ON THE YUKAWA PREDICTION OF THE MESON EXISTENCE
Physicists measure the mass of particles in fractions of kilograms but they also measure it in another unit, the MeV/c
2. The values that come to follow are presented in this unit.
The theory of Yukawa foresaw that the mass of meson had to be 100.
The mass detected from the experiences was 140. Therefore, it had a 40% difference, and the forecast of the theory might be felt unremarkable but there are other problems with the model. Note how many mesons exists in Nature:
Type mass
Meson π 140
Méson K 490
Méson η 549
Méson η' 958
Let us consider then that 40% error is a good forecast since physicists had considered the error made by Yukawa acceptable. Then:
1. If the forecast mass was 230 then, if his theory had foreseen a mass of 230, an allowed error of 40% results in 92 (that is, 230±92). As 230-92=138, this value would be confirmed by the real value of 140 detected experimentally. Therefore, if he had foreseen a mass between 100 and 230 he would have been felt right as well.
2. If the forecast mass was 350, then the allowed error would be 140. As 350+140 = 490, this value fits to the mass of the K meson. In this case, if the theory had foreseen a mass 350, the forecast would be confirmed once again.
3. If the forecast mass was between 350 and 1000, then any value foreseen in this band would give good result because the forecast would give a value next to 490, 549, or 958.
Conclusion: Yukawa could have foreseen the following masses:
Any value between 100 and 230
Any value between 350 and 1000
All these would be confirmed experimentally.
Only with a mass of 300 would he produce an unacceptable forecast. However, in a band between 100 the 1000, any forecast, except in the range between 270 and 320, would give a good result according to the acceptance criterion that physicists had adopted when considering Yukawa’s forecast as acceptable.
The possibility of error is very remote. Any forecast would come out right. One perceives that the rightness of Yukawa cannot even be considered coincidence, because he did not have the chance to make a mistake. If somebody hides a needle in a straw-loft, and we thread the hand in the straw and find the needle at the first attempt, this is coincidence. But if somebody places thousands of needles in the straw-loft and, at the first attempt, we find a needle, this is not coincidence since there was only a small possibility of failure. However, if we regard Yukawa’s forecast as coincidence, doesn’t it seem surprising that physicists accepted it so readily as confirmation of the theory?
Further, consider the irony that physicists consider the successes of the Bohr model of the atom as coincidences and do so although, because of the laws of probability, it is impossible that they are accidental. There really must be some link with reality in the Bohr model of the atom.
Therefore, the trust of physicists in mathematics seems highly subjective.
They happily accept the fruits of mathematics when it supplies results that suit them but, if the mathematics opposes their expectations, they reject the results in the same way that a religious rejects reasonable arguments to explain a supposed miracle that he insists on attributing to supernatural causes.
good stuff nonetheless.
