As to Daniel’s question. Collins obviously has some understanding of gravitational waves. The formulation of the question seams to require a binary definition of understanding which I reject. However a physicist working in the area would have a deeper understanding. I find that obvious.

A physicist would be able to make quantative predictions from the theories of gravitational waves. Making quantative predictions shows a deeper understanding than making qualitive predictions, since a qualitive prediction is really just quantative prediction where you’ve only kept the sign of the answer.

A mathematician on the other hand would have gaps in her understanding because she would not neccessarily know how to translate a fact about the mathematical framework into something you expect to see in the real world. So she would not be able either to make any quantative predictions about the real world. Thus, knowing the math is neccessary but not sufficient for a full understanding of physics.

The question of why experiments to measure gravity waves have not in fact measured gravity waves is one that no current gravity wave theorist can answer, no matter how much mathematics they deploy in the effort.

Are gravity waves simply not strong enough to be measured with the apparatus? Are gravity waves strong enough to be detected by the apparatus simply very infrequent, or very infrequent in our local neighborhood, or damped somehow? Do they not exist at all?

A single unambiguous detection of a gravity wave would eliminate the “they don’t exist” option without using any math.

And that single reading plus piles and piles of math wouldn’t help at all in deciding which of many alternate gravitaional wave theories is correct, due to the sort of non-mathematical possible explanations for low readings that I just mentioned.

I think what you’re saying is that it will take lots of math to build more sensitive experimental apparatus.

I’d agree, of course, but I’d also point out that most of the math deployed in that effort would be for the engineering involved, and not at all related to the kind of math used by purely theoretical gravitational radiation physicists (and perhaps entirely unknown to them).

It will also take quite a lot of money to build more sensitive experimental apparatus, but I don’t think anyone is suggesting one needs a degree in finance to understand gravity waves.

Has anyone been able to answer this question? I’m sure many people have come up with answers to this question (some saying the experiments weren’t sensitive enough and some saying the theories were wrong, and some saying we were testing the wrong theories), but does anyone have really good reason to believe that one of them (rather than one of the others) is the right answer? Some day I’m sure we will, and Collins probably won’t be the one to do it, but as Daniel pointed out, the fact that he hasn’t yet doesn’t distinguish him from most (or perhaps even any) gravity wave researchers. We don’t expect every researcher to be able to have achieved every breakthrough in the field.

You’re right that mathematics is more than notation. After all, algebra predates modern algebraic notation by thousands of years. However, “more inconvenient” is a staggering understatement. Even using a poor notation can make problems orders of magnitude more difficult (expand the tensor calculus of Einstein’s gravity equation into the many equivalent linear equations, then try to work with them for one example). English is going to be much more verbose and complex than the linear equations.

For many problems, the additional memory required to hold the expanded information exceeds the capacity of the brain and calculations take longer than a human lifetime to complete. To look at another mathematical notation, look at software. MS Windows is already 50 million lines of code. Translating it to machine language (a less abstract notation, like the linear equations in place of tensor calculus in Einstein’s equation) would require about 500 million lines. It would be much longer in English. Could anyone understand it well enough to produce the next version?

Feynman was a great popularizer of physics, but he knew that you had to understand the math to do physics. He told his physics students that they didn’t understand particle physics until they could get all of the factors of 2 pi (in computing the integral from a feynman diagram) right. While he thought everyone could gain some understanding of physics and knew that there’s more to physics than math, he certainly didn’t confuse the level of understanding of a physics practitioner who could do the math with a layman who couldn’t.

None have observed gravity waves to date. Whether this is because the experiments were not sensitive enough or because theories of how gravity waves are generated is incorrect is a question that is fundamental to understanding gravity wave physics to answer, requires math to answer, and (I suspect, but am not certain) Collins would not have been able to answer.

There is indirect evidence in the form of astronomical observations; i.e. “the observed system appears to be losing energy at a rate consistent with all viable theories of gravitational radiation.”

There have been several experiments designed to observe gravitational waves directly. None have succeeded to date.

If a person must confirm (or be able to confirm) theories with predictions and experiments and direct observation and all the rest of the scientific method before that person can be said to “understand” a scientific theory, then no physicist today can be said to “understand” gravitational radiation very well.

Daniel’s question does not stem from any lack of understanding of the scientific method.

Personally, I think this whole debate is rooted in a lack of distinction between a scientific theory and a mathematical model based on that theory. In physics, of course, this distinction is rarely made— compare with, say, evolutionary biology, where you have theories (e.g., punctuated equilibrium) with little or partial or even no accompanying mathematics at all (or mathematical models that arrive long after the underlying ideas).

In a typical scientific situation, I would say that a person understands a mathematical model when one understands how it can be derived from the non-mathematical ideas underlying the theory, and I would accept such an understanding of any model involved as a necessary condition for a “real” and “scientific” understanding of the theory. Whether or not said theory is itself “real” (or, if you prefer, “confirmed”) I would treat as a separate question entirely. I may differ with Daniel on that last one, I’m not sure.

The problem with the specific case of gravitational radiation is that even if we stipulate that there is a single mathematical model to “understand,” (that model being general relativity, and so ignoring viable alternate gravitaional models), there is, as yet, no widely accepted or experimentally confirmed derivation of that model starting from fundamental, non-mathematical principles. There are, in fact many different theories of gravitational radiation, none of them sufficiently compelling or problem-free to produce consensus in the rarified community Harry Collins studies.

Now, back to Daniel’s question. I must assume that he is asking us about Harry Collins’ understanding of actual gravitational waves, if they do in fact exist, rather than about Harry Collins’ understanding of any particular theory of gravitational waves, which is trivially inferior to that of a physicist working on that particular theory.

We can answer Daniel’s question using numerical methods. Let there be i working theories in the gravity-waves community and k physicists in that community. Let ct(n) denote Collins’ degree of familiarity with theory n, where 0 as a whole has a better understanding of actual real gravity waves than Harry Collins does. Two heads are better than one, indeed.

The interesting question, however, is whether the statistically average gravitational wave physicist has a better understanding than Harry Collins. To resolve this, we…

[earnest calculation, reasonable assumptions, margins of error estimated, etc]

…and thus we can see that while the average gravitational physicist does indeed have a better understanding of actual real gravity waves than Harry Collins, the advantage doesn’t seem all that impressive, what with both scores being so low.

That’s me! I program hydraulic models used in civil engineering and I understand neither the physics nor the math. I just know how to write a program that will produce the numbers my customers are expecting ;)

I almost forgot something. It is not naive, it is wrong to say the ultraviolet catastrophe was not a physical problem. The Rayleigh-Jeans law, derived from observation of blackbodies, implied that you would get an energy density going to infinity as the frequency of light emitted by a blackbody increases. This has energy conservation implications. However, we also have a couple of centuries of experimental evidence that energy gets conserved in closed systems, so something that looks like a violation of an established principle is exciting and important, simply wonderful. This means there is a place we can improve our description of the world and make it look more like reality. In this case, Planck made an ad hoc hypothesis about the atoms in the walls of blackbodies and their energy levels, thus starting the development of one of the most important and exciting developments in all of human understanding ever, quantum mechanics.