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Difference between revisions of "The Road to Reality Study Notes"
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The Road to Reality Study Notes (view source)
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, 16:43, 20 June 2020→5.5 Some Relations To Modern Particle Physics
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The notion of [https://en.wikipedia.org/wiki/Parity_(physics) parity] is introduced as approximately a multiplicative quantum number with n=2, and an example is the family of particles called [https://en.wikipedia.org/wiki/Boson bosons]. Penrose notes that [https://en.wikipedia.org/wiki/Fermion fermions] could also be considered a parity group but it is not the normal convention. The distinction between these two particles are that bosons are completely restored to their original states under a $$2π$$ rotation, whereas fermions require $$4π$$ (two rotations). Thus a multiplicative quantum number of $$-1$$ can be assigned to a fermion and $$+1$$ to a boson. | The notion of [https://en.wikipedia.org/wiki/Parity_(physics) parity] is introduced as approximately a multiplicative quantum number with n=2, and an example is the family of particles called [https://en.wikipedia.org/wiki/Boson bosons]. Penrose notes that [https://en.wikipedia.org/wiki/Fermion fermions] could also be considered a parity group but it is not the normal convention. The distinction between these two particles are that bosons are completely restored to their original states under a $$2π$$ rotation, whereas fermions require $$4π$$ (two rotations). Thus a multiplicative quantum number of $$-1$$ can be assigned to a fermion and $$+1$$ to a boson. | ||
An example of a multiplicative quantum number with $$n=3$$ relates to quarks, which have values for electric charge that are not integer multiples of the electron’s charge, but in fact $$\frac{1}{3}$$ multiples. If $$q$$ is the value of electric charge with respect to an electron ($$q=-1$$ for electron charge), then quarks have q=$$\frac{2}{3}$$ or $$-\frac{1}{3}$$ and antiquarks q=$$\frac{1}{3}$$ or $$-\frac{2}{3}$$. If we take the multiplicative quantum number <math>e^{-2qπi}</math>, then we find the values 1,ω, | An example of a multiplicative quantum number with $$n=3$$ relates to quarks, which have values for electric charge that are not integer multiples of the electron’s charge, but in fact $$\frac{1}{3}$$ multiples. If $$q$$ is the value of electric charge with respect to an electron ($$q=-1$$ for electron charge), then quarks have q=$$\frac{2}{3}$$ or $$-\frac{1}{3}$$ and antiquarks q=$$\frac{1}{3}$$ or $$-\frac{2}{3}$$. If we take the multiplicative quantum number <math>e^{-2qπi}</math>, then we find the values $$1,ω,ω^2$$ from section 5p4, which constitute the cyclic group Z<sub>3</sub>. | ||
== Chapter 6 Real-number calculus == | == Chapter 6 Real-number calculus == | ||