You are no doubt familiar with Einstein’s famous dictum that a theory should be “as simple as possible, but not more so”. When I taught elementary mathematic logic, I set exercises to translate such sentences into the contrapositive. A theory should be “as complicated as necessary, but not more so”. That, I feel, is where physicists have gone wrong in the past half century. The Standard Model of Particle Physics was, in the 1970s, pretty clearly as complicated as necessary, but not more so. All attempts to go beyond the Standard Model, almost without exception, have been, equally clearly, more complicated than necessary, since they all, almost without exception, predict physical phenomena which have not been observed in the real world, despite extensive and very expensive searches.

My own attempts in this direction have been guided especially by the principle that the theory should be as complicated as necessary, but not more so. Some of my models are not complicated enough. Some of them are too complicated. But my guiding principle for many years has been to steer a middle ground. Of particular importance is to estimate how many free parameters there are. If there are more than 24 free parameters, the theory is too complicated. If there are fewer than 24 free parameters, the theory is probably not complicated enough.

Of course, this is only half the story. If there are 24 free parameters, then these parameters cannot be explained. This means that we need to assess the Standard Model as being *more* complicated than necessary, if we want to explain these unexplained parameters. That is where I get into trouble, when everybody else is looking for models that are *more* complicated than the Standard Model, and I insist that we should be looking for models that are *less* complicated than the Standard Model.

But I insist that Einstein was right: a model should be as complicated as necessary, but not more so.

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September 29, 2022 at 7:54 pm |

I have the impression that physicists would fail my class, by giving as the supposed contrapositive “as complicated as necessary, but more so”, or perhaps “as complicated as possible, but not more so”, or even worse “as complicated as possible, but more so”. These are certainly the kinds of answers that I frequently received. I do get the impression that string theory is based on the idea that a theory should be “as complicated as possible, but more so”.

September 30, 2022 at 5:30 pm |

Since you’re a group theorist, I’d like to ask (please), if there is a known connection between the 26 sporadic groups and the volume, mass of observable universe. Or if it has been considered and not accepted.

If one equates the Compton wavelength of a particle with the Hubble radius, one gets what some people call the Hubble scale (or the inverse Hubble scale) with minimal mass of 9.1×10^-33 eV/1.62×10^-68 kg and a volume of 1.75×10^-285 m^3. This gives us about 2.10×10^365 elementary volumes in the universe at present (with error related to the Hubble constant, tension… about 15 %). Now, the direct product of all the 26 sporadic groups is ~ 2.32×10^365. Almost the same value! What’s more, the cube root of the product is ~ 6×10^121 which if taken in the elementary masses is just below 10^54 kg – coincidentaly the estimated baryonic + dark matter content of the universe (+/- 10 %). I feel that this is too much for it to be a mere coincidence.

Thank you very much for any kind of response!!! Since nobody (so far) has been able to react to this.

September 30, 2022 at 6:27 pm |

The thing with coincidences like this is, you have to ask yourself how much of a surprise is it? How likely is is that you can find coincidences like this just by looking at some random numbers? My estimate is that it is not a surprise at all, and that it is easy to come up with coincidences like this.

When I look at numerical coincidences, first of all I need to have a good reason why such a coincidence should exist at all. Second of all, I don’t even bother thinking about it until I get down to about a 1 in a million chance, and I don’t write about it until it’s down to one in a billion. And I don’t send off a paper to a journal until it’s nearer 1 in a billion billion.

September 30, 2022 at 7:07 pm

Yes, that’s pretty much what I though. The problem here is that we’re limited by the imprecise knowledge of the Hubble constant/radius of the universe. That’s why I wanted to know if there is a ~ known mechanism that could hide behind this observation. I presumed that this coincidence is known and explained away but I found nothing. Only that the minimum length, time and volumes in the universe almost match the estimates of Stephen Wolfram (based on an independent method).

What bothers me the most is that it holds true just about now, it didn’t hold true before and will never be true for ~ infinity (according to ΛCDM). It also almost satisfies I went looking for something like this because I noticed that the square of the diameter of the universe (~ 8×10^53 m^2) is almost the same as its mass (in kg) and I’d like to know if there is a some kind of mechanism behind this. I really don’t like the fact that it works in kg/m.

Thanks for your answer!