On the surface mass, like space, seems like a simple and straightforward concept but there are deep subtleties involved here too. In order to bring out the subtleties about mass, I had a practice of asking students in my introductory physics classes to explain what they understood when they spoke of the mass of some object. The would usually give some vague formulation along the lines ‘the amount of stuff’ it has. When I pressed them by asking how that differs from their concept of volume, they would sharpen their answer, usually saying that volume was a measure of the amount of space that was occupied by the object but mass was a measure of how heavy it was. There are teachers who insist that we must emphasize that mass and weight are different but I am not one of them. After all, we all know from experience that objects with greater mass are heavier to lift. The intuitive idea that mass has a relationship to weight is a good enough starting point for learning about the subtleties of mass.
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Take a look at this graph that disaggregates the rates of covid-19 deaths according to vaccination status.

Note that if you are unvaccinated you have at least a five-fold greater risk of dying. This is a massive difference. And yet, many people choose to ignore information that is effectively smacking them upside the head and telling them to get vaccinated.

Compare this with how people are willing to adopt all manner of practices that promise even small benefits. People start taking things like turmeric, acai berries, pomegranate, and adopt all manner of diets, exercise routines, and things like detoxing even though the promised benefits may be just a few percent reduction in cancer or a slight increase in longevity, and the like. And even those benefits have been shown to not be that robust or are even spurious. This behavior reminds me of something that Jesus said in Matthew 23:24 about people straining at a gnat while swallowing a camel.
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How do you tell if you are in an inertial frame or not? According to Newton’s model of a fixed space, an inertial frame is one which is at rest or moving with constant velocity through that fixed space. We saw that determining this required us to observe the state of motion through that space of an object Q that was known to be not under the influence of any forces. If you observe Q to be at rest or moving with constant velocity, then you are in an inertial frame. If however, even in the absence of forces, the freely floating object Q appears to be accelerating in some direction with respect to you, you could conclude that this must be because you are in a frame that is an accelerating in a straight line in the opposite direction and hence you are not in an inertial frame.
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As a computational matter, when we are in a rotating frame such as the Earth, we have a choice. We could work with inertial frames where Newton’s laws and Maxwell’s equation are valid, use real forces only, and make sure to include all the accelerations introduced due to the rotational motions. Or we could use a frame that is embedded in the Earth and thus rotating but treat it as an inertial frame by including via the fictitious Coriolis and centrifugal forces the non-inertial effects caused by its rotation. The two methods are mathematically equivalent but conceptually different. It is sometimes easier to treat the Earth as an inertial frame that is not spinning and incorporate fictitious forces and that is often done in the field of meteorology.

It is the search for genuine inertial frames that is of interest in this series of posts because it is important in the resolution of the radiation paradoxes.
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In trying to understand and resolve the paradox I wrote about in the first post in this series, I will be taking a somewhat circuitous route in order to lay some important groundwork before we can directly confront the paradox.

We can start the journey by looking at one of the most fundamental concepts in physics, that of the nature of space. On the surface, space seems like a very straightforward concept. It is seen as a kind of container in which everything in the universe exists. But difficulties arise when one asks questions such as whether space can be viewed as something positive, a tangible entity that has its own properties that can be detected, or whether it is viewed as something negative, that signifies the absence of matter in a region. Another way of posing the distinction is asking whether, if one can conceive of removing all the matter and energy in the universe, what would we be left with? Just ’empty space’? In the absence of matter, would such a thing have any meaning at all?
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The concept of ‘wellness’ has been gaining ground in the US. It is a vague term and, as I understand it, it means taking proactive steps to maintain one’s health, such as eating healthily, getting exercise, avoiding harmful practices like smoking, getting enough rest, and so forth. The idea is that by doing so, one can stave off some of the ailments and illnesses that can affect one’s wellbeing.

An additional layer is laid on in the name of holistic’ approaches to health, with the idea that the mind and body are connected and that one should also try and maintain a healthy mindset. These could include practices like yoga, meditation, relaxation techniques, and other activities that seek to reduce stress, blood pressure, and the like.

All that is perfectly reasonable.
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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.
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