When the electron, the first subatomic particle to be identified, was discovered in 1897, it was thought to be a tiny speck with electric charge, moving around on a path governed by the forces of electricity, magnetism and gravity. This was just as one would expect for any small object, given the incredibly successful approach to physics that had been initiated by Galileo and Newton and carried onward into the 19th century.
But this view didn’t last long. Less than 15 years later, physicists learned that an atom has a tiny nucleus with positive electric charge and most of an atom’s mass. This made it clear that something was deeply wrong, because if Newton’s and Maxwell’s laws applied, then all the electrons in an atom should have spiraled into the nucleus in less than a second.
From 1913 to 1925, physicists struggled toward a new vision of the electron. They had great breakthroughs and initial successes in the late 1920s. But still, something was off. They did not really find what they were looking for until the end of the 1940s.
Most undergraduates in physics, philosophers who are interested in physics, and general readers mainly learn about quantum physics of the 1920s, that of Heisenberg, Born, Jordan and of Schrödinger. The methods developed at that time, often called “quantum mechanics” for historical reasons, represented the first attempt by physicists to make sense of the atomic, molecular, and subatomic world. Quantum mechanics is all you need to know if you just want to do chemistry, quantum computing, or most atomic physics. It forms the basis of many books about the applications of quantum physics, including those read by most non-experts. The strange puzzles of quantum physics, including the double-slit experiment that I reviewed recently, and many attempts to interpret or alter quantum physics, are often phrased using this 1920s-era approach.
What often seems to be forgotten is that 1920s quantum physics does not agree with data. It’s an approximation, and sometimes a very good one. But it is inconsistent with Einstein’s relativity principle, a cornerstone of the cosmos. This is in contrast to the math and concepts that replaced it, known as relativistic quantum field theory. Importantly, electrons in quantum field theory are very different from the electrons of the 1920s.
And so, when trying to make ultimate conceptual sense of the universe, we should always be careful to test our ideas using quantum field theory, not relying on the physics of the 1920s. Otherwise we risk developing an interpretation which is inconsistent with data, at a huge cost in wasted time. Meanwhile, when we do use the 1920s viewpoint, we should always remember its limitations, and question its implications.
Overview
Before I go into details, here’s an overview.
I have argued strongly in my book and on this blog that calling electrons “particles” is misleading, and one needs to remember this if one wants to understand them. One might instead consider calling them “wavicles“, a term itself from the 1920s that I find appropriate. You may not like this term, and I don’t insist that you adopt it. What’s important is that you understand the conceptual point that the term is intended to convey.
Most crucially, electrons as wavicles is an idea from quantum field theory, not from the 1920s (though a few people, like de Broglie, were on the right track.) In the viewpoint of 1920s quantum physics, electrons are not wavicles. They are particles. Quantum particles.
Before quantum physics, an electron was described as an object with a position and a velocity (or a momentum, which is the electron’s mass times its velocity), moving through the world along a precise path. But in 1920s quantum physics, an electron is described as a particle with a position or a momentum, or some compromise between the two; its path is not definite.
In Schrödinger’s viewpoint [and I emphasize that there are others — his approach is just the most familiar to non-experts], there is a quantum wave function (or more accurately, a quantum state) that tells us the probabilities for the particle’s behavior: where we might find it, and where it might be going.
A wave function must not be identified with the particle itself. No matter how many particles there are, there is only one wave function. Specifically, if there are two electrons, then a single quantum wave function tells us the probabilities for their joint behavior — for the behavior of the system of two electrons. The two electrons are not independent of one another; in quantum physics I can’t say what one’s behavior might be without worrying about what the other is doing. The wave function describes the two electrons, but it is not either one of them.
Then we get to quantum field theory of the late 1940s and beyond. Now we view an electron as a wave — as a ripple in a field, known as the electron field. The whole field, across all of space, has to be described by the wave function, not just the one electron. (In fact, that’s not right either: our wave function has to simultaneously describe all the universe’s fields.) This is very different conceptually from the ’20s; the electron is never an object with a precise position, and instead it is generally spread out.
