In several of Neil Turok's talks, he talks about this equation that encompasses all of physics. Here it is:

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How much of it is true? If it isn't, then is it possible to put all of our knowledge of physics into one equation? Finally, can you explain where each term comes from (I understand till 'Einstein' and 'Newton' terms)? EDIT:

Is this a path integral formulation of some sort?

  • 2
    $\begingroup$ This is the standard model in quite schematic form. $\endgroup$
    – Meng Cheng
    Jun 23 '15 at 3:35
  • $\begingroup$ How did Newton's gravitation constant move from the numerator to the denominator? $\endgroup$
    – LDC3
    Jun 23 '15 at 3:39
  • $\begingroup$ @MengCheng can u expand that into an answer maybe? Also, is general relativity in the Standard Model since there's a term for gravity as well... $\endgroup$
    – TanMath
    Jun 23 '15 at 3:39
  • $\begingroup$ @LDC3 I was thinking about that, but it is a general relativity term... $\endgroup$
    – TanMath
    Jun 23 '15 at 3:40
  • 2
    $\begingroup$ And that is "How physics doesn't work for beginners". Worse still, it looks like it's taken from a nerd T-shirt... :-) $\endgroup$
    – CuriousOne
    Jun 23 '15 at 4:56

This equation suggests a path integral, of a Lagrangian that contains terms for both general relativity and the Standard Model in highly abbreviated form. Compressing it all into one line is a stunt, of course, rather than an actually useful equation. :) It glosses over many technical issues (for instance that we don't actually know how to do quantum gravity!) and it doesn't include anything about dark matter or dark energy (you can argue whether those qualify as "known physics" or not). Those caveats aside, it is basically correct insofar as it depicts all known physics coexisting in a single mathematical framework.

I'll try to label the parts of it...

  • $\Psi$ — represents the quantum-mechanical amplitude to find a system in a particular state
  • $\displaystyle \int e^{i/\hbar \int \mathcal{L}}$ — path-integral formulation due to Feynman, expresses the amplitude due to a Lagrangian density $\mathcal{L}$, which is a sum of terms for all the different fields that exist in the theory. In the Lagrangian, derivatives of a field cause the field to oscillate and form waves (and quantized packets of waves, i.e. particles); products of two or more fields cause those fields/particles to interact.
  • $\displaystyle \frac{R}{16\pi G}$ is the Einstein–Hilbert Lagrangian, which is the Lagrangian formulation of general relativity.
  • $-\tfrac{1}{4}F^2$ stands for the kinetic energy terms for all the gauge bosons: photons (electromagnetic field) and the gluons and W and Z bosons (Yang-Mills fields) that give rise to the strong and weak forces. The $F$ stands for the field tensor, which is made of derivatives of the potential; this article explains it more for electromagnetism, and Yang-Mills theory is a generalization of that, so they're all represented by one term here.
  • $\bar\psi i \not D \psi$ stands for the kinetic energy terms for all the fermions: electrons, neutrinos, and quarks. Again, they they all share the same formalism, that of Dirac fields, so they are all compressed into one term here. The $\not D$ notation represents a special kind of derivative that accounts for the interaction with the gauge fields, so this term also includes all the interactions between the fermions and the gauge bosons. Note that the fermions are all massless here, because massive fermions are incompatible with gauge invariance. This is fixed by...
  • $-\lambda H \bar \psi \psi$ stands for the Yukawa interaction between the Higgs field $H$ and the fermion fields $\psi$. This is part of the Higgs mechanism and is what gives the fermions an effective mass.
  • $|DH|^2$ is the kinetic energy term for the Higgs field. Again $D$ is a gauge-covariant derivative, so it also includes interactions between the Higgs and the gauge bosons, giving the W and Z bosons their effective mass.
  • Finally, $-V(H)$ is the Higgs potential.

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