Once upon a time, physics was simple and beautiful. Everything we knew about the universe could be derived from a small set of brief, elegant expressions called "Lagrangians." If you wanted to predict how a particle would behave in an electric or magnetic field, for example, you would start with this Lagrangian (from classical electrodynamics):
ϵ0⋅||E||2−c2||B||22−ρϕ+j⋅Aϵ0⋅||E||2−c2||B||22−ρϕ+j⋅A
where EE is the electric field, BB is the magnetic field, ρρ is the charge density, and jj is the current density vector. You would plug this expression into the Euler-Lagrange equation, which minimizes the integral of the Lagrangian (also called the "action"). And just a few mathematical steps later, voilà! You had a complete description of the particle's motion.
If you wanted to know how a particle would behave in a gravitational field, well, then, you used this Lagrangian (from general relativity):
116π(R−2Λ)−g116π(R−2Λ)−g
Solving the resulting equation was fairly complicated, but at least the Lagrangian itself was simple and easy to understand. And to make things even easier, you had the perfectly respectable option of ignoring the ΛΛ. Everyone knew that the cosmological constant was just a blunder.
Then came the Standard Model. Its Lagrangian looks like this:
−12νgaμνgaμ−gsfabcμgaνgbμgcν−14g2sfabcfadegbμgcνgdμgeν−12∂νgμa∂νgμa−gsfabc∂μgνagμbgνc−14gs2fabcfadegμbgνcgμdgνe
+12ig2s(q¯σiγμqσj)gaμ+G¯a2Ga+gsfabcμG¯aGbgcμ−∂νW+μνWμ−M2W+μWμ+12igs2(q¯iσγμqjσ)gμa+G¯a∂2Ga+gsfabc∂μG¯aGbgμc−∂νWμ+∂νWμ−−M2Wμ+Wμ−
−12νZ0μνZ0μ−12c2wM2Z0μZ0μ−12μAνμAν−12∂νZμ0∂νZμ0−12cw2M2Zμ0Zμ0−12∂μAν∂μAν
−12μHμH−12m2hH2−∂μϕ+μϕ−M2ϕ+ϕ−12μϕ0μϕ0−12c2wMϕ0ϕ0−12∂μH∂μH−12mh2H2−∂μϕ+∂μϕ−−M2ϕ+ϕ−−12∂μϕ0∂μϕ0−12cw2Mϕ0ϕ0
−βh[2M2g2+2MgH+12(H20ϕ0+2ϕ+ϕ)]+2M4g2αh−βh[2M2g2+2MgH+12(H2+ϕ0ϕ0+2ϕ+ϕ−)]+2M4g2αh
−igcw[∂νZ0μ(W+μWν−W+νWμ)−Z0ν(W+μνWμ−WμνW+μ)+Z0μ(W+ννWμ−WννW+μ)]−igcw[∂νZμ0(Wμ+Wν−−Wν+Wμ−)−Zν0(Wμ+∂νWμ−−Wμ−∂νWμ+)+Zμ0(Wν+∂νWμ−−Wν−∂νWμ+)]
−igsw[∂νAμ(W+μWν−W+νWμ)−Aν(W+μνWμ−WμνW+μ)+Aμ(W+ννWμ−WννW+μ)]−igsw[∂νAμ(Wμ+Wν−−Wν+Wμ−)−Aν(Wμ+∂νWμ−−Wμ−∂νWμ+)+Aμ(Wν+∂νWμ−−Wν−∂νWμ+)]
−12g2W+μWμW+νWν+12g2W+μWνW+μWν−12g2Wμ+Wμ−Wν+Wν−+12g2Wμ+Wν−Wμ+Wν−
