Is the electron ever a wave?

Question

I'm coming back to rewrite this question I asked years ago. My wording then was apparently too caustic to allow the question to last long enough for many on PSE to consider its meaning. I realize now that presentation can be everything for some people and some forums, so I am coming back to make another attempt at asking the same question with same meaning albeit with a different demeanor.

I'm taking on an interesting task: explaining to an advanced high school student that much of what he hears and reads from popular physics videos and TV isn't accurate. I need to decide if I go so far as to explain that while there is evidence that an electron (for instance) behaves in a wave-like manner there is no evidence showing that an electron actually is a wave. There is, rather, much evidence showing that when an electron interacts with something else that the system involved in the interaction appears to be wave-like. It is quite the ontological leap, in my opinion, for one to use this as evidence that therefore the electron is a wave.

I realize that many physics PhDs will disagree. This is why I'm posing the question. Some disagree. Many others do not. Physicists on both sides are equally as bright and equally as versed on theory and experimental observation.

Regarding what I tell this student, I can explain what a probability function is, and that it's a solution to a wave equation. I can explain that this probability function is not the electron itself, but rather a mathematical function utilized to describe and predict behavior of electrons and their interactions. But how best to, at a not-so-advanced level, explain the difference between "is a wave" and "behaves in a wave-like manner"?

At that age my understanding of QM would have advanced by 2 years or more if someone explained this. I'd like to know what others think, but if you're someone who is so sure that an electron is actually a wave please bring strong evidence to support your claim. To state something like "I know it's a wave because I see it diffract every day!" is disingenuous in my opinion. It's just another way of stopping the discussion, because you don't want to consider contrary arguments.

More details to explain my position:

The probability function (or superposition thereof) has meaning because it is directly related to the solution to a special wave equation that has proven to glean deep meaning. When considering wave equations related to an electron influenced by a potential, it is my opinion that the electron is not the solution to this wave equation. We can learn things about electron behavior from the solutions to this wave equation, but I think it makes little sense to believe that the electron is the solution to this same wave equation.

When we measure it we observe an energy and momentum exchange event. We do not measure "a wave". This is why many excellent theorists and experimentalists call it wave-like. I.E. because of its behavior.

If you believe that an electron is actually a wave what it your evidence?

Answer 1

Whether an electron's probability function should be thought of as distinct from the electron itself is pretty much a completely philosophical question with very little physical content, and so saying that its "DEFINITELY NOT" true is wrong. (Note I'm not saying that it's true that an electron is the same thing as its probability function. I'm saying that it's not true that an electron is definitely not the same thing as its probability function.) Presenting this as a "common misconception" is just going to confuse him and set back his physics understanding.

In fact, based on the confidence with which you present the incorrect statement in your question, I would recommend thinking twice about clearing up the "misconceptions" that his physics teachers are spreading and letting the professionals do their job.

Answer 2

And electron is not a wave. However, describing matter with the use of wave functions has proven to be very effective in giving a mathematical framework for quantifying empirical observations regarding the probabilistic nature of interactions of small particles, and our uncertainty of their momentum/position, or energy/time relationship.

To say "an electron is not a wave" is not going to clear up any misconceptions - it is likely to perpetuate them in the same way that you seem to be having some misconceptions (and strongly held opinions masquerading as facts).

If this 11 year old is so bright, you might want to take him through some of the experimental work that has been done to explain optical diffraction (is a photon a particle or a wave?), the photoelectric effect, and electron diffraction. Three beautiful experiments that cannot, between them, be explained unless you accept that particles "sometimes are like particles, and at other times are like waves". Note - I don't say "are waves"; I say "like waves".

At the age of 11, having a clear and well grounded intuition for the behavior of the world (including some of that "fuzzy duality") is appropriate; telling a child something "absolute" when you are not actually an expert is likely to set them back.

I applaud your desire to help this child grow; please consider the advice given in the sense it was given - we both want the next generation to be equipped to deal with the challenges of their time, and we'll need some first class scientists...