The Universe, Vol. 5, No. 1 January-March 2017 Regular Article Relativity in Physics for the 21st Century W-Y. Pauchy Hwang∗1 1Asia Pacific Organization for Cosmology and Particle Astrophysics, Center for Theoretical Sciences, Department of Physics, and Institute of Astrophysics, National Taiwan University, Taipei, Taiwan 106 At the beginning of the 21st Century, we may declare that we are living in the quantum 4-dimensional Minkowski space-time with, via the gauge principle, the force-fields gauge-group structure, SUc(3) × SUL(2) × U(1) or SUL(2) × U(1) × SUf (3), built-in from the very beginning. From there, it emerges the Standard Model that describes the smallest units of matter such as electrons, neutrinos, and quarks. I would like to point out as well as to discuss a few major century errors dictated by the God, throughout the 20th Century. We, as the human being, are sometimes so helpless in the struggles for the true knowledge. 1 A Question to Dirac and thus we don't need the infinite sea of elec- trons. P.A.M. Dirac discovers the Dirac equation, rather than inventing this equation [1]. In our Apparently, Dirac knew these also, since he World (or, our Universe), the basic units of mat- knows the language so well. Later on, he pub- ter, such as electrons, neutrinos, and quarks, lished \Quantum Mechanics" which the mean- are the smallest objects ever exist in nature. ing of quantization was elucidated in great de- These smallest units of matter obey Pauli's ex- tail. There is no \second quantization" and, clusion principle, as fermions, satisfying the anti- also, there is no \electron sea" whatsoever. The commuting Dirac algebra. consistency and, perhaps, the completeness are At 1928, we already knew the electrons, but absolutely demanded for the language (and its not the positrons. This gave a few then-famous logic). \physicists" a real puzzle to tackle. In fact, Einstein's 1905 revolution was not What if the positron still has not had discov- complete at E2 = ~p 2 + m2, which implies the ered till now? This would be refute to Einstein's Klein-Gordon equation and which is not suitable relativity principle, rather than the \invention" in the description of the matter. The Einstein's of the infinite \electron sea", etc. Fortunately, revolution is thus completed by Dirac's lineariza- the position is there and its company with the tion, the discovery of the Dirac equation. electron makes the four components that are In my personal opinion, the idea of the \elec- needed by Dirac's linearization of Einstein's re- tron sea" could not stand out since there is no lation E2 = ~p 2 + m2. This fact consolidates stopover at the bottom, at the negative infinity. the status of Einstein's relativity principle and The quantization of the Dirac field begins with Dirac's linearization, paving the way of describ- the field operator Ψ(x) that is the combination ing the motion using Newton's doctrine. of the terms - the particle annihilation operators a(+)(~p;s) and the antiparticle creation operators a(−)∗(~p;s); there is no difference between these Thus, the God could fool all of us, the human two terms. In terms of the language, the anni- being, if so far there had not been positrons dis- hilation and the creation have the same status covered in our world. Then, Dirac had to figure and, if needed, they could be interchanged. The out why his equation has four components but mathematical framework is perfectly consistent the Nature only needed two (for the electron). It seems that the mathematics and the physics ac- ∗Email: [email protected] tually converge to only one thing. 13 Regular Article The Universe, Vol. 5, No. 1 January-March 2017 2 Another Century Error Dic- the existence of dark-matter lumps interpreted tated by the God as some simple adjustable outlet. Remember- ing that a star of five solar mass, in terms of Schwarzschild's solution was given on 13 January the smallest units of matter (such as electrons, 60 1916 by Einstein (on behalf of Schwarzschild). quarks, etc.), has 10 units of matter - a gigantic The horizon idea was developed by Wheeler and number, the re-scaling of Newton's gravitational others in 1960's, leading to Hawking's black constant has to be acceptable. holes. The mathematics is correct, so further pursuing is reasonable. However, at the turn of the 21st Century, it 3 Why Relativity for the 21st was realized that our Universe is composed by Century and Onward? 