One of the questions to which I alluded in Q&A that came up not long ago was why mass curves space. The answer to this, as measured by curiosity fulfillment, is an unsatisfying “we don’t know”. The reason the discussion doesn’t end right here is that it’s important to know why one can’t answer that question, and why not having an answer is not a scientific flaw or crisis.

This is a cousin to a question that one can answer, which is why space is curved. That one is relatively straightforward: we have length contraction, which is a logical consequence of a constant speed of light in an inertial frame. (Logical here is not necessarily synonymous with intuitive, but the premise of a constant c and physics being the same everywhere — the postulates of special relativity — lead directly to the phenomena of time dilation and length contraction) Moving objects are contracted along their direction of motion. So what happens to an object or system moving in a circle? At some radius r, the circumference is no longer given by the familiar 2*pi*r, since any length one measure will be length contracted. In other words, the flat Cartesian coordinates of Euclidean geometry we are used to using is no longer adequate to describe the details of the system. It’s not flat anymore. That’s the thought process that led Einstein to develop the curved geometry of General Relativity, which describes the kinematics when we include gravity. There’s an acceleration, and the coordinate system has to change. (Deeper understanding is impeded by the realization that freefall is an inertial frame, which is another counter-intuitive concept one must wrap their head around. Then there’s all the math.) That’s it in a nutshell.

But why does mass (in a Newtonian sense, energy in relativity) do this? Can’t help you. This is, to many non-scientists, the Rolling Stones issue: Can’t Get No Satisfaction from that answer. It’s been implied (and sometimes declared) that this, or some other question to which science has no answer, should really bother me, and it just doesn’t keep me up at night. But unanswered questions are supposed to haunt me, right?

No, not really. Unanswered scientific questions, perhaps, and especially ones in our field of study might cause me to lose sleep, but not metaphysical ones. And that’s really what this boils down to: science is about building models to explain what’s happening around us, and there are limits to those models. I can do a whole lot of science without knowing why mass attracts another mass or (closer to my field) exactly what the mechanism is that causes an atom to emit a photon. I know what transitions are possible, I know how the emitted photon will be polarized, I know the atom will recoil as a result — all of those things are measurable effects, and fit into a model of how the atom-photon interaction behaves.

But wouldn’t it be great if we knew why all of this was happening? Yes, and I imagine there are people who spend time thinking about such things. But any answer they come up with has to be checked to see if it’s right, and that’s the problem. Science progresses, in a very broad sense, by either theory driving experiment, or experiment driving theory. But both have to happen. Special relativity is an example of theory driving experiment — there were no observations of time dilation or length contraction that had identified a hole in our physics knowledge. The framework came first, and experiment verified it. Similarly with Einstein’s model of spontaneous and stimulated emission, which led to the development of the laser. Quantum mechanics has some prominent examples in the other direction — observed phenomena (photoelectric effect, and Stern-Gerlach, which is actually an example of both phenomena) that did not fit in with existing the theory and demanded an explanation based on new thinking. But the new theories, and the models based on them, are not accepted merely because they explain the one observation that prompted them — that’s too ad hoc. One has to be sure the model works under a wide range of conditions, which prompts further experiment. Only then do you accept it.

Which is why some of these deep questions do not beget a scientific explanation. There is no unexplained phenomenon to require a model be built, and there is no experiment to test a model that someone comes up with. A question that does not carry one of those banners is generally not going to be something that science addresses.

I saw this via @JenLucPiquant, and I have to say, the video only explains half the answer. It’s true that if a photon doesn’t have enough energy to promote an electron to a higher energy level, it won’t be absorbed — there is no allowable state for the electron, so the photon passes through unscathed. That’s all good. It explains why a material that is transparent in the visible part of the spectrum becomes opaque somewhere in the UV.

But what this doesn’t explain is why the same transparent material also becomes opaque in the IR. Here are a few transmission curves, and we see for BK7 glass, it is indeed transparent in the visible and the transmission falls sharply when we get to 300 nm. But over at the other end of the graph, we also see that the transmission falls when we get out near 2 – 3 microns, i.e. photons that have a bit more than 10% of the energy to bridge the gap being discussed in the video. It’s not just that, either. There are more substances on that data page, and other materials still, all with the same general behavior; the details are different, which is nice, because you can find a material that is transparent a little further into the UV, or out into the IR, according to your needs. That way you aren’t limited to strictly being in the visible part of the spectrum for your work.

Why is this the case? A visible photon has a few electron-Volts of energy, and that’s not enough to promote an electron, but the material becomes opaque at photon energies of less than one eV! The key here is that photons and molecules are choosier than was implied in the video. Not only do you have to have enough energy to complete the excitation, you can’t have too much, either. A photon cannot give up only part of its energy in an absorption — it’s all or nothing. For simple systems, like an atom, the photon energy has to be exactly the right value. (This being quantum mechanics, though, “exact” means “exact to within the limits of the Heisenberg Uncertainty Principle,” but it’s still close enough for government work). For composite systems, the energy levels can thicken into bands, but the same principle holds: too little, or too much energy, landing you in a region where the electron’s energy isn’t permitted, and there will be no interaction. Transparent materials are those that lack those energy levels. The light can’t interact, so it passes through.