Aristotle divides change in two ways, change by contact, and change in-itself; for example, I hold a cup and move or rotate it - this is change by contact; or a rose grows by itself - it has some inner law of change or growth.

A quantum system, to be specific: a single particle in empty space; does it change by contact or by some inner law?

In the classical situation it's simply at rest; but in QM, Schrodingers equation means its wave evolves:

When it is not interacting with an external system that can detect its position, the electron can spread out over 'different positions'; in the jargon of the theory one says that the electron is in a 'quantum superposition' of one or many different positions.

if we give the wave some kind of ontological weight, then it appears it's never at rest - or is this language inappropriate?


A single electron in empty space evolves as predicted by the Schrodinger equation or some similar equation of motion. And even if the electron doesn't interact with anything else in a given region, to understand what happens in a given region, you have to know its state throughout that region. For example, an electron whose wave function is a Gaussian wave packet will spread out differently in space than an electron whose wave function is a plane wave. The resulting difference is physically measurable and the only available explanation is that the electron actually has the relevant evolving state.

  • But the shape of space and the other fields present predict the solution to Schroedinger's equations. So it is not possible for the electron to "just have" these various internal states, is it?
    – user9166
    Mar 23 '16 at 14:50
  • You're wrong about the shape of the space and the other fields predicting the solution. You left out the boundary/initial conditions.
    – alanf
    Mar 24 '16 at 9:43
  • @alanf Let's assume that the space under consideration is 3-dimensional real space without boundary. Let's consider quantum mechanics as described by Schroedinger equation. Then the state of a free electron develops according to the Schroedinger equation. In this case, what is your answer to the OP's question: Change in-itself or by contact?
    – Jo Wehler
    Mar 24 '16 at 11:00
  • If you are going to be that pedantic, they you are wrong on other counts. 'The resulting difference is physically measurable' by what? There are no other particles in the space...
    – user9166
    Mar 24 '16 at 15:53

An electron in empty space may change its kinematic state due to an electromagnetic field.

In quantum electrodynamics this kind of change is explained by the interaction with a photon. If you want to apply Aristotelian terms, the change is by contact.

Aside: Where do you see the benefit in applying Aristotelian terms to a physical phenomenon which was unknown to Aristotle?

  • Isn't the EM field something additional to empty space? The EM field whose source is the electron, as far as I understand it, has no reaction on it; well, Aristotle does actually consider the motion of a single particle in empty space; he suggests it moves in all directions at once which is his argument for dismissing the concept of empty space; but one can consider the wavefunction that describes the electron as 'travelling' in all directions at once. Mar 22 '16 at 20:24
  • I find this consonance intriguing; but really the question is about change in the simplest physical context and what it means. Mar 22 '16 at 20:26

By the common model, combining the two earlier answers, which both seem correct, the answer has to be 'both'.

It will be pushed around by electromagnetic fields, if alone, then only by the way the shape of space redistributes its own field. This is as close to 'contact' as the fields that keep your fingers from being part of the cup. So it is only fair to subsume the two effects under the same name.

It also 'waves' in the sense that when approached at different times in the same way it would interfere constructively or destructively with other particles in slightly different ways. This is a constant mutation of its internal state, again to the degree that the probability distribution that extends everywhere is 'internal'.

By more abstract models

  1. The thing simply is not alone in space, and the model is not obligated to answer the thought experiment.
  2. If it were, it would eventually no longer be so, so it is the space that really has state, and not the particle.
  3. Until there is something else, the particle would have no state, since a particle's state is a function predicting responses to potential interactions, and here couldn't be any.

So in a truly modern view of quantum behavior, your question disappears.

  • 'The thing is simply not alone'; I've just read of a thought experiment of Newton where he takes an atom as pure void and impenetrable! Mar 24 '16 at 4:44
  • I've changed the electron, which I chose for definiteness, to a particle - as this was distracting from the ontological question. Mar 24 '16 at 4:56

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