So it’s really, really important to remember that it is relativistic quantum field theory that universally agrees with experiments, not the quantum physics of the ’20s. If we forget this, we risk drawing wrong conclusions from the latter. Moreover, it becomes impossible to understand what modern particle physicists are talking about, because our description of the physics of “particles” relies on relativistic quantum field theory.
The Electron Over Time
Let me now go into more detail, with hope of giving you some intuition for how things have changed from 1900 to 1925 to 1950.
1900: Electrons Before Quantum Physics
A Simple Particle
Pre-quantum physics (such as one learns in a first-year undergraduate course) treats an electron as a particle with a definite position which changes in a definite way over time; it has a definite speed v which represents the rate of the change of its position. The particle also has definite momentum p equal to its mass m times its speed v. Scientists call this a “classical particle”, because it’s what Isaac Newton himself, the founder of old-school (“classical”) physics would have meant by the word “particle”.
Two Simple Particles
Two particles are just two of these objects. That’s obvious, right? [Seems as though it ought to be. But as we’ll see, quantum physics says that not only isn’t it obvious, it’s false.]
Two Particles in the “Space of Possibilities”
But now I’m going to do something that may seem unnecessarily complicated — a bit mind-bending for no obvious purpose. I want to describe the motion of these two particles not in the physical space in which they individually move but instead in the space of possibilities for two-particle system, viewed as a whole.
Why? Well, in classical physics, it’s often useful, but it’s also unnecessary. I can tell you where the two particles are in physical space and be done with it. But in quantum physics I cannot. The two particles do not, in general, exist independently. The system must be viewed as a whole. So to understand how quantum physics works, we need to understand the space of possibilities for two classical particles.
This isn’t that hard, even if it’s unfamiliar. Instead of depicting the two particles as two independent dots at two locations A and B along the line shown in Fig. 2, I will instead depict the system by indicating a point in a two-dimensional plane, where
- the horizontal axis depicts where the first particle is located
- the vertical axis depicts where the second particle is located
To make sure that you remember that I am not depicting any one particle but rather the system of two particles, I have drawn what the system is doing at this moment as a star in this two-dimensional space of possibilities. Notice the star is located at A along the horizontal axis and at B along the vertical axis, indicating that one particle is at A and the other is at B.
Moreover, in contrast to the two arrows in physical space that I have drawn in Fig. 2, each one indicating the motion of the corresponding particle, I have drawn a single arrow in the space of possibilities, indicating how the system is changing over time. As you can see from Fig. 2,
- the first particle is moving from A to the right in physical space, which corresponds to rightward motion along the horizontal axis of Fig. 3;
- the second particle is moving from B to the left in physical space, which corresponds to downward motion along the vertical axis in Fig. 3;
and so the arrow indicating how the system is changing over time points downward and to the right. It points more to the right than downward, because the motion of the particle at A is faster than the motion of the particle at B.
Why didn’t I bother to make a version of Fig. 3 for the case of just one particle? That’s because for just one particle, physical space and the space of possibilities are the same, so the pictures would be identical.
I suggest you take some time to compare Figs. 2 and 3 until the relationship is clear. It’s an important conceptual step, without which even 1920s quantum physics can’t make sense.
If you’re having trouble with it, try this post, in which I gave another example, a bit more elaborate but with more supporting discussion.
1925: Electrons in 1920s Quantum Physics
A Quantum Particle
1920s quantum physics, as one learns in an upper-level undergraduate course, treats an electron as a particle with position x and momentum p that are never simultaneously definite, and both are generally indefinite to a greater or lesser degree. The more definite the position, the less definite the momentum can be, and vice versa; that’s Heisenberg’s uncertainty principle applied to a particle. Since these properties of a particle are indefinite, quantum physics only tells us about their statistical likelihoods. A single electron is described by a wave function (or “state vector”) that gives us the probabilities of it having, at a particular moment in time, a specific location x0 or specific momentum p0. I’ll call this a “quantum particle”.
