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(Updated the cube with NS (Newton-Schrödinger) as opposed to NRQG (Non-relativistic Quantum Gravity))
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# <ol start=7><div style="color:black; position:relative; left:-50px;">
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# NRQG or [[Non-relativistic quantum gravity]].</div></ol></div>
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# NS for Newton-Schrödinger but properly [[Non-relativistic quantum gravity]].</div></ol></div>
  
 
The 8th corner is the grail of Physics:
 
The 8th corner is the grail of Physics:
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# GR: $G_{\mu \nu }+\Lambda g_{\mu \nu }=\kappa T_{\mu \nu }$.
 
# GR: $G_{\mu \nu }+\Lambda g_{\mu \nu }=\kappa T_{\mu \nu }$.
 
# QFT: $i\hbar\gamma^\mu\partial_\mu\psi=mc\psi$.  
 
# QFT: $i\hbar\gamma^\mu\partial_\mu\psi=mc\psi$.  
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# NRQT: ?!
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# NS: $\nabla^2\Phi =4\pi Gm|\Psi |^2$.
 
# TOE: ?!
 
# TOE: ?!
  
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But {{I}}'m not quite sure yet what to put for 7 & 8.
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But {{I}}'m not quite sure yet what to put for 8 (maybe some action or Lagrangian). Note that NS is also a fairly simplified approach to this corner of the cube.
  
 
More topics tackled by Physics with a finer distinction:
 
More topics tackled by Physics with a finer distinction:

Revision as of 09:51, 26 December 2023

Physics

Physics is the Art of finding things out. Hear Feynman talk about it:

Physics is the core of all Science, as emphatically expressed by Rutherford, deemed the greatest experimentalist since Faraday by the Encyclopædia Britannica, who famously expressed that “all science is either physics or stamp collecting”.

There is no scientific discipline, in fact hardly any discipline at all, where the concepts of motion, space, time, matter, energy, causality, information, error, etc., are not invoked, and these are what Physics is about. When applied to particular cases, Physics becomes Chemistry (the science of how matter is structured), Optics (the science of how light propagates), Astronomy (the science of celestial objects), Climatology (the science of atmosphere and oceans), Engineering (the science of implementing technology), etc. Even seemingly more remote fields such as Biology, Medicine or Geology, or more fundamental ones such as Mathematics or Computing Sciences, are deeply rooted into Physics and increasingly so as scientific expertise progresses. The field of Quantum Biology and Quantum Computation, for instance, are quickly evolving and will shape the tomorrow’s landscape of these disciplines. In a sufficiently advanced technology, everything comes back to the rule of physical laws. In this way, a computer bit becomes a qubit encoded on a bunch of few particles ruled by the principle of atomic physics, rather than by those of abstract platonic mathematics.

Physics is therefore the keystone of Science.

A fundamental classification can be made with the $cGh$ cube of Physics:

CGh.png

This relates the various corners, or pillars, of Modern Physics around its historical foundation, which also serves as the pre-University syllabus: classical mechanics (oscillators, derivatives, etc.):

  1. CM or Classical Mechanics.

Bringing one "ingredient" of complexity at a time, be it fast speed or high energies through the speed of light $c$, small objects through Planck's constant $h$ or heavy/curved geometry through the gravitational constant $G$, we would normally cover the first three corners of the cube:

though it happens that the non-relativistic, non-quantum but heavy/extended-objects gets a treatment of its own:

    1. NC or Newton-Cartan theory (also known as Non-Relativistic Gravity).

NC is little studied on its own. The bulk of it is incorporated in CM as Newtonian Gravity but this fails to include modern insights. NC can be regarded as a geometrized version of Newton's equations, still relying on absolute (not proper) time and through Galilean transformations as opposed to Lorentz's but on curved spacetime and relying on geodesics there [2]. See also Ref. [1]

Combining two ingredients brings us to the major developments of modern physics:

Here too, one corner stands on its own, the geometric non-relativistic gravity, but quantized:

    1. NS for Newton-Schrödinger but properly Non-relativistic quantum gravity.

The 8th corner is the grail of Physics:

I would love to update the cube with the main equations of the respective theories. This could be:

  1. CM: $\vec F=m\vec a$.
  2. QM: $i\hbar\partial_t\psi=H\psi$.
  3. SR: $E=\gamma mc^2$.
  4. NC: $R_{00}=4\pi G\rho$.
  5. GR: $G_{\mu \nu }+\Lambda g_{\mu \nu }=\kappa T_{\mu \nu }$.
  6. QFT: $i\hbar\gamma^\mu\partial_\mu\psi=mc\psi$.
  7. NS: $\nabla^2\Phi =4\pi Gm|\Psi |^2$.
  8. TOE: ?!

But I'm not quite sure yet what to put for 8 (maybe some action or Lagrangian). Note that NS is also a fairly simplified approach to this corner of the cube.

More topics tackled by Physics with a finer distinction:

Not part of physics per se, but related:

See also the other scales.

Fundamentals

Fundamental concepts of Physics, historically, include conservation laws (e.g., conservation of energy or momentum). Later, with Noether's theorem, it got clarified that symmetries are a more fundamental underlying concept. In its wake follows the idea of gauge theory[2] impulsed by Hermann Weyl and the rise of group theory. Maybe the latest step forward is the understanding of the role played by topology.

Follows a list of what I regard as the basic, fundamental ideas which support the whole edifice and to which one should give much attention:

References

  1. ↑ Newton-Cartan gravity revisited, Roel Andringa's PhD thesis (1984) [1]
  2. ↑ Which symmetry? Noether, Weyl and conservation of electric charge. K. A. Brading in Stud. Hist. Philos. Sci. B 33:3 (2002).

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