One of the fundamental questions for any freshman studying physics is the following: if an electron orbits around a nucleus, the various accelerations and decelerations should cause it to emit electromagnetic radiation. Hence, it should gradually lose energy and, therefore, the orbital cannot be stable. Therefore, the atom cannot be stable. So we have a problem. 🙂
A related but different question is: why don’t the electron and the nucleus simply crash into each other? They attract each other, very strongly, right? Well… Yes. But, as I said, that’s a related but different question. Let me first try to handle the first one – as good as I can. 🙂
So… Well… It’s a simple question but – as you know by now – the science of physics seldom gives us simple answers to simple questions. Worse, I’ve studied physics for many years now – admittedly, in my own stubborn, critical and generally limited way 🙂 – and I feel the answer I am getting is not only complicated but also not very real. So… Well… We might want to think we probably do not quite understand what is going on really.
This lack of understanding is nothing to be ashamed of, as great physicists such as Richard Feynman (and others) acknowledge: “Atomic behavior appears peculiar and mysterious to everyone—both to the novice and to the experienced physicist. Even the experts do not understand it the way they would like to.” So… Well… If you’d be in need of a rather spectacular acknowledgement of the shortcomings of physics as a science, there you have it: physicists don’t understand their own science, it seems. 🙂 But let’s go beyond that. Let’s talk about the wavefunction because… Well… You know it’s supposed to describe the electron, right? So what is it?
Well… Unfortunately, physics textbooks won’t tell you what the wavefunction is. They’ll tell you it’s a mathematical construct. A solution to some differential equation (Schrödinger’s equation), to be precise. 😦 However, they will you – from time to time, at least – tell you what it isn’t. For example, Feynman’s most precise description of the model of an electron – or an electron orbital, I should say – might be the one he offers when, while deriving the electron orbitals from Schrödinger’s equation, he says what the wavefunction is surely not:
“The wave function Ψ(r) for an electron in an atom does not describe a smeared-out electron with a smooth charge density. The electron is either here, or there, or somewhere else, but wherever it is, it is a point charge.” (Feynman’s Lectures, Vol. III, p. 21-6)
So… Well… That’s not too bad as an explanation. 🙂 But… Well… While fairly precise, I’d think we can improve on Feynman’s language. For starters, we should distinguish the concept of an electron and the concept of its charge. When the electron is in some stable configuration – i.e. in an orbital as described by its wavefunction Ψ(r) – the idea of the electron combines both the orbital and the point charge. Let’s be precise here:
- The charge is what, when probing, we’ll effectively find “here, there, or somewhere else” in the space that is being described by our wavefunction Ψ(r).
- As for the electron… Well… We know that – by applying operators to the wavefunction – we’ll not only get information about its position, but also about its linear or angular momentum, its energy, and whatever other characteristic of the electron that we’re describing. In that sense, we might say that the wavefunction completely describes the electron and that, therefore, the electron is not the point charge itself, but the orbital, as described by the wavefunction, with its point charge somewhere.
In short, for all practical purposes, we might say that the electron is the wavefunction, and vice versa. 🙂 Indeed, when studying quantum mechanics, one effectively does end up equating the particle with its wavefunction, not with its charge. And rightly so ! An elementary particle – be it an electron or a quark – is more than just its charge: it has energy, momentum (linear or angular), occupies some space and – in the case of quarks – has a color too ! 🙂
But that still doesn’t answer the simple question I started out with: the electrons – or the point charges in those orbitals – don’t emit radiation. Why not? Well… If I’d be your professor, and you’d be sitting for an exam in front of me, then I’d expect you to start talking about the Uncertainty Principle, wavefunctions, energy states and what have you. But I am not your professor (I am not a professor at all, in fact), and so I don’t want hear that answer. To be precise, I don’t like that answer because, just like Feynman, I don’t quite understand it the way I would like to understand it! So… What other answer can we think of? Can we think of something that is, perhaps, more intuitive?
I think we can. I, for one, am thinking, once more, of that profound statement that Einstein made back in 1916, when explaining his relativity theory to a broader audience:
“Physical objects are not in space, but these objects are spatially extended. In this way, the concept “empty space” loses its meaning.”
In fact, I’d go one step further and say: objects create their own space.
Huh? Yes. Think of the planets – including Earth – going around the Sun. Einstein’s general relativity theory tells us they are in their own space. Indeed, Einstein told us we should not think of gravitation as a force: the masses involved just curve the space-time fabric around them in such a way that these planets just keep going and going around and around. They are basically moving in free space: their path just happens to be curved from our perspective. If we wouldn’t impose this abstract (or mathematical, I should say) rectangular Cartesian coordinate space on our description of them, but accept this system of large objects creates its own space, we’d understand why it’s stable: it doesn’t need any energy from the outside to keep going. Nor does it radiate anything out.
Let me emphasize this point: they are in their own space because they don’t radiate anything out. And, I should add, nor do they absorb any energy from the outside. Of course, you’ve heard about gravitational waves – and most notably the one detected by the LIGO Lab last year – but note that gravitational wave was created when two black holes spectacularly merged. That’s because black holes do emit radiation, as a result of which do lose mass and, therefore, this system of large objects became unstable. Of course, if we’d detonate all of the atomic bombs we’ve built, we might also cause our planetary system to become unstable, but you’ll understand that’s a different discussion altogether. 🙂
So… Well… I like to think a wavefunction for an orbital represents the same: we’re looking at a charge that moves around in its own space. In our Cartesian reference frame, this looks like a terribly complicated oscillation. In fact, the oscillation is not only complicated but also – literally – complex, because we’re keeping track of two dimensions simultaneously: the real and imaginary component of the wavefunction. Both are equally real, of course, in a physical sense (and we can argue about what that means, exactly, but not about the statement itself). But so… Well… It’s just a spacetime blob. The charge itself just moves around along a geodesic in its spacetime, and that’s why it doesn’t emit or absorb any energy from the outside. 🙂
Of course, the question now becomes: if an electron orbital is nothing but a weird blob of curved spacetime – in which our charge moves around like a planet moves around in a planetary system – then what’s causing the curvature of space? For our planetary system, we know it’s mass.
So… Well… What can I say? Well… What’s mass? Energy has an equivalent mass, and mass has an equivalent energy. In my previous posts, I look at mass as an oscillation itself and, as I show in one of my papers, that might allow us to interpret Schrödinger’s wave equation as an energy diffusion equation, and the wavefunction itself as a self-contained and self-sustaining gravitational wave. So… Well… If the wavefunction represents a blob of energy – some two-dimensional oscillation – then… Well… Then it could create its own space, right? Just like our Sun and the planets create their own space, in which they move without absorbing or radiating any energy away. In other words, they move in a straight line in their own space. I am tempted to think our pointlike charge must also be moving in a straight line in its own space because… Well… It would, effectively, be emitting radiation otherwise. 🙂
So what’s the nature of Nature, then? Well… All is movement, it seems. Panta rhei ! 🙂 And… Well… I’ll let you do the philosophy now. For example, if objects create their own space, how should we think of their interactions? 🙂