How can we depict this? For a single particle, it’s easy — so easy that it’s misleading, as we’ll see when we go to two particles. All we have to do is show what the wave function looks like; and the wave function [actually the square of the wave function] tells us about the probability of where we might find the particle. This is indicated in Fig. 4.
As I mentioned earlier, the case of one particle is special, because the space of possibilities is the same as physical space. That’s potentially misleading. So rather than think too hard about this picture, where there are many potentially misleading elements, let’s go to two particles, where things look much more complicated, but are actually much clearer once you understand them.
Two Quantum Particles
Always remember: it’s not one wave function per particle. It’s one wave function for each isolated system of particles. Two electrons are also described by a single wave function, one that gives us the probability of, say, electron 1 being at location A while electron 2 is simultaneously at location B. That function cannot be expressed in physical space! It can only be expressed in the space of possibilities, because it never tells us the probability of finding the first electron at position 1 independent of what electron 2 is doing.
In other words, there is no analogue of Fig. 2. Quantum physics is too subtle to be squeezed easily into a description in physical space. Instead, all we can look for is a generalization of Fig. 3.
And when we do, we might find something like what is shown in Fig. 5; in contrast to Fig. 4, where the wave function gives us a rough idea of where we may find a single particle, now the wave function gives us a rough idea of what the system of two particles may be doing — and more precisely, it gives us the probability for any one thing that the two particles, collectively, might be doing. Compare this figure to Fig. 2.
In Fig. 2, we know what the system is doing; particle 1 is at position A and particle 2 is at position B, and we know how their positions are changing with time. In Fig. 5 we know the wave function and how it is changing with time, but the wave function only gives us probabilities for where the particles might be found — namely that they are near position A and position B, respectively, but exactly can’t be known known until we measure, at which point the wave function will change dramatically, and all information about the particles’ motions will be lost. Nor, even though roughly that they are headed right and left respectively, we can’t know exactly where they are going unless we measure their momenta, again changing the wave function dramatically, and all information about the particles’ positions will be lost.
And again, if this is too hard to follow, try this post, in which I gave another example, a bit more complicated but with more supporting discussion.
1950: Electrons in Modern Quantum Field Theory
1940s-1950s relativistic quantum field theory, as a future particle physicist typically learns in graduate school, treats electrons as wave-like objects — as ripples in the electron field.
[[[NOTA BENE: I wrote “the ElectrON field”, not “the electrIC field”. The electrIC field is something altogether different!!!]]]
The electron field (like any cosmic field) is found everywhere in physical space.
(Be very careful not to confuse a field, defined in physical space, with a wave function, which is defined on the space of possibilities, a much larger, abstract space. The universe has many fields in its physical space, but only one wave function across the abstract space of all its possibilities.)
In quantum field theory, an electron has a definite mass, but as a ripple, it can be given any shape, and it is always undergoing rapid vibration, even when stationary. It does not have a position x, unlike the particles found in 1920s quantum field theory, though it can (very briefly) be shaped into a rather localized object. It cannot be divided into pieces, even if its shape is very broadly spread out. Nevertheless it is possible to create or destroy electrons one at a time (along with either a positron [the electron’s anti-particle] or an anti-neutrino.) This rather odd object is what I would mean by a “wavicle”; it is a particulate, indivisible, faint wave.
Meanwhile, there is a wave function for the whole field (really for all the cosmic fields at once), and so that whole notion is vastly more complicated than in 1920s physics. In particular, the space of possibilities, where the wave function is defined, is the space of all possible shapes for the field! This is a gigantic space, because it takes an infinite amount of information to specify a field’s shape. (After all, you have to tell me what the field’s strength is at each point in space, and there are an infinite number of such points.) That means that the space of possibilities now has an infinite number of dimensions! So the wave function is a function of an infinite number of variables, making it completely impossible to draw, generally useless for calculations, and far beyond what any human brain can envision.
