I have recently fallen down a rabbit hole in physics trying to resolve some paradoxes that I stumbled upon. In spending a lot of time and mental effort trying to understand what is going on, I realized that although I have spent my life studying and teaching physics, I did not fully understand some very fundamental aspects of space and motion and the way that the laws of physics operate. That is part of the fascination that physics provides, that it can always surprise you, leading you to learn new things.
In an occasional series of posts, I will share with readers my journey through this maze, trying to make things as clear as possible to the non-physicists out there. This will not be easy because an important prerequisite to explaining something to someone else is for you to understand it first. I cannot claim to understand completely what I am going to be writing about, for which I apologize in advance. But it is well known among teachers that it is in trying to explain something to someone else that one starts more deeply understanding what one is trying to say. Like many teachers I have used students as sounding boards for tentative ideas.
And so it is with this issue. This series of posts will largely consist of me trying to work my way through some paradoxes and puzzles to a satisfactory understanding and I hope readers will find journeying with me at least partly enlightening and will also provide them an opportunity to contribute their insights. At times I may seem overly pedantic but that is because there are a lot of subtleties involved and I am trying to pick my way gingerly through them as carefully as possible so as not to go astray, though I cannot guarantee that I will succeed in avoiding all the pitfalls.
So where to start? Perhaps it is best to start with something that almost all of us are familiar with from the time of Galileo and that is that any two objects dropped from the same height will fall at the same rate and hit the ground at the same time. Of course, when we do this under everyday conditions on Earth, this will not hold true because air resistance can affect the rate of fall of each differently. But if the experiment can be done in a vacuum, the result is expected to hold. The famous experiment done on the moon by dropping a feather and hammer seemed to support this and there have been similar experiments done on Earth in high-vacuum chambers. (See this post for videos of the two experiments.)
So let us take as a given what I will call Postulate #1, that if we can eliminate all other forces such as friction, all objects that are dropped from the same height in a gravitational field will fall at the same rate and hit the ground at the same time.
Another well-known result in physics is one that I will call Postulate #2, that an accelerating charge will radiate energy. This is a consequence of Maxwell’s equations (ME), which are foundational laws of physics. The laws expressed in ME are so fundamental that they played a key role in the transition from Newtonian physics to special relativity. The radiation of energy by accelerating charges is the basis of the electromagnetic phenomena that undergirds so much of the technology that we take for granted in our lives today. The textbook Classical Electrodynamics by J. D. Jackson is a staple of graduate physics curricula in the US and is an exhaustive and authoritative treatment of electrodynamic phenomena. In such esteem is the book held that saying, “Jackson says …” is usually enough to end an argument. In his second edition, he begins chapter 14 that has the title Radiation By Moving Charges by stating flatly, “It is well known that accelerated charges emit electromagnetic radiation”. The statement is not accompanied by any qualifications or conditions or caveats whatsoever. It helped convince me (and doubtless countless other physicists) that accelerating charges always radiate energy, period.
But if that is the case then these two Postulates that each seem to be incontrovertibly true and have a wealth of evidence supporting them lead immediately to the paradox that I came across while idly thinking. (I confess to being such a nerd that these are the kinds of things I idly think about.) The paradox is this: If we drop an electric charge and a neutral particle from a height in a gravitational field, say the ceiling of a building, Postulate #1 says that they should both hit the ground at the same time. But since the electric charge is accelerating, then by Postulate #2, it must radiate energy and this loss of energy will slow it down and it will hit the ground after the neutral particle does.
It seems like both Postulates cannot hold simultaneously. So is Postulate #1 not applicable when it comes to charged particles? Alternatively, does Postulate #2 break down so that an electric charge does not radiate when its acceleration is due to it falling in a gravitational field? Neither solution seemed palatable.
This was the seeming paradox that I encountered and that started my investigations. While the answer should be an empirical fact that should be conclusively decided by experiment, the actual experiment is not easy to do. Dropping two large items in a vacuum chamber is hard enough. Trying to do it with one charged object and one neutral one would be very difficult and, as far as I am aware, has not been done. So we are left with trying to resolve this issue theoretically.
I was of course not surprised to learn that such a fundamental issue has been recognized for a long time and has been examined by many eminent physicists. What did surprise me was that there seems to be no simple theoretical resolution to the paradox, with more than one conclusion arrived at, and that even among the experts who agree on a conclusion, they sometimes do not agree on the reasons. What also surprised me was that there is no widespread discussion of this question within the larger physics community. I would have thought that it would have been discussed at least in graduate physics curricula as a topic of interest since it involves so many fundamental questions but none of my professors did so and none of the textbooks that I used mentioned it either. The issues raised all involve very basic concepts involving the laws of physics that I once thought I understood fairly well but had clearly missed many subtleties.
So let us begin the exploration of those subtleties. I hope you enjoy going on this ride with me.
(To be continued.)