Curiously, if you go to the source for this proton/electron mass ratio claim you'll find the original author is well aware that it's dimensionally incorrect and... well... it's hard to describe what he does next. You'll have to have a look yourself. You might want a stiff drink ready though:
http://eprints.ucl.ac.uk/19084/1/19084.pdf page 54.
In the voice of Slim Pickens:
Well, I've been to one world's fair, a picnic, and a rodeo, and that's the stupidest thing I ever heard come over a set of earphones.
Worsley's dimensions go nuts already on page 29, where he computes "a fundamental quantum mass" by taking Planck's constant h as the energy E in E=mc
2:
mq = h/(c2)
Realizing that the dimensions of his
mq are mass times time, he adds a footnote advising us to "multiply by n, which is the number of quanta
per unit time".
On page 32 he calculates "the wavelength of this quintessential quantum" in SI units "with a frequency of 1 per unit time", as though the SI unit of time (the second) were some fundamental constant of mathematics or nature, obtaining 2.9979245 ⋅ 10
8 m.
(If you pay attention to how he uses n in his calculations, n is really just the number of seconds per unit time. Worsley never explains why n should have the value 1 when he's using the SI unit of time. It's crackpot numerology, and nothing more.)
On page 33, he writes:
Dr Andrew Worsley said:
The fascinating thing is that for a single quintessence travelling at the speed of light, then the wavelength is itself equivalent to the distance travelled by the speed of light in a single unit of time, whatever units you use. In the above example (see Box 2) we use two standard units, Standard International (S.I.), and centimetres, grams and seconds (cgs), the answer comes out exactly the same in each case.
The answer comes out the same because he used 1 second as his unit of time in both calculations. Had he used a different unit of time, he'd either have gotten a wrong answer or he'd have had to give n a more explicit role in his calculation that would have revealed the naked unit-dependence of n.
Worsley's also using a crackpot notion of wavelength. The standard notion of wavelength is a pure distance (for a pure sine wave, the distance between wave crests), independent of your chosen unit of time. Worsley's notion depends on the unit of time.
That's how Worsley comes up with the truly remarkable coincidence that, for a radio wave whose frequency is 105.6 MHz, there are "effectively 105.6 million quanta".
Dr Andrew Worsley said:
This relationship between time and wavelength may be a surprise to some, for it is taught that units are arbitrary, but in reality they are not.
That's crackpottery at its (finest)
-1.
[size=+1]
So Why Is There So Much Crackpot Physics?[/size]
It's hard to discuss that question without considering the backgrounds and motivations of individuals who promote crackpot physics.
Dr Andrew Worsley probably thinks he's doing the math correctly, just as Michael Mozina probably thinks he's doing science.
Reading their crackpot science is like watching children play with toy trucks or baby dolls.
For children, that's healthy play. When they grow up, they may drive real trucks and change real diapers.
We seldom see adults whose experience is limited to toy trucks and dolls say other adults are driving or changing diapers wrongly. Real trucks and dirty diapers are too concrete; even a child knows toy trucks and dolls aren't the same as real trucks and real people.
Math and theoretical physics are a lot more abstract, so some adults are able to convince themselves their play-math and pretend physics are real. A few convince themselves their play-math and pretend physics are more real than what the professionals are doing. After all, the Dunning-Kruger effect is real too.
Crackpots are often compared to fundamentalists, but I don't think that's a particularly useful comparison. In my opinion, fundamentalist religion is more social than intellectual. Fundamentalism has much to do with a religious community's peculiar sense of identity, us versus them, and the members of that community derive social benefits from sticking to the party line.
There is, to be sure, some boost to the individual ego that comes from thinking you know the Truth, unlike all those pointy-headed infidels, but few fundamentalists are able to maintain that faith over long periods of time without social support from others who share at least some aspects of that faith.
It seems to me that those who promote crackpot physics are more likely to be proudly iconoclastic. (There are exceptions, as with the plasma cosmology folks, especially the Velikovskian wing.) Dr Andrew Worsley comes across as more of a lone prophet than just another sheep in the herd.
We shouldn't generalize too much. Gerhard Gerlich, a professor of theoretical physics who says the atmospheric greenhouse effect discovered over a century ago by Fourier/Tyndall/Arrhenius can't possibly exist in any way, shape, or form, has been active in organizations that oppose several different kinds of government regulation. Although I hate to judge before all the facts are in, it's beginning to look like his political passions may have exceeded his scientific judgment.
That's a more likely explanation for Gerlich's crackpot physics than any lack of skill in mathematics. Judging by the Gerlich and Tscheuschner paper and their reply to Halpern
et al.'s rebuttal, Gerlich uses (irrelevant or trivial) mathematics to intimidate. Worsley, on the other hand, uses (dimensionally incorrect) mathematics to amaze. No one explanation for crackpot physics is likely to fit both of them.