It’s almost impossible to figure out how to convey all this in a picture. Below is my best attempt, and it’s not one I’m very proud of. Someday I may think of something better.
I’ve drawn the single electron in physical space, and indicated one possible shape for the field representing this electron, along with a blur and a question mark to emphasize that we don’t generally know the shape for the field — analogous to the fact that when I drew one electron in Fig. 4, there was a blur and question mark that indicated that we don’t generally know the position of the particle in 1920s quantum physics.
[There actually is a way to draw what a single, isolated particle’s wave function looks like in a space of possibilities, but you have to scramble that space in a clever way, far beyond what I can explain right now. We’ll see it later this year.]
Ugh. Writing about quantum physics, even about non-controversial issues, is really hard. The only thing I can confidently hope to have conveyed here is that there is a very big difference between electrons as they were understood and described in 1920’s quantum physics and electrons as they are described in modern quantum field theory. If we get stuck in the 1920’s, the math and concepts that we apply to puzzles like the double slit experiment and “spooky action at a distance” are never going to be quite right.
As for what’s wrong with Figure 6, there are so many things, some incidental, some fundamental:
- The picture I’ve drawn would be somewhat accurate for a Higgs boson as a ripple in the Higgs field. But an electron is a fermion, not a boson, and trying to draw the ripple without being misleading is kind of impossible.
- The electron field is given by a complex number, and in fact more than one, so drawing it as though it has a shape like the one shown in Fig. 6 is an oversimplification.
- At best, Fig. 6 sketches how an electron would look if it didn’t experience any forces. But because electrons are electrically charged and do experience electric and magnetic forces, we can’t just show the electron field without showing the electromagnetic field too; the wave function for an electron deeply involves both. That gets super-complicated.
- The wave function is suggested by a vague blur, but in fact it always has more structure than can be depicted here.
- And there are probably more issues, as I’m sure some readers will point out. Go ahead and do so; it’s better to state all the flaws out loud.
What about two electrons — two ripples in the electron field? This is currently beyond my abilities to sketch. Even ignoring the effects of electric and magnetic forces, describing two electrons in quantum field theory in a picture like Fig. 6 seems truly impossible. For one thing, because electrons are precisely identical in quantum field theory, there are always correlations between the two electrons that cannot be avoided — they can never be independent, in the way that two classical electrons are. (In fact this correlation even affects Fig. 5; I ignored this issue to keep things simpler.) So they really cannot be depicted in physical space. But the space of possibilities is far too enormous for any depiction (unless we do some serious rescrambling — again, something for later in the year, and even then it will only work for bosons.)
And what should you take away from this? Some things about quantum physics can be understood using 1920’s language, but not the nature of electrons and other elementary “particles”. When we try to extract profound lessons from quantum physics without using quantum field theory, we have to be very careful to make sure that those lessons still apply when we try to bring them to the cosmos we really live in — a cosmos for which 1920’s quantum physics proved just as imperfect, though still useful, as the older laws of Newton and Maxwell.
33 Responses
I suppose you could replace the two electrons with neutrinos and thus avoid the EM field. But that introduces the Weak force and I have no idea if two neutrinos interact that way.
It doesn’t really help; first, the correlations between the two neutrinos are still there, and second, although the weak nuclear force’s effects are small and can often be ignored, they’re still there, and sometimes they might matter, as inside a forming supernova. Gravity, too, is small but can’t always be ignored.
And in any case, we still need to be able to describe electrons!
Hello, thanks for your explanations. The main question as far as I am concerned is that the wave function is a complex function that does not exist in the 3D physical space and still is used to describe the quantum objects like electrons, protons, etc that’s presumably exist in 3D space ( + time). This is fundamental contraction that causes all these uncertainties as what election really is, how it can be described and so on, including completely unexplainable property of spin. The conclusion is that we do not have the adequate equations for quantum mechanics yet, and if and when we have those equations all these contradictions will disappear. What do you think? Thanks BT
I don’t know what to think. My goal here is to lay out what we know clearly enough that more of us can understand the conceptual problems well. But whether and how these problems will ever be resolved, I have no idea.