+g2c2w(Z0μW+μZ0νWν−Z0μZ0μW+νWν)+g2cw2(Zμ0Wμ+Zν0Wν−−Zμ0Zμ0Wν+Wν−)
+g2s2w(AμW+μAνWν−AμAμW+νWν)+g2sw2(AμWμ+AνWν−−AμAμWν+Wν−)
+g2swcw[AμZ0ν(W+μWν−W+νWμ)−2AμZ0μW+νWν]+g2swcw[AμZν0(Wμ+Wν−−Wν+Wμ−)−2AμZμ0Wν+Wν−]
−gα[H3+Hϕ0ϕ0+2Hϕ+ϕ]−gα[H3+Hϕ0ϕ0+2Hϕ+ϕ−]
−18g2αh[H4+(ϕ0)4+4(ϕ+ϕ)2+4(ϕ0)2ϕ+ϕ+4H2ϕ+ϕ+2(ϕ0)2H2]−18g2αh[H4+(ϕ0)4+4(ϕ+ϕ−)2+4(ϕ0)2ϕ+ϕ−+4H2ϕ+ϕ−+2(ϕ0)2H2]
−gMW+μWμH−12gMc2wZ0μZ0μH−gMWμ+Wμ−H−12gMcw2Zμ0Zμ0H
−12ig[W+μ0μϕ−ϕμϕ0)−Wμ0μϕ+−ϕ+μϕ0)]−12ig[Wμ+(ϕ0∂μϕ−−ϕ−∂μϕ0)−Wμ−(ϕ0∂μϕ+−ϕ+∂μϕ0)]
+12g[W+μ(Hμϕ−ϕμH)−Wμ(Hμϕ+−ϕ+μH)]+12g[Wμ+(H∂μϕ−−ϕ−∂μH)−Wμ−(H∂μϕ+−ϕ+∂μH)]
+12g1cw(Z0μ(Hμϕ0−ϕ0μH)−igs2wcwMZ0μ(W+μϕ−Wμϕ+)+12g1cw(Zμ0(H∂μϕ0−ϕ0∂μH)−igsw2cwMZμ0(Wμ+ϕ−−Wμ−ϕ+)
+igswMAμ(W+μϕ−Wμϕ+)+igswMAμ(Wμ+ϕ−−Wμ−ϕ+)
−ig1−2c2w2cwZ0μ+μϕ−ϕμϕ+)+igswAμ+μϕ−ϕμϕ+)−ig1−2cw22cwZμ0(ϕ+∂μϕ−−ϕ−∂μϕ+)+igswAμ(ϕ+∂μϕ−−ϕ−∂μϕ+)
−14g2W+μWμ[H2+(ϕ0)2+2ϕ+ϕ]−14g2Wμ+Wμ−[H2+(ϕ0)2+2ϕ+ϕ−]
−14g21c2wZ0μZ0μ[H2+(ϕ0)2+2(2s2w−1)2ϕ+ϕ]−14g21cw2Zμ0Zμ0[H2+(ϕ0)2+2(2sw2−1)2ϕ+ϕ−]
−12g2s2wcwZ0μϕ0(W+μϕ+Wμϕ+)−12ig2s2wcwZ0μH(W+μϕ−Wμϕ+)−12g2sw2cwZμ0ϕ0(Wμ+ϕ−+Wμ−ϕ+)−12ig2sw2cwZμ0H(Wμ+ϕ−−Wμ−ϕ+)
+12g2swAμϕ0(W+μϕ+Wμϕ+)+12ig2swAμH(W+μϕ−Wμϕ+)+12g2swAμϕ0(Wμ+ϕ−+Wμ−ϕ+)+12ig2swAμH(Wμ+ϕ−−Wμ−ϕ+)
−g2swcw(2c2w−1)Z0μAμϕ+ϕ−g2swcw(2cw2−1)Zμ0Aμϕ+ϕ−
−g1s2wAμAμϕ+ϕ−e¯λ+mλe)eλ−ν¯λγνλ−g1sw2AμAμϕ+ϕ−−e¯λ(γ∂+meλ)eλ−ν¯λγ∂νλ
−u¯λj+mλu)uλj−d¯λj+mλd)dλj−u¯jλ(γ∂+muλ)ujλ−d¯jλ(γ∂+mdλ)djλ
+igswAμ[−(e¯λγμeλ)+23(u¯λjγμuλj)−13(d¯λjγμdλj)]+igswAμ[−(e¯λγμeλ)+23(u¯jλγμujλ)−13(d¯jλγμdjλ)]
+ig4cwZ0μ[(ν¯λγμ(1+γ5λ)+(e¯λγμ(4s2w−1−γ5)eλ)+(u¯λjγμ(43s2w−1−γ5)uλj)+(d¯λjγμ(1−83s2w−γ5)dλj)]+ig4cwZμ0[(ν¯λγμ(1+γ5)νλ)+(e¯λγμ(4sw2−1−γ5)eλ)+(u¯jλγμ(43sw2−1−γ5)ujλ)+(d¯jλγμ(1−83sw2−γ5)djλ)]
+ig22W+μ[(ν¯λγμ(1+γ5)eλ)+(u¯λjγμ(1+γ5)Cλκdκj)]+ig22Wμ+[(ν¯λγμ(1+γ5)eλ)+(u¯jλγμ(1+γ5)Cλκdjκ)]
+ig22Wμ[(e¯λγμ(1+γ5λ)+(d¯κjCλκγμ(1+γ5)uλj)]+ig22Wμ−[(e¯λγμ(1+γ5)νλ)+(d¯jκCλκ†γμ(1+γ5)ujλ)]
+ig22mλeM[−ϕ+¯λ(1−γ5)eλ)+ϕ(e¯λ(1+γ5λ)]+ig22meλM[−ϕ+(ν¯λ(1−γ5)eλ)+ϕ−(e¯λ(1+γ5)νλ)]
−g2mλeM[H(e¯λeλ)+iϕ0(e¯λγ5eλ)]−g2meλM[H(e¯λeλ)+iϕ0(e¯λγ5eλ)]
+ig2M2ϕ+[−mκd(u¯λjCλκ(1−γ5)dκj)+mλu(u¯λjCλκ(1+γ5)dκj]+ig2M2ϕ+[−mdκ(u¯jλCλκ(1−γ5)djκ)+muλ(u¯jλCλκ(1+γ5)djκ]
+ig2M2ϕ[mλd(d¯λjCλκ(1+γ5)uκj)−mκu(d¯λjCλκ(1−γ5)uκj]+ig2M2ϕ−[mdλ(d¯jλCλκ†(1+γ5)ujκ)−muκ(d¯jλCλκ†(1−γ5)ujκ]
