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Description
Some of the most essential equations in the two branches of fundamental physics (general relativity and quantum theory) are arranged into a venn diagram.

Outside are the general principles which transcend all physics, the principles of stationary action (top left) and entropy increase (top right), and the continuity equation (bottom left). (General equations like the wave or diffusion equations are not shown since these are consequences of fundamental laws).

To keep the equations as simple and compact as possible, Planck units are used (bottom right), and no index notation.

The graphics on the left are geodesics of a sphere forming part of the diagram. The equations are (top to bottom): line element, energy-momentum relation (a stronger form of the E=mc^2), energy-momentum conservation, Einstein field equations, geodesic equation, and geodesic deviation (the uparrow ↑ is just a blank placeholder). General relativity describes gravitation as curvature of spacetime, and mass-energy generates curvature.

The graphics on the right shows quantization of stationary states around a circle (integer number of wavelengths around circumference), inside are "cones" of allowed quantized spin (a fundamental property of elementary particles, the cones are a common heuristic depiction not a literal representation, similar "cones" exist for orbital and total angular momenta also). The equations (top to bottom) are: observables as operators (eigenvalues are allowed results of measurement), De Broglie relation, normalization condition on wave functions, Schrödinger equation, Dirac's quantization condition, the uncertainty relations between two observables A and B, and energy-time.

Yes I have biased quantum mechanics rather than quantum field theory, but its dead simple to write down compact and broadly applicable equations in QM, in QFT (which I understand less) I wasn't sure where to start (commutation/anticommutation relations for bosonic/fermionic operators? S-matrix expansion? etc?).

Then the middle overlap is the unification of the two theories. We don't know what the equations are because currently there is no widely accepted unified theory of QM and GR.

Fonts used are Times New Roman and Univers LT Std 45 Light.

For those with interest in such things, the picture could be used for a background on books/phones/desktops or maybe a classroom/conference poster...

See also: PDF version , PNG version .

Description
Some of the most essential equations in the two branches of fundamental physics (general relativity and quantum theory) are arranged into a venn diagram.

Outside are the general principles which transcend all physics, the principles of stationary action (top left) and entropy increase (top right), and the continuity equation (bottom left). (General equations like the wave or diffusion equations are not shown since these are consequences of fundamental laws).

To keep the equations as simple and compact as possible, Planck units are used (bottom right), and no index notation.

The graphics on the left are geodesics of a sphere forming part of the diagram. The equations are (top to bottom): line element, energy-momentum relation (a stronger form of the E=mc^2), energy-momentum conservation, Einstein field equations, geodesic equation, and geodesic deviation (the uparrow ↑ is just a blank placeholder). General relativity describes gravitation as curvature of spacetime, and mass-energy generates curvature.

The graphics on the right shows quantization of stationary states around a circle (integer number of wavelengths around circumference), inside are "cones" of allowed quantized spin (a fundamental property of elementary particles, the cones are a common heuristic depiction not a literal representation, similar "cones" exist for orbital and total angular momenta also). The equations (top to bottom) are: observables as operators (eigenvalues are allowed results of measurement), De Broglie relation, normalization condition on wave functions, Schrödinger equation, Dirac's quantization condition, the uncertainty relations between two observables A and B, and energy-time.

Yes I have biased quantum mechanics rather than quantum field theory, but its dead simple to write down compact and broadly applicable equations in QM, in QFT (which I understand less) I wasn't sure where to start (commutation/anticommutation relations for bosonic/fermionic operators? S-matrix expansion? etc?).

Then the middle overlap is the unification of the two theories. We don't know what the equations are because currently there is no widely accepted unified theory of QM and GR.

Fonts used are Times New Roman and Univers LT Std 45 Light.

For those with interest in such things, the picture could be used for a background on books/phones/desktops or maybe a classroom/conference poster...

See also: PDF version , PNG version .