I was able to derive the mass of the electron muon and tau proportionally using geometric volumes.. suggesting electrons are inverted space along with the familiar particle when measured.
https:// [Link removed by host]
Zephyr: what you say seems to make sense: could you give me some of your resources?
We are describing what an electron does better, but don’t really know what or why it is. Electron fields sidestep the issue entirely. There are certainly hints from Dirac theories and his electron hole model, black hole electron model, and approximate equivalence of electron and self field energies, but I fear we are missing a very important part of the picture. One thing I think is for sure is that once we have a satisfactory epistemological theory that can calculate the fine structure constant (and thus electron mass) we will understand a lot more about quarks, gluons, and even quantum gravity than we do now. I fear we’ve taken the “shut up and calculate model” to far. It certainly produces useful results more quickly, but if we are in this for the long haul, we need to think outside of the box about what we really do and do not know. My bias is that we are using the wrong substrate by relying too much upon a Euclidean or nonEuclidean continuous metric space, and this has something to do with how we could create spatial backdrop from observations through time alone. A complete theory would let space and all its potential topological and other defects arise naturally. There should be some impetus also with regards to untested assumptions. For example, with regards to how an electron (or any charged particle) reacts with gravity, we really don’t know as the forces are so extremely different that no experiment to my knowledge can verify even that an electron falls down, up, or something different in a gravitational field. All we know now is that neutral matter and antimatter appears to.
Thank you for these posts! Yours is the only blog where I have encountered the concept of a particle being a disturbance in a field. If that is true, here is a question I wish you would address sometime: what makes the disturbance stable? Why doesn’t it simply dissipate like a ripple in a pond? What keeps the disturbance localized? And when a particle does disintegrate into multiple particles, what makes that happen?
Thanks
You’re using the word “dissipate” in two natural ways, but they are different and conflating them is going to be very confusing. So let’s separate them carefully.
A localized object can dissipate in the sense of spreading out, yet without losing any energy. A better word would simply be “spread”.
An object with energy can suffer dissipation, as with friction, in which some of its energy is dissipated away into other forms, such as heat. This is how physicistst use the term “dissipate”.
Nothing stops a “particle” like an electron from spreading (without losing energy) and indeed that’s exactly what they do if you leave them alone. If you put an electron into a box, it will eventually spread out across the box — because it is more wave than particle, and that’s what waves do. You can’t put a localized wave in a box and expect it to remain localized. So the answer to your 2nd and 3rd questions are: it doesn’t remain localized unless something is keeping it localized; it spreads out (without dissipating its energy), somewhat like a ripple in a pond but potentially more slowly because it has mass. I’ve written several blog posts in the past year about how a stationary electron behaves; the links to these posts are all found in the first paragraph of this webpage on chapter 17 of my recent book. I hope they will help you get the intuition you’re looking for. Also, stay tuned for my next blog post, which is also relevant.
As for your first and fourth question, they are related. The disturbance may or may not be stable (now we are talking not about its shape, which will generally spread out, but about its very existence) and if it is unstable it will disintegrate into multiple particles. Simply put, it will be stable if there are no ways for it to disintegrate without violating consistency conditions; only electrons, photons, gluons in a sense, the lightest quark, the lightest neutrino, and gravitons if they exist, satisfy such conditions. I went through those conditions here: https://profmattstrassler.com/articles-and-posts/particle-physics-basics/why-do-particles-decay/most-particles-decay-yet-some-dont/
Otherwise it will inevitably disintegrate, and that disintegration is a quantum form of dissipation (again, in the physics sense, since the particle’s energy is now stolen and given to other particles.) Unlike friction, which steals the energy gradually, quantum dissipation steals the energy all at once. An intuitive sense of this is that it is not entirely unlike the vibrational energy of a guitar string being dissipated into sound waves — one type of vibration being converted into another and carrying the energy away, only suddenly instead of gradually. This is indeed a pretty good analogy, but not a precise one. If you want something more precise, and you are comfortable with first-year university math, you might want to read my series https://profmattstrassler.com/articles-and-posts/particle-physics-basics/fields-and-their-particles-with-math/ When you get to the eight and final page in that series, you’ll see how interactions among fields sometimes allow one particle to be created from two others. The disintegration process is essentially the same thing reversed in time.