−g2mλuMH(u¯λjuλj)−g2mλdMH(d¯λjdλj)+ig2mλuMϕ0(u¯λjγ5uλj)−g2muλMH(u¯jλujλ)−g2mdλMH(d¯jλdjλ)+ig2muλMϕ0(u¯jλγ5ujλ)
−ig2mλdMϕ0(d¯λjγ5dλj)−ig2mdλMϕ0(d¯jλγ5djλ)
+X¯+(∂2−M2)X++X¯(∂2−M2)X+X¯0(∂2−M2c2w)X0+Y¯2Y+X¯+(∂2−M2)X++X¯−(∂2−M2)X−+X¯0(∂2−M2cw2)X0+Y¯∂2Y
+igcwW+μ(∂μX¯0X−∂μX¯+X0)+igswW+μ(∂μY¯X−∂μX¯+Y)+igcwWμ+(∂μX¯0X−−∂μX¯+X0)+igswWμ+(∂μY¯X−−∂μX¯+Y)
+igcwWμ(∂μX¯X0−∂μX¯0X+)+igswWμ(∂μX¯Y−∂μY¯X+)+igcwWμ−(∂μX¯−X0−∂μX¯0X+)+igswWμ−(∂μX¯−Y−∂μY¯X+)
+igcwZ0μ(∂μX¯+X+−∂μX¯X)+igswAμ(∂μX¯+X+−∂μX¯X)+igcwZμ0(∂μX¯+X+−∂μX¯−X−)+igswAμ(∂μX¯+X+−∂μX¯−X−)
−12gM[X¯+X+H+X¯XH+1c2wX¯0X0H]−12gM[X¯+X+H+X¯−X−H+1cw2X¯0X0H]
+1−2c2w2cwigM[X¯+X0ϕ+−X¯X0ϕ]+12cwigM[X¯0Xϕ+−X¯0X+ϕ]+1−2cw22cwigM[X¯+X0ϕ+−X¯−X0ϕ−]+12cwigM[X¯0X−ϕ+−X¯0X+ϕ−]
+igMsw[X¯0Xϕ+−X¯0X+ϕ]+12igM[X¯+X+ϕ0−X¯Xϕ0]+igMsw[X¯0X−ϕ+−X¯0X+ϕ−]+12igM[X¯+X+ϕ0−X¯−X−ϕ0]
But that's not even the worst part! Trying to get a prediction out of this untidy jumble of Greek letters yields infinity in pretty much any nontrivial situation. So physicists had to introduce a trick called "renormalization" to remove the infinities. Renormalization doesn't have any particularly strong mathematical justification, but it gives the right results, so we kept using it.
Then another problem came up: no one could explain why particles had mass. This was a… massive… problem. (Sorry.) In the 1960's, some clever physicists came up with a kludge called the Higgs mechanism that mostly filled the gap, but the ad hoc introduction of a new scalar field wasn't exactly satisfying.
In the end, we have the Standard Model: a patchwork quilt of quick fixes and unsightly workarounds that barely fits together. There are 17 fundamental particles (no one knows why) and somewhere around 18 arbitrarily adjustable parameters. Yet somehow this convoluted mishmash is the most accurate scientific theory of all time.
For physicists, that’s a deeply unsettling state of affairs. We want to believe the universe isn’t really this ugly. We want a better theory to exist, a more beautiful theory that will unify quantum mechanics and general relativity in one simple and lovely set of equations. But so far, we haven’t been able to find anything convincing. A Nobel Prize awaits the first person who does.