In the Standard Model the masses of quarks and leptons take values proportional to the coupling constants in the interaction of these fermions with s… - Steven Weinberg
" "In the Standard Model the masses of quarks and leptons take values proportional to the coupling constants in the interaction of these fermions with scalar fields, constants that in the context of this model are entirely arbitrary. But the peculiar hierarchical pattern of lepton and quark masses seems to call for a larger theory, in which in some leading approximation the only quarks and leptons with non-zero mass are those of the third generation, the tau, top, and bottom, with the other lepton and quark masses arising from some sort of radiative correction. Such theories were actively considered ... soon after the completion of the Standard Model, but interest in this program seems to have lapsed subsequently ...
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About Steven Weinberg
Steven Weinberg (born 3 May 1933 – 23 July 2021) was an American physicist. He was awarded the 1979 Nobel Prize in Physics (with colleagues Abdus Salam and Sheldon Glashow) for combining electromagnetism and the weak force into the electroweak force.
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In 1929 Hubble announced... a "roughly linear" relation between and distance. ...His data points ...did not really support a linear relation. But in the early 1930s he had measured redshifts and distances out to the , with a redshift <math>z \eqsim 0.02</math>, corresponding to... 7,000 km/sec and a linear relation... was evident. The conclusion... the universe is really expanding. ...At the time of writing, the largest... <math>z=6.96</math>.
It may eventually become possible to measure the expansion rate <math>H(t) \equiv \dot{a}(t)/a(t)</math> at times <math>t</math> earlier than the present, by observing the change in very accurately measured redshifts of individual galaxies over times as short as a decade.
In the case where the universe does not recollapse, the proper distance to the is...<math>d_{MAX}(t) = a(t) \int_{0}^{r_{MAX}(t)} \frac{dr}{\sqrt{1-Kr^2}} = a(t)\int_{0}^{\infty} \frac{dt'}{a(t')}</math>... In the absence of a cosmological constant, <math>a(t)</math> grows like <math>t^{\frac{2}{3}}</math>, and the integral diverges, so there is no event horizon. But with a cosmological constant, <math>a(t)</math> will eventually grow as exp(<math>Ht</math>) with <math>H = H_0 \Omega^{1/2}_\Lambda</math> constant and... an event horizon... approaches... <math>d_{MAX}(\infty) = 1/H</math>. As time passes all sources of light outside our gravitationally bound will move beyond this... and become unobservable. The same is true for the quintessence theory... In that case <math>a(t)</math> eventually grows as exp(const <math>\times\, t^{2/{(2+\frac{\alpha}{2})}}</math>), so for any <math>\alpha \ge 0</math> the integral... [<math>d_{MAX}(t)</math>] converges.
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Velocity, acceleration, and force are vectors... they have direction as well as magnitude. It is often convenient to describe... [vectors] in terms of their components along specified directions. ...Components of vectors can be negative as well as positive ...Newton's Second Law applies separately to each component... it says... the component of force in any direction is equal to the mass times the corresponding component of acceleration.
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