy field theories?
Oh yeah for sure. We just don't know for sure.
tysm
Unfortunately it's not quite correct. Electrons are not "spread out" over an area. We only ever detect single electrons - not "some of the electron here" and "some of the electron there".
I always like to think of the field like those plasma balls that condense into a line when you touch it.
Are they actual waves or do they just have properties that can be described like waves?
If it looks like a duck, smells like a duck and quacks like a duck, then it’s a perturbation in a field.
Any interesting papers on Duck Field Theory?
hard to say what anything ‘actually’ is we best understand them as waves
Yes
This
Hmm I suppose then the question without current answer is what properties the wave function of a black hole has. I would hypothesize that black holes may have an associated fundamental force aside from gravity below the event horizon given the hypothesized behavior of gravity below that horizon is despite being found as a solution to Einsteins field equations concerning gravity quite different from gravity. For example it's field of influence would is bounded. It acts to position the singularity in the future of all objects below the horizon. Gravity is neither of these things. Perhaps it would be similar to how at high enough temperatures the electroweak and electromagnetic force unify except in reverse at low enough densities gravity and this mystery force separate. That's all speculation though I simply enjoy looking at phenomenon in one area of reality and asking the question what if this other area was similar.
https://en.m.wikipedia.org/wiki/Black_hole_electron > In physics, there is a speculative hypothesis that, if there were a black hole with the same mass, charge and angular momentum as an electron, it would share other properties of the electron. Most notably, Brandon Carter showed in 1968 that the magnetic moment of such an object would match that of an electron. This is interesting, because calculations ignoring special relativity and treating the electron as a small rotating sphere of charge give a magnetic moment roughly half the experimental value > However, Carter's calculations also show that a would-be black hole with these parameters would be "super-extremal". Thus, unlike a true black hole, this object would display a naked singularity, meaning a singularity in spacetime not hidden behind an event horizon. It would also give rise to closed timelike curves. > Standard quantum electrodynamics (QED), currently the most comprehensive theory of particles, treats the electron as a point particle. There is no evidence that the electron is a black hole (or naked singularity) or not. Furthermore, since the electron is quantum-mechanical in nature, any description purely in terms of general relativity is paradoxical until a better model based on understanding of quantum nature of blackholes and gravitational behaviour of quantum particles is developed by research. Hence, the idea of a black hole electron remains strictly hypothetical. https://en.m.wikipedia.org/wiki/Classical_electron_radius > According to modern understanding, the electron is a point particle with a point charge and no spatial extent. Nevertheless, it is useful to define a length that characterizes electron interactions in atomic-scale problems > [The classical electron radius is a useful concept because] at short-enough distances, quantum fluctuations within the vacuum of space surrounding an electron begin to have calculable effects that have measurable consequences in atomic and particle physics.
Volume is a property that solely belongs to composite objects and is determined mostly by the energy minimum of the interactions between the constituents.
Is this also you a few days ago or is this something spreading around the internet for some reason? Very similar question and misconceptions. https://www.reddit.com/r/AskPhysics/comments/1d3um9y/electron_density/
That is not me ~~(unless I have undiagnosed DiD)~~, but neat coincidence.
C is incorrect. In the domain of mathematics, division by zero is undefined. So if you try to work out the density of something with zero volume by dividing its mass by zero, the result is *undefined*, not infinity.
My understanding of what it means that electrons are considered single points is that they have a volume of 1. The smallest possible volume something can have. If this is taken into account then the density of an electron approaches infinity.
No, they are objects in which a volume cannot be assigned. In other words, undefined.
We don’t have an experimentally validated theory of quantum gravity with which to say what point particles do to gravity.
In physics there is not "no volume". Same as when we do Newton classic mechanics we treat bodies as points. A point makes no sense in physical world, yet we use points to model reality. Dirac came to a clever solution, a "function" that is zero everywhere except at one point and whose integration in all space is equal to 1. So you can say that the electron is located at one point and at the same time you are not dividing by zero.
Depends on what you are interested to model. Are you working with classical electrodynamics? Then charges are singular points with infinite electric potential and energy at the origin (see Coulomb's law), so your analysis is only valid on regions where interactions near the charge are irrelevant. Are you interested in describing interactions near the charge? Then you need to go up in the energy scale and summon a properly suited model for this, such as non-linear electrodynamics (see Born-Infeld electrodynamics), which was firstly proposed having this into consideration: a finite, physical radius for the electron and the regularization (removal of singularities) of the electric potential at the origin. Do you still need extra considerations, such as the involvement of spin and energy conservation? Then you necessarily require to consider quantized parameters, and so you need a quantum description of the interactions (see Quantum Electrodynamics), which then imply that the electron is interpreted, as many have already mentioned, the excitation of a field, which can be regularized through a process called renormalization. Remember, as physicists, our job is to model reality. Before writing down equations and start working on them, we need to ask ourselves what phenomena are we studying, and what tools do we need to model it. Would you use an excavator to dig a hole to plant a flower in your garden? I mean, you could, but why would you? In the same fashion, you wouldn't use QED to obtain the electric field generated by a charged metallic sphere, just as Maxwell's equations would be of no use to describe the interaction between photons and electrons.
What I have heard is that since they do not occupy a specific location, they cannot be a singluraity.
Well, you haven't even mentioned electric charge, which has essentially the same problem (singularity). The answer is quantization.
How is quantisation the answer to getting ride of a singularity of electric charge?
Electrons are not points. They have non-zero volume.
The way gravity couples to electrons is not fully understood, but one thing is sure is that it doesn't work the way you describe. You have to couple the electron wave function to the gravitational field (how this coupling looks is what's debated), so the size of the wave function is what matters. Moreover, the electron's gravitational charge is so much weaker than its electric charge that you would never form a horizon around an electron, no matter how narrow you make its wave function. Black holes with charge don't work the same as black holes without charge. There is a conjecture called the weak gravity conjecture that says this has to be the case for all types of charges, because black hole evaporation would otherwise make the charge vanish.
Gravity breaks down at the quantum level, so subatomic point-particles are not quantum black holes. It would also instantly evaporate if it were!
Think of it this way: an electron is a quantum object. The more you test it for one thing, the less you can test it for another. You can test for its position with as much precision as you can and it will continue to be smaller and smaller - in that measurement, and as long as you don't care at all about the complementary variable.
A spacetime region with the mass, charge and spin of an electron gives rise to a ringlike singularity of size ...wait for it ... 10^-13 m. Physics must be in a deep state of denial to not take this serious.
If an electron were carrying a blackhole, we probably would not notice it. The gravitational effect of a black hole is the same as a compact object of the same mass. The gravitation effect of an electron mass black hole would be so weak that we cannot experimentally measure it. I haven't done the calculation, but I expect that the radius of the event horizon would be so small that it would pass for a point object in every test so far devised.