70% dark energy, 25% dark matter, and only 5% visual ordinary matter. According to the Stan- In the 20th Century, we have firmly established dard Model [2] (that describes our Universe), the the two pillars of modern physics, Einstein's rel- 25% dark matter are neutrino halos, made up ativity principle and the quantum principle. In from cosmic background neutrinos (of three fla- the beginning of the 21st Century, we have real- vors, and antineutrinos) (CBν0s), just like cos- ized that there exist the smallest units of mat- mic microwave background (CMB), from the ter, including electrons, neutrinos, and quarks. Early Universe. To describe these smallest units of matter, we Neutrino halos, which are Fermi-Dirac gases, have the Standard Model [2] as the mathemati- obey the quantum principle, or Pauli's exclusion cal framework. ν principle. For the Earth, the Fermi energy kF It is not outrageous to declare [4, 2] that of the Fermi-Dirac sphere would be 600 GeV , as we're in fact living in the quantum 4-dimensional suggested by the Sam Ting's Space-Station AMS Minkowski space-time with, via the gauge prin- experiments [3]. ciple, the force-fields gauge-group structure, The distance dictated by the quantum prin- SUc(3) × SUL(2) × U(1) or SUL(2) × U(1) × ciple, or by Pauli's exclusion principle, is deter- SUf (3), built-in from the very beginning. In the mined by the Planck constant ~, which is many Standard Model [2], the language is \relativis- orders bigger than the Schwarzschild's radius rh. tic quantum mechanics and quantum fields” [5]. So, if we consider a realistic physical sys- Since the left-handed and right-handed compo- tem that has five times in weight the neutrino nents of fermions enter the theory differently, the halo (the 25% dark matter) and the ordinary- Standard Model is a completely massless theory, matter object (such as the visual Earth), then, apart from the \ignition" term of the sponta- due to the universal gravitational force, the vi- neous symmetry breaking (SSB) [6]. sual ordinary-matter part, at the \last" stage, In fact, when we declare that we're living would be dragged by the \incompressible" neu- in the quantum 4-dimensional Minkowski space- trino halo - thus, that a black hole cannot ex- time, we also need to know how the unit of mat- ist (i.e., that the final destiny of the neutrino ter know from the space-time point xµ to another halo determines the final destiny of the entire point xµ + δxµ; that is, the content of the gauge system). principle @µ ! Dµ (the change in the derivatives, Therefore, this is the mistake (or error) dic- or in the velocities). This is the centerpiece of tated by the God. Our Universe is described, the Newton's description of motions. This is also mathematically, by the Standard Model [2] and the centerpiece of the Standard Model [2]. this Universe has CBν0s and CMB upon its To begin our discussions about the nuclear and birth. The physicists in the generations of the particle physics for the 21st Century, we may be 1960's, 1970's and 1980's didn't know the con- overwhelmed by lots of \non-relativistic approxi- tents of our Universe, thus fooled by the God. mations" in our theoretical languages. Although Some might argue that Newton's universal we don't know how much revisions that might gravitational law may have trouble in light of be involved, the attitude that we actually ac- such dark-matter halos. But the re-scaling of knowledge to live in the quantum 4-dimensional Newton's gravitational constant can always treat Minkowski space-time should be a positive first 14 The Universe, Vol. 5, No. 1 January-March 2017 Regular Article step. It means the basic change [7] into our rel- the gauge principle, the gauge-group structure, ativistic quantum attitude from that based on SUc(3) × SUL(2) × U(1) or SUL(2) × U(1) × Newton's classic era - in fact, we could just look SUf (3), built-in from the very beginning. into the textbooks (of the 20th Century) in gen- There are plenty of evidences for the family eral physics, into how we were taught in ordinary gauge symmetry - the existence of three \gener- quantum mechanics, and so on. We believe that ations" for leptons (if without the family gauge the recognition of where we are living (in the concept), the phenomenon of neutrino oscilla- quantum 4-dimensional Minkowski space-time) tions, etc. What if this family gauge symmetry should be the first revolution in our altitude - is not a gauge symmetry? It does not look like then the realization of electrons, neutrinos, and so - indeed, if yes, it solves a lot of puzzles; while quarks as the smallest units of matter will come if not, many questions remain [1]. as the next revolution in our altitude. In fact, the meaning of \generations" dis- appears completely, when the family SUf (3) gauge group is adopted for leptons while, for 4 We're Living in the Quantum quarks, all the entries as the triplets of the quark 4-Dimensional Minkowski group SUQ(3) (not a gauge symmetry) are used.