In dense aether model space-time (i.e. the classical vacuum) is foamy system embedded in false vacuum (something like density fluctuations of supercritical fluid), which gets more dense temporarily once some energy wave passes through it in similar way, like the soap foam inside of evacuated vessel once it gets shaken. The space-time will get deformed and curved and it will start to behave like gravitational lens for another energy waves passing this particular place in similar way like water surface for surface ripples once it gets shaken. This behavior follows from mass-energy equivalence, which has many apparent consequences, which are recognized but still ignored by mainstream physics so far.
One of them is, that every electromagnetic wave is connected with density blob of vacuum, so-called graviton, which gives soliton character to it (photon) and which also slows-down the wave propagation. When this wave gets sufficient energy density (for instance when two photons will met), then the vacuum will get so dense in this moment, that the portion of its energy will start to undulate at place inside of resulting blob, which is what we call an electron. The electron is thus a standing wave of transverse and longitudinal wave of vacuum, which resonate mutually and which orbit each other in structure resembling Mobius strip or tiny toroidal black hole.
The OP article reflects confusion of mainstream physics, because it doesn’t touches subject too much and it interchanges notion of electron, i.e. particle itself with quantum field i.e. pilot wave around it. Once some energy gets localized, then it will start to shield surrounding density wave of vacuum, which results in local excess of virtual photons around it, i.e. pilot wave. But this pilot wave isn’t part of electron by itself, it’s just a “quantum atmosphere” of it and it changes size and geometry, once the electron gets into motion in similar way, like wake wave around boat floating at the water surface.
‘given by a complex numbers’; is that a single complex number or more than one? My mathematical understanding is too weak to guess.
Issues like this are why I am not a fan of any attempt to retain particle terminology. The more we learn, the less little round balls of stuff seem to matter.
Fermions are complicated. It can depend how you count, which is why I punted on being specific. In 3+1 space-time dimensions, the Dirac fermion has four (but that reduces to 2 when you account for the equations of motion); Weyl and Majorana fermions have half as many. (And for quarks, which each come in three “colors”, multiply these numbers by 3.)
Dr. Strassler, thank you for your efforts to explain these concepts to the public! I’ve been trying for quite a while to figure out how to understand quantum foundations / different interepretations of quantum mechanics in the context of QFT, so definitely looking forward to your further posts on this subject.
Are there mathematical problems with defining a wavefunction on an infinite-dimensional configuration space? From what I understand it isn’t possible to normalize such a function, and my sources on QFT get pretty handwavy about this. (Granted, my main QFT resource has been Lancaster and Blundell’s “QFT for the Gifted Amateur”, which is probably not the most rigorous!)
When you say that it is possible to “scramble” the space of possibilities for the field in a way that makes it possible to visualize the quantum state for an isolated particle – is this referring to Fock space?
One more question – as I understand it, for a bosonic field, it is possible to view the quantum state as a superposition of states with definite field configurations, much as it is possible to view the wavefunction in 1920’s QM as a superposition of states with definite particle positions. However, for a fermionic field, because the field operators do not commute, there are no states corresponding to definite field configurations. (I’m assuming this is why you indicated that Figure 6 is not as accurate for an electron as it would be for a Higgs boson.) But I see that we can find states with definite numbers of excitations of the field at each spatial location (which essentially looks like a configuration of point-like charges after all!?), and describe the full state as superpositions of those – or we can use a basis of states with definite numbers of excitations for each plane-wave mode instead. So are there also states where the field is definitely excited with some arbitrary shape (intermediate between point-localization and plane-wave)?
Thanks!
Okay, these questions are too advanced for me to answer with details here; if you want more details, ask me at https://profmattstrassler.com/contact-me/ The short answers are
Yes, I’m sure there are horrendous problems defining a wave function for interacting field theory. For free field theory the wave function factorizes easily [into an infinite set of harmonic oscillators]; but who cares?
Yes, the scrambling refers to Fock space [again, harmonic oscillator states]. And again: easy for free field theory, and horrendously hard in the interesting, interacting case.
“States with definite numbers of exictations of the field at each spatial location” — I’m not following what you mean, so send me the math.
In general, most interacting field theories have not been defined to the satisfaction even of a physicist, much less a mathematician.
Thanks for the reply! I will try to clarify the last question and send you a message through your contact form.
Hi Matt, Not sure if you were able to answer Matthew’s questions offline but I’m wondering about it too.
When I read Matthew’s question with “States with definite numbers of excitations of the field at each spatial location” I was thinking that he was talking about what is happening inside the “wave function” and if you can get more “definite numbers” for the “point-like charges” throughout of the wave function duration or is it just values in at the start and out at the end? Is that what he was referring to?
Also when you say “most interacting field theories have not been defined to the satisfaction even of a physicist”, are those “interacting field theories” the ones needed for particle accelerator calculations and is that a problem?
Thanks, Pete
Dr.Strassler:
in figure 6. I know you said that you want to avoid being misleading, but would a somewhat correct interpretation be that the electron is somewhat localized around position A, which I’m assuming means the highest probability is that it is somewhere near A……..however, the tails of the blue blur trail off asymptotically towards zero. So, while the highest probability is the electron is around A, the probability of it being somewhere in the tails is never exactly Zero. Would that be a correct understanding?
It’s a great question, because it really nails what the problem is when we try to draw anything that tries to capture the whole situation.
Remember the wave function is telling us the probability of the field’s shape. And the field’s shape (like a particle’s position in 1920s quantum physics) is generally indefinite — or rather, we cannot know both the field’s shape and how it is changing (just as we cannot know a particle’s position and motion simultaneously in 1920s quantum physics.) And therefore, the blue blur is telling us what we do not know about the field’s shape, and not necessarily what we do not know about the electron’s position.
In fact, if there were no electron there at all, there would still be a blue blur, because even in the vacuum of empty space, the field’s shape and the change in its shape cannot be simultaneously known.
Maybe, when I revise this post after I get some comments like yours, I’ll make a figure that shows this explicitly. Thanks for the question.
Dr.Strassler:
I posted a similar question on your other post, but after rereading this post, I realized that figure 6 gives “visualization” of my question. In figure 6, what would the DeBroglie wavelength be defined as? Would it be the distance between crests, even though the amplitude of the crests is getting smaller in the tails of the blue blur?
The DeBroglie wavelength is only defined as the inverse of the momentum, lambda = h/p, where h is Planck’s constant. If the momentum is uncertain, as it is in most states, then so is the DeBroglie wavelength. In Fig. 6 the momomentum (and wavelength) have small but non-zero uncertainty; we cannot say exactly what either of them is. This corresponds to the fact that we know rather roughly where the particle is, whereas the location of the particle would be completely unknown if the momentum and deBroglie wavelength were precisely known.
“our wave function has to simultaneously describe all the universe’s fields”
Interesting. Doesn’t that violate the speed of light limit? If I use classical confinement to capture an electron within a well-define container, how long does it take that new relationship to other electrons to propagate outward? I’m not talking about entanglement, of course, just the spread of wavefunction change information as limited by lightspeed.
According to quantum field theory, this universe is a quantum universe. The wave function already describes everything, and there is no such thing as “classical confinement” that somehow exists outside the wave function.
Now you could dispute this (and some do.) But if you do so, then you have to argue that the wave function collapses when classical physics comes into contact with quantum physics. That collapse must indeed be faster than c (if you are to explain the famous spooky action at a distance and Bell’s theorem.) That’s okay, because the wave function is not a thing, and does not exist in physical space, only in the space of possibilities.
Einstein’s theory of relativity applies to objects in physical space — to things — whereas the wave function, as a description of things, a description that exists only in the space of possibilities, need not satisfy some naive notion of relativity. There is no notion of speed in the space of possibilities, so in fact the wave function *cannot* satisfy the relativity principle. Instead, the wave function need only assure that the things that it describes remain constrained by the speed c.
“The wave function already describes everything, and there is no such thing as ‘classical confinement’ that somehow exists outside the wave function.”
This sounds like Everett’s MWI quantum wave function, which develops with infinite complexity regardless of mass and energy constraints on information density. Are you an MWI advocate?
Not so; I am simply describing the solution to the Schrodinger wave equation.
The Many-Worlds Interpretation says that we must view the Schrodinger wave function as capturing reality — that every branch of the wave function is equally real. I am not advocating for that, or for any other interpretation; I view the question as open.
What is an electric charge? Please, don’t describe it as a charged particle affected by the electric and magnetic fields.
What is it? Fundamental, how does this small space filled with “energy” get charged?
Same question can also be asked about the color charge.
I ask it because it seems like all QFT can be derived by “charged particles”.
We do not know the origin or fundamental cause of electric charge. We know what electric charge does (it causes effects on and feels effects of electric and magnetic fields.) But we do not know what it is, or whether that’s even a meaningful question.
We do know many possibilities for how electric charge might arise, especially from theories with extra dimensions of space. But we don’t know if any of them are correct. Nor can we be sure that electric charge even has a more fundamental cause. Some basic things may just exist, no explanation possible.
Is it remotely possible that “charge” is the phase shift (+ and -) to maintain symmetry, i.e. keep the atom neutral and stable.
So, assume the can be describes by one wavefunction, composed of quarks and elections the + charged protons have a + phase shift w.r.t. the election and hence the election will acquire a – phase shift (charge) to keep the atom from decay.
So, why would a free electron keep it’s – charge? Because it’s “floating in a sea of + charged vacuum energy, ZPE.
Is this a plausible theory? This concept of charge could very well explain the strong force by way of quantum gravity.
Hi Professor, I really don’t want to bother you but this question is a doozy! Since you’re not coming to the March APS mtg,.. Anytime you want to review a theory that provides a mechanism of how an electric charge is formed along with the mechanism of what creates an electric field and a magnetic field (along with why elementary magnetic monopole particles are not possible), just contact me and I’ll fly up to Boston for you to review this theory. Again I think you will be fascinated.
Thanks, very clear (under the circumstances)!
Makes me curious about the scrambled version (but there are several months left of this year).
“struggled toward _struggled_toward_a_new_vision” -> “_struggled_toward_a_new_vision”
“a definite speed v which represents the rate of the change of its motion” -> “… position”
“[[[NOTA BENE: …]” -> “[NOTA BENE: …]”
“it is always undergoing rapid vibration” and “it is a … gentle wave” are … difficult to reconcile.
It can be fun/challenging to understand the changes of physical interpretation in the past. It is more challenging to understand such changes during one’s lifetime. For me, I was surprised to learn that what was the strong force of my youth became the residual strong force of today. (I’m used to it now.)
Thanks for pointing out the typos.
The question is: what is going to happen to the space-time of your youth.
Thank you for this attempt that makes us think. Is it not necessary to add that from 1920 onward, an electron not only has a position and a momentum, but also a spin ?
It is true that the idea of spin was a new one, and only possible in quantum physics. But I didn’t want to get into it today, as the fact that the electron has spin is tangential to the issues I focused on here, all of which would have been the same even if the electron been spinless.