Is there a maximum number of types of elementary particles?

Doing a Google search i found a paper called The maximum number of elementary particles in a super symmetric extension of the standard model.

It claims in the abstract that the upper bound is 84 (i don't have access to the article)

My question is: Is there a max number of types of elementary particles predicted in advanced physics theories such as string theory? What are the reasons for this?Are the arguments purely mathematical?

• Hi Mark, I suggest you go read the blog El Naschie Watch. I find it amazing that Elsevier kept Chaos, Solitons and Fractals going instead of letting it rest in peace. – Simon Apr 15 '11 at 2:36
• Cool i was going to ask the same question, particularly, will there be a simple classifiction of particles similar to chemical elements, with families, upper bounds of stability, a kind of quantum particle classification system. Regards your quesiton, for me it is the same as asking: can there be a limit to time forwards and backwards... can there be a limit on the division of time into small sections, until nothing periodic happens on any scale? Peering into a mandelbrot fractal zoom, it seems that mathematically, complexity of some string formulas increase and do not have a boundary. – com.prehensible Feb 15 '17 at 19:16

The paper you cite employs Mohammed El Naschie's "E-infinity theory" of physics, which is one big exercise in what physicists call "numerology". Numerology is where you match up numbers - e.g. the three generations of particles in the standard model, and the three dimensions of space - and then you state or insinuate that there is a connection; but you cannot justify the connection logically (deductively). Another common example is where people find formulae for particle masses and other unexplained quantities, using combinations of transcendental numbers, other particle masses, and so on.

This "numerology" sometimes does work in physics and mathematics. That is, the search for quantitative coincidences sometimes does stumble upon relationships which have a deeper origin. Balmer's formula for the emissions of the hydrogen atom was explained by quantum mechanics; the coincidence in mathematics known as "monstrous moonshine" was proven to be true by Richard Borcherds; there are many other examples. But it is also possible to make extremely contrived relationships - e.g. you can approximate any real number arbitrarily closely, using combinations of e and $\pi$, if you use enough of them. You can also pile up lots of deductively unjustified "connections", and claim to have a theory of everything. "E-infinity theory" is in the latter category. These papers don't contain even the moderately difficult sorts of calculation that you see in real particle physics papers - I mean scattering amplitudes, particle lifetimes, and all the other detailed quantities which come from employing a theory with a proper equation of motion. Instead, these papers are full of basic algebra equations in which various known quantities are "explained" in a meaningless way. But these papers don't actually explain anything, nor do they predict anything, and the journal which publishes most of them is considered low-quality for this reason.

• I just read the paper. Sadly its not just "low quality", but pure garbage! I cannot understand how these "E-infinity" papers were able to get published for so many years. – Heidar Apr 13 '11 at 10:44
• good way to make money though, a little more cool than motivation speeches :) – jokoon Apr 13 '11 at 11:09
• @4tnemele, google for El Nashie You will find reason for this publications in the fact that he was editor of that "paper". The "case" El Nashie is setteled meanwhile. – Georg Apr 13 '11 at 13:29
• @Gokoon at least with a motivational speech you know you're getting fed BS. – corsiKa Apr 13 '11 at 18:55
• Do you think it's possible to get El Nashie's papers (and most of the garbage published in "his" journal) withdrawn and removed from reputable search engines? I got tricked by his BS during a summer project a while back (before he became infamous) and wasted a fair chunk of time trying to understand what he was doing. As evidenced by this question, I'm not the only one whose been fooled. Elsevier should really made to be held accountable for packaging up CS&F and basically forcing libraries to buy it. And yes, I know that Baez et al have already tried... – Simon Apr 15 '11 at 2:18

There is no finite limit, at least in string theory, where the closed string mass spectrum is:

$$m=2\pi\sqrt{N+\tilde N-a-\tilde a}$$

Where $a,\tilde a$ are the normal ordering constants, and the number operators $N,\tilde N$ can be any integer or half-integer, without limit. So the spectrum is infinite, and since each mass corresponds to a different particle, there is an infinite particle spectrum.

• This is true, but the "particles" we see in accelerators are just the massless particles, and there are a finite number of these. This is probably the best interpretation of the question. – Ron Maimon Aug 22 '13 at 22:14

The number of particles depends on the theory assumed. Symmetries, such as super symmetry impose limits, but who knows what the theory of everything is?

Yes, the arguments are purely mathematical, until some experiment at a future date will chose among the multiplicity of theoretical models.

• In the case of string theory,particles are understood as tiny vibrating strings with certain frequencies,so there is a finite number of possible frequencies?Are these frequencies quantized? – Mark Apr 13 '11 at 5:45
• Also,the electromagnetic spectrum is related to the photon's energy.Does it imply that at the string level the string is vibrating faster? – Mark Apr 13 '11 at 5:58
• @Mark: The frequencies are quantised, but there are an infinite number of modes. – Abhimanyu Pallavi Sudhir Jul 21 '13